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Learning Objectives
• In what senses can financial markets be efficient or inefficient?
• What is portfolio diversification and sectoral asset allocation, and how do they help investors to earn market returns?
Now here is the freaky thing. While at any given moment, most investors’ valuations are wrong (too low or too high), the market’s valuation, given the information available at that moment, is always correct, though in a tautological or circular way only. You may recall from your principles course that markets “discover” prices and quantities. If the market price of anything differs from the equilibrium price (where the supply and demand curves intersect), market participants will bid the market price up or down until equilibrium is achieved. In other words, a good, including a financial security, is worth precisely what the market says it is worth.
At any given time, some people expect the future market price of an asset will move higher or that it is currently underpriced, a value or bargain, so to speak. They want to buy. Others believe it will move lower, that it is currently overpriced. They want to sell. Sometimes the buyers are right and sometimes the sellers are, but that is beside the point, at least from the viewpoint of economic efficiency. The key is that the investor who values the asset most highly will come to own it because he’ll be willing to pay the most for it. Financial markets are therefore allocationally efficient. In other words, where free markets reign, assets are put to their most highly valued use, even if most market participants don’t know what that use or value is. That’s really remarkable when you think about it and goes a long way to explaining why many economists grow hot under the collar when governments create barriers that restrict information flows or asset transfers.
Financial markets are also efficient in the sense of being highly integrated. In other words, prices of similar securities track each other closely over time and prices of the same security trading in different markets are identical, or nearly so. Were they not, arbitrage, or the riskless profit opportunity that arises when the same security at the same time has different prices in different markets, would take place. By buying in the low market and immediately selling in the high market, an investor could make easy money. Unsurprisingly, as soon as an arbitrage opportunity appears, it is immediately exploited until it is no longer profitable. (Buying in the low market raises the price there, while selling in the high market decreases the price there.) Therefore, only slight price differences that do not exceed transaction costs (brokerage fees, bid-ask spreads, etc.) persist.
The size of those price differences and the speed with which arbitrage opportunities are closed depend on the available technology. Today, institutional investors can complete international financial market trades in just seconds and for just a few hundredths or even thousandths of a percent. In the early nineteenth century, U.S.-London arbitrageurs (investors who engage in arbitrage) confronted lags of several weeks and transaction costs of several percent. Little wonder that price differentials were larger and more persistent in the early nineteenth century. But the early markets were still rational because they were as efficient as they could be at the time. (Perhaps in the future, new technology will make seconds and hundredths of a percent look pitifully archaic.)
Arbitrage, or the lack thereof, has been the source of numerous jokes and gags, including a two-part episode of the 1990s comedy sitcom Seinfeld. In the episodes, Cosmo Kramer and his rotund friend Newman (the postal worker) decide to try to arbitrage the deposit on cans and bottles of soda, which is 5 cents in New York, where Seinfeld and his goofy friends live, and 10 cents in Michigan. The two friends load up Newman’s postal truck with cans and head west, only to discover that the transaction costs (fuel, tolls, hotels, and what not) are too high, especially given the fact that Kramer is easily sidetracked.[1] High transaction costs also explain why people don’t arbitrage the international price differentials of Big Macs and many other physical things.[2] Online sites like eBay, however, have recently made arbitrage in nonperishables more possible than ever by greatly reducing transaction costs.
In another joke (at least I hope it’s a joke!), two economics professors think they see an arbitrage opportunity in wheat. After carefully studying all the transaction costs—freight, insurance, brokerage, weighing fees, foreign exchange volatility, weight lost in transit, even the interest on money over the expected shipping time—they conclude that they can make a bundle buying low in Chicago and selling high in London. They go for it, but when the wheat arrives in London, they learn that a British ton (long ton, or 2,240 pounds) and a U.S. ton (short ton, or 2,000 pounds) are not the same thing. The price of wheat only appeared to be lower in Chicago because a smaller quantity was being priced.
Some economists believe financial markets are so efficient that unexploited profit opportunities like arbitrage are virtually impossible. Such extreme views have also become the butt of jokes, like the one where a young, untenured assistant professor of economics bends over to pick up a \$20 bill off the sidewalk, only to be chided by an older, ostensibly wiser, and indubitably tenured colleague who advises him that if the object on the ground were real money, somebody else would have already have picked it up.[3] But we all know that money is sometimes lost and that somebody else is lucky enough to pocket it. At the same time, however, some people stick their hands into toilets to retrieve authentic-looking \$20 bills, so we also know that things are not always what they seem. Arbitrage and other unexploited profit opportunities are not unicorns. They do exist on occasion. But especially in financial markets, they are so fleeting that they might best be compared to kaons or baryons, rare and short-lived subatomic particles.
In an efficient market, all unexploited profit opportunities, not just arbitrage opportunities, will be eliminated as quickly as the current technology set allows. Say, for example, the rate of return on a stock is 10 percent but the optimal forecast or best guess rate of return, due to a change in information or in a valuation model, was 15 percent. Investors would quickly bid up the price of the stock, thereby reducing its return. Remember that R = (C + Pt1 – Pt0)/Pt0. As Pt0 , the price now, increases, R must decrease. Conversely, if the rate of return on a stock is currently 10 percent but the optimal forecast rate of return dropped to 5 percent, investors would sell the stock until its price decreased enough to increase the return to 10 percent. In other words, in an efficient market, the optimal forecast return and the current equilibrium return are one and the same.
Financial market efficiency means that it is difficult or impossible to earn abnormally high returns at any given level of risk. (Remember, returns increase with risk.) Yes, an investor who invests 100 percent in hedge funds will likely garner a higher return than one who buys only short-dated Treasury notes. Holding risk (and liquidity) constant, though, returns should be the same, especially over long periods. In fact, creating a stock portfolio by throwing darts at a dartboard covered with ticker symbols returns as much, on average, as the choices of experienced stock pickers choosing from the same set of companies. Chimpanzees and orangutans have also done as well as the darts and the experts. Many studies have shown that actively managed mutual funds do not systematically outperform (provide higher returns than) the market. In any given period, some funds beat the market handily, but others lag it considerably. Over time, some stellar performers turn into dogs, and vice versa. (That is why regulators force financial firms to remind investors that past performance is not a guarantee of future returns.)
That is not to say, however, that you shouldn’t invest in mutual funds. In fact, mutual funds are much less risky (have lower return variability) than individual stocks or any set of stocks you are likely to pick on your own. Portfolio diversification, the investment strategy often described as not putting all of your eggs (money) in one basket (asset), is a crucial concept. So-called indexed mutual funds provide diversification by passively or automatically buying a broad sample of stocks in a particular market (e.g., the Dow or NASDAQ) and almost invariably charge investors relatively low fees.
Sectoral asset allocation is another important concept for investors. A basic strategy is to invest heavily in stocks and other risky assets when young but to shift into less volatile assets, like short-term bonds, as one nears retirement or other cash-out event. Proper diversification and allocation strategies will not help investors to “beat the market,” but they will definitely help the market from beating them. In other words, those strategies provide guidelines that help investors to earn average market returns safely and over the long term. With luck, pluck, and years of patience, modest wealth can be accumulated, but a complete bust will be unlikely.
Stop and Think Box
I once received the following hot tip in my e-mail:
Saturday, March 17, 2007
Dear Friend:
If you give me permission…I will show you how to make money in a high-profit sector, starting with just \$300–\$600. The profits are enormous. You can start with as little as \$300. And what’s more, there is absolutely no risk because you will “Test Drive” the system before you shell out any money. So what is this “secret” high-profit sector that you can get in on with just \$300–\$600 or less??? Dear Friend, it’s called “penny stocks”—stocks that cost less than \$5 per share. Don’t laugh—at one time Wal-Mart was a “penny stock.” So was Microsoft. And not too long age, America Online was selling for just .59 cents a share, and Yahoo was only a \$2 stock. These are not rare and isolated examples. Every month people buy penny stocks at bargain prices and make a small fortune within a short time.
Very recently, these three-penny stocks made huge profits. In January ARGON Corp. was at \$2.69. Our indicators picked up the beginning of the upward move of this stock. Within three months the stock shot up to \$28.94 a share, turning a \$300 investment into \$3,238 in just three months. In November Immugen (IMGN) was at \$2.76 a share. We followed the decline of this stock from \$13 to as little as \$1.75 a share. But our technicals were showing an upward move. Stock went up to \$34.10 a share. An investment of \$500 would have a net gain of \$5,677. RF Micro Devices was at \$1.75 in August 1999. It exploded to \$65.09 a share by April 2000. An investment of only \$500 in this stock would have a net profit of \$18,097. In fact, the profits are huge in penny stocks. And smart investors who picked these so-called penny stocks made huge profits. They watched their money double seemingly day after day, week after week, month after month. Double, triple, quadruple, and more.
Should I buy? Why or why not?
I did not invest, and you shouldn’t either if confronted with a similar scenario. If the individual who sent the message really knows that the stock is going to appreciate, why should he tell anyone? Shouldn’t he buy the shares himself, borrowing to the hilt if necessary to do so? So why would he try to entice me to buy this stock? He probably owns a few (hundred, thousand, million) shares and wants to drive their price up by finding suckers and fools to buy it so he can sell. This is called “pumping and dumping”[4] and it runs afoul of any number of laws, rules, and regulations, so you shouldn’t think about sending such e-mails yourself, unless you want to spend some time in Martha Stewart’s prison.[5] And don’t think you can free-ride on the game, either. One quirky fellow named Joshua Cyr actually tracks the prices of the hot stock tips he has received, pretending to buy 1,000 shares of each. On one day in March 2007, his Web site claimed that his pretend investment of \$70,987.00 was then worth a whopping \$9,483.10, a net gain of −\$61,503.90. (To find out how he is doing now, browse http://www.spamstocktracker.com.) Even if he had bought and sold almost immediately, he would have still lost money because most stocks experienced very modest and short-lived “pops” followed by quick deflations. A few of us are idiots, but most are not (or we are too poor or too lazy to act on the tips). Learning this, the scammers started to pretend that they were sending the message to a close friend to make it seem as though the recipient stumbled upon important inside information. (For a hilarious story about this, browse www.marketwatch.com/news/story/errant-e-mails-nothing-more-another/story.aspx?guid={1B1B5BF1-26DE-46BE-BA34-C068C62C92F7}.) Beware, because their ruses are likely to grow increasingly sophisticated.
In some ways, darts and apes are better stock pickers than people because the fees and transaction costs associated with actively managed funds often erase any superior performance they provide. For this reason, many economists urge investors to buy passively managed mutual funds or exchange traded funds (ETFs) indexed to broad markets, like the S&P or the Dow Jones Industrial Average, because they tend to have the lowest fees, taxes, and trading costs. Such funds “win” by not losing, providing investors with an inexpensive way of diversifying risk and earning the market rate of return, whatever that happens to be over a given holding period (time frame).
KEY TAKEAWAYS
• Markets are efficient if they allocate resources to their most highly valued use and if excess profit opportunities are rare and quickly extinguished.
• Financial markets are usually allocationally efficient. In other words, they ensure that resources are allocated to their most highly valued uses, and outsized risk-adjusted profits (as through arbitrage, the instantaneous purchase and sale of the same security in two different markets to take advantage of price differentials) are uncommon and disappear rapidly.
• Portfolio diversification and sectoral asset allocation help investors to earn average market returns by spreading risks over numerous assets and by steering investors toward assets consistent with their age and financial goals.
[3] robotics.caltech.edu/~mason/ramblings/efficientSidewalkTheory.html; www.indexuniverse.com/sections/research/123.html
[4] www.fool.com/foolu/askfoolu/2002/askfoolu020107.htm | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/07%3A_Rational_Expectations_Efficient_Markets_and_the_Valuation_of_Corporate_Equities/7.03%3A_Financial_Market_Efficiency.txt |
Learning Objectives
• How efficient are our markets?
Sophisticated statistical analyses of stock and other securities prices indicate that they follow a “random walk.” That is why stock charts often look like the path of a drunk staggering home after a party, just as in Figure 7.1. As noted at the beginning of this chapter, securities prices in efficient markets are not random. They are determined by fundamentals, particularly interest rate, inflation, and profit expectations. What is random is their direction, up or down, in the next period. That’s because relevant news cannot be systematically predicted. (If it could, it wouldn’t be news.) So-called technical analysis, the attempt to predict future stock prices based on their past behavior, is therefore largely a chimera. On average, technical analysts do not outperform the market. Some technical analysts do, but others do not. The differences are largely a function of luck. (The fact that technical analysts and actively managed funds persist, however, suggests that financial markets are still far short of perfect efficiency.)
In fact, in addition to allocational efficiency, economists talk about three types of market efficiency: weak, semistrong, and strong. These terms are described in Figure 7.2. Today, most financial markets appear to be semistrong at best. As it turns out, that’s pretty good.
Some markets are more efficient than others. Thanks to technology improvements, today’s financial markets are more efficient (though not necessarily more rational) than those of yore. In every age, financial markets tend to be more efficient than real estate markets, which in turn tend to be more efficient than commodities markets and labor and many services markets. That’s because financial instruments tend to have a very high value compared to their weight (indeed they have no weight whatsoever today), are of uniform quality (a given share of Microsoft is the same as any other share[1]), and are little subject to wastage (you could lose bearer bonds or cash, but most other financial instruments are registered, meaning a record of your ownership is kept apart from physical possession of the instruments themselves). Most commodities are relatively bulky, are not always uniform in quality, and deteriorate over time. In fact, futures markets have arisen to make commodities markets (for gold, wheat, orange juice, and many others)[2] more efficient. Financial markets, particularly mortgage markets, also help to improve the efficiency of real estate markets. Nevertheless, considerable inefficiencies persist. As the Wall Street Journal reported in March 2007, it was possible to make outsized profits by purchasing homes sold at foreclosure, tax, and other auctions, then selling them at a hefty profit, accounting for transaction costs, without even going through the trouble or expense of fixing them up. That is nothing short of real estate arbitrage![3]
Labor and services markets are the least efficient of all. People won’t or can’t move to their highest valued uses; they adapt very slowly to technology changes; and myriad regulations, some imposed by government and others by labor unions, limit their flexibility on the job. Some improvements have been made in recent years thanks to global outsourcing, but it is clear that the number of unexploited profit opportunities in labor markets far exceeds those in the financial markets. Finally, markets for education,[4] health care,[5] and custom construction services[6] are also highly inefficient, probably due to high levels of asymmetric information.
Stop and Think Box
A friend urges you to subscribe to a certain reputable investment report. Should you buy? Another friend brags about the huge returns she has made by buying and selling stocks frequently. Should you emulate her trading strategies?
Buying an investment report makes more sense than following the unsolicited hot stock tip discussed above, but it still may not be a good idea. Many legitimate companies try to sell information and advice to investors. The value of that information and advice, however, may be limited. The information may be tainted by conflicts of interest. Even if the research is unbiased and good, by the time the newsletter reaches you, even if it is electronic, the market has probably already priced the information, so there will be no above-market profit opportunities remaining to exploit. In fact, only one investment advice newsletter, Value Line Survey (VLS), has consistently provided advice that leads to abnormally high risk-adjusted returns. It isn’t clear if VLS has deeper insights into the market, if it has simply gotten lucky, or if its mystique has made its predictions a self-fulfilling prophecy: investors believe that it picks super stocks, so they buy its recommendations, driving prices up, just as it predicted! The three explanations are not, in fact, mutually exclusive. Luck and skill may have created the mystique underlying VLS’s continued success.
As far as emulating your friend’s trading strategies, you should investigate the matter more thoroughly first. For starters, people tend to brag about their gains and forget about their losses. Even if your friend is genuinely successful at picking stocks, she is likely just getting lucky. Her luck could turn just as your money gets in the game. To the extent that markets are efficient, investors are better off choosing the level of risk they are comfortable with and earning the market return. That usually entails buying and holding a diverse portfolio via an indexed mutual fund, which minimizes taxes and brokerage fees, both of which can add up. Long-term index investors also waste less time tracking stocks and worrying about market gyrations.
As noted above, none of this should be taken to mean that financial markets are perfectly efficient. Researchers have uncovered certain anomalies, situations where it is or was possible to outperform the market, holding risk and liquidity constant. I say was because exposing an anomaly will often induce investors to exploit it until it is eliminated. One such anomaly was the so-called January Effect, a predictable rise in stock prices that for many years occurred each January until its existence was recognized and publicized. Similarly, stock prices in the past tended to display mean reversion. In other words, stocks with low returns in one period tended to have high returns in the next, and vice versa. The phenomenon appears to have disappeared, however, with the advent of trading strategies like the Dogs of the Dow, where investors buy beaten-down stocks in the knowledge that they can only go up (though a few will go to zero and stay there).[7]
Other anomalies, though, appear to persist. The prices of many financial securities, including stocks, tend to overshoot when there is unexpected bad news. After a huge initial drop, the price often meanders back upward over a period of several weeks. This suggests that investors should buy soon after bad news hits, then sell at a higher price a few weeks later. Sometimes, prices seem to adjust only slowly to news, even highly specific announcements about corporate profit expectations. That suggests that investors could earn above-market returns by buying immediately on good news and selling after a few weeks when the price catches up to the news.
Some anomalies may be due to deficiencies in our understanding of risk and liquidity rather than market inefficiency. One of these is the small-firm effect. Returns on smaller companies, apparently holding risk and liquidity constant, are abnormally large. Why then don’t investors flock to such companies, driving their stock prices up until the outsized returns disappear? Some suspect that the companies are riskier, or at least appear riskier to investors, than researchers believe. Others believe the root issues are asymmetric information, the fact that the quality and quantity of information about smaller firms is inferior to that of larger ones, and inaccurate measurement of liquidity. Similarly, some researchers believe that stock prices are more volatile than they should be given changes in underlying fundamentals. That finding too might stem from the fact that researchers aren’t as prescient as the market.
The most important example of financial market inefficiencies are so-called asset bubbles or manias. Periodically, market prices soar far beyond what the fundamentals suggest they should. During stock market manias, like the dot-com bubble of the late 1990s, investors apparently popped sanguine values for g into models like the Gordon growth model or, given the large run-up in prices, large P1 values into the one-period valuation model. In any event, starting in March 2000, the valuations for most of the shares were discovered to be too high, so share prices rapidly dropped. Bubbles are not necessarily irrational, but they are certainly inefficient to the extent that they lead to the misallocation of resources when prices are rising and unexploited profit opportunities when prices head south.
Asset bubbles are very common affairs. Literally thousands of bubbles have arisen throughout human history, typically when assets
1. can be purchased with cheap, borrowed money;
2. attract the attention of numerous, inexperienced traders;
3. cannot be easily “sold short” (when nobody can profit from a declining price);
4. are subject to high levels of moral hazard due to the expectation of a bailout (rescue funds provided by the government or other entity);
5. are subject to high agency costs (e.g., poorly aligned incentives between investors and intermediaries or market facilitators).
Agricultural commodities (e.g., tulips, tea, sheep, and sugar beets) have experienced bubbles most frequently but the precious metals (gold and silver), real estate, equities, bonds, and derivatives have also witnessed bubble activity. Most bubbles caused relatively little economic damage, but a real estate bubble in the early 1760s helped to foment the American Revolution, one in Treasury bonds helped to form the two party system in the 1790s, and one in stocks exacerbated the Great Depression. Since the tech bubble burst in 2000, we’ve already experienced another, in housing and home mortgages. Recurrent investor euphoria may be rooted in the deepest recesses of the human mind. Whether we evolved from the great apes or were created by some Divine Being, one thing is clear: our brains are pretty scrambled, especially when it comes to probabilities and percentages. For example, a recent study[8] published in Review of Finance showed that investors, even sophisticated ones, expect less change in future stock prices when asked to state their forecasts in currency (so many dollars or euros per share) than when asked to state them as returns (a percentage gain or loss).[9]
Behavioral finance uses insights from evolutionary psychology, anthropology, sociology, the neurosciences, and psychology to try to unravel how the human brain functions in areas related to finance.[10] For example, many people are averse to short selling, selling (or borrowing and then selling) a stock that appears overvalued with the expectation of buying it back later at a lower price. (Short sellers profit by owning more shares of the stock, or the same number of shares and a sum of cash, depending on how they go about it.) A dearth of short selling may allow stock prices to spiral too high, leading to asset bubbles. Another human foible is that we tend to be overly confident in our own judgments. Many actually believe that they are smarter than the markets in which they trade! (As noted above, many researchers appear to fall into the same trap.) People also tend to herd. They will, like the common misconception about lemmings, run with the crowd, seemingly oblivious to the cliff looming just ahead.
Many people also fail the so-called Linda Problem. When asked if a twenty-seven-year-old philosophy major concerned about social issues is more likely to be either (a) a bank teller or (b) a bank teller active in a local community activist organization, most choose the latter. The former, however, is the logical choice because b is a subset of a. The St. Petersburg Paradox also points to humanity’s less-than-logical brain: most people will pay \$1 for a one-in-a-million chance to win \$1 million dollars but they will not receive \$1 for a one-in-a-million chance of losing \$1 million dollars, although the two transactions, as opposite sides of the same bet, are mathematically equivalent.[11] Most people, it seems, are naturally but irrationally risk averse.
Finally, as noted above, another source of inefficiency in financial (and nonfinancial) markets is asymmetric information, when one party to a transaction has better information than the other. Usually, the asymmetry arises due to inside information as when the seller, for instance, knows the company is weak but the buyer does not. Regulators try to reduce information asymmetries by outlawing outright fraud and by encouraging timely and full disclosure of pertinent information to the public. In short, they try to promote what economists call transparency. Some markets, however, remain quite opaque.[12]
In short, our financial markets appear to be semistrong form efficient. Greater transparency and more fervent attempts to overcome the natural limitations of human rationality would help to move the markets closer to strong form efficiency.
KEY TAKEAWAYS
• Beyond allocational efficiency, markets may be classed as weak, semistrong, or strong form efficient.
• If the market is weak form efficient, technical analysis is useless because securities prices already reflect past prices.
• If the market is semistrong form efficient, fundamental analysis is also useless because prices reflect all publicly available information.
• If the market is strong form efficient, inside information is useless too because prices reflect all information.
• Securities prices tend to track each other closely over time and in fact usually display random walk behavior, moving up and down unpredictably.
• Neither technical analysis nor fundamental analysis outperforms the market on average, but inside information apparently does, so most financial markets today are at best semistrong form efficient.
• Although more efficient than commodities, labor, and services markets, financial markets are not completely efficient.
• Various anomalies, like the January and small-firm effects, market overreaction and volatility, mean reversion, and asset bubbles, suggest that securities markets sometimes yield outsized gains to the quick and the smart, people who overcome the mushy, often illogical brains all humans are apparently born with. But the quest is a never-ending one; no strategy works for long.
[1] Any share of the same class, that is. As noted above, some corporations issue preferred shares, which differ from the common shares discussed in this chapter. Other corporations issue shares, usually denominated Class A or Class B, that have different voting rights.
[2] www2.barchart.com/futures.asp
[3] James R. Hagerty, “Foreclosure Rise Brings Business to One Investor,” Wall Street Journal, March 14, 2007, A1.
[4] www.forbes.com/columnists/2005/12/29/higher-education-partnerships-cx_rw_1230college.html
[5] www.amazon.com/Fubarnomics-Lighthearted-Serious-Americas-Economic/dp/1616141913/ref=ntt_at_ep_dpi_3
[6] www.amazon.com/Broken-Buildings-Busted-Budgets-Trillion-Dollar/dp/0226472671/ref=sr_1_1/002-2618567-2654432?ie
[8] Markus Glaser, Thomas Langer, Jens Reynders, and Martin Weber, “Framing Effects in Stock Market Forecasts: The Differences Between Asking for Prices and Asking for Returns,” Review of Finance (2007) 11:325–357.
[9] This is a new example of the well-known framing effect. Predict the future stock price of a stock that goes from \$35 to \$37 to \$39 to \$41 to \$43 to \$45. Now predict the future stock price of a stock whose returns are +\$2, +\$2, +\$2, +\$2, +\$2, and +\$2. If you are like most people, your answer to the first will be less than \$45 but your answer to the second will be +\$2 even though both series provide precisely the same information. In other words, the way a problem is set up or framed influences the way people respond to it.
[11] Not even lottery or raffle organizations make such a bet. Instead, they promise to pay the winner only a percentage of total ticket sales and pocket the rest. That is a major reason why lotteries and other forms of gambling are closely regulated.
7.05: Suggested Reading
Bernstein, Peter. Against the Gods: The Remarkable Story of Risk. Hoboken, NJ: John Wiley and Sons, 1998.
Burnham, Terry. Mean Markets and Lizard Brains: How to Profit from the New Science of Irrationality. Hoboken, NJ: John Wiley and Sons, 2008.
English, James. Applied Equity Analysis: Stock Valuation Techniques for Wall Street Professionals. New York: McGraw-Hill, 2001.
Mackay, Charles, and Joseph de la Vega. Extraordinary Popular Delusions and the Madness of Crowds and Confusion de Confusiones. Hoboken, NJ: John Wiley and Sons, 1995.
Malkiel, Burton. A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing, 9th ed. New York: W. W. Norton, 2007. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/07%3A_Rational_Expectations_Efficient_Markets_and_the_Valuation_of_Corporate_Equities/7.04%3A_Evidence_of_Market_Efficiency.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Describe how nonfinancial companies meet their external financing needs.
• Explain why bonds play a relatively large role in the external financing of U.S. companies.
• Explain why most external finance is channeled through financial intermediaries.
• Define transaction costs and explain their importance.
• Define and describe asymmetric information and its importance.
• Define and explain adverse selection, moral hazard, and agency problems.
• Explain why the financial system is heavily regulated.
Thumbnail: Image by Foxy_ from Pixabay
08: Financial Structure Transaction Costs and Asymmetric Information
Learning Objectives
• How can companies meet their external financing needs?
Thus far, we have spent a lot of time discussing financial markets and learning how to calculate the prices of various types of financial securities, including stocks and bonds. Securities markets are important, especially in the U.S. economy. But you may recall from Chapter 2 that the financial system connects savers to spenders or investors to entrepreneurs in two ways, via markets and via financial intermediaries. It turns out that the latter channel is larger than the former. That’s right, in dollar terms, banks, insurance companies, and other intermediaries are more important than the stock and bond markets. The markets tend to garner more media attention because they are relatively transparent. Most of the real action, however, takes place behind closed doors in banks and other institutional lenders.
Not convinced? Check out Figure 8.1, which shows the sources of external funds for nonfinancial businesses in four of the world’s most advanced economies: the United States, Germany, Japan, and Canada. In none of those countries does the stock market (i.e., equities) supply more than 12 percent of external finance. Loans, from banks and nonbank financial companies, supply the vast bulk of external finance in three of those countries and a majority in the fourth, the United States. The bond market supplies the rest, around 10 percent or so of total external finance (excluding trade credit), except in the United States, where bonds supply about a third of the external finance of nonfinancial businesses. (As we’ll learn later, U.S. banking has been relatively weak historically, which helps to explain why the bond market and loans from nonbank financial companies are relatively important in the United States. In short, more companies found it worthwhile to borrow from life insurance companies or to sell bonds than to obtain bank loans.)
As noted above, the numbers in Figure 8.1 do not include trade credit. Most companies are small and most small companies finance most of their activities by borrowing from their suppliers or, sometimes, their customers. Most such financing, however, ultimately comes from loans, bonds, or stock. In other words, companies that extend trade credit act, in a sense, as nonbank intermediaries, channeling equity, bonds, and loans to small companies. This makes sense because suppliers usually know more about small companies than banks or individual investors do. And information, we’ll see, is key.
Also note that the equity figures are somewhat misleading given that, once sold, a share provides financing forever, or at least until the company folds or buys it back. The figures above do not account for that, so a \$1,000 year-long bank loan renewed each year for 20 years would count as \$20,000 of bank loans, while the sale of \$1,000 of equities would count only as \$1,000. Despite that bias in the methodology, it is clear that most external finance does not, in fact, come from the sale of stocks or bonds. Moreover, in less economically and financially developed countries, an even higher percentage of external financing comes to nonfinancial companies via intermediaries rather than markets.
What explains the facts highlighted in Figure 8.1? Why are bank and other loans more important sources of external finance than stocks and bonds? Why does indirect finance, via intermediaries, trump direct finance, via markets? For that matter, why are most of those loans collateralized? Why are loan contracts so complex? Why are only the largest companies able to raise funds directly by selling stocks and bonds? Finally, why are financial systems worldwide one of the most heavily regulated economic sectors?
Those questions can be answered in three ways: transaction costs, asymmetric information, and the free-rider problem. Explaining what those three terms mean, however, will take a little doing.
KEY TAKEAWAYS
• To meet their external financing needs, companies can sell equity (stock) and commercial paper and longer-term bonds and they can obtain loans from banks and nonbank financial institutions.
• They can also obtain trade credit from suppliers and customers, but most of those funds ultimately come from loans, bonds, or equity.
• Most external financing comes from loans, with bonds and equities a distant second, except in the United States, where bonds provide about a third of external financing for nonfinancial companies.
• Bonds play a relatively larger role in the external financing of U.S. companies because the U.S. banking system has been weak historically. That weakness induced companies to obtain more loans from nonbank financial institutions like life insurance companies and also to issue more bonds. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/08%3A_Financial_Structure_Transaction_Costs_and_Asymmetric_Information/8.01%3A_The_Sources_of_External_Finance.txt |
Learning Objectives
• Why is most external finance channeled through financial intermediaries?
Minimum efficient scale in finance is larger than most individuals can invest. Somebody with \$100, \$1,000, \$10,000, even \$100,000 to invest would have a hard time making any profit at all, let alone the going risk-adjusted return. That is because most of his or her profits would be eaten up in transaction costs like banking and brokerage fees, dealer spreads, attorney fees, and the opportunity cost of his or her time, and liquidity and diversification losses. Many types of bonds come in \$10,000 increments and so are out of the question for many small investors. A single share of some companies, like Berkshire Hathaway, costs thousands or tens of thousands of dollars and so is also out of reach.[1] Most shares cost far less, but transaction fees, even after the online trading revolution of the early 2000s, are still quite high, especially if an investor were to try to diversify by buying only a few shares of many companies. Financial markets are efficient enough that arbitrage opportunities are rare and fleeting. Those who make a living engaging in arbitrage, like hedge fund D. E. Shaw, do so mainly by exploiting scale economies. They need superfast (read “expensive”) computers and nerdy (read “expensive”) employees to operate custom (read “expensive”) programs on them. They also need to engage in large-scale transactions because of high fixed costs. With a flat brokerage fee of \$50, for example, you won’t profit making .001 percent on a \$1,000 trade, but you will on a \$1,000,000,000 one.
What about making loans directly to entrepreneurs or other borrowers? Fuggeddaboutit! The time, trouble, and cash (e.g., for advertisements like that in Figure 8.2) it would take to find a suitable borrower would likely wipe out any profits from interest. The legal fees alone would swamp you! (It helps if you can be your own lawyer, like John C. Knapp.) And, as we’ll learn below, making loans isn’t all that easy. You’ll still occasionally see advertisements like those that used to appear in the eighteenth century, but they are rare and might in fact be placed by predators, people who are more interested in robbing you (or worse) than lending to you. A small investor might be able to find a relative, co-religionist, colleague, or other acquaintance to lend to relatively cheaply. But how could the investor know if the borrower was the best one, given the interest rate charged? What is the best rate, anyway? To answer those questions even haphazardly would cost relatively big bucks. And here is another hint: friends and relatives often think that a “loan” is actually a “gift,” if you catch my “drift.”
A new type of banking, called peer-to-peer banking, might reduce some of those transaction costs. In peer-to-peer banking, a financial facilitator, like Zopa.com or Prosper.com, reduces transaction costs by electronically matching individual borrowers and lenders. Most peer-to-peer facilitators screen loan applicants in at least a rudimentary fashion and also provide diversification services, distributing lenders’ funds to numerous borrowers to reduce the negative impact of any defaults.[2] Although the infant industry is currently growing, the peer-to-peer concept is still unproven and there are powerful reasons to doubt its success. Even if the concept succeeds (and it might given its Thomas Friedman–The World Is Flatishness[3]), it will only reinforce the point made here about the inability of most individuals to invest profitably without help.
Financial intermediaries clearly can provide such help. They have been doing so for at least a millennium (yep, a thousand years, maybe more). One key to their success is their ability to keep credit information that they have created a secret. Bankers have incentives to discover who the best borrowers are because it is difficult for others to steal that information. Insurers cannot simply wait for another insurer to discern good from bad risks and then exploit the information. Free riding, in other words, is minimal in traditional financial intermediation.
Another key is the ability of financial intermediaries to achieve minimum efficient scale. Banks, insurers, and other intermediaries pool the resources of many investors. That allows them to diversify cheaply because instead of buying 10 shares of XYZ’s \$10 stock and paying \$7 for the privilege (7/100 = .07) they can buy 1,000,000 shares for a brokerage fee of maybe \$1,000 (\$1,000/1,000,000 = .001). In addition, financial intermediaries do not have to sell assets as frequently as individuals (ceteris paribus, of course) because they can usually make payments out of inflows like deposits or premium payments. Their cash flow, in other words, reduces their liquidity costs. Individual investors, on the other hand, often find it necessary to sell assets (and incur the costs associated therewith) to pay their bills.
As specialists, financial intermediaries are also experts at what they do. That does not mean that they are perfect—far from it, as we learned during the financial crisis that began in 2007—but they are certainly more efficient at accepting deposits, making loans, or insuring risks than you or I will ever be (unless we work for a financial intermediary, in which case we’ll likely become incredibly efficient in one or at most a handful of functions). That expertise covers many areas, from database management to telecommunications. But it is most important in the reduction of asymmetric information.
Asymmetric information is the devil incarnate, a scourge of humanity second only to scarcity. Seriously, it is a crucial concept to grasp if you want to understand why the financial system exists, and why it is, for the most part, heavily regulated. Asymmetric information makes our markets, financial and otherwise, less efficient than they otherwise would be by allowing the party with superior information to take advantage of the party with inferior information. Where asymmetric information is high, resources are not put to their most highly valued uses, and it is possible to make outsized profits by cheating others. Asymmetric information helps to give markets, including financial markets, the bad rep they have acquired in some circles.
Financial intermediaries and markets can reduce or mitigate asymmetric information, but they can no more eliminate it than they can end scarcity. Financial markets are more transparent than ever before, yet dark corners remain.[4] The government and market participants can, and have, forced companies to reveal important information about their revenues, expenses, and the like, and even follow certain accounting standards.[5] As a CEO in a famous Wall Street Journal cartoon once put it, “All these regulations take the fun out of capitalism.” But at the edges of every rule and regulation there is ample room for shysters to play.[6] When managers found that they could not easily manipulate earnings forecasts (and hence stock prices, as we learned in Chapter 7), for example, they began to backdate stock options to enrich themselves at the expense of stockholders and other corporate stakeholders.
What is the precise nature of this great asymmetric evil? Turns out this devil, this Cerberus, has three heads: adverse selection, moral hazard, and the principal-agent problem. Let’s lop off each head in turn.
KEY TAKEAWAYS
• Transaction costs, asymmetric information, and the free-rider problem explain why most external finance is channeled through intermediaries.
• Most individuals do not control enough funds to invest profitably given the fact that fixed costs are high and variable costs are low in most areas of finance. In other words, it costs almost as much to buy 10 shares as it does to buy 10,000.
• Also, individuals do not engage in enough transactions to be proficient or expert at it.
• Financial intermediaries, by contrast, achieve minimum efficient scale and become quite expert at what they do, though they remain far from perfect.
• Transaction costs are any and all costs associated with completing an exchange.
• Transaction costs include, but are not limited to, broker commissions; dealer spreads; bank fees; legal fees; search, selection, and monitoring costs; and the opportunity cost of time devoted to investment-related activities.
• They are important because they detract from bottom-line profits, eliminating or greatly reducing them in the case of individuals and firms that have not achieved minimum efficient scale.
• Transaction costs are one reason why institutional intermediaries dominate external finance.
[2] For details, see “Options Grow for Investors to Lend Online,” Wall Street Journal, July 18, 2007.
[5] www.fasb.org | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/08%3A_Financial_Structure_Transaction_Costs_and_Asymmetric_Information/8.02%3A_Transaction_Costs_Asymmetric_Information_and_the_Free-Rider_Problem.txt |
Learning Objectives
• What problems do asymmetric information and, more specifically, adverse selection cause and how can they be mitigated?
Adverse selection is precontractual asymmetric information. It occurs because the riskiest potential borrowers and insureds have the greatest incentive to obtain a loan or insurance.
The classic case of adverse selection, the one that brought the phenomenon backClassical economists like Adam Smith recognized adverse selection and asymmetric information more generally, but they did not label or stress the concepts.to the attention of economists in 1970, is the market for “lemons,” which is to say, breakdown-prone automobiles. The lemons story, with appropriate changes, applies to everything from horses to bonds, to lemons (the fruit), to construction services. That is because the lemons story is a simple but powerful one. People who offer lemons for sale know that their cars stink. Most people looking to buy cars, though, can’t tell that a car is prone to breakdown. They might kick the tires, take it for a short spin, look under the hood, etc., all without discovering the truth. The seller has superior information and indeed has an incentive to increase the asymmetry by putting a Band-Aid over any obvious problems. (He might, for example, warm the car up thoroughly before showing it, put top-quality gasoline in the tank, clean up the oil spots in the driveway, and so forth.) He may even explain that the car was owned by his poor deceased grandmother, who used it only to drive to church on Sundays (for services) and Wednesdays (for bingo), and that she took meticulous care of it. The hapless buyer, the story goes, offers the average price for used cars of the particular make, model, year, and mileage for sale. The seller happily (and greedily if you want to be moralistic about it) accepts. A day, week, month, or year later, the buyers learns that he has overpaid, that the automobile he purchased is a lemon. He complains to his relatives, friends, and neighbors, many of whom tell similar horror stories. A consensus emerges that all used cars are lemons.
Of course, some used cars are actually “peaches,” very reliable means of personal transportation. The problem is that owners of peaches can’t credibly inform buyers of the car’s quality. Oh, she can say, truthfully, that the car was owned by her poor deceased grandmother who used it only to drive to church on Sundays (for services) and Wednesdays (for bingo) and that she took meticulous care of it. But that sounds a lot like what the owner of the lemon says too. (In fact, we just copied and pasted it from above!) So the asymmetric information remains and the hapless buyer offers the average price for used cars of the particular make, model, year, and mileage for sale. (Another copy and paste job!) But this time the seller, instead of accepting the offer, gets offended and storms off (or at least declines). So the buyer’s relatives, friends, and neighbors are half right—not all the used cars for sale are lemons, but those that are bought are!
Now appears our hero, the used car dealer, who is literally a dealer in the same sense a securities dealer is: he buys from sellers at one (bid) price and then sells to buyers at a higher (ask) price. He earns his profits or spread by facilitating the market process by reducing asymmetric information. Relative to the common person, he is an expert at assessing the true value of used automobiles. (Or his operation is large enough that he can hire such people and afford to pay them. See the transaction costs section above.) So he pays more for peaches than lemons (ceteris paribus, of course) and the used car market begins to function at a much higher level of efficiency. Why is it, then, that the stereotype of the used car salesman is not very complimentary? That the guy in Figure 8.4 "Shady used car salesman" seems more typical than the guy in Figure 8.5?
Several explanations come to mind. The market for used car dealers may be too competitive, leading to many failures, which gives dealers incentives to engage in rent seeking (ripping off customers) and disincentives to establish long-term relationships. Or the market may not be competitive enough, perhaps due to high barriers to entry. Because sellers and buyers have few choices, dealers find that they can engage in sharp business practiceswww.m-w.com/dictionary/sharp and still attract customers as long as they remain better than the alternative, the nonfacilitated market. I think the latter more likely because in recent years, many used car salesmen have cleaned up their acts in the face of national competition from the likes of AutoNation and similar companies.en.Wikipedia.org/wiki/AutoNation Moreover, CarFax.com and similar companies have reduced asymmetric information by tracking vehicle damage using each car’s unique vehicle identification number (VIN), making it easier for buyers to reduce asymmetric information without the aid of a dealer.
What does this have to do with the financial system? Plenty, as it turns out. As noted above, adverse selection applies to a wide variety of markets and products, including financial ones. Let’s suppose that, like our friend Mr. Knapp above, you have some money to lend and the response to your advertisement is overwhelming. Many borrowers are in the market. Information is asymmetric—you can’t really tell who the safest borrowers are. So you decide to ration the credit as if it were apples, by lowering the price you are willing to give for their bonds (raising the interest rate on the loan). Big mistake! As the interest rate increases (the sum that the borrower/securities seller will accept for his IOU decreases), the best borrowers drop out of the bidding. After all, they know that their projects are safe, that they are the equivalent of an automotive peach. People with riskier business projects continue bidding until they too find the cost of borrowing too high and bow out, leaving you to lend to some knave, to some human lemon, at a very high rate of interest. That, our friend, is adverse selection.
Adverse selection also afflicts the market for insurance. Safe risks are not willing to pay much for insurance because they know that the likelihood that they will suffer a loss and make a claim is low. Risky people and companies, by contrast, will pay very high rates for insurance because they know that they will probably suffer a loss. Anyone offering insurance on the basis of premium alone will end up with the stinky end of the stick, just as the lender who rations on price alone will.
Like used car dealers, financial facilitators and intermediaries seek to profit by reducing adverse selection. They do so by specializing in discerning good from bad credit and insurance risks. Their main weapon here is called screening and it’s what all those forms and questions are about when you apply for a loan or insurance policy. Potential lenders want to know if you pay your bills on time, if your income minus expenses is large and stable enough to service the loan, if you have any collateral that might protect them from loss, and the like. Potential insurers want to know if you have filed many insurance claims in the past because that may indicate that you are clumsy; not very careful with your possessions; or worse, a shyster who makes a living filing insurance claims. They also want to know more about the insured property so they don’t insure it for too much, a sure inducement to start a fire or cause an accident. They also need to figure out how much risk is involved, how likely a certain type of car is to be totaled if involved in an accident,www.edmunds.com/ownership/safety/articles/43804/article.html the probability of a wood-frame house burning to the ground in a given area,www.usfa.dhs.gov/statistics/national/residential.shtm the chance of a Rolex watch being stolen, and so forth.
Stop and Think Box
Credit-protection insurance policies promise to make payments to people who find themselves unemployed or incapacitated. Whenever solicited to buy such insurance, I (Wright) always ask how the insurer overcomes adverse selection because there are never any applications or premium schedules, just one fixed rate. Why do I care?
I care because I’m a peach of a person. I know that if I lived a more dangerous lifestyle or was employed in a more volatile industry that I’d snap the policy right up. Given my current situation, however, I don’t think it very likely that I will become unemployed or incapacitated, so I don’t feel much urgency to buy such a policy at the same rate as some guy or gal who’s about to go skydiving instead of going to work. I don’t want to subsidize them or to deal with a company that doesn’t know the first thing about insurance.
Financial intermediaries are not perfect screeners. They often make mistakes. Insurers like State Farm, for example, underestimated the likelihood of a massive storm like Katrina striking the Gulf Coast. And subprime mortgage lenders, companies that lend to risky borrowers on the collateral of their homes, grossly miscalculated the likelihood that their borrowers would default. Competition between lenders and insurers induces them to lower their screening standards to make the sale. (In a famous cartoon in the Wall Street Journal, a clearly nonplussed father asks a concerned mom how their son’s imaginary friend got preapproved for a credit card.) At some point, though, adverse selection always rears its ugly head, forcing lenders and insurance providers to improve their screening procedures and tighten their standards once again. And, on average, they do much better than you or I acting alone could do.
Another way of reducing adverse selection is the private production and sale of information. Before the 1970s, companies like Standard and Poor’s, Bests, Duff and Phelps, Fitch’s, and Moody’s compiled and analyzed data on companies, rated the riskiness of their bonds, and then sold that information to investors in huge books. The free-rider problem, though, killed off that business model. Specifically, the advent of cheap photocopying induced people to buy the books, photocopy them, and sell them at a fraction of the price that the bond-rating agencies could charge. (The free riders had to pay only the variable costs of publication; the rating agencies had to pay the large fixed costs of compiling and analyzing the data.) So in the mid-1970s, the bond-rating agencies began to give their ratings away to investors and instead charged bond issuers for the privilege of being rated. The new model greatly decreased the effectiveness of the ratings because the new arrangement quickly led to rating inflation similar to grade inflation. (Pleasure flows with the cash. Instead of pleasing investors, the agencies started to please the issuers.) After every major financial crisis, including the subprime mortgage mess of 2007, academics and former government regulators lambaste credit-rating agencies for their poor performance relative to markets and point out the incentive flaws built into their business model. Thus far, little has changed, but encrypted databases might allow a return to the investor-pay model. But then another form of free riding would arise as investors who did not subscribe to the database would observe and mimic the trades of those investors known to have subscriptions. Due to the free-rider problem inherent in markets, banks and other financial intermediaries have incentives to create private information about borrowers and people who are insured. This helps to explain why they trump bond and stock markets.
Adverse selection can also be reduced by contracting with groups instead of individuals. Insurers, for example, offer group health and life insurance policies to employers because doing so reduces adverse selection. Chronically or terminally ill people usually do not seek employment, so the riskiest part of the population is excluded from the insurance pool. Moreover, it is easier for insurers to predict how many claims a group of people will submit over some period of time than to predict the probability that a specific individual will make a claim. Life expectancy tables,www.ssa.gov/oact/STATS/table4c6.html for example, accurately predict how many people will die in a given year but not which particular individuals will perish.
Governments can no more legislate away adverse selection than they can end scarcity by decree. They can, however, give markets and intermediaries a helping hand. In the United States, for example, the Securities and Exchange Commission (SEC) tries to ensure that corporations provide market participants with accurate and timely information about themselves, reducing the information asymmetry between themselves and potential bond- and stockholders.www.sec.gov Like sellers of lemons, however, bad companies often outfox the SEC (and similar regulators in other countries) and investors, especially when said investors place too much confidence in government regulators. In 2001, for example, a high-flying energy trading company named Enron suddenly encountered insurmountable financial difficulties and was forced to file for bankruptcy, the largest in American history at that time. Few saw Enron’s implosion coming because the company hid its debt and losses in a maze of offshore shell companies and other accounting smokescreens. Some dumbfounded investors hadn’t bothered watching the energy giant because they believed the government was doing it for them. It wasn’t.
KEY TAKEAWAYS
• Asymmetric information decreases the efficiency of financial markets, thereby reducing the flow of funds to entrepreneurs and injuring the real economy.
• Adverse selection is precontractual asymmetric information.
• It can be mitigated by screening out high-risk members of the applicant pool.
• Financial market facilitators can also become expert specialists and attain minimum efficient scale, but financial markets are hampered by the free-rider problem.
• In short, few firms find it profitable to produce information because it is easy for others to copy and profit from it. Banks and other intermediaries, by contrast, create proprietary information about their borrowers and people they insure. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/08%3A_Financial_Structure_Transaction_Costs_and_Asymmetric_Information/8.03%3A_Adverse_Selection.txt |
Learning Objectives
• What is moral hazard and how can it be mitigated?
Moral hazard is postcontractual asymmetric information. It occurs whenever a borrower or insured entity (an approved borrower or policyholder, not a mere applicant) engages in behaviors that are not in the best interest of the lender or insurer. If a borrower uses a bank loan to buy lottery tickets instead of Treasuries, as agreed upon with the lender, that’s moral hazard. If an insured person leaves the door of his or her home or car unlocked or lets candles burn all night unattended, that’s moral hazard. It’s also moral hazard if a borrower fails to repay a loan when he or she has the wherewithal to do so, or if an insured driver fakes an accident.
We call such behavior moral hazard because it was long thought to indicate a lack of morals or character and in a sense it does. But thinking about the problem in those terms does not help to mitigate it. We all have a price. How high that price is can’t be easily determined and may indeed change, but offered enough money, every human being (except maybe Gandhi, prophets, and saints) will engage in immoral activities for personal gain if given the chance. It’s tempting indeed to put other people’s money at risk. As we’ve learned, the more risk, the more reward. Why not borrow money to put to risk? If the rewards come, the principal and interest are easily repaid. If the rewards don’t come, the borrower defaults and suffers but little. Back in the day, as they say, borrowers who didn’t repay their loans were thrown into jail until they paid up. Three problems eventually ended that practice. First, it is difficult to earn money to repay the loan when you’re imprisoned! (The original assumption was that the borrower had the money but wouldn’t cough it up.) Second, not everyone defaults on a loan due to moral hazard. Bad luck, a soft economy, and/or poor execution can turn the best business plan to mush. Third, lenders are almost as culpable as the borrowers for moral hazard if they don’t take steps to try to mitigate it. A locked door, an old adage goes, keeps an honest man honest. Don’t tempt people, in other words, and most won’t rob you. There are locks against moral hazard. They are not foolproof but they get the job done most of the time.
Stop and Think Box
Investment banks engage in many activities, two of which, research and underwriting, have created conflicts of interest. The customers of ibanks’ research activities, investors, want unbiased information. The customers of ibanks’ underwriting activities, bond issuers, want optimistic reports. A few years back, problems arose when the interests of bond issuers, who provided ibanks with most of their profits, began to supersede the interests of investors. Specifically, ibank managers forced their research departments to avoid making negative or controversial comments about clients. The situation grew worse during the Internet stock mania of the late 1990s, when ibank research analysts like Jack Grubman (a Dickensian name but true!) of Citigroup (then Salomon Smith Barney) made outrageous claims about the value of high-tech companies. That in itself wasn’t evil because everyone makes mistakes. What raised hackles was that the private e-mails of those same analysts indicated that they thought the companies they were hyping were extremely weak. And most were. What sort of problem does this particular conflict of interest represent? How does it injure the economy? What can be done to rectify the problem?
This is an example of asymmetric information and, more specifically, moral hazard. Investors contracted with the ibanks for unbiased investment research but instead received extremely biased advice that induced them to pay too much for securities, particularly the equities of weak tech companies. As a result, the efficiency of our financial markets decreased as resources went to firms that did not deserve them and could not put them to their most highly valued use. That, of course, injured economic growth. One way to solve this problem would be to allow ibanks to engage in securities underwriting or research, but not both. That would make ibanks less profitable, though, as doing both creates economies of scope. (That’s why ibanks got into the business of selling research in the first place.) Another solution is to create a “Chinese wall” within each ibank between their research and underwriting departments. This apparent reference to the Great Wall of China, which despite its grandeur was repeatedly breached by “barbarian” invaders with help from insiders, also belies that strategy’s weakness.en.Wikipedia.org/wiki/Great_Wall_of_China If the wall is so high that it is impenetrable, then the economies of scope are diminished to the vanishing point. If the wall is low or porous, then the conflict of interest can again arise. Rational expectations and transparency could help here. Investors now know (or at least could/should know) that ibanks can provide biased research reports and hence should remain wary. Government regulations could help here by mandating that ibanks completely and accurately disclose their interests in the companies that they research and evaluate. That extra transparency would then allow investors to discount rosy prognostications that appear to be driven by ibanks’ underwriting interests. The Global Legal Settlement of 2002, which was brokered by Eliot Spitzer (then New York State Attorney General and New York’s governor until he ran into a little moral hazard problem himself!), bans spinning, requires investment banks to sever the links between underwriting and research, and slapped a \$1.4 billion fine on the ten largest ibanks.
The main weapon against moral hazard is monitoring, which is just a fancy term for paying attention! No matter how well they have screened (reduced adverse selection), lenders and insurers cannot contract and forget. They have to make sure that their customers do not use the superior information inherent in their situation to take advantage. Banks have a particularly easy and powerful way of doing this: watching checking accounts. Banks rarely provide cash loans because the temptation of running off with the money, the moral hazard, would be too high. Instead, they credit the amount of the loan to a checking account upon which the borrower can draw funds. (This procedure has a second positive feature for banks called compensatory balances. A loan for, say, \$1 million does not leave the bank at once but does so only gradually. That raises the effective interest rate because the borrower pays interest on the total sum, not just that drawn out of the bank.) The bank can then watch to ensure that the borrower is using the funds appropriately. Most loans contain restrictive covenants, clauses that specify in great detail how the loan is to be used and how the borrower is to behave. If the borrower breaks one or more covenants, the entire loan may fall due immediately. Covenants may require that the borrower obtain life insurance, that he or she keep collateral in good condition, or that various business ratios be kept within certain parameters.www.toolkit.cch.com/text/P06_7100.asp Often, loans will contain covenants requiring borrowers to provide lenders with various types of information, including audited financial reports, thus minimizing the lender’s monitoring costs.
Another powerful way of reducing moral hazard is to align incentives. That can be done by making sure the borrower or insured has some skin in the game,www.answers.com/topic/skin-in-the-game that he, she, or it will suffer if a loan goes bad or a loss is incurred. That will induce the borrower or insured to behave in the lender’s or insurer’s best interest. Collateral, property pledged for the repayment of a loan, is a good way to reduce moral hazard. Borrowers don’t take kindly to losing, say, their homes. Also, the more equity they have—in their home or business or investment portfolio—the harder they will fight to keep from losing it. Some will still default, but not purposely. In other words, the higher one’s net worth (market value of assets minus market value of liabilities), the less likely one is to default, which could trigger bankruptcy proceedings that would reduce or even wipe out the borrower’s net worth. This is why, by the way, it is sometimes alleged that you have to have money to borrow money. That isn’t literally true, of course. What is true is that owning assets free and clear of debt makes it much easier to borrow.
Similarly, insurers long ago learned that they should insure only a part of the value of a ship, car, home, or life. That is why they insist on deductibles or co-insurance. If you will lose nothing if you total your car, you might attempt that late-night trip on icy roads or sign up for a demolition derby. If an accident will cost you \$500 (deductible) or 20 percent of the costs of the damage (co-insurance), you will think twice or thrice before doing something risky with your car.
When it comes to reducing moral hazard, financial intermediaries have advantages over individuals. Monitoring is not cheap. Indeed, economists sometimes refer to it as “costly state verification.” Economies of scale give intermediaries an upper hand. Monitoring is also not easy, so specialization and expertise also render financial intermediaries more efficient than individuals at reducing moral hazard. If nothing else, financial intermediaries can afford to hire the best legal talent to frighten the devil out of would-be scammers. Borrowers can no longer be imprisoned for defaulting, but they can go to prison for fraud. Statutes against fraud are one way that the government helps to chop at the second head of the asymmetric information Cerberus.
Financial intermediaries also have monitoring advantages over markets. Bondholder A will try to free-ride on Bondholder B, who will gladly let Bondholder C suffer the costs of state verification, and all of them hope that the government will do the dirty work. In the end, nobody may monitor the bond issuer.
KEY TAKEAWAYS
• Moral hazard is postcontractual asymmetric information.
• Moral hazard can be mitigated by monitoring counterparties after contracting. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/08%3A_Financial_Structure_Transaction_Costs_and_Asymmetric_Information/8.04%3A_Moral_Hazard.txt |
Learning Objectives
• What are agency problems and how can they be mitigated?
The principal-agent problem is an important subcategory of moral hazard that involves postcontractual asymmetric information of a specific type. In many, nay, most instances, principals (owners) must appoint agents (employees) to conduct some or all of their business affairs on their behalf. Stockholders in joint-stock corporations, for example, hire professional managers to run their businesses. Those managers in turn hire other managers, who in turn hire supervisors, who then hire employees (depending on how hierarchical the company is). The principal-agent problem arises when any of those agents does not act in the best interest of the principal, for example, when employees and/or managers steal, slack off, act rudely toward customers, or otherwise cheat the company’s owners. If you’ve ever held a job, you’ve probably been guilty of such activities yourself. (We admit we have, but it’s best not to get into the details!) If you’ve ever been a boss, or better yet an owner, you’ve probably been the victim of agency problems. (Wright has been on this end too, like when he was eight years old and his brother told him their lemonade stand had revenues of only \$1.50 when in fact it brought in \$10.75. Hey, that was a lot of money back then!)
Stop and Think Box
As the author of this textbookideas.repec.org/a/taf/acbsfi/v12y2002i3p419-437.html and many others have pointed out, investment banks often underprice stock initial public offerings (IPOs). In other words, they offer the shares of early-stage companies that decide to go public for too little money, as evidenced by the large first day “pops” or “bumps” in the stock price in the aftermarket (the secondary market). Pricing the shares of a new company is tricky business, but the underpricing was too prevalent to have been honest errors, which one would think would be too high about half of the time and too low the other half. All sorts of reasons were proffered for the systematic underpricing, including the fact that many shares could not be “flipped” or resold for some weeks or months after the IPO. Upon investigation, however, a major cause of underpricing turned out to be a conflict of interest called spinning: ibanks often purposely underpriced IPOs so that there would be excess demand, so that investors would demand a larger quantity of shares than were being offered. Whenever that occurs, shares must be rationed by nonprice mechanisms. The ibanks could then dole out the hot shares to friends or family, and, in return for future business, the executives of other companies! Who does spinning hurt? Help? Be as specific as possible.
Spinning hurts the owners of the company going public because they do not receive as much from the IPO as they could have if the shares were priced closer to the market rate. It may also hurt investors in the companies whose executives received the underpriced shares who, in reciprocation for the hot shares, might not use the best ibank when their companies later issue bonds or stock or attempt a merger or acquisition. Spinning helps the ibank by giving it a tool to acquire more business. It also aids whoever gets the underpriced shares.
Monitoring helps to mitigate the principal-agent problem. That’s what supervisors, cameras, and corporate snitches are for. Another, often more powerful way of reducing agency problems is to try to align the incentives of employees with those of owners by paying efficiency wages, commissions, bonuses, stock options, and the like. Caution is the watchword here, though, because people will do precisely what they have incentive to do. Failure to recognize that apparently universal human trait has had adverse consequences for some organizations, a point made in business schools through easily understood case stories. In one story, a major ice cream retailer decided to help out its employees by allowing them to consume, free of charge, any mistakes they might make in the course of serving customers. What was meant to be an environmentally sensitive (no waste) little perk turned into a major problem as employee waistlines bulged and profits shrank because hungry employees found it easy to make delicious frozen mistakes. (“Oh, you said chocolate. I thought you said my favorite flavor, mint chocolate chip. Excuse me because I am now on break.”)
In another story, a debt collection agency reduced its efficiency and profitability by agreeing to a change in the way that it compensated its collectors. Initially, collectors received bonuses based on the dollars collected divided by the dollars assigned to be collected. So, for example, a collector who brought in \$250,000 of the \$1 million due on his accounts would receive a bigger bonus than a collector who collected only \$100,000 of the same denominator (250/1,000 = .25 > 100/1,000 = .10). Collectors complained, however, that it was not fair to them if one or more of their accounts went bankrupt, rendering collection impossible. The managers of the collection agency agreed and began to deduct the value of bankrupt accounts from the collectors’ denominators. Under the new incentive scheme, a collector who brought in \$100,000 would receive a bigger bonus than his colleague if, say, \$800,000 of his accounts claimed bankruptcy (100/[1,000 – 800 = 200] = .5, which is > 250/1,000 = .25). Soon, the collectors transformed themselves into bankruptcy counselors! The new scheme inadvertently created a perverse incentive, that is, one diametrically opposed to the collection agency’s interest, which was to collect as many dollars as possible, not to help debtors file for bankruptcy.
In a competitive market, pressure from competitors and the incentives of managers would soon rectify such mishaps. But when the incentive structure of management is out of kilter, bigger and deeper problems often appear. When managers are paid with stock options, for instance, they are given an incentive to increase stock prices, which they almost invariably do, sometimes by making their companies’ more efficient but sometimes, as investors in the U.S. stock market in the late 1990s learned, through accounting legerdemain. Therefore, corporate governance looms large and requires constant attention from shareholders, business consulting firms, and government regulators.
A free-rider problem, however, makes it difficult to coordinate the monitoring activities that keep agents in line. If Stockholder A watches management, then Stockholder B doesn’t have to but he will still reap the benefits of the monitoring. Ditto with Stockholder A, who sits around hoping Stockholder B will do the dirty and costly work of monitoring executive pay and perks, and the like. Often, nobody ends up monitoring managers, who raise their salaries to obscene levels, slack off work, go empire-building, or all three!www.investopedia.com/terms/e/empirebuilding.asp This governance conundrum helps to explain why the sale of stocks is such a relatively unimportant form of external finance worldwide.
Governance becomes less problematic when the equity owner is actively involved in management. That is why investment banker J. P. Morgan used to put “his people” (principals in J. P. Morgan and Company) on the boards of companies in which Morgan had large stakes. A similar approach has long been used by Warren Buffett’s Berkshire Hathaway. Venture capital firms also insist on taking some management control and have the added advantage that the equity of startup firms does not, indeed cannot, trade. (It does only after it holds an IPO or direct public offering [DPO]). So other investors cannot free-ride on its costly state verification. The recent interest in private equity, funds invested in privately owned (versus publicly traded) companies, stems from this dynamic as well as the desire to avoid costly regulations like Sarbanes-Oxley.www.sec.gov/info/smallbus/pnealis.pdf
Stop and Think Box
Investment banks are not the only financial services firms that have recently suffered from conflicts of interest. Accounting firms that both audit (confirm the accuracy and appropriateness of) corporate financial statements and provide tax, business strategy, and other consulting services found it difficult to reconcile the conflicts inherent in being both the creator and the inspector of businesses. Auditors were too soft in the hopes of winning or keeping consulting business because they could not very well criticize the plans put in place by their own consultants. One of the big five accounting firms, Arthur Andersen, actually collapsed after the market and the SEC discovered that its auditing procedures had been compromised. How could this type of conflict of interest be reduced?
In this case, simply informing investors of the problem would probably not work. Financial statements have to be correct; the free-rider problem ensures that no investor would have an incentive to verify them him- or herself. The traditional solution to this problem was the auditor and no better one has yet been found. But the question is, how to ensure that auditors do their jobs? One answer, enacted in the Sarbanes-Oxley Act of 2002 (aka SOX and Sarbox), is to establish a new regulator, the Public Company Accounting Oversight Board (PCAOB) to oversee the activities of auditors.www.pcaobus.org The law also increased the SEC’s budget (but it’s still tiny compared to the grand scheme of things), made it illegal for accounting firms to offer audit and nonaudit services simultaneously, and increased criminal charges for white-collar crimes. The most controversial provision in SOX requires corporate executive officers (CEOs) and corporate financial officers (CFOs) to certify the accuracy of corporate financial statements and requires corporate boards to establish unpaid audit committees composed of outside directors, that is, directors who are not members of management. The jury is still out on SOX. The consensus so far appears to be that it is overkill: that it costs too much given the benefits it provides.
Government regulators try to reduce asymmetric information. Sometimes they succeed. Often, however, they do not. Asymmetric information is such a major problem, however, that their efforts will likely continue, whether all businesses like it or not.
KEY TAKEAWAYS
• Agency problems are a special form of moral hazard involving employers and employees or other principal-agent relationships.
• Agency problems can be mitigated by closely aligning the incentives of the agents (employees) with those of the principal (employer).
• Regulations are essentially attempts by the government to subdue the Cerberus of asymmetric information.
• Some government regulations, like laws against fraud, are clearly necessary and highly effective.
• Others, though, like parts of Sarbanes-Oxley, may add to the costs of doing business without much corresponding gain.
8.06: Suggested Reading
Allen, Franklin, and Douglas Gale. Comparing Financial Systems. Cambridge, MA: MIT Press, 2001.
Demirguc-Kunt, Asli, and Ross Levine. Financial Structure and Economic Growth: A Cross-Country Comparison of Banks, Markets, and Development. Cambridge, MA: MIT Press, 2004.
Laffont, Jean-Jacques, and David Martimort. The Theory of Incentives: The Principal-Agent Model. Princeton, NJ: Princeton University Press, 2001. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/08%3A_Financial_Structure_Transaction_Costs_and_Asymmetric_Information/8.05%3A_Agency_Problems.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Explain what a balance sheet and a T-account are.
• Explain what banks do in five words and also at length.
• Describe how bankers manage their banks’ balance sheets.
• Explain why regulators mandate minimum reserve and capital ratios.
• Describe how bankers manage credit risk.
• Describe how bankers manage interest rate risk.
• Describe off-balance sheet activities and explain their importance.
Thumbnail: Image by Mudassar Iqbal from Pixabay
09: Bank Management
Learning Objectives
• What is a balance sheet and what are the major types of bank assets and liabilities?
Thus far, we’ve studied financial markets and institutions from 30,000 feet. We’re finally ready to “dive down to the deck” and learn how banks and other financial intermediaries are actually managed. We start with the balance sheet, a financial statement that takes a snapshot of what a company owns (assets) and owes (liabilities) at a given moment. The key equation here is a simple one:
ASSETS (aka uses of funds) = LIABILITIES (aka sources of funds) + EQUITY (aka net worth or capital).
Liabilities are money that companies borrow in order to buy assets, which is why liabilities are sometimes called “sources of funds” and assets, “uses of funds.” The hope is that the liabilities will cost less than the assets will earn, that a bank, for example, will borrow at 2 percent and lend at 5 percent or more. The difference between the two, called the gross spread, is the most important aspect of bank profitability. (The bank’s expenses and taxes, its cost of doing business, is the other major factor in its profitability.)
The equity, net worth, or capital variable is a residual that makes the two sides of the equation balance or equal each other. This is because a company’s owners (stockholders in the case of a joint stock corporation, depositors or policyholders in the case of a mutual) are “junior” to the company’s creditors. If the company shuts down, holders of the company’s liabilities (its creditors) get paid out of the proceeds of the assets first. Anything left after the sale of the assets is then divided among the owners.
If a company is economically viable, the value of what it owns will exceed the value of what it owes. Equity, therefore, will be positive and the company will be a going concern (will continue operating). If a company is not viable, the value of what it owes will exceed what it owns. Equity, therefore, will be negative, and the company will be economically bankrupt. (This does not mean, however, that it will cease operating at that time. Regulators, stockholders, or creditors may force a shutdown well before equity becomes zero, or they may allow the company to continue operating “in the red” in the hope that its assets will increase and/or its liabilities decrease enough to return equity to positive territory.)
The value of assets and liabilities (and, hence, equity) fluctuates due to changes in interest rates and asset prices. How to account for those changes is a difficult yet crucial subject because accounting rules will affect the residual equity and perceptions of a company’s value and viability. Sometimes, it is most appropriate to account for assets according to historical cost—how much the company paid to acquire it. Other times, it is most appropriate to account for assets according to their current market value, a process called “marking to market.” Often, a blend of the two extremes makes the best sense. For instance, a bank might be allowed to hold a bond at its historical cost unless the issuer defaults or is downgraded by a rating agency.
Figure 9.1 lists and describes the major types of bank assets and liabilities, and Figure 9.2 shows the combined balance sheet of all U.S. commercial banks on March 7, 2007. For the most recent figures, browse www.federalreserve.gov/releases/h8/current.
Stop and Think Box
In the first half of the nineteenth century, bank reserves in the United States consisted solely of full-bodied specie (gold or silver coins). Banks pledged to pay specie for both their notes and deposits immediately upon demand. The government did not mandate minimum reserve ratios. What level of reserves do you think those banks kept? (Higher or lower than today’s required reserves?) Why?
With some notorious exceptions known as wildcat banks, which were basically financial scams, banks kept reserves in the range of 20 to 30 percent, much higher than today’s required reserves. They did so for several reasons. First, unlike today, there was no fast, easy, cheap way for banks to borrow from the government or other banks. They occasionally did so, but getting what was needed in time was far from assured. So basically borrowing was closed to them. Banks in major cities like Boston, New York, and Philadelphia could keep secondary reserves, but before the advent of the telegraph, banks in the hinterland could not be certain that they could sell the volume of bonds they needed to into thin local markets. In those areas, which included most banks (by number), secondary reserves were of little use. And the potential for large net outflows was higher than it is today because early bankers sometimes collected the liabilities of rival banks, then presented them all at once in the hopes of catching the other guy with inadequate specie reserves. Also, runs by depositors were much more frequent then. There was only one thing for a prudent early banker to do: keep his or her vaults brimming with coins.
KEY TAKEAWAYS
• A balance sheet is a financial statement that lists what a company owns (its assets or uses of funds) and what it owes (its liabilities or sources of funds).
• Major bank assets include reserves, secondary reserves, loans, and other assets.
• Major bank liabilities include deposits, borrowings, and shareholder equity. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.01%3A_The_Balance_Sheet.txt |
Learning Objectives
• In five words, what do banks do?
• Without a word limitation, how would you describe what functions they fulfill?
As Figure 9.1 and Figure 9.2 show, commercial banks own reserves of cash and deposits with the Fed; secondary reserves of government and other liquid securities; loans to businesses, consumers, and other banks; and other assets, including buildings, computer systems, and other physical stuff. Each of those assets plays an important role in the bank’s overall business strategy. A bank’s physical assets are needed to conduct its business, whether it be a traditional brick-and-mortar bank, a full e-commerce bank (there are servers and a headquarters someplace), or a hybrid click-and-mortar institution. Reserves allow banks to pay their transaction deposits and other liabilities. In many countries, regulators mandate a minimum level of reserves, called required reserves. When banks hold more than the reserve requirement, the extra reserves are called excess reserves. When reserves paid zero interest, as they did until recently, U.S. bankers usually kept excess reserves to a minimum, preferring instead to hold secondary reserves like Treasuries and other safe, liquid, interest-earning securities. Banks’ bread-and-butter asset is, of course, their loans. They derive most of their income from loans, so they must be very careful who they lend to and on what terms. Banks lend to other banks via the federal funds market, but also in the process of clearing checks, which are called “cash items in process of collection.” Most of their loans, however, go to nonbanks. Some loans are uncollateralized, but many are backed by real estate (in which case the loans are called mortgages), accounts receivable (factorage), or securities (call loans).
Stop and Think Box
Savings banks, a type of bank that issues only savings deposits, and life insurance companies hold significantly fewer reserves than commercial banks do. Why?
Savings banks and life insurance companies do not suffer large net outflows very often. People do draw down their savings by withdrawing money from their savings accounts, cashing in their life insurance, or taking out policy loans, but remember that one of the advantages of relatively large intermediaries is that they can often meet outflows from inflows. In other words, savings banks and life insurance companies can usually pay customer A’s withdrawal (policy loan or surrender) from customer B’s deposit (premium payment). Therefore, they have no need to carry large reserves, which are expensive in terms of opportunity costs.
Where do banks get the wherewithal to purchase those assets? The right-hand side of the balance sheet lists a bank’s liabilities or the sources of its funds. Transaction deposits include negotiable order of withdrawal accounts (NOW) and money market deposit accounts (MMDAs), in addition to good old checkable deposits. Banks like transaction deposits because they can avoid paying much, if any, interest on them. Some depositors find the liquidity that transaction accounts provide so convenient they even pay for the privilege of keeping their money in the bank via various fees, of which more anon. Banks justify the fees by pointing out that it is costly to keep the books, transfer money, and maintain sufficient cash reserves to meet withdrawals.
The administrative costs of nontransaction deposits are lower so banks pay interest for those funds. Nontransaction deposits range from the traditional passbook savings account to negotiable certificates of deposit (NCDs) with denominations greater than \$100,000. Checks cannot be drawn on passbook savings accounts, but depositors can withdraw from or add to the account at will. Because they are more liquid, they pay lower rates of interest than time deposits (aka certificates of deposit), which impose stiff penalties for early withdrawals. Banks also borrow outright from other banks overnight via what is called the federal funds market (whether the banks are borrowing to satisfy Federal Reserve requirements or for general liquidity purposes), and directly from the Federal Reserve via discount loans (aka advances). They can also borrow from corporations, including their parent companies if they are part of a bank holding company.
That leaves only bank net worth, the difference between the value of a bank’s assets and its liabilities. Equity originally comes from stockholders when they pay for shares in the bank’s initial public offering (IPO) or direct public offering (DPO). Later, it comes mostly from retained earnings, but sometimes banks make a seasoned offering of additional stock. Regulators watch bank capital closely because the more equity a bank has, the less likely it is that it will fail. Today, having learned this lesson the hard way, U.S. regulators will close a bank down well before its equity reaches zero. Provided, that is, they catch it first. Even well-capitalized banks can fail very quickly, especially if they trade in the derivatives market, of which more below.
At the broadest level, banks and other financial intermediaries engage in asset transformation. In other words, they sell liabilities with certain liquidity, risk, return, and denominational characteristics and use those funds to buy assets with a different set of characteristics. Intermediaries link investors (purchasers of banks’ liabilities) to entrepreneurs (sellers of banks’ assets) in a more sophisticated way than mere market facilitators like dealer-brokers and peer-to-peer bankers do.
More specifically, banks (aka depository institutions) engage in three types of asset transformation, each of which creates a type of risk. First, banks turn short-term deposits into long-term loans. In other words, they borrow short and lend long. This creates interest rate risk. Second, banks turn relatively liquid liabilities (e.g., demand deposits) into relatively illiquid assets like mortgages, thus creating liquidity risk. Third, banks issue relatively safe debt (e.g., insured deposits) and use it to fund relatively risky assets, like loans, and thereby create credit risk.
Other financial intermediaries transform assets in other ways. Finance companies borrow long and lend short, rendering their management much easier than that of a bank. Life insurance companies sell contracts (called policies) that pay off when or if (during the policy period of a term policy) the insured party dies. Property and casualty companies sell policies that pay if some exigency, like an automobile crash, occurs during the policy period. The liabilities of insurance companies are said to be contingent because they come due if an event happens rather than after a specified period of time.
Asset transformation and balance sheets provide us with only a snapshot view of a financial intermediary’s business. That’s useful, but, of course, intermediaries, like banks, are dynamic places where changes constantly occur. The easiest way to analyze that dynamism is via so-called T-accounts, simplified balance sheets that list only changes in liabilities and assets. By the way, they are called T-accounts because they look like a T. Sort of. Note in the T-accounts below the horizontal and vertical rules that cross each other, sort of like a T.
Suppose somebody deposits \$17.52 in cash in a checking account. The T-account for the bank accepting the deposit would be the following:
Some Bank
Assets Liabilities
Reserves +\$17.52 Transaction deposits +\$17.52
If another person deposits in her checking account in Some Bank a check for \$4,419.19 drawn on Another Bank,If that check were drawn on Some Bank, there would be no need for a T-account because the bank would merely subtract the amount from the account of the payer, or in other words, the check maker, and add it to the account of the payee or check recipient. the initial T-account for that transaction would be the following:
Some Bank
Assets Liabilities
Cash in collection +\$4,419.19 Transaction deposits +\$4,419.19
Once collected in a few days, the T-account for Some Bank would be the following:
Some Bank
Assets Liabilities
Cash in collection −\$4,419.19
Reserves +\$4,419.19
The T-account for Another Bank would be the following:
Another Bank
Assets Liabilities
Reserves −\$4,419.19
Transaction deposits +\$4,419.19
Gain some practice using T-accounts by completing the exercises, keeping in mind that each side (assets and liabilities) of a T-account should balance (equal each other) as in the examples above.
EXERCISES
Write out the T-accounts for the following transactions.
1. Larry closes his \$73,500.88 account with JPMC Bank, spends \$500.88 of that money on consumption goods, then places the rest in W Bank.
2. Suppose regulators tell W Bank that it needs to hold only 5 percent of those transaction deposits in reserve.
3. W Bank decides that it needs to hold no excess reserves but needs to bolster its secondary reserves.
4. A depositor in W bank decides to move \$7,000 from her checking account to a CD in W Bank.
5. W Bank sells \$500,000 of Treasuries and uses the proceeds to fund two \$200,000 mortgages and the purchase of \$100,000 of municipal bonds.
(Note: This is net. The bank merely moved \$100,000 from one type of security to another.)
KEY TAKEAWAYS
• In five words, banks lend (1) long (2) and (3) borrow (4) short (5).
• Like other financial intermediaries, banks are in the business of transforming assets, of issuing liabilities with one set of characteristics to investors and of buying the liabilities of borrowers with another set of characteristics.
• Generally, banks issue short-term liabilities but buy long-term assets.
• This raises specific types of management problems that bankers must be proficient at solving if they are to succeed. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.02%3A_Assets_Liabilities_and_T-Accounts.txt |
Learning Objectives
• What are the major problems facing bank managers and why is bank management closely regulated?
Bankers must manage their assets and liabilities to ensure three conditions:
1. Their bank has enough reserves on hand to pay for any deposit outflows (net decreases in deposits) but not so many as to render the bank unprofitable. This tricky trade-off is called liquidity management.
2. Their bank earns profits. To do so, the bank must own a diverse portfolio of remunerative assets. This is known as asset management. It must also obtain its funds as cheaply as possible, which is known as liability management.
3. Their bank has sufficient net worth or equity capital to maintain a cushion against bankruptcy or regulatory attention but not so much that the bank is unprofitable. This second tricky trade-off is called capital adequacy management.
In their quest to earn profits and manage liquidity and capital, banks face two major risks: credit risk, the risk of borrowers defaulting on the loans and securities it owns, and interest rate risk, the risk that interest rate changes will decrease the returns on its assets and/or increase the cost of its liabilities. The financial panic of 2008 reminded bankers that they also can face liability and capital adequacy risks if financial markets become less liquid or seize up completely (trading is greatly reduced or completely stops; q* approaches 0).
Stop and Think Box
What’s wrong with the following bank balance sheet?
Flower City Bank Balance Sheet June 31, 2009 (Thousands USD)
Liabilities Assets
Reserves \$10 Transaction deposits \$20
Security \$10 Nontransaction deposits \$50
Lones \$70 Borrowings (?\$15)
Other assets \$5 Capitol worth \$10
Totals \$100 \$100
There are only 30 days in June. It can’t be in thousands of dollars because this bank would be well below efficient minimum scale. The A-L labels are reversed but the entries are okay. By convention, assets go on the left and liabilities on the right. Borrowings can be 0 but not negative. Only equity capital can be negative. What is “Capitol worth?” A does not equal L. Indeed, the columns do not sum to the purported “totals.” It is Loans (not Lones) and Securities (not Security). Thankfully, assets is not abbreviated!
Let’s turn first to liquidity management. Big Apple Bank has the following balance sheet:
Big Apple Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$10 Transaction deposits \$30
Securities \$10 Nontransaction deposits \$55
Loans \$70 Borrowings \$5
Other assets \$10 Capital \$10
Totals \$100 \$100
Suppose the bank then experiences a net transaction deposit outflow of \$5 million. The bank’s balance sheet (we could also use T-accounts here but we won’t) is now like this:
Big Apple Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$5 Transaction deposits \$25
Securities \$10 Nontransaction deposits \$55
Loans \$70 Borrowings \$5
Other assets \$10 Capital \$10
Totals \$95 \$95
The bank’s reserve ratio (reserves/transaction deposits) has dropped from 10/30 = .3334 to 5/25 = .2000. That’s still pretty good. But if another \$5 million flows out of the bank on net (maybe \$10 million is deposited but \$15 million is withdrawn), the balance sheet will look like this:
Big Apple Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$0 Transaction deposits \$20
Securities \$10 Nontransaction deposits \$55
Loans \$70 Borrowings \$5
Other assets \$10 Capital \$10
Totals \$90 \$90
The bank’s reserve ratio now drops to 0/20 = .0000. That’s bound to be below the reserve ratio required by regulators and in any event is very dangerous for the bank. What to do? To manage this liquidity problem, bankers will increase reserves by the least expensive means at their disposal. That almost certainly will not entail selling off real estate or calling in or selling loans. Real estate takes a long time to sell, but, more importantly, the bank needs it to conduct business! Calling in loans (not renewing them as they come due and literally calling in any that happen to have a call feature) will likely antagonize borrowers. (Loans can also be sold to other lenders, but they may not pay much for them because adverse selection is high. Banks that sell loans have an incentive to sell off the ones to the worst borrowers. If a bank reduces that risk by promising to buy back any loans that default, that bank risks losing the borrower’s future business.) The bank might be willing to sell its securities, which are also called secondary reserves for a reason. If the bankers decide that is the best path, the balance sheet will look like this:
Big Apple Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$10 Transaction deposits \$20
Securities \$0 Nontransaction deposits \$55
Loans \$70 Borrowings \$5
Other assets \$10 Capital \$10
Totals \$90 \$90
The reserve ratio is now .5000, which is high but prudent if the bank’s managers believe that more net deposit outflows are likely. Excess reserves are insurance against further outflows, but keeping them is costly because the bank is no longer earning interest on the \$10 million of securities it sold. Of course, the bank could sell just, say, \$2, \$3, or \$4 million of securities if it thought the net deposit outflow was likely to stop.
The bankers might also decide to try to lure depositors back by offering a higher rate of interest, lower fees, and/or better service. That might take some time, though, so in the meantime they might decide to borrow \$5 million from the Fed or from other banks in the federal funds market. In that case, the bank’s balance sheet would change to the following:
Big Apple Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$5 Transaction deposits \$20
Securities \$10 Nontransaction deposits \$55
Loans \$70 Borrowings \$10
Other assets \$10 Capital \$10
Totals \$95 \$95
Notice how changes in liabilities drive the bank’s size, which shrank from \$100 to \$90 million when deposits shrank, which stayed the same size when assets were manipulated, but which grew when \$5 million was borrowed. That is why a bank’s liabilities are sometimes called its “sources of funds.”
Now try your hand at liquidity management in the exercises.
EXERCISES
Manage the liquidity of the Timberlake Bank given the following scenarios. The legal reserve requirement is 5 percent. Use this initial balance sheet to answer each question:
Timberlake Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$5 Transaction deposits \$100
Securities \$10 Nontransaction deposits \$250
Loans \$385 Borrowings \$50
Other assets \$100 Capital \$100
Totals \$500 \$500
1. Deposits outflows of \$3.5 and inflows of \$3.5.
2. Deposit outflows of \$4.2 and inflows of \$5.8.
3. Deposit outflows of \$3.7 and inflows of \$0.2.
4. A large depositor says that she needs \$1.5 million from her checking account, but just for two days. Otherwise, net outflows are expected to be about zero.
5. Net transaction deposit outflows are zero, but there is a \$5 million net outflow from nontransaction deposits.
Asset management entails the usual trade-off between risk and return. Bankers want to make safe, high-interest rate loans but, of course, few of those are to be found. So they must choose between giving up some interest or suffering higher default rates. Bankers must also be careful to diversify, to make loans to a variety of different types of borrowers, preferably in different geographic regions. That is because sometimes entire sectors or regions go bust and the bank will too if most of its loans were made in a depressed region or to the struggling group. Finally, bankers must bear in mind that they need some secondary reserves, some assets that can be quickly and cheaply sold to bolster reserves if need be.
Today, bankers’ decisions about how many excess and secondary reserves to hold is partly a function of their ability to manage their liabilities. Historically, bankers did not try to manage their liabilities. They took deposit levels as given and worked from there. Since the 1960s, however, banks, especially big ones in New York, Chicago, and San Francisco (the so-called money centers), began to actively manage their liabilities by
1. actively trying to attract deposits;
2. selling large denomination NCDs to institutional investors;
3. borrowing from other banks in the overnight federal funds market.
Recent regulatory reforms have made it easier for banks to actively manage their liabilities. In typical times today, if a bank has a profitable loan opportunity, it will not hesitate to raise the funds by borrowing from another bank, attracting deposits with higher interest rates, or selling an NCD.
That leaves us with capital adequacy management. Like reserves, banks would hold capital without regulatory prodding because equity or net worth buffers banks (and other companies) from temporary losses, downturns, and setbacks. However, like reserves, capital is costly. The more there is of it, holding profits constant, the less each dollar of it earns. So capital, like reserves, is now subject to minimums called capital requirements.
Consider the balance sheet of Safety Bank:
Safety Bank Balance Sheet (Billions USD)
Assets Liabilities
Reserves \$1 Transaction deposits \$10
Securities \$5 Nontransaction deposits \$75
Loans \$90 Borrowings \$5
Other assets \$4 Capital \$10
Totals \$100 \$100
If \$5 billion of its loans went bad and had to be completely written off, Safety Bank would still be in operation:
Safety Bank Balance Sheet (Billions USD)
Assets Liabilities
Reserves \$1 Transaction deposits \$10
Securities \$5 Nontransaction deposits \$75
Loans \$85 Borrowings \$5
Other assets \$4 Capital \$5
Totals \$95 \$95
Now, consider Shaky Bank:
Shaky Bank Balance Sheet (Billions USD)
Assets Liabilities
Reserves \$1 Transaction deposits \$10
Securities \$5 Nontransaction deposits \$80
Loans \$90 Borrowings \$9
Other assets \$4 Capital \$1
Totals \$100 \$100
If \$5 billion of its loans go bad, so too does Shaky.
Shaky Bank Balance Sheet (Billions USD)
Assets Liabilities
Reserves \$1 Transaction deposits \$10
Securities \$5 Nontransaction deposits \$80
Loans \$85 Borrowings \$9
Other assets \$4 Capital ?\$4
Totals \$95 \$95
You don’t need to be a certified public accountant (CPA) to know that red numbers and negative signs are not good news. Shaky Bank is a now a new kind of bank, bankrupt.
Why would a banker manage capital like Shaky Bank instead of like Safety Bank? In a word, profitability. There are two major ways of measuring profitability: return on assets (ROA) and return on equity (ROE).
ROA = net after-tax profit/assets
ROE = net after-tax profit/equity (capital, net worth)
Suppose that, before the loan debacle, both Safety and Shaky Bank had \$10 billion in profits. The ROA of both would be 10/100 = .10. But Shaky Bank’s ROE, what shareholders care about most, would leave Safety Bank in the dust because Shaky Bank is more highly leveraged (more assets per dollar of equity).
Shaky Bank ROE = 10/1 = 10
Safety Bank ROE = 10/10 = 1
This, of course, is nothing more than the standard risk-return trade-off applied to banking. Regulators in many countries have therefore found it prudent to mandate capital adequacy standards to ensure that some bankers are not taking on high levels of risk in the pursuit of high profits.
Bankers manage bank capital in several ways:
1. By buying (selling) their own bank’s stock in the open market. That reduces (increases) the number of shares outstanding, raising (decreasing) capital and ROE, ceteris paribus
2. By paying (withholding) dividends, which decreases (increases) capital, increasing (decreasing) ROE, all else equal
3. By increasing (decreasing) the bank’s assets, which, with capital held constant, increases (decreases) ROE
These same concepts and principles—asset, liability, capital, and liquidity management, and capital-liquidity and capital-profitability trade-offs—apply to other types of financial intermediaries as well, though the details, of course, differ.
KEY TAKEAWAYS
• Bankers must manage their bank’s liquidity (reserves, for regulatory reasons and to conduct business effectively), capital (for regulatory reasons and to buffer against negative shocks), assets, and liabilities.
• There is an opportunity cost to holding reserves, which pay no interest, and capital, which must share the profits of the business.
• Left to their own judgment, bankers would hold reserves > 0 and capital > 0, but they might not hold enough to prevent bank failures at what the government or a country’s citizens deem an acceptably low rate.
• That induces government regulators to create and monitor minimum requirements. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.03%3A_Bank_Management_Principles.txt |
Learning Objectives
• What is credit risk and how do bankers manage it?
As noted above, loans are banks’ bread and butter. No matter how good bankers are at asset, liability, and capital adequacy management, they will be failures if they cannot manage credit risk. Keeping defaults to a minimum requires bankers to be keen students of asymmetric information (adverse selection and moral hazard) and techniques for reducing them.
Bankers and insurers, like computer folks, know about GIGO—garbage in, garbage out. If they lend to or insure risky people and companies, they are going to suffer. So they carefully screen applicants for loans and insurance. In other words, to reduce asymmetric information, financial intermediaries create information about them. One way they do so is to ask applicants a wide variety of questions.
Financial intermediaries use the application only as a starting point. Because risky applicants might stretch the truth or even outright lie on the application, intermediaries typically do two things: (1) make the application a binding part of the financial contract, and (2) verify the information with disinterested third parties. The first allows them to void contracts if applications are fraudulent. If someone applied for life insurance but did not disclose that he or she was suffering from a terminal disease, the life insurance company would not pay, though it might return any premiums. (That may sound cruel to you, but it isn’t. In the process of protecting its profits, the insurance company is also protecting its policyholders.) In other situations, the intermediary might not catch a falsehood in an application until it is too late, so it also verifies important information by calling employers (Is John Doe really the Supreme Commander of XYZ Corporation?), conducting medical examinations (Is Jane Smith really in perfect health despite being 3' 6'' tall and weighing 567 pounds?), hiring appraisers (Is a one-bedroom, half-bath house on the wrong side of the tracks really worth \$1.2 million?), and so forth. Financial intermediaries can also buy credit reports from third-party report providers like Equifax, Experian, or Trans Union. Similarly, insurance companies regularly share information with each other so that risky applicants can’t take advantage of them easily.
To help improve their screening acumen, many financial intermediaries specialize. By making loans to only one or a few types of borrowers, by insuring automobiles in a handful of states, by insuring farms but not factories, intermediaries get very good at discerning risky applicants from the rest. Specialization also helps to keep monitoring costs to a minimum. Remember that, to reduce moral hazard (postcontractual asymmetric information), intermediaries have to pay attention to what borrowers and people who are insured do. By specializing, intermediaries know what sort of restrictive covenants (aka loan covenants) to build into their contracts. Loan covenants include the frequency of providing financial reports, the types of information to be provided in said reports, working capital requirements, permission for onsite inspections, limitations on account withdrawals, and call options if business performance deteriorates as measured by specific business ratios. Insurance companies also build covenants into their contracts. You can’t turn your home into a brothel, it turns out, and retain your insurance coverage. To reduce moral hazard further, insurers also investigate claims that seem fishy. If you wrap your car around a tree the day after insuring it or increasing your coverage, the insurer’s claims adjuster is probably going to take a very close look at the alleged accident. Like everything else in life, however, specialization has its costs. Some companies overspecialize, hurting their asset management by making too many loans or issuing too many policies in one place or to one group. While credit risks decrease due to specialization, systemic risk to assets increases, requiring bankers to make difficult decisions regarding how much to specialize.
Forging long-term relationships with customers can also help financial intermediaries to manage their credit risks. Bankers, for instance, can lend with better assurance if they can study the checking and savings accounts of applicants over a period of years or decades. Repayment records of applicants who had previously obtained loans can be checked easily and cheaply. Moreover, the expectation (there’s that word again) of a long-term relationship changes the borrower’s calculations. The game, if you will, is to play nice so that loans will be forthcoming in the future.
One way that lenders create long-term relationships with businesses is by providing loan commitments, promises to lend \$x at y interest (or y plus some market rate) for z years. Such arrangements are so beneficial for both lenders and borrowers that most commercial loans are in fact loan commitments. Such commitments are sometimes called lines of credit, particularly when extended to consumers. Because lines of credit can be revoked under specific circumstances, they act to reduce risky behavior on the part of borrowers.
Bankers also often insist on collateral—assets pledged by the borrower for repayment of a loan. When those assets are cash left in the bank, the collateral is called compensating or compensatory balances. Another powerful tool to combat asymmetric information is credit rationing, refusing to make a loan at any interest rate (to reduce adverse selection) or lending less than the sum requested (to reduce moral hazard). Insurers also engage in both types of rationing, and for the same reasons: people willing to pay high rates or premiums must be risky, and the more that is lent or insured (ceteris paribus) the higher the likelihood that the customer will abscond, cheat, or set aflame, as the case may be.
As the world learned to its chagrin in 2007–2008, banks and other lenders are not perfect screeners. Sometimes, under competitive pressure, they lend to borrowers they should not have. Sometimes, individual bankers profit handsomely by lending to very risky borrowers, even though their actions endanger their banks’ very existence. Other times, external political or societal pressures induce bankers to make loans they normally wouldn’t. Such excesses are always reversed eventually because the lenders suffer from high levels of nonperforming loans.
Stop and Think Box
In the first quarter of 2007, banks and other intermediaries specializing in originating home mortgages (called mortgage companies) experienced a major setback in the so-called subprime market, the segment of the market that caters to high-risk borrowers, because default rates soared much higher than expected. Losses were so extensive that many people feared, correctly as it turned out, that they could trigger a financial crisis. To stave off such a potentially dangerous outcome, why didn’t the government immediately intervene by guaranteeing the subprime mortgages?
The government must be careful to try to support the financial system without giving succor to those who have screwed up. Directly bailing out the subprime lenders by guaranteeing mortgage payments would cause moral hazard to skyrocket, it realized. Borrowers might be more likely to default by rationalizing that the crime is a victimless one (though, in fact, all taxpayers would suffer—recall that there is no such thing as a free lunch in economics). Lenders would learn that they can make crazy loans to anyone because good ol’ Uncle Sam will cushion, or even prevent, their fall.
KEY TAKEAWAYS
• Credit risk is the chance that a borrower will default on a loan by not fully meeting stipulated payments on time.
• Bankers manage credit risk by screening applicants (taking applications and verifying the information they contain), monitoring loan recipients, requiring collateral like real estate and compensatory balances, and including a variety of restrictive covenants in loans.
• They also manage credit risk by trading off between the costs and benefits of specialization and portfolio diversification. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.04%3A_Credit_Risk.txt |
Learning Objectives
• What is interest rate risk and how do bankers manage it?
Financial intermediaries can also be brought low by changes in interest rates. Consider the situation of Some Bank, which like most depository institutions borrows short and lends long:
Some Bank (Billions USD)
Assets Liabilities
Interest-rate-sensitive assets like variable rate and short-term loans and short-term securities \$10 Interest-rate-sensitive liabilities like variable rate CDs and MMDAs \$20
Fixed-rate assets like reserves, long-term loans and securities \$50 Fixed-rate liabilities like checkable deposits, CDs, equity capital \$40
If interest rates increase, Some Bank’s gross profits, the difference between what it pays for its liabilities and earns on its assets, will decline (assuming the spread stays the same) because the value of its rate-sensitive liabilities (short-term and variable-rate time deposits) exceeds that of its rate-sensitive assets (short-term and variable- rate loans and securities). Say, for instance, it today pays 3 percent for its rate-sensitive liabilities and receives 7 percent on its rate-sensitive assets. That means it is paying 20 × .03 = \$.6 billion to earn 10 × .07 = \$.7 billion. (Not bad work if you can get it.) If interest rates increase 1 percent on each side of the balance sheet, Some Bank will be paying 20 × .04 = \$.8 billion to earn 10 × .08 = \$.8 billion. (No profits there.) If rates increase another 1 percent, it will have to pay 20 × .05 = \$1 billion to earn 10 × .09 = \$.9 billion, a total loss of \$.2 billion (from a \$.1 billion profit to a \$.1 billion loss).
Stop and Think Box
Inflation was unexpectedly high in the 1970s. Given what you learned about the relationship between inflation and nominal interest rates (as inflation increases, so too must nominal interest rates, all else equal), and between interest rates and bank profitability in this chapter, what happened in the 1980s?
Bank profitability sank to the point that many banks, the infamous savings and loans (S&Ls), went under. Inflation (via the Fisher Equation) caused nominal interest rates to increase, which hurt banks’ profitability because they were earning low rates on long-term assets (like thirty-year bonds) while having to pay high rates on their short-term liabilities. Mounting losses induced many bankers to take on added risks, including risks in the derivatives markets. A few restored their banks to profitability, but others destroyed all of their bank’s capital and then some.
Of course, if the value of its risk-sensitive assets exceeded that of its liabilities, the bank would profit from interest rate increases. It would suffer, though, if interest rates decreased. Imagine Some Bank has \$10 billion in interest rate-sensitive assets at 8 percent and only \$1 billion in interest rate-sensitive liabilities at 5 percent. It is earning 10 × .08 = \$.8 billion while paying 1 × .05 = \$.05 billion. If interest rates decreased, it might earn only 10 × .05 = \$.5 billion while paying 1 × .02 = \$.02 billion; thus, ceteris paribus, its gross profits would decline from .8 − .05 = \$.75 billion to .5 − .02 = \$.48 billion, a loss of \$.27 billion. More formally, this type of calculation, called basic gap analysis, is
\[C_ρ = ( A_r - L_r ) × △ i\]
where:
• \(C_ρ\) is the changes in profitability
• \(A_r\) is the risk-sensitive assets
• \(L_r\) is the risk-sensitive liabilities
• \(Δi\) is the change in interest rates
So, returning to our first example,
\[C_ρ = ( 10 - 20 ) × 0.02 = - 10 × 0.02 = - \$0.2 billion ,\]
and the example above,
\[C_ρ = ( 10 - 1 ) - ( - 0.03 ) = - \$0.27 billion .\]
Complete the exercise to get comfortable conducting basic gap analysis.
EXERCISE
1. Use the basic gap analysis formula to estimate Some Bank’s loss or gain under the following scenarios.
\[C \? = ( A r - L r ) × △ i\]
Risk Sensitive Assets (Millions USD) Risk Sensitive Liabilities (Millions USD) Change in Interest Rates (%) Answer: CP (Millions USD)
100 100 100 0
100 200 10 −10
100 200 −10 10
199 200 10 −0.1
199 200 −10 0.1
200 100 10 10
200 100 −10 −10
200 199 10 0.1
200 199 −10 −0.1
1000 0 1 10
0 1000 1 −10
Now, take a look at Figure 9.3, which summarizes, in a 2 × 2 matrix, what happens to bank profits when the gap is positive (Ar > Lr) or negative (Ar < Lr) when interest rates fall or rise. Basically, bankers want to have more interest-sensitive assets than liabilities if they think that interest rates are likely to rise and they want to have more interest rate-sensitive liabilities than assets if they think that interest rates are likely to decline.
Of course, not all rate-sensitive liabilities and assets have the same maturities, so to assess their interest rate risk exposure bankers usually engage in more sophisticated analyses like the maturity bucket approach, standardized gap analysis, or duration analysis. Duration, also known as Macaulay’s Duration, measures the average length of a security’s stream of payments.www.riskglossary.com/link/duration_and_convexity.htm In this context, duration is used to estimate the sensitivity of a security’s or a portfolio’s market value to interest rate changes via this formula:
△ % P = - △ % i × d
Δ%P = percentage change in market value
Δi = change in interest (not decimalized, i.e., represent 5% as 5, not .05. Also note the negative sign. The sign is negative because interest rates and prices are inversely related.)
d = duration (years)
So, if interest rates increase 2 percent and the average duration of a bank’s \$100 million of assets is 3 years, the value of those assets will fall approximately −2 × 3 = −6%, or \$6 million. If the value of that bank’s liabilities (excluding equity) is \$95 million, and the duration is also 3 years, the value of the liabilities will also fall, 95 × .06 = \$5.7 million, effectively reducing the bank’s equity (6 − 5.7= ) \$.3 million. If the duration of the bank’s liabilities is only 1 year, then its liabilities will fall −2 × 1 = −2% or 95 × .02 = \$1.9 million, and the bank will suffer an even larger loss (6 − 1.9 =) of \$4.1 million. If, on the other hand, the duration of the bank’s liabilities is 10 years, its liabilities will decrease −2 × 10 = −20% or \$19 million and the bank will profit from the interest rate rise.
A basic interest rate risk reduction strategy when interest rates are expected to fall is to keep the duration of liabilities short and the duration of assets long. That way, the bank continues to earn the old, higher rate on its assets but benefits from the new lower rates on its deposits, CDs, and other liabilities. As noted above, borrowing short and lending long is second nature for banks, which tend to thrive when interest rates go down. When interest rates increase, banks would like to keep the duration of assets short and the duration of liabilities long. That way, the bank earns the new, higher rate on its assets and keeps its liabilities locked in at the older, lower rates. But banks can only go so far in this direction because it runs against their nature; few people want to borrow if the loans are callable and fewer still want long-term checkable deposits!
KEY TAKEAWAYS
• Interest rate risk is the chance that interest rates may increase, decreasing the value of bank assets.
• Bankers manage interest rate risk by performing analyses like basic gap analysis, which compares a bank’s interest rate risk-sensitive assets and liabilities, and duration analysis, which accounts for the fact that bank assets and liabilities have different maturities.
• Such analyses, combined with interest rate predictions, tell bankers when to increase or decrease their rate-sensitive assets or liabilities, and whether to shorten or lengthen the duration of their assets or liabilities. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.05%3A_Interest-Rate_Risk.txt |
Learning Objectives
• What are off-balance-sheet activities and why do bankers engage in them?
To protect themselves against interest rate increases, banks go off road, engaging in activities that do not appear on their balance sheets.This is not to say that these activities are not accounted for. It isn’t illegal or even slimy. These activities will appear on revenue statements, cash flow analyses, etc. They do not, however, appear on the balance sheet, on the list of the bank’s assets and liabilities.Banks charge customers all sorts of fees, and not just the little ones that they sometimes slap on retail checking depositors. They also charge fees for loan guarantees, backup lines of credit, and foreign exchange transactions. Banks also now sell some of their loans to investors. Banks usually make about .15 percent when they sell a loan, which can be thought of as their fee for originating the loan, for, in other words, finding and screening the borrower. So, for example, a bank might discount the \$100,000 note of XYZ Corp. for 1 year at 8 percent. We know from the present value formula that on the day it is made, said loan is worth PV = FV/(1 + i) = 100,000/1.08 = \$92,592.59. The bank might sell it for 100,000/1.0785 = \$92,721.37 and pocket the difference. Such activities are not without risks, however. Loan guarantees can become very costly if the guaranteed party defaults. Similarly, banks often sell loans with a guarantee or stipulation that they will buy them back if the borrower defaults. (If they didn’t do so, as noted above, investors would not pay much for them because they would fear adverse selection, that is, the bank pawning off their worse loans on unsuspecting third parties.) Although loans and fees can help keep up bank revenues and profits in the face of rising interest rates, they do not absolve the bank of the necessity of carefully managing its credit risks.
Banks (and other financial intermediaries) also take off-balance-sheet positions in derivatives markets, including futures and interest rate swaps. They sometimes use derivatives to hedge their risks; that is, they try to earn income should the bank’s main business suffer a decline if, say, interest rates rise. For example, bankers sell futures contracts on U.S. Treasuries at the Chicago Board of Trade. If interest rates increase, the price of bonds, we know, will decrease. The bank can then effectively buy bonds in the open market at less than the contract price, make good on the contract, and pocket the difference, helping to offset the damage the interest rate increase will cause the bank’s balance sheet.
Bankers can also hedge their bank’s interest rate risk by engaging in interest rate swaps. A bank might agree to pay a finance company a fixed 6 percent on a \$100 million notational principal (or \$6 million) every year for ten years in exchange for the finance company’s promise to pay to the bank a market rate like the federal funds rate or London Interbank Offering Rate (LIBOR) plus 3 percent. If the market rate increases from 3 percent (which initially would entail a wash because 6 fixed = 3 LIBOR plus 3 contractual) to 5 percent, the finance company will pay the net due to the bank, (3 + 5 = 8 − 6 = 2% on \$100 million =) \$2 million, which the bank can use to cover the damage to its balance sheet brought about by the higher rates. If interest rates later fall to 2 percent, the bank will have to start paying the finance company (6 − [3 + 2] = 1% on \$100 million) \$1 million per year but will well be able to afford it.
Banks and other financial intermediaries also sometimes speculate in derivatives and the foreign exchange markets, hoping to make a big killing. Of course, with the potential for high returns comes high levels of risk. Several hoary banks have gone bankrupt because they assumed too much off-balance-sheet risk. In some cases, the failures were due to the principal-agent problem: rogue traders bet their jobs, and their banks, and lost. In other cases, traders were mere scapegoats, instructed to behave as they did by the bank’s managers or owners. In either case, it is difficult to have much sympathy for the bankers, who were either deliberate risk-takers or incompetent. There are some very basic internal controls that can prevent traders from risking too much of the capital of the banks they trade for, as well as techniques, called value at riskwww.gloriamundi.org and stress testing,financial-dictionary.thefreedictionary.com/Stress+Testing that allow bankers to assess their bank’s derivative risk exposure.
KEY TAKEAWAYS
• Off-balance-sheet activities like fees, loan sales, and derivatives trading help banks to manage their interest rate risk by providing them with income that is not based on assets (and hence is off the balance sheet).
• Derivatives trading can be used to hedge or reduce interest rate risks but can also be used by risky bankers or rogue traders to increase risk to the point of endangering a bank’s capital cushion and hence its economic existence.
9.07: Suggested Reading
Choudhry, Moorad. Bank Asset and Liability Management: Strategy, Trading, Analysis. Hoboken, NJ: John Wiley and Sons, 2007.
Dermine, Jean, and Youssef Bissada. Asset and Liability Management: A Guide to Value Creation and Risk Control. New York: Prentice Hall, 2002.
Ketz, J. Edward. Hidden Financial Risk: Understanding Off Balance Sheet Accounting. Hoboken, NJ: John Wiley and Sons, 2003.
Kolari, James, and Benton Gup. Commercial Banking: The Management of Risk. Hoboken, NJ: John Wiley and Sons, 2004. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/09%3A_Bank_Management/9.06%3A_Off_the_Balance_Sheet.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Explain why bankers and other financiers innovate.
• Explain how widespread unit banking in the United States affected financial innovation.
• Explain how the Great Inflation of the 1970s affected banks and banking.
• Define loophole mining and lobbying and explain their importance.
• Describe how technology changed the banking industry after World War II.
• Define traditional banking and describe the causes of its demise.
• Define industry consolidation and explain how it is measured.
• Define financial conglomeration and explain its importance.
• Define industry concentration and explain how it is measured.
Thumbnail: Image by mohamed Hassan from Pixabay
10: Innovation and Structure in Banking and Finance
Learning Objectives
• Why do bankers and other financiers innovate in the face of branching restrictions and other regulations?
Banking today is much the same everywhere. And, at the broadest level, today’s banks are not much different from banks hundreds of years ago. Philadelphian Thomas Willing, America’s first banker and life insurer, and a marine insurance pioneer, would likely understand the functioning of today’s largest, most complex banks and insurance companies with little trouble.www.augie.edu/academics/areas-study/nef-family-chair-political-economy/thomas-willing-institute (He’d certainly understand interest-only mortgages because he used them extensively as early as the 1760s.) Despite broad similarities, banking and other aspects of the financial system vary in detail over time and place, thanks in large part to innovations: new ideas, products, and markets. Innovation, in turn, is driven by changes in the financial environment, specifically in macroeconomic volatility, technology, competition, and regulation. (I discuss the economics of regulation in detail elsewhere. Here, I’ll simply mention regulations that have helped to spur innovation.)
The first U.S. commercial bank, the Bank of North America, began operations in early 1782. For the next two centuries or so, banking innovation in the United States was rather glacial because regulations were relatively light, pertinent technological changes were few, and competition was sparse. Before the Civil War, all but two of America’s incorporated banks were chartered by one of the state governments rather than the national government. Most states forbade intrastate branching; interstate branching was all but unheard of, except when conducted by relatively small private (unincorporated) banks. During the Civil War, Congress passed a law authorizing the establishment of national banks, but the term referred only to the fact that the national government chartered and regulated them. Despite their name, the banks that came into existence under the national banking acts could not branch across state lines, and their ability to branch within their state of domicile depended on the branching rules imposed by that state. As before the war, most states forbade branching. Moreover, state governments continued to charter banks too. The national government tried to dissuade them from doing so by taxing state bank notes heavily, but the banks responded nimbly, issuing deposits instead. Unlike most countries, which developed a few, large banks with extensive systems of branches, the United States was home to hundreds, then thousands, then tens of thousands of tiny branchless, or unit, banks.
Most of those unit banks were spread evenly throughout the country. Because banking was essentially a local retail business, most unit banks enjoyed near-monopolies. If you didn’t like the local bank, you were free to do your banking elsewhere, but that might require putting one’s money in a bank over hill and over dale, a full day’s trek away by horse. Most people were reluctant to do that, so the local bank got their business, even if its terms were not particularly good. Little regulated and lightly pressed by competitors, American banks became stodgy affairs, the stuff of WaMu commercials.www.youtube.com/watch?v=BJ7EIKbnnkw Spreads between sources of funds and uses of funds were large and stable, leading to the infamous 3-6-3 rule: borrow at 3 percent, lend at 6 percent, and golf at 3 p.m. Reforming the system proved difficult because the owners and managers of small banks enjoyed significant local political clout.Raghuram Ragan and Rodney Ramcharan, “Constituencies and Legislation: Fight Over the McFadden Act of 1927,” NBER Working Paper No. w17266 (August 2011). papers.ssrn.com/sol3/papers.cfm?abstract_id=1905859.
Near-monopoly in banking, however, led to innovation in the financial markets. Instead of depositing money in the local bank, some investors looked for higher returns by lending directly to entrepreneurs. Instead of paying high rates at the bank, some entrepreneurs sought cheaper funds by selling bonds directly into the market. As a result, the United States developed the world’s largest, most efficient, and most innovative financial markets. The United States gave birth to large, liquid markets for commercial paper (short-dated business IOUs) and junk bonds (aka BIG, or below investment grade, bonds), which are high-yielding but risky bonds issued by relatively small or weak companies. Markets suffer from higher levels of asymmetric information and more free-rider problems than financial intermediaries do, however, so along with innovative securities markets came instances of fraud, of people issuing overvalued or fraudulent securities. And that led to several layers of securities regulation and, inevitably, yet more innovation.
Stop and Think Box
Unlike banks, U.S. life insurance companies could establish branches or agencies wherever they pleased, including foreign countries. Life insurers must maintain massive accumulations of assets so that they will certainly be able to pay claims when an insured person dies. From the late nineteenth century until the middle of the twentieth, therefore, America’s largest financial institutions were not its banks, but its life insurers, and competition among the biggest ones—Massachusetts Mutual, MetLife, Prudential, New York Life, and the Equitable—was fierce. Given that information, what do you think innovation in life insurance was like compared to commercial banking?
Innovation in life insurance should have been more rapid because competition was more intense. Data-processing innovations, like the use of punch-card-tabulating machines,www.officemuseum.com/IMagesWWW/Tabulating_Machine_Co_card_punch_left_end.JPG automated mechanical mailing address machines,www.officemuseum.com/IMagesWWW/1904_1912_Graphotype_Addressograph_Co_Chicago_OM.JPG and mainframe computers,ccs.mit.edu/papers/CCSWP196.html occurred in life insurers before they did in most banks.
KEY TAKEAWAYS
• Bankers and financiers innovate to continue to earn profits despite a rapidly evolving financial environment, including changes in competition, regulation, technology, and the macroeconomy.
• Unit banks enjoyed local monopolies and were lightly regulated, so there was little incentive for them to innovate but plenty of reason for investors and borrowers to meet directly via the second major conduit of external finance, markets.
• Unit banking dampened banking innovation but spurred financial market innovation.
• Traditionally, bankers earned profits from the spread between the cost of their liabilities and the earnings on their assets. It was a staid business characterized by the 3-6-3 rule. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/10%3A_Innovation_and_Structure_in_Banking_and_Finance/10.01%3A_Early_Financial_Innovations.txt |
Learning Objectives
• Why did the Great Inflation spur financial innovation?
Competition keeps gross spreads (the difference between what borrowers pay for loans and what depositors receive) down, but it is also important because it drives bankers to adopt new technologies and search for ways to reduce the negative effects of volatility. It is not surprising, therefore, that as changing regulations, globalization, computerization, and unprecendented macroeconomic volatility rendered the U.S. financial system more competitive in the 1970s and 1980s, the pace of financial innovation increased dramatically. As Figure 10.1 shows, beginning in the late 1960s, inflation rose steadily and grew increasingly erratic. Not surprisingly, nominal interest rates rose as well, via the Fisher Equation. Interest rate risk, particularly rising interest rates, is one of the things that keeps bankers awake at night. They could not have slept much during the Great Inflation of 1968 to 1982, when the aggregate price level rose over 110 percent all told, more than any fifteen-year period before or since.
Bankers responded to the increased interest rate risk by inducing others to assume it. Bankers can use financial derivatives, like options, futures, and swaps, to hedge their interest rate risks. It is no coincidence that the modern revival of such markets occurred during the 1970s. Also in the 1970s, bankers began to make adjustable-rate mortgage loans. Traditionally, mortgages had been fixed rate. The borrower promised to pay, say, 6 percent over the entire fifteen-, twenty-, or thirty-year term of the loan. Fixed-rate loans were great for banks when interest rates declined (or stayed the same). But when rates rose, banks got stuck with long-term assets that earned well below what they had to pay for their short-term liabilities. One solution was to get borrowers to take on the risk by inducing them to promise to pay some market rate, like the six-month Treasury rate, plus 2, 3, 4, or 5 percent. That way, when interest rates rise, the borrower has to pay more to the bank, helping it with its gap problem. Of course, when rates decrease, the borrower pays less to the bank. The key is to realize that with adjustable-rate loans, interest rate risk, as well as reward, falls on the borrower, rather than the bank. To induce borrowers to take on that risk, banks must offer them a more attractive (lower) interest rate than on fixed-rate mortgages. Fixed-rate mortgages remain popular, however, because many people don’t like the risk of possibly paying higher rates in the future. Furthermore, if their mortgages contain no prepayment penalty clause (and most don’t), borrowers know that they can take advantage of lower interest rates by refinancing—getting a new loan at the current, lower rate and using the proceeds to pay off the higher-rate loan. Due to the high transaction costs (“closing costs” like loan application fees, appraisal costs, title insurance, and so forth) associated with home mortgage re-fis, however, interest rates must decline more than a little bit before it is worthwhile to do one.www.bankrate.com/brm/calc_vml/refi/refi.asp
Bankers also responded to increased competition and disintermediation (removal of funds by depositors looking for better returns) by finding new and improved ways to connect to customers. ATMs (automated teller machines), for example, increased the liquidity of deposits by making it easier for depositors to make deposits and withdrawals during off hours and at locations remote from their neighborhood branch.
Stop and Think Box
In the 1970s and 1980s, life insurance companies sought regulatory approval for a number of innovations, including adjustable-rate policy loans and variable annuities. Why? Hint: Policy loans are loans that whole life insurance policyholders can take out against the cash value of their policies. Most policies stipulated a 5 or 6 percent fixed rate. Annuities, annual payments made during the life of the annuitant, were also traditionally fixed.
Life insurance companies, like banks, were adversely affected by disintermediation during the Great Inflation. (In other words, policyholders, like bank depositors, reduced the amount that they lent to insurers.) Policyholders astutely borrowed the cash values of their life insurance policies at 5 or 6 percent, then re-lent the money to others at the going market rate, which was often in the double digits. By making the policy loans variable, life insurers could adjust them upward when rates increased to limit such arbitrage. Similarly, fixed annuities were a difficult sell during the Great Inflation because annuitants saw the real value (the purchasing power) of their annual payments decrease dramatically. By promising to pay annuitants more when interest rates and inflation were high, variable-rate annuities helped insurers to attract customers.
KEY TAKEAWAYS
• By increasing macroeconomic instability, nominal interest rates, and competition between banks and financial markets, the Great Inflation forced bankers and other financiers to innovate.
• Bankers innovated by introducing new products, like adjustable-rate mortgages and sweep accounts; new techniques, like derivatives and other off-balance-sheet activities; and new technologies, including credit card payment systems and automated and online banking facilities. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/10%3A_Innovation_and_Structure_in_Banking_and_Finance/10.02%3A_Innovations_Galore.txt |
Learning Objectives
• What are loophole mining and lobbying, and why are they important?
Competition for profits also drives bankers and other financiers to look for regulatory loopholes, a process sometimes called loophole mining. Loophole mining is both legal and ethical and works better in nations, like the United States, with a permissive regulatory system rather than a restrictive one, or, in other words, in places where anything is allowed unless it is explicitly forbidden.Doug Arner, Financial Stability, Economic Growth, and the Role of Law (New York: Cambridge University Press, 2007), 263. During the Great Inflation, banks could not legally pay any interest on checking deposits or more than about 6 percent on time deposits, both far less than going market rates. Banks tried to lure depositors by giving them toasters and other gifts, attempting desperately to skirt the interest rate caps by sweetening the pot. Few depositors bit. Massive disintermediation ensued because depositors pulled their money out of banks to buy assets that could provide a market rate of return. Financiers responded by developing money market mutual funds (MMMFs), which offered checking account–like liquidity while paying interest at market rates, and by investing in short-term, high-grade assets like Treasury Bills and AAA-rated corporate commercial paper. (The growth of MMMFs in turn aided the growth and development of the commercial paper markets.)
Stop and Think Box
To work around regulations against interstate banking, some banks, particularly in markets that transcended state lines, established so-called nonbank banks. Because the law defined banks as institutions that “accept deposits and make loans,” banks surmised, correctly, that they could establish de facto branches that did one function or the other, but not both. What is this type of behavior called and why is it important?
This is loophole mining leading to financial innovation. Unfortunately, this particular innovation was much less economically efficient than establishing real branches would have been. The banks that created nonbank banks likely profited, but not as much as they would have if they had not had to resort to such a technicality. Moreover, the nonbank bank’s customers would have been less inconvenienced!
Bankers also used loophole mining by creating so-called sweep accounts, checking accounts that were invested each night in (“swept” into) overnight loans. The interest earned on those loans was credited to the account the next morning, allowing banks to pay rates above the official deposit rate ceilings. Sweep accounts also allowed banks to do the end around on reserve requirements, legal minimums of cash and Federal Reserve deposits. Recall that banks earn limited interest on reserves, so they often wish that they could hold fewer reserves than regulators require, particularly when interest rates are high. By using computers to sweep checking accounts at the close of business each day, banks reduced their de jure deposits and thus their reserve requirements to the point that reserve regulations today are largely moot, a point to which we shall return.
Bank holding companies (BHCs), parent companies that own multiple banks and banking-related service companies, offered bankers another way to use loophole mining because regulation of BHCs was, for a long time, more liberal than unit bank regulation. In particular, BHCs could circumvent restrictive branching regulations and earn extra profits by providing investment advice, data processing, and credit card services. Today, bank holding companies own almost all of the big U.S. banks. J. P. Morgan Chase, Bank of America, and Citigroup are all BHCs.www.ffiec.gov/nicpubweb/nicweb/top50form.aspx
Not all regulations can be circumvented cost effectively via loophole mining, however, so sometimes bankers and other financiers have to push for regulatory reforms. The Great Inflation and the decline of traditional banking, we’ll learn below, induced bankers to lobby to change the regulatory regime they faced. Like loophole mining, lobbying in and of itself is legal and ethical so long as the laws and social mores related to such activities are not violated. The bankers largely succeeded, aided in part by a banking crisis.
KEY TAKEAWAYS
• Loophole mining is a legal and ethical type of innovation where bankers and other financiers look for creative ways of circumventing regulations.
• Lobbying is a legal and ethical type of innovation where bankers and other financiers try to change regulations.
• The Great Inflation also induced bankers to use loophole mining (for example, by using bank holding companies). When that was too costly, bankers lobbied to change the regulatory system, generally to make it less restrictive. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/10%3A_Innovation_and_Structure_in_Banking_and_Finance/10.03%3A_Loophole_Mining_and_Lobbying.txt |
Learning Objectives
• How has technology aided financial innovation?
Proliferation of the telegraph and the telephone in the nineteenth century did little to change banking. Bankers in remote places could place orders with securities brokers more quickly and cheaply than before, customers could perform certain limited transactions by talking with a teller by phone rather than in person, and mechanical computers made certain types of data storage and number crunching faster. The widespread use of automobiles led to the adoption of drive-up teller windows in the 1950s. None of those technologies, however, transformed the face of the business. The advent of cheap electronic computing and digital telecommunications after World War II, however, did eventually spur significant innovation.
Retail-level credit has always been a major component of the American economy, but it began to get crimped in the late nineteenth and early twentieth centuries in large urban areas where people no longer knew their neighbors and clerks left for new jobs with alarming frequency. Some stores began to issue credit cards to their customers. These credit cards were literally identification cards that let the clerks know that the customer had a credit account with the store. The system was inefficient because consumers needed a different card for each store in which they shopped. Moreover, screening good borrowers from bad isn’t easy and minimum efficient scale is quite high, so even large department store chains were not very efficient at issuing the cards. Observers realized that economies of scale could be exploited if one company decided who was creditworthy and provided a payment system that allowed participation by a large percentage of retailers.
After World War II, Diners Club applied the idea to restaurants, essentially telling restaurateurs that it would pay their customers’ bills. (Diners Club later collected from the customers.) The service was very costly, however, so new credit card systems did not spread successfully until the late 1960s, when improvements in computer technology and telecommunications made it possible for machines to conduct the transactions at both the point of sale and card issuer sides of the transaction. Since then, several major credit card networks have arisen, and thousands of institutions, including many nonbanks, now issue credit cards.
Basically, Visa and MasterCard have created private payment systems that are win-win-win. Retailers win because they are assured of getting paid (checks sometimes bounce days after the fact, but credit and debit cards can be verified before goods are given or services are rendered). Retailers pay a small fixed fee (that’s why a shopkeeper might not let you charge a 25 cent pack of gum) and a few percentage points for each transaction because they believe that their customers like to pay by credit card. Indeed many do. Carrying a credit card is much easier and safer than carrying around cash. By law, cardholders are liable for no more than \$50 if their card is lost or stolen, provided they report it in a timely manner. Credit cards are small and light, especially compared to large sums of cash, and they eliminate the need for small change. They also allow consumers to smooth their consumption over time by allowing them to tap a line of credit on demand. Although interest rates on credit cards are generally high, the cardholder can avoid interest charges by paying the bill in full each month. Finally, banks and other card issuers win because of the fees they receive from vendors. Some also charge cardholders an annual fee. Competition, however, has largely ended the annual fee card and indeed driven issuers to refund some of the fees they collect from retailers to cardholders to induce people to pay with their cards rather than with cash, check, or competitors’ cards. That’s what all of the business about cash back, rewards, frequent flier points, and the like, is about.
Debit cards look like credit cards but actually tap into the cardholder’s checking account much like an instantaneous check. Retailers like them better than checks, though, because a debit card can’t bounce, or be returned for insufficient funds days after the customer has walked off with the store owner’s property. Consumers who find it difficult to control their spending find debit cards useful because it gives them firm budget constraints, that is, the sums in their respective checking accounts. If a debit card is lost or stolen, however, the cardholder’s liability is generally much higher than it is with a credit card. Today, many debit cards are also automatic teller machine (ATM) cards, cards that allow customers to withdraw cash from ATMs. That makes sense because, like debit cards, ATM cards are linked directly to each cardholder’s checking (and sometimes savings) accounts. ATMs are much smaller, cheaper, and more convenient than full-service branches, so many banks established networks of them instead of branches. Before bank branching restrictions were lifted, ATMs also received more favorable regulatory treatment than branches. There are more than 250,000 ATMs in the United States today, all linked to bank databases via the miraculous telecom devices developed in the late twentieth century.
Further technological advances have led to the creation of automated banking machines (ABMs); online banking, home banking, or e-banking; and virtual banks. ABMs are combinations of ATMs, Web sites, and dedicated customer service telephone lines that allow customers to make deposits, transfer funds between accounts, or engage in even more sophisticated banking transactions without stepping foot in the bank. Online banking allows customers to bank from their home or work computers. Banks have found online banking so much cheaper than traditional in-bank methods that some have encouraged depositors and other customers to bank from home or via machines by charging them fees for the privilege of talking to a teller! A few banks are completely virtual, having no physical branches. So-called click-and-mortar, or hybrid, banks appear more viable than completely virtual banks at present, however, because virtual banks seem a little too ephemeral, a little too like the wild cat banks of old. As during the good old days, a grand edifice still inspires confidence in depositors and policyholders. The bank in Figure 10.2, for some reason, evokes more confidence than the bank in Figure 10.3.
Technological improvements also made possible the rise of securitization, the process of transforming illiquid financial assets like mortgages, automobile loans, and accounts receivable into marketable securities. Computers make it relatively easy and cheap to bundle loans together, sell them to investors, and pass the payments through to the new owner. Because they are composed of bundles of smaller loans, the securitized loans are diversified against default risk and are sold in the large round sums that institutional investors crave. Securitization allows bankers to specialize in originating loans rather than in holding assets. They can improve their balance sheets by securitizing and selling loans, using the cash to fund new loans. As we’ll see shortly, however, securitization has also opened the door to smaller competitors.
KEY TAKEAWAYS
• Technology, particularly digital electronic computers and telecommunication devices, made possible sweep accounts, securitization, credit and debit card networks, ATMs, ABMs, and online banking.
• ATMs, ABMs, and online banking reduced a bank’s expenses.
• Sweep accounts reduced the cost of required reserves.
• Securitization allows banks to specialize in making loans, as opposed to holding assets.
• Credit card issuance is often lucrative. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/10%3A_Innovation_and_Structure_in_Banking_and_Finance/10.04%3A_Banking_on_Technology.txt |
Learning Objectives
• What role does market structure (concentration, consolidation, conglomeration) play in the banking industry’s profitability?
Despite their best innovation efforts, banks have been steadily losing market share as sources of loans to nonfinancial borrowers. In the 1970s, commercial banks and other depository institutions (the so-called thrifts—credit unions, savings and loans, savings banks) controlled over 60 percent of that market. Today, they have only about a third. The market for loans to nonfinancial borrowers grew very quickly over the last quarter century, however, so that decline is a relative one only. Banks are still extremely profitable, so much so that many new banks form each year. But bankers have to work harder than ever for those profits; the good old days of traditional banking and the 3-6-3 rule are long gone. Fees and other off-balance-sheet activities now account for almost half of bank income, up from about 7 percent in 1980. The traditional source of profit, the spread between the cost of liabilities and the returns on assets, has steadily eroded from both ends.
As noted above, the interest rates that banks could pay on deposits were capped (under so-called Regulation Q) at 0 for checking deposits and about 6 percent on time deposits. (The hope was that, if they faced limited competition for funds, banks would be safer.) Until the Great Inflation, bankers loved the caps because they limited competition for deposits. When interest rates rose enough to cause disintermediation, to cause funds to flow out of banks to higher-yielding investments like money market mutual funds, bankers lobbied for an end to the interest rate restrictions and their request was granted in the 1980s. Since then, banks have had to compete with each other as well as with money market mutual funds for deposits. Unsurprisingly, banks’ gross spreads have eroded, and deposits have become relatively less important as sources of funds.
On the asset side, banks can’t charge as much for loans, ceteris paribus, as they once did because they face increasingly stiff competition from the commercial paper and bond markets, especially the so-called junk bond market. Now, instead of having to cozy up to a bank, smaller and riskier companies can sell bonds directly to investors. Issuing bonds incurs costs besides interest charges—namely, mandatory information disclosure and constant feedback from investors on the issuing firm’s performance via its bond prices—but companies are willing to bear those costs if they can get a better interest rate than banks offer.
As mentioned above, securitization has also hurt banks by giving rise to numerous small lenders that basically sell every loan they originate. Such companies can be efficient at smaller scale because they do not have to attract and retain deposits or engage in more sophisticated asset and liability management techniques. All they have to do is originate loans and sell them to investors, using the proceeds to make new loans. Finance companies especially have eaten into banks’ market share in commercial lending, and a slew of specialized mortgage lenders made major inroads into the home mortgage market. What is good for the goose, as they say, is good for the gander.www.bartleby.com/59/3/whatsgoodfor.html
As a result of those competitive pressures, many banks exited the business, some by going bankrupt, others by merging with larger institutions. The banking crisis of the 1980s enabled bankers and regulators to make further reforms, including greatly easing restrictions on branch banking and investment banking (securities) activities. In 1933, at the nadir of the Great Depression, commercial (receiving deposits and making loans) and investment banking activities (underwriting securities offerings) were strictly separated by legislation usually called Glass-Steagall, after the congressional members who cooked it up. The gradual de facto erosion of Glass-Steagall in the late 1980s and 1990s (by means of bank holding companies and a sympathetic Federal Reserve) and its de jure elimination in 1999 allowed investment and commercial banks to merge and to engage in each other’s activities. Due to those and other regulatory changes, usually called deregulation, and the decline of traditional banking, banks began to merge in large numbers, a process called consolidation, and began to enter into nonbanking financial activities, like insurance, a process called conglomeration.
As Figure 10.4 "Number of FDIC commercial banks, year-end, 1980–2010" and Figure 10.5 "U.S. banks: return on equity, 1935–2010" show, consolidation and conglomeration have left the nation with fewer but larger and more profitable (and ostensibly more efficient) banks. Due to the demise of Glass-Steagall, conglomerate banks can now more easily tap economies of scope, the ability to use a single resource to supply numerous products or services. For example, banks can now use the information they create about borrowers to offer loans or securities underwriting and can use branches to schlep insurance. Consolidation has also allowed banks to diversify their risks geographically and to tap economies of scale. That is important because minimum efficient scale may have increased in recent decades due to the high initial costs of employing the latest and greatest computer and telecommunications technologies. Larger banks may be safer than smaller ones, ceteris paribus, because they have more diversified loan portfolios and more stable deposit bases. Unlike most small banks, large ones are not reliant on the economic fortunes of one city or company, or even one country or economic sector.
The Federal Reserve labels the entities that have arisen from the recent wave of mergers large, complex banking organizations (LCBOs) or large, complex financial institutions (LCFIs). Those names, though, also point to the costs of the new regime. Consolidation may have made banks and other financial institutions too big, complex, and politically potent to regulate effectively. Also, to justify their merger activities to shareholders, many banks have increased their profitability, not by becoming more efficient, but by taking on higher levels of risk. Finally, conglomerates may be able to engage in many different activities, thereby diversifying their revenues and risks, but they may not do any of them very well, thereby actually increasing the risk of failure. A combination of consolidation, conglomeration, and concentration helped to trigger a systemic financial crisis acute enough to negatively affect the national and world economies.
Today, the U.S. banking industry is far more concentrated than during most of its past. In other words, a few large banks have a larger share of assets, deposits, and capital than ever before. That may in turn give those banks considerable market power, the ability to charge more for loans and to pay less for deposits. Figure 10.6 "Concentration in the U.S. banking sector, 1984–2010" shows the increase in the industry’s Herfindahl index, which is a measure of market concentration calculated by taking the sum of the squares of the market shares of each firm in a particular industry. Whether scaled between 0 and 1 or 0 and 10,000, the Herfindahl index is low (near zero) if an industry is composed of numerous small firms, and it is high (near 1 or 10,000) the closer an industry is to monopoly (1 × 1 = 1; 100 × 100 = 10,000). While the Herfindahl index of the U.S. banking sector has increased markedly in recent years, thousands of small banks keep the national index from reaching 1,800, the magic number that triggers greater antitrust scrutiny by the Justice Department. At the end of 2006, for example, 3,246 of the nation’s 7,402 commercial banks had assets of less than \$100 million. Another 3,662 banks had assets greater than \$100 million but less than \$1 billion, leaving only 494 banks with assets over \$1 billion.
Those 500 or so big banks, however, control the vast bulk of the industry’s assets (and hence liabilities and capital too). As Figure 10.7 shows, the nation’s ten largest banks are rapidly gaining market share. Nevertheless, U.S. banking is still far less concentrated than the banking sectors of most other countries. In Canada, for example, the commercial bank Herfindahl index hovers around 1,600, and in Colombia and Chile, the biggest five banks make more than 60 percent of all loans. The United States is such a large country and banking, despite the changes wrought by the Information Revolution, is still such a local business that certain regions have levels of concentration high enough that some fear that banks there are earning quasi-monopoly rents, the high profits associated with oligopolistic and monopolistic market structures. The good news is that bank entry is fairly easy, so if banks become too profitable in some regions, new banks will form to compete with them, bringing the Herfindahl index, n-firm concentration ratios, and ultimately bank profits back in line. Since the mid-1980s, scores to hundreds of new banks, called de novo banks, began operation in the United States each year.
Stop and Think Box
In 2003, Canada was home to the banks (and a handful of small ones that can be safely ignored) listed in the following chart. How concentrated was the Canadian banking sector as measured by the five-firm concentration ratio? The Herfindahl index?
The five-firm concentration ratio is calculated simply by summing the market shares of the five largest banks:
So the five-bank concentration ratio (for assets) in Canada in 2003 was 86 percent.
The Herfindahl index is calculated by summing the squares of the market shares of each bank:
So the Herfindahl index for bank assets in Canada in 2003 was 1,590.
Starting a new bank is not as difficult as it sounds. About twenty or so incorporators need to put about \$50,000 each at risk for the year or two it takes to gain regulatory approval. They must then subscribe at least the same amount in a private placement of stock that provides the bank with some of its capital. The new bank can then begin operations, usually with two branches, one in an asset-rich area, the other in a deposit-rich one. Consultants like Dan Hudson of NuBank.com help new banks to form and begin operations.www.nubank.com Due to the ease of creating new banks and regulations that effectively cap the size of megabanks, the handful of U.S. banks with over \$1 trillion of assets, many observers think that the U.S. banking sector will remain competitive, composed of numerous small banks, a few (dozen, even score) megabanks, and hundreds of large regional players. The small and regional banks will survive by exploiting geographical and specialized niches, like catering to depositors who enjoy interacting with live people instead of machines. Small banks also tend to lend to small businesses, of which America has many. Despite funny television commercials to the contrary, large banks will also lend to small businesses, but smaller, community banks are often better at it because they know more about local markets and borrowers and hence can better assess their business plans.www.icba.org/communitybanking/index.cfm?ItemNumber=556&sn.ItemNumber=1744
The United States also allows individuals to establish other types of depository institutions, including savings and loan associations, mutual savings banks, and credit unions. Few new savings banks are created, and many existing ones have taken commercial bank charters or merged with commercial banks, but new credit union formation is fairly brisk. Credit unions are mutual (that is, owned by depositors rather than shareholders) depository institutions organized around a group of people who share a common bond, like the same employer. They are tax-exempt and historically quite small. Recently, regulators have allowed them to expand so that they can maintain minimum efficient scale and diversify their asset portfolios more widely.
The U.S. banking industry is also increasingly international in scope. Thus, foreign banks can enter the U.S. market relatively easily. Today, foreign banks hold more than 10 percent of total U.S. bank assets and make more than 16 percent of loans to U.S. corporations. Foreign banks can buy U.S. banks or they can simply establish branches in the United States. Foreign banks used to be subject to less stringent regulations than domestic banks, but that was changed in 1978. Increasingly, bank regulations worldwide have converged.
The internationalization of banking also means that U.S. banks can operate in other countries. To date, about 100 U.S. banks have branches abroad, up from just eight in 1960. International banking has grown along with international trade and foreign direct investment. International banking is also a way to diversify assets, tap markets where spreads are larger than in the United States, and get a piece of the Eurodollar market. Eurodollars are dollar-denominated deposits in foreign banks that help international businesses to conduct trade and banks to avoid reserve requirements and other taxing regulations and capital controls. London, Singapore, and the Cayman Islands are the main centers for Eurodollars and, not surprisingly, favorite locations for U.S. banks to establish overseas branches. To help finance trade, U.S. banks also have a strong presence elsewhere, particularly in East Asia and in Latin America.
The nature of banking in the United States and abroad is changing, apparently converging on the European, specifically the British, model. In some countries in continental Europe, like Germany and Switzerland, so-called universal banks that offer commercial and investment banking services and insurance prevail. In other countries, like Great Britain and its commonwealth members, full-blown financial conglomerates are less common, but most banks engage in both commercial and investment banking activities. Meanwhile, foreign securities markets are modeling themselves after American markets, growing larger and more sophisticated. Increasingly, the world’s financial system is becoming one. That should make it more efficient, but it also raises fears of financial catastrophe, a point to which we shall return.
KEY TAKEAWAYS
• Industry consolidation is measured by the number of banks in existence at a given time.
• As the number of banks declines (because mergers and bankruptcies exceed new bank formation), the industry is said to become more consolidated. It is important because a more consolidated industry may be safer and more profitable as smaller, weaker institutions are swallowed up by larger, stronger ones.
• However, consolidation can also lead to higher costs for consumers and borrowers and poorer service.
• Bigger banks are likely to be more diversified than smaller ones, but they might also take on higher levels of risk, thereby threatening the stability of the financial system.
• Conglomeration refers to the scope of activities that a bank or other financial intermediary is allowed to engage in.
• Traditionally, U.S. banks could engage in commercial banking activities or investment banking activities, but not both, and they could not sell or underwrite insurance. Due to recent regulatory changes, however, banks and other financial intermediaries and facilitators like brokerages can now merge into the same company or exist under the same holding company umbrella.
• This deregulation may increase competition for financial intermediaries, thereby driving innovation. It could also lead, however, to the creation of financial conglomerates that are too large and complex to regulate adequately.
• Industry concentration is a proxy for competition and is measured by the n-firm concentration of assets (revenues, capital, etc., where n is 1, 3, 5, 10, 25, 50, etc.) or by the Herfindahl index, the sum of the square of the market shares (again for assets, deposits, revenues, capital, etc.) of each company in the industry or in a given city, state, or region.
• Concentration is important because a highly concentrated industry may be less competitive, leading to less innovation, higher costs for borrowers, outsized profits for suppliers (in this case banks), and a more fragile (prone to systemic crisis) banking system.
• On the other hand, as banking has grown more concentrated, individual banks have become more geographically diversified, which may help them to better weather economic downturns.
10.06: Suggested Reading
Anderloni, Luisa, David Llewellyn, and Reinhard Schmidt. Financial Innovation in Retail and Corporate Banking. Northampton, MA: Edward Elgar, 2009.
Banner, Stuart. Anglo-American Securities Regulation: Cultural and Political Roots, 1690–1860. New York: Cambridge University Press, 2002.
Freedman, Roy. Introduction to Financial Technology. New York: Academic Press, 2006.
Shiller, Robert. The New Financial Order: Risk in the 21st Century. Princeton, NJ: Princeton University Press, 2004.
Wright, Robert E. The Wealth of Nations Rediscovered: Integration and Expansion in American Financial Markets, 1780–1850. New York: Cambridge University Press, 2002.
Wright, Robert E., and David J. Cowen. Financial Founding Fathers: The Men Who Made America Rich. Chicago, IL: Chicago University Press, 2006.
Wright, Robert E., and George D. Smith. Mutually Beneficial: The Guardian and Life Insurance in America. New York: New York University Press, 2004. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/10%3A_Innovation_and_Structure_in_Banking_and_Finance/10.05%3A_Banking_Industry_Profitability_and_Structure.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Explain why the government can’t simply legislate bad things out of existence.
• Describe the public interest and private interest models of government and explain why they are important.
• Explain how asymmetric information interferes with regulatory efforts.
• Describe how government regulators exacerbated the Great Depression.
• Describe how government regulators made the Savings and Loan Crisis worse.
• Assess recent regulatory reforms in the United States and both Basel accords.
Thumbnail: Image by Pixabay
11: The Economics of Financial Regulation
Learning Objectives
• Why can’t the government legislate bad things out of existence and which model of government, public interest or private interest, is the most accurate depiction of reality?
Some regulations are clearly salubrious and should be retained. The main justifications for financial system regulation—market failures—do occur, and government regulations can, and sometimes have, helped to mitigate them. Like everything else in life, however, regulations are costly (not gratis) and hence entail trade-offs. As detailed in another chapter, they induce perfectly legal but bureaucratically disruptive loophole mining and lobbying activities. They can also lead to severely twisted, unintended consequences, like banks purposely making bad loans.
The goal of this chapter is not to bash all regulation but rather to critique specific financial regulations in the hopes of creating better regulatory policies in the (hopefully near) future. The place to start, I believe, is to think about what regulators and regulations cannot do, and that is fix the world by decree. Simply making an activity illegal does not mean that it will stop. Because the government faces a budget constraint and opportunity costs, it can’t afford to monitor everyone all the time. What’s bad for some is often good for others, so many people willingly supply illegal goods or activities. As a result, many illegal activities are commonplace; in no particular order, sodomy, drug use, reckless use of automobiles, and music piracy come to mind. This may seem like a simple point, but many people believe that regulation can really work if only regulations, and the regulators charged with enforcing them, are strengthened. If regulations failed in the past, they believe that means regulators needed more money or authority, or both.
The problem with this view, however, is that government officials may not be the angels many people assume they are. It’s not their fault. Especially if they went through the U.S. public school system, they likely learned an interpretation of government called the public interest model. As its name suggests, the public interest model posits that government officials work in the interests of the public, of “the people,” if you will. It’s the sort of thing Abraham Lincoln had in mind in his famous Gettysburg Address when he said “that government of the people, by the people, for the people, shall not perish from the earth.”showcase.netins.net/web/creative/lincoln/speeches/gettysburg.htm That’s outstanding political rhetoric, better than anything current spin artists concoct, but is it a fair representation of reality?
Many economists think not. They believe that private interest prevails, even in the government. According to their model, called the public choice or, less confusingly, the private interest model, politicians and bureaucrats often behave in their own interests rather than those of the public. Of course, they don’t go around saying that we need law X or regulation Y to help me to get rich via bribes, to bailout my brother-in-law, or to ensure that I soon receive a cushy job in the private sector. Rather, they say that we need law X or regulation Y to protect widows and orphans, to stymie the efforts of bad guys, or to make the rich pay for their success.
In many countries, the ones we will call “predatory” in the context of the Growth Diamond model, the private interest model clearly holds sway. In rich countries, the public interest model becomes more plausible. Nevertheless, many economic regulations, though clothed in public interest rhetoric, appear on close inspection to conform to the private interest model. As University of Chicago economist and Nobel Laureate George Stiglerwww.econlib.org/LIBRARY/Enc/bios/Stigler.html pointed out decades ago, regulators are often “captured”en.Wikipedia.org/wiki/Regulatory_capture by the industry they regulate. In other words, the industry establishes regulations for itself by influencing the decisions of regulators. Financial regulators, as we’ll see, are no exception.
Regardless of regulators’ and politicians’ motivations, another very sticky question arises: could regulators stop bad activities, events, and people even if they wanted to? The answer in many contexts appears to be an unequivocal “No!” The reason is our old nemesis, asymmetric information, which, readers should recall, inheres in nature and pervades all. It flummoxes governments as much as markets and intermediaries. The implications of this insight are devastating for the effectiveness of regulators and their regulations, as Figure 11.1 makes clear.
Although Figure 11.1 is esthetically pleasing (great job, guys!) it does not paint a pretty picture. Due to multiple levels of nearly intractable problems of asymmetric information, democracy is no guarantee that government will serve the public interest. Matters are even worse in societies still plagued by predatory government, where corruption further fouls up the works by giving politicians, regulators, and bankers (and other financiers) incentives to perpetuate the current system, no matter how suboptimal it may be from the public’s point of view.
And if you really want to get your head spinning, consider this: agency problems within the government, within regulatory bureaucracies, and within banks abound. Within banks, traders and loan officers want to keep their jobs, earn promotions, and bring home large bonuses. They can do the latter two by taking large risks, and sometimes they choose to do so. Sometimes shareholders want to take on much larger risks than managers or depositors or other debt holders do. Sometimes it’s the managers who have incentives to place big bets, to get their stock options “in the money.”www.investorwords.com/2580/in_the_money.html Within bureaucracies, regulators have incentives to hide their mistakes and to take credit for good outcomes, even if they had little or nothing to do with them. The same is true for the government, where the legislature may try to discredit the executive’s policies, or vice versa, and withhold information or even spread disinformation to “prove” its case.
Stop and Think Box
In the 1910s and early 1920s, a majority of U.S. states passed securities regulations called Blue Sky Laws that ostensibly sought to prevent slimy securities dealers from selling nothing but the blue sky to poor, defenseless widows and orphans. Can you figure out what was really going on? (Hint: Recall that this was a period of traditional banking, unit banks, the 3-6-3 rule, and all that. Recall, too, that securities markets are an alternative method of linking investors to borrowers.)
We probably gave it away with that last hint. Blue Sky Laws, scholars now realize, were veiled attempts to protect the monopolies of unit bankers upset about losing business to the securities markets. Unable to garner public sympathy for their plight, the bankers instead spoke in terms of public interest, of defrauded widows and orphans. There were certainly some scams about, but not enough to warrant the more virulent Blue Sky Laws, which actually gave state officials the power to forbid issuance of securities they didn’t like, and in some states, that was most of them!
It’s okay if you feel a bit uneasy with these new ideas. I think that as adults you can handle straight talk. It’ll be better for everyone—you, me, our children and grandchildren—if you learn to look at the government’s actions with a critical eye. Regulators have failed in the past and will do so again unless we align the interests of all the major parties depicted in Figure 11.1 more closely, empowering market forces to do most of the heavy lifting.
KEY TAKEAWAYS
• The government can’t legislate bad things away because it can’t be every place at once. Like the rest of us, government faces budget constraints and opportunity costs. Therefore, it cannot stop activities that some people enjoy or find profitable.
• According to the public interest model, government tries to enact laws, regulations, and policies that benefit the public.
• The private interest (or public choice) model, by contrast, suggests that government officials enact laws that are in their own private interest.
• It is important to know which model is a more accurate description of reality because the models have very different implications for our attitudes toward regulation.
• If one believes the public interest model is usually correct, then one will be more likely to call for government regulation, even if one admits that regulatory goals may in fact be difficult to achieve regardless of the intentions of politicians and bureaucrats.
• If one believes the private interest model is a more accurate depiction of the real world, one will be more skeptical of government regulation.
• Asymmetric information creates a principal-agent problem between the public and elected officials, another principal-agent problem between those officials and regulators, and yet another principal-agent problem between regulators and banks (and other financial firms) because in each case, one party (politicians, regulators, banks) knows more than the other (public, politicians, regulators).
• So there are at least three places where the public’s interest can be stymied: in political elections, in the interaction between Congress and the president and regulatory agencies, and in the interaction between regulators and the regulated. And that’s ignoring the often extensive agency problems found within governments, regulatory agencies, and financial institutions! | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/11%3A_The_Economics_of_Financial_Regulation/11.01%3A_Market_Failures_and_Public_Choice.txt |
Learning Objectives
• How did the government exacerbate the Great Depression?
Time again, government regulators have either failed to stop financial crises or have exacerbated them. Examples are too numerous to discuss in detail here, so we will address only two of the more egregious cases, the Great Depression of the 1930s and the Savings and Loan (S&L) Crisis of the 1980s.
Generally when economic matters go FUBAR (Fouled Up Beyond All Recognition in polite circles), observers blame either “market failures” like asymmetric information and externalities, or they blame the government. Reality is rarely that simple. Most major economic foul-ups stem from a combination of market and government failures, what I like to call hybrid failures. So while it would be an exaggeration to claim that government policies were the only causes of the Great Depression or the Savings and Loan Crisis, it is fair to say that they made matters worse, much worse.
The stock market crash of 1929 did not start the Great Depression, but it did give the economy a strong push downhill.stocks.fundamentalfinance.com/stock-market-crash-of-1929.php A precipitous decline in stock prices like that of 1929 can cause uncertainty to increase and balance sheets to deteriorate, worsening asymmetric information problems and leading to a decline in economic activity. That, in turn, can cause bank panics, further increases in asymmetric information, and yet further declines in economic activity followed by an unanticipated decline in the price level. As Figure 11.2 "Major macro variables during the Great Depression" shows, that is precisely what happened during the Great Depression—per capita gross domestic product (GDP) shrank, the number of bankruptcies soared, M1 and M2 (measures of the money supply) declined, and so did the price level.
Weren’t evil financiers completely responsible for this mess, as nine out of ten people thought at the time? Absolutely not. For starters, very few financiers benefited from the depression and they did not have the ability to cause such a mess. Most would have stopped the downward spiral if it was in their power to do so, as J. P. Morgan did when panic seized the financial system in 1907.www.bos.frb.org/about/pubs/panicof1.pdf In fact, only the government had the resources and institutions to stop the Great Depression and it failed to do so. Mistake number one occurred during the 1920s, when the government allowed stock and real estate prices to rise to dizzying heights. (The Dow Jones Industrial Average started the decade at 108.76, dropped to around 60, then began a slow climb to 200 by the end of 1927. It hit 300 by the end of 1928 and 350 by August 1929.)measuringworth.com/datasets/DJA By slowly raising interest rates beginning in, say, mid-1928, the Federal Reserve (Fed) could have deflated the stock market bubble before it grew to enormous proportions and burst in 1929.
Mistake number two occurred after the crash, in late 1929 and 1930, when the Federal Reserve raised interest rates. A much better policy response at that point would have been to lower interest rates in order to help troubled banks and stimulate business investment and hence private job growth. In addition, the Federal Reserve did not behave like a lender of last resort (LLR) during the crisis and follow Bagehot’s/Hamilton’s Rule. Before the Fed began operations in the fall of 1914, regional clearinghouses had acted as LLRs, but during the Depression they assumed, wrongly as it turned out, that the Fed had relieved them of that responsibility. They were, accordingly, unprepared to thwart major bank runs.Michael Bordo and David Wheelock, “The Promise and Performance of the Federal Reserve as Lender of Last Resort,” Norges Bank Working Paper 201 (20 January 2011). papers.ssrn.com/sol3/papers.cfm?abstract_id=1847472
The government’s third mistake was its banking policy. The United States was home to tens of thousands of tiny unit banks that simply were not large or diversified enough to ride out the depression. If a factory or other major employer succumbed, the local bank too was doomed. Depositors understood this, so at the first sign of trouble they ran on their banks, pulling out their deposits before they went under. Their actions guaranteed that their banks would indeed fail. Meanwhile, across the border in Canada, which was home to a few large and highly diversified banks, few bank disturbances took place. California also weathered the Great Depression relatively well, in part because its banks, which freely branched throughout the large state, enjoyed relatively well-diversified assets and hence avoided the worst of the bank crises.
The government’s fourth failure was to raise tariffs in a misguided attempt to “beggar thy neighbor.”www.state.gov/r/pa/ho/time/id/17606.htm Detailed analysis of this failure, which falls outside the bailiwick of finance, I’ll leave to your international economics textbook and a case elsewhere in this book. Here, we’ll just paraphrase Mr. Mackey from South Park: “Tariffs are bad, mmmkay?”en.Wikipedia.org/wiki/List_of_staff_at_South_Park_Elementary#Mr._Mackey
But what about Franklin Delano Roosevelt (FDR)www.whitehouse.gov/history/presidents/fr32.html and his New Deal?newdeal.feri.org Didn’t the new administration stop the Great Depression, particularly via deposit insurance, Glass-Steagall, securities market reforms, and reassuring speeches about having nothing to fear but fear itself?historymatters.gmu.edu/d/5057 The United States did suffer its most acute banking crisis in March 1933, just as FDR took office on March 4.www.bartleby.com/124/pres49.html (The Twentieth Amendment, ratified in 1938, changed the presidential inauguration date to January 20, which it is to this day.) But many suspect that FDR himself brought the crisis on by increasing uncertainty about the new administration’s policy path. Whatever the cause of the crisis, it shattered confidence in the banking system. FDR’s creation of a deposit insurance scheme under the aegis of a new federal agency, the Federal Deposit Insurance Corporation (FDIC), did restore confidence, inducing people to stop running on the banks and thereby stopping the economy’s death spiral. Since then, bank runs have been rare occurrences directed at specific shaky banks and not system-wide disturbances as during the Great Depression and earlier banking crises.
But as with everything in life, deposit insurance is far from cost-free. In fact, the latest research suggests it is a wash. Deposit insurance does prevent bank runs because depositors know the insurance fund will repay them if their bank goes belly up. (Today, it insures \$250,000 per depositor per insured bank. For details, browsewww.fdic.gov/deposit/deposits/insured/basics.html) However, insurance also reduces depositor monitoring, which allows bankers to take on added risk. In the nineteenth century, depositors disciplined banks that took on too much risk by withdrawing their deposits. As we’ve seen, that decreases the size of the bank and reduces reserves, forcing bankers to decrease their risk profile. With deposit insurance, depositors (quite rationally) blithely ignore the adverse selection problem and shift their funds to wherever they will fetch the most interest. They don’t ask how Shaky Bank is able to pay 15 percent for six-month certificates of deposit (CDs) when other banks pay only 5 percent. Who cares, they reason, my deposits are insured! Indeed, but as we’ll learn below, taxpayers insure the insurer.
Another New Deal financial reform, Glass-Steagall, in no way helped the U.S. economy or financial system and may have hurt both. For over half a century, Glass-Steagall prevented U.S. banks from simultaneously engaging in commercial (taking deposits and making loans) and investment banking (underwriting securities and advising on mergers) activities. Only two groups clearly gained from the legislation, politicians who could thump their chests on the campaign stump and claim to have saved the country from greedy financiers and, ironically enough, big investment banks. The latter, it turns out, wrote the act and did so in such a way that it protected their oligopoly from the competition of commercial banks and smaller, more retail-oriented investment banks. The act was clearly unnecessary from an economic standpoint because most countries had no such legislation and suffered no ill effects because of its absence. (The Dodd-Frank Act’s Volcker Rule represents a better approach because it outlaws various dubious practices, like proprietary trading, not valid organizational forms).
The Security and Exchange Commission’s (SEC) genesis is almost as tawdry and its record almost as bad. The SEC’s stated goal, to increase the transparency of America’s financial markets, was a laudable one. Unfortunately, the SEC simply does not do its job very well. As the late, great, free-market proponent Milton Friedman put it:
“You are not free to raise funds on the capital marketsThis part is inaccurate. Financiers went loophole mining and found a real doozy called a private placement. As opposed to a public offering, in a private placement securities issuers can avoid SEC disclosure requirements by selling directly to institutional investors like life insurance companies and other “accredited investors” (legalese for “rich people”). unless you fill out the numerous pages of forms the SEC requires and unless you satisfy the SEC that the prospectus you propose to issue presents such a bleak picture of your prospects that no investor in his right mind would invest in your project if he took the prospectus literally.This part is all too true. Check out the prospectus of Internet giant Google at www.sec.gov/Archives/edgar/data/1288776/000119312504142742/ds1a.htm. If you don’t dig Google, check out any company you like via Edgar, the SEC’s filing database, at www.sec.gov/edgar.shtml. And getting SEC approval may cost upwards of \$100,000—which certainly discourages the small firms our government professes to help.”
Stop and Think Box
As noted above, the FDIC insures bank deposits up to \$250,000 per depositor per insured bank. What if an investor wants to deposit \$1 million or \$1 billion? Must the investor put most of her money at risk?
Depositors can loophole mine as well as anyone. And they did, or, to be more precise, intermediaries known as deposit brokers did. Deposit brokers chopped up big deposits into insured-sized chunks, then spread them all over creation. The telecommunications revolution made this relatively easy and cheap to do, and the S&L crisis created many a zombie bank willing to pay high interest for deposits.
KEY TAKEAWAYS
• In addition to imposing high tariffs, the government exacerbated the Great Depression by (1) allowing the asset bubble of the late 1920s to continue; (2) responding to the crash inappropriately by raising the interest rate and restricting M1 and M2; and (3) passing reforms of dubious long-term efficacy, including deposit insurance, Glass-Steagall, and the SEC. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/11%3A_The_Economics_of_Financial_Regulation/11.02%3A_The_Great_Depression_as_Regulatory_Failure.txt |
Learning Objectives
• How did regulators exacerbate the Savings and Loan Crisis of the 1980s?
Although the economy improved after 1933, regulatory regimes did not. Ever fearful of a repeat of the Great Depression, U.S. regulators sought to make banks highly safe and highly profitable so none would ever dare to fail. Basically, the government regulated the interest rate, assuring banks a nice profit—that’s what the 3-6-3 rule was all about. Regulators also made it difficult to start a new bank to keep competition levels down, all in the name of stability. The game worked well until the late 1960s, then went to hell in a handbasket as technological breakthroughs and the Great Inflation conspired to destroy traditional banking.
Here’s where things get interesting. Savings and loan associations were particularly hard hit by the changed financial environment because their gaps were huge. The sources of their funds were savings accounts and their uses were mortgages, most of them for thirty years at fixed rates. Like this:
Typical Savings and Loan Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$10 Deposits \$130
Securities \$10 Borrowings \$15
Mortgages \$130 Capital \$15
Other assets \$10
Totals \$160 \$160
Along comes the Great Inflation and there go the deposits. Then S&L’s balance sheets looked like this:
Typical Savings and Loan Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$1 Deposits \$100
Securities \$1 Borrowings \$30
Mortgages \$130 Capital \$10
Other assets \$8
Totals \$140 \$140
This bank is clearly in deep doodoo. Were it alone, it soon would have lost its remaining capital and failed. But there were some 750 of them in like situation. So they went to the regulators and asked for help. The regulators were happy to oblige because they did not want to have a bunch of failed banks on their hands, especially given that the deposits of those banks were insured. So regulators eliminated the interest rate caps and allowed S&Ls to engage in a variety of new activities, like making commercial real estate loans and buying junk bonds, hitherto forbidden. Given the demise of traditional banking, that was a reasonable response. The problem was that most S&L bankers didn’t have a clue about how to do anything other than traditional banking. Most of them got chewed. Their balance sheets then began to resemble a train wreck:
Typical Savings and Loan Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$1 Deposits \$120
Securities \$1 Borrowings \$22
Mortgages \$130 Capital \$0
Other assets \$10
Totals \$142 \$142
Now comes the most egregious part. Fearful of losing their jobs, regulators kept these economically dead (capital < \$0) banks alive. Instead of shutting them down, they engaged in what is called regulatory forbearance. Specifically, they allowed S&Ls to add “goodwill” to the asset side of their balance sheets, restoring them to life—on paper. (Technically, they allowed the banks to switch from generally accepted accounting principles [GAAP] to regulatory accounting principles [RAP].) Seems like a cool thing for the regulators to do, right? Wrong! A teacher can pass a kid who can’t read, but the kid still can’t read. Similarly, a regulator can pass a bank with no capital, but still can’t make the bank viable. In fact, the bank situation is worse because the kid has other chances to learn to read. By contrast zombie banks, as these S&Ls were called, have little hope of recovery. Regulators should have shot them in the head instead, which as any zombie-movie fan knows is the only way to stop the undead dead in their tracks.www.margrabe.com/Devil/DevilU_Z.html;www.ericlathrop.com/notld
Recall that if somebody has no capital, no skin in the game, to borrow Warren Buffett’s phrase again, moral hazard will be extremely high because the person is playing only with other people’s money. In this case, the money wasn’t even that of depositors but rather of the deposit insurer, a government agency. The managers of the S&Ls did what anyone in the same situation would do: they rolled the dice, engaging in highly risky investments funded with deposits and borrowings for which they paid a hefty premium. In other words, they borrowed from depositors and other lenders at high rates and invested in highly risky loans. A few got lucky and pulled their banks out of the red. Most of the risky loans, however, quickly turned sour. When the whole thing was over, their balance sheets looked like this:
Typical Savings and Loan Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$10 Deposits \$200
Securities \$10 Borrowings \$100
Mortgages \$100 Capital −\$60
Goodwill \$30
Crazy, risky loans \$70
Other assets \$20
Totals \$240 \$240
The regulators could no longer forbear. The insurance fund could not meet the deposit liabilities of the thousands of failed S&Ls, so the bill ended up in the lap of U.S. taxpayers.
Stop and Think Box
In the 1980s, in response to the Great Inflation and the technological revolution, regulators in Scandinavia (Sweden, Norway, and Finland) deregulated their heavily regulated banking systems. Bankers who usually lent only to the best borrowers at government mandated rates suddenly found themselves competing for both depositors and borrowers. What happened?
Scandinavia suffered from worse banking crises than the United States. In particular, Scandinavian bankers were not very good at screening good from bad borrowers because they had long been accustomed to lending to just the best. They inevitably made many mistakes, which led to defaults and ultimately asset and capital write-downs.
The most depressing aspect of this story is that the United States has unusually good regulators. As Figure 11.3 "Banking crises around the globe through 2002" shows, other countries have suffered through far worse banking crises and losses. Note that at 3 percent of U.S. GDP, the S&L crisis was no picnic, but it pales in comparison to the losses in Argentina, Indonesia, China, Jamaica and elsewhere.
KEY TAKEAWAYS
• First, regulators were too slow to realize that traditional banking—the 3-6-3 rule and easy profitable banking—was dying due to the Great Inflation and technological improvements.
• Second, they allowed the institutions most vulnerable to the rapidly changing financial environment, savings and loan associations, too much latitude to engage in new, more sophisticated banking techniques, like liability management, without sufficient experience or training.
• Third, regulators engaged in forbearance, allowing essentially bankrupt companies to continue operations without realizing that the end result, due to very high levels of moral hazard, would be further losses. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/11%3A_The_Economics_of_Financial_Regulation/11.03%3A_The_Savings_and_Loan_Regulatory_Debacle.txt |
Learning Objectives
• Have regulatory reforms and changes in market structure made the U.S. banking industry safer?
The S&L crisis and the failure of a few big commercial banks induced a series of regulatory reforms in the United States. The first such act, the Financial Institutions Reform, Recovery, and Enforcement Act (FIRREA), became law in August 1989. That act canned the old S&L regulators, created new regulatory agencies, and bailed out the bankrupt insurance fund. In the end, U.S. taxpayers reimbursed depositors at the failed S&Ls. FIRREA also re-regulated S&Ls, increasing their capital requirements and imposing the same risk-based capital standards that commercial banks are subject to. Since passage of the act, many S&Ls have converted to commercial banks and few new S&Ls have been formed.
In 1991, the government enacted further reforms in the Federal Deposit Insurance Corporation Improvement Act (FDICIA), which continued the bailout of the S&Ls and the deposit insurance fund, raised deposit insurance premiums, and forced the FDIC to close failed banks using the least costly method. (Failed banks can be dismembered and their pieces sold off one by one. That often entails selling assets at a discount. Or an entire bank can be sold to a healthy bank, which, of course, wants a little sugar [read, “cash”] to induce it to embrace a zombie!) The act also forced the FDIC to charge risk-based insurance premiums instead of a flat fee. The system it developed, however, resulted in 90 percent of banks, accounting for 95 percent of all deposits, paying the same premium. The original idea of taxing risky banks and rewarding safe ones was therefore subverted.
FDICIA’s crowning glory is that it requires regulators to intervene earlier and more stridently when banks first get into trouble, well before losses eat away their capital. The idea is to close banks before they go broke, and certainly before they arise from the dead. See Figure 11.4 for details. Of course, banks can go under, have gone under, in a matter of hours, well before regulators can act or even know what is happening. Regulators do not and, of course, cannot monitor banks 24/7/365. And despite the law, regulators might still forbear, just like your neighbor might still smoke pot, even though it’s illegal.
The other problem with FDICIA is that it weakened but ultimately maintained the too-big-to-fail (TBTF) policy. Regulators cooked up TBTF during the 1980s to justify bailing out a big shaky bank called Continental Illinois. Like deposit insurance, TBTF was ostensibly a noble notion. If a really big bank failed and owed large sums to lots of other banks and nonbank financial institutions, it could cause a domino effect that could topple numerous companies very quickly. That, in turn, would cause asymmetric information and uncertainty to rise, risk premia on bonds to jump, stock prices to fall…you get the picture.If not, read an article that influenced policymakers: Ben Bernanke, “Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression,” American Economic Review 73 (June 1983): 257–76.The problem is that if a bank thinks it is too big to be allowed to fail, it has an incentive to take on a lot of risk, confident that the government will have its back if it gets into trouble. (Banks in this respect are little different from drunken frat boys, or so I’ve heard.) Financier Henry Kaufman has termed this problem the Bigness DilemmaThe dilemma is that big banks in other regards are stabilizing rather than destabilizing because they have clearly achieved efficient scale and maintain a diversified portfolio of assets. and long feared that it could lead to a catastrophic economic meltdown, a political crisis, or a major economic slump. His fears came to fruition during the financial crisis of 2007–2008, of which we will learn more in another chapter. Similarly some analysts believe that Japan’s TBTF policy was a leading cause of its recent fifteen-year economic funk. So like most other regulations, TBTF imposes costs that may exceed its benefits, depending on the details of how each are tallied. Such tallies, unfortunately, are often suffused with partisan ideological assumptions.
In 1994, the Riegle-Neal Interstate Banking and Branching Efficiency Act finally overturned most prohibitions on interstate banking. That law led to considerable consolidation, the effects of which are still unclear. Nevertheless, the act was long overdue, as was the Gramm-Leach-Bliley Financial Services Modernization Act of 1999, which repealed Glass-Steagall, allowing the same institutions to engage in both commercial and investment banking activities. The act has led to some conglomeration, but not as much as many observers expected. Again, it may be some time before the overall effects of the reform become clear. So far, both acts appear to have strengthened the financial system by making banks more profitable and diversified. Some large complex banking organizations and large complex financial institutions (LCBOs and LCFIs, respectively) have held up well in the face of the subprime mortgage crisis, but others went bankrupt. The recent crisis appears to have been rooted in more fundamental issues, like TBTF and a dearth of internal incentive alignment within financial institutions, big and small, than in the regulatory reforms of the 1990s.
KEY TAKEAWAYS
• To some extent, it is too early to tell what the effects of financial consolidation, concentration, and conglomeration will be.
• Overall, it appears that recent U.S. financial reforms range from salutary (repeal of branching restrictions and Glass-Steagall) to destabilizing (retention of the too-big-to-fail policy). | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/11%3A_The_Economics_of_Financial_Regulation/11.04%3A__Better_but_Still_Not_Good-_U.S._Regulatory_Reforms.txt |
Learning Objectives
• Will Basel II render the banking industry safe? If not, what might?
Due to the prevalence of banking crises worldwide and the financial system’s increasingly global and integrated nature, international regulators, especially the Bank for International Settlements in Basel, Switzerland, have also been busy. Their recommendations are not binding on sovereign nations, but to date they have obtained significant buy-in worldwide. America’s financial reforms in the 1990s, for example, were influenced by the so-called Basel I recommendations of 1988. Almost all countries have complied, on paper anyway, with Basel I rules on minimum and risk-weighted capitalization. Risk-weighting was indeed an improvement over the older capitalization requirements, which were simply a minimum leverage ratio:
Capital assets
So the leverage ratio of the following bank would be 6 percent (6/100 = .06, or 6%), which in the past was generally considered adequate.
Some Bank Balance Sheet (Millions USD)
Assets Liabilities
Reserves \$10 Deposits \$80
Securities \$10 Borrowings \$14
Loans \$70 Capital \$6
Other assets \$10
Totals \$100 \$100
Of course, leverage ratios are much too simplistic because a bank with a leverage ratio of only 4 percent but with a diversified portfolio of very safe loans would be much safer than one with a leverage ratio of 10 percent but whose assets were invested entirely in lottery tickets!
The concept of weighting risks is therefore a solid one. A bank holding nothing but reserves would need very little capital compared to one holding mostly high-risk loans to biotech and nanotech startups. Bankers, however, consider the Basel I weights too arbitrary and too broad. For example, Basel I suggested weighting sovereign bonds at zero. That’s great for developed countries, but plenty of poorer nations regularly default on their bonds. Some types of assets received a weighting of .5, others 1, others 1.5, and so forth, as the asset grew riskier. So, for example, the following assets would be weighted according to their risk before being put into a leverage ratio:
Reserves \$100,000,000 × 0 = 0
Governments \$50,000,000 × 0 = 0
Commercial loans \$600,000,000 × 1 = 600,000,000
Mortgages \$100,000,000 × 1.5 = 150,000,000
And so forth. But the weights were arbitrary. Are mortgages exactly half again as risky as commercial loans? Basel I basically encouraged banks to decrease their holdings of assets that the regulations overweighted and to stock up on assets that it underweighted. Not a pretty sight.
In response to such criticism, the Basel Committee on Banking Supervision announced in June 2004 a new set of guidelines, called Basel II, initially slated for implementation in 2008 and 2009 in the G10 countries. Basel II contains three pillars: capital, supervisory review process, and market discipline. According to the latest and greatest research, Rethinking Bank Regulation by James Barth, Gerard Caprio, and Ross Levine, the first two pillars are not very useful ways of regulating banks. The new risk weighting is an improvement, but it still grossly oversimplifies risk management and is not holistic enough. Moreover, supervisors cannot monitor every aspect of every bank all the time. Banks have to make periodic call reports on their balance sheets, income, and dividends but, like homeowners selling their homes, they pretty up the place before the prospective buyers arrive. In more developed countries, regulators also conduct surprise on-site examinations during which the examiners rate banks according to the so-called CAMELS formulation:
C = capital adequacy
A = asset quality
M = management
E = earnings
L = liquidity (reserves)
S = sensitivity to market risk.
A, M, and S are even more difficult to ascertain than C, E, and L and, as noted above, any or all of the variables can change very rapidly. Moreover, much banking activity these days takes place off the balance sheet, where it is even more difficult for regulators to find and accurately assess. Finally, in many jurisdictions, examiners are incorrecty compensated and hence do not do a very thorough job.
Barth, Caprio, and Levine argue that the third pillar of Basel II, financial market monitoring, is different. In aggregate, market participants can and in fact do monitor banks and bankers much more often and much more astutely than regulators can because they have much more at stake than a relatively low-paying job. Barth, Caprio, and Levine argue persuasively that instead of conceiving of themselves as police officers, judges, and juries, bank regulators should see themselves as aides, as helping bank depositors (and other creditors of the bank) and stockholders to keep the bankers in line. After all, nobody gains from a bank’s failure. The key, they believe, is to ensure that debt and equity holders have incentives and opportunities to monitor bank management to ensure that they are not taking on too much risk. That means reducing asymmetric information by ensuring reliable information disclosure and urging that corporate governance best practices be followed.Frederick D. Lipman, Corporate Governance Best Practices: Strategies for Public, Private, and Not-for-Profit Organizations (Hoboken, N.J.: Wiley, 2006).
Regulators can also provide banks with incentives to keep their asset bases sufficiently diversified and to prevent them from engaging in inappropriate activities, like building rocket ships or running water treatment plants. Screening new banks and bankers, if regulators do it to reduce adverse selection (omit shysters or inexperienced people) rather than to aid existing banks (by blocking all or most new entrants and hence limiting competition) or to line their own pockets (via bribes), is another area where regulators can be effective. By focusing on a few key reachable goals, regulators can concentrate their limited resources and get the job done, the job of letting people look after their own property themselves. The market-based approach, scholars note, is most important in less-developed countries where regulators are more likely to be on the take (to enact and enforce regulations simply to augment their incomes via bribes).
U.S. implementation of Basel II was disrupted by the worst financial dislocation in 80 years. Intense lobbying pressure combined with the uncertainties created by the 2008 crisis led to numerous changes and implementation delays. As of writing (September 2011), the move to Basel II had barely begun in the United States, though full implementation of yet newer regulations, Basel III, are currently slated to take effect in 2019.Pierre-Hugues Verdier, “U.S. Implementation of Basel II: Lessons for Informal International Law-Making,” University of Virginia School of Law Working Paper (30 June 2011). papers.ssrn.com/sol3/papers.cfm?abstract_id=1879391
In July 2010, the U.S. government also attempted to make the financial system less fragile by passing the Dodd-Frank Wall Street Reform and Protection Act. Over the next several years, the law mandates the creation of a new
• Financial Stability Oversight Council;
• Office of Financial Research;
• Consumer Financial Protection Bureau;
• advanced warning system that will attempt to identify and address systemic risks before they threaten financial institutions and markets.
It also calls for:
• more stringent capital and liquidity requirements for LCFIs;
• tougher regulation of systemically important non-bank financial companies;
• the breakup of LCFIs, if necessary;
• tougher restrictions on bailouts;
• more transparency for asset-backed securities and other “exotic” financial instruments;
• improved corporate governance rules designed to give shareholders more say over the structure of executive compensation.
Despite the sweeping nature of those reforms, some scholars remain skeptical of the new law because it has not clearly eliminated the problems associated with TBTF policy, bailouts, and other causes of the financial crisis of 2007-2009.
KEY TAKEAWAYS
• Basel I and II have provided regulators with more sophisticated ways of analyzing the adequacy of bank capital.
• Nevertheless, it appears that regulators lag behind banks and their bankers, in part because of agency problems within regulatory bureaucracies and in part because of the gulf of asymmetric information separating banks and regulators, particularly when it comes to the quality of assets and the extent and risk of off-balance-sheet activities.
• If scholars like Barth, Caprio, and Levine are correct, regulators ought to think of ways of helping financial markets, particularly bank debt and equity holders, to monitor banks.
• They should also improve their screening of new bank applicants without unduly restricting entry, and set and enforce broad guidelines for portfolio diversification and admissible activities.
11.06: Suggested Reading
Acharya, Viral et al, eds. Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance. Hoboken, NJ: John Wiley and Sons, 2011.
Arner, Douglas. Financial Stability, Economic Growth, and the Role of Law. New York: Cambridge University Press, 2007.
Barth, James, Gerard Caprio, and Ross Levine. Rethinking Bank Regulation. New York: Cambridge University Press, 2006.
Barth, James, S. Trimbath, and Glenn Yago. The Savings and Loan Crisis: Lessons from a Regulatory Failure. New York: Springer, 2004.
Benston, George. Regulating Financial Markets: A Critique and Some Proposals. Washington, DC: AEI Press, 1999.
Bernanke, Ben S. Essays on the Great Depression. Princeton, NJ: Princeton University Press, 2000.
Gup, Benton. Too Big to Fail: Policies and Practices in Government Bailouts. Westport, CT: Praeger, 2004.
Stern, Gary, and Ron Feldman. Too Big to Fail: The Hazards of Bank Bailouts. Washington, DC: Brookings Institution Press, 2004.
Tullock, Gordon, Arthur Seldon, and Gordon Brady. Government Failure: A Primer in Public Choice. Washington, DC: Cato Institute, 2002.
Winston, Clifford. Government Failure Versus Market Failure: Microeconomics Policy Research and Government Performance. Washington, DC: AEI-Brookings Joint Center for Regulatory Studies, 2006. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/11%3A_The_Economics_of_Financial_Regulation/11.05%3A_Basel_II_Basel_III_and_Dodd-Frank.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Define financial derivative and explain the economic functions that financial derivatives fulfill.
• Define and describe the four major types of derivatives: forwards, futures, options, and swaps.
• Explain the economic functions of hedging and speculating.
Thumbnail: Image by Gino Crescoli from Pixabay
12: Financial Derivatives
Learning Objectives
• What are financial derivatives and what economic needs do they fulfill?
Financial derivatives are special types of financial instruments, the prices of which are ultimately derived from the price or performance of some underlying asset. Investors use derivatives to hedge (decrease return volatility) or to speculate (increase the volatility of returns).
Although often derided in the press and movies, derivatives are inherently neither good nor bad, they are merely tools used to limit losses (hedge) or to multiply gains and losses (speculate). Speculation has a bad rep but in fact it makes hedging possible because investors can hedge only if they can find a speculator willing to assume the risks that they wish to eschew.
Ultimately, the prices of derivatives are a function of supply and demand, both of which are subject to valuation models too mathematically complex to address here. The basic forms and functions of the four main types of derivatives—forwards, futures, options, and swaps—are easily narrated and understood, however, and form the basis of this chapter.
Stop and Think Box
If you could, would you receive a guaranteed grade of B for this course? Or would you rather have a chance of receiving an A even if that meant that you might fail the course?
If you take the guaranteed B, you are hedging or reducing your return (grade) variability. If you are willing to accept an A or an F, you are acting like a speculator and may end up on the dean’s list or on academic probation. Neither choice is wrong or bad but is merely a tool by which you can achieve your preferences.
KEY TAKEAWAYS
• Derivatives are instruments, the price of which derives from the price or performance of some underlying asset.
• Derivatives can be used to hedge (reduce risk) or to speculate (increase risk).
• Derivatives are just tools that investors can use to increase or decrease return volatility and hence are not inherently bad. Speculation is the obverse of hedging, which would be impossible to do without speculators serving as counterparties.
12.02: Forwards and Futures
Learning Objectives
• What is a forward contract and what is it used for?
• What is a futures contract and what is its economic purpose?
Imagine you want to throw a party at the end of the semester and have a budget of \$100 for beer. (If you are underage or a teetotaler think about root beer instead.) You know your buddies will drink up any (root) beer you bring into the house before the party so you have to wait until the day of the event to make your purchases. The problem is that the price of your favorite beer jumps around. Sometimes it costs \$20 per case but other times it is \$30. Having 5 cases of the good stuff would mean an awesome party but having 3 cases of the good stuff and a case of (insert your favorite word for bad \$10/case beer here) would be…like totally lame. What to do?
Buyers naturally fear increases in the prices of the things they want to own in the future. Sellers, by contrast, fear price decreases. Those mutual fears can lead to the creation of a financial instrument known as a forward. In a forward contract, a buyer and a seller agree today on the price of an asset to be purchased and delivered in the future. That way, the buyer knows precisely how much he will have to pay and the seller knows precisely how much she will receive. You could sign a forward contract with your beer distributor pegging the price of your favorite beer at \$25 per case and thus ensure that you will have 4 cases of the good stuff at your end of semester bash. Similarly, a farmer and a grocer could contract at planting to fix the price of watermelons, corn, and so forth at harvest time.
Agricultural forward contracts like that just described have been used for centuries if not millennia. Their use is limited by three major problems with forward contracts: (1) it is often costly/difficult to find a willing counterparty; (2) the market for forwards is illiquid due to their idiosyncratic nature so they are not easily sold to other parties if desired; (3) one party usually has an incentive to break the agreement. Imagine, for example, that the price of your favorite beer dropped to only \$15 per case. You might feel cheated at having to pay \$25 and renege on your promise. Conversely, if your beer went to \$40 per case the distributor might tell you to get lost when you tried to pay \$25 under the forward contract.
Exchanges like the Chicago Board Options Exchange (CBOE), Chicago Mercantile Exchange (CME), Chicago Board of Trade (CBOT), and Minneapolis Grain Exchange (MGEX) developed futures to obviate the difficulties with forward contracts by: (1) efficiently linking buyers and sellers; (2) developing standardized weights, definitions, standards, and expiration dates for widely traded commodities, currencies, and other assets; (3) enforcing contracts between counterparties. Each contract specifies the underlying asset (which ranges from bonds to currencies, butter to orange juice, ethanol to oil, and gold to uranium), its amount and quality grade, and the type (cash or physical) and date of settlement or contract expiration. CME, for example, offers a futures contract on copper in which physical settlement of 25,000 pounds of copper is due on any of the last three business days of the delivery month.www.cmegroup.com/trading/metals/base/copper_contract_specifications.html In many contracts, especially for financial assets, physical delivery is not desired or demanded. Instead, a cash settlement representing the difference between the contract price and the spot market price on the expiration date is made.
To lock in the price that it will have to pay for an asset in the future, a business should purchase a futures contract, thereby committing another party to supply it at the contract price. To lock in the price it will receive for an asset in the future, a business should sell a futures contract, thereby committing a buyer to purchase it at the contract price.
Here is a concrete example of how a futures contract can be used to hedge against price movements in an underlying asset: If you wanted to hedge the sale of 1 million barrels of crude oil you could sell a 3-month futures contract for \$100 per barrel. If the market price of crude was \$90 per barrel at the expiration date, you would get \$10 per barrel from the buyer of the contract plus the market price (\$90), or \$100 per barrel. If the market price of crude was \$110 at the end of the contract, by contrast, you would have to pay \$10 per barrel to the buyer of the contract. Again, you would net \$100 per barrel, \$110 in the market minus the \$10 paid to the contract counterparty.
To ensure that you would not renege in the latter case by not paying \$10 per barrel to the counterparty, futures exchanges require margin accounts and other safeguards. As the contract and market prices diverge, the incentive to default increases and exchanges know it. So they require investors to post bonds or to increase the deposits in their margin accounts or they will pay the money in the margin account to the counterparty and close the contract.
Stop and Think Box
Could a futures contract price ever be lower than the current market price? If not, why not? If so, how?
Futures contract prices will be lower than current market prices if market participants anticipate lower future prices due to deflation, changes in relative prices, or changes in supply or demand conditions. Cold weather in Florida, for example, can make orange juice futures soar on the expectation of a damaged crop (decreased supply) but unexpectedly mild weather in climatically marginal groves can have the opposite effect. Similarly, the expected completion of a new refinery might make gasoline futures decline.
KEY TAKEAWAYS
• Buyers and sellers can hedge or lock in the price they will pay/receive for assets in the future by contracting for the price today.
• Such contracts, called forwards, are costly to consummate, illiquid, and subject to high levels of default risk.
• Standardized forward contracts, called futures, were developed by exchanges to reduce the problems associated with forwards and have proliferated widely across asset classes. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/12%3A_Financial_Derivatives/12.01%3A_Derivatives_and_Their_Functions.txt |
Learning Objectives
• What are options and how can they be used to hedge and speculate?
• What are swaps and how are they used to hedge and speculate?
Options are aptly named financial derivatives that give their holders the option (which is to say the right, but not the obligation) to purchase (call) or sell (put) an underlying asset at a predetermined strike price, on (if a so-called European option) or before (if a so-called American option) a predetermined expiration date. Options are most often written on stocks (equities) but can be linked to other types of assets as well. To induce investors to issue an option and thereby obligate themselves to make a disadvantageous trade, option holders must pay a premium to the option issuer based on the option type, strike price, expiration date, interest rates, and volatility of the underlying asset. (The most famous option valuation model is called Black-Scholes.en.Wikipedia.org/wiki/Black–Scholes It is rather complicated, but various online calculators will painlessly compute the option premium for users who input the values of the key variables.www.money-zine.com/Calculators/Investment-Calculators/Black-Scholes-Calculator)
Options can be used to hedge or speculate in various ways. An investor might buy a call option on a stock in the hopes that the stock price will rise above the strike price, allowing her to buy the stock at the strike price (e.g., \$90) and immediately resell it at the higher market price (e.g., \$100). Or an investor might buy a put option to minimize his losses. If the stock fell from \$100 to \$50 per share, for example, a put option at \$75 would be profitable or “in the money” because the investor could buy the stock in the market at \$50 and then exercise his option to sell the stock to the option issuer at \$75 for a gross profit of \$25 per share.
Buying and selling calls and puts can be combined to create a variety of investment strategies with colorful names like bear put spreads and bull collars. Do yourself a favor and study the subject more thoroughly before dabbling in options, especially before selling them. The purchaser of an option can never lose more than the premium paid because the worst case scenario is that the option remains “out of the money.” For example, if the market price of a share on which you hold a European call option is below the option’s strike price on the expiration date the option would expire valueless. (If the market price was \$15 you would not want to exercise your right to buy at \$20.) Similarly, if the market price (e.g., \$25 to \$30 range) of an American put option remains above the strike price (e.g., \$15) for the entire term of the contract, the option would be out of the money. (Why exercise your right to sell something for \$15 that you could sell for \$25 plus?!) The seller of an option, by contrast, can lose a large sum if an option goes a long way into the money. For example, the seller of a call option with a strike price of \$50 would lose \$950 per share if the price of the underlying share soared to \$1,000. (The holder of the option would exercise its right to call or buy the shares from the option issuer at \$50.) Such large movements are rare, of course, but it would only take one instance to ruin most individual option issuers.
Stop and Think Box
All else equal, what should cost more to purchase, an American or a European option? Why?
American options are more valuable than European options, ceteris paribus, because the American option is more likely to be valuable or “in the money” as it can be exercised on numerous days, not just one.
Swaps are very different from options (though they can be combined to form a derivative called a swaption, or an option to enter into a swap). As the name implies, swaps are exchanges of one asset for another on a predetermined, typically repeated basis. A savings bank, for example, might agree to give \$50,000 per year to a finance company in exchange for the finance company’s promise to pay the savings bank \$1 million times a variable interest rate such as LIBOR. Such an agreement, called an interest rate swap, would buffer the bank against rising interest rates while protecting the finance company from lower ones, as in the following table:
Table 12.3 Payments Under an Interest Rate Swap
Year Savings bank owes (\$) LIBOR (%) Finance company owes (\$) Net payment to/from bank (\$) Net payment to/from finance company (\$)
1 50,000 5.00 50,000 0 0
2 50,000 6.00 60,000 10,000 −10,000
3 50,000 4.00 40,000 −10,000 10,000
4 50,000 1.25 12,500 −37,500 37,500
A credit default swap (CDS) is a type of swap used to create an unregulated form of insurance against a default by a bond issuer such as a country or corporation. In a CDS, the holder of bonds promises to make a relatively small payment (similar to an insurance premium) to a counterparty in exchange for a large payment if the bond issuer does not pay principal or interest on its bonds as promised. CDSs exacerbated the financial crisis of 2008 because many counterparties failed to make good on their promise to indemnify bondholders in case of default. CDSs are still largely unregulated and present systemic risks that most other derivatives do not.
KEY TAKEAWAYS
• Options are financial derivatives that in exchange for a premium provide holders with the option (the right but not the obligation) to buy or sell a stock or other underlying asset at a predetermined price up to or on a predetermined date.
• Option holders/buyers can never lose more than the premium paid for the option, the value of which is a function of interest rates, the strike price, the expiration date, and the volatility of the underlying asset.
• Swaps are derivatives in which two parties agree to swap or exchange one asset for another at one or more future dates. Like options, they can be used to hedge or speculate.
• Credit Default Swaps are a special form of swap akin to an insurance policy on bonds. Despite their ability to increase systemic volatility, they remain largely unregulated.
12.04: Suggested Reading
Durbin, Michael. All About Derivatives. 2nd ed. New York: McGraw-Hill, 2010.
Kolb, Robert and James Overdahl. Financial Derivatives: Pricing and Risk Management. Hoboken, NJ: John Wiley and Sons, 2009. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/12%3A_Financial_Derivatives/12.03%3A_Options_and_Swaps.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Define financial crisis and differentiate between systemic and nonsystemic crises.
• Describe a generic asset bubble.
• Define leverage and explain its role in asset bubble formation.
• Explain why bubbles burst, causing financial panics.
• Define and explain the importance of lender of last resort.
• Define and explain the importance of bailouts.
• Narrate the causes and consequences of the financial crisis that began in 2007.
Thumbnail: Image by Mediamodifier from Pixabay
13: Financial Crises- Causes and Consequences
Learning Objectives
• What is a financial crisis?
• How do financial shocks and crises affect the real economy?
A financial crisis occurs when one or more financial markets or intermediaries cease functioning or function only erratically and inefficiently. A nonsystemic crisis involves only one or a few markets or sectors, like the Savings and Loan Crisis. A systemic crisis involves all, or almost all, of the financial system to some extent, as during the Great Depression and the crisis of 2008.
Financial crises are neither new nor unusual. Thousands of crises, including the infamous Tulip Mania and South Sea Company episodes, have rocked financial systems throughout the world in the past five hundred years. Two such crises, in 1764–1768 and 1773, helped lead to the American Revolution.Tim Arango, “The Housing-Bubble and the American Revolution,” New York Times (29 November 2008), WK5. www.nytimes.com/2008/11/30/weekinreview/30arango .html?_r=2&pagewanted=1&ref=weekinreview After its independence, the United States suffered systemic crises in 1792, 1818–1819, 1837–1839, 1857, 1873, 1884, 1893–1895, 1907, 1929–1933, and 2008. Nonsystemic crises have been even more numerous and include the credit crunch of 1966, stock market crashes in 1973–1974 (when the Dow dropped from a 1,039 close on January 12, 1973, to a 788 close on December 5, 1973, to a 578 close on December 6, 1974) and 1987, the failure of Long-Term Capital Management in 1998, the dot-com troubles of 2000, the dramatic events following the terrorist attacks in 2001, and the subprime mortgage debacle of 2007. Sometimes, nonsystemic crises burn out or are brought under control before they spread to other parts of the financial system. Other times, as in 1929 and 2007, nonsystemic crises spread like a wildfire until they threaten to burn the entire system.
Financial crises can be classified in other ways as well. Some affect banks but not other parts of the financial system. Others mostly involve government debt and/or currency, as in bouts of inflation or rapid depreciation in foreign exchange markets. All types can spread to the other types and even to other nations via balance sheet deterioration and increases in asymmetric information. Five shocks, alone or in combination, have a strong propensity to initiate financial crises.
Increases in uncertainty. When companies cannot plan for the future and when investors feel they cannot estimate future corporate earnings or interest, inflation, or default rates, they tend to play it safe. They hold cash instead of investing in a new factory or equipment. That, of course, reduces aggregate economic activity.
Increases in interest rates. Higher interest rates make business projects less profitable and hence less likely to be completed, a direct blow to gross domestic product (GDP). Also, higher interest rates tend to exacerbate adverse selection by discouraging better borrowers but having little or no effect on the borrowing decisions of riskier companies and individuals. As a result, lenders are saddled with higher default rates in high interest-rate environments. So, contrary to what one would think, high rates reduce their desire to lend. To the extent that businesses own government or other bonds, higher interest rates decrease their net worth, leading to balance sheet deterioration, of which we will soon learn more. Finally, higher interest rates hurt cash flow (receipts minus expenditures), rendering firms more likely to default.
Government fiscal problems. Governments that expend more than they take in via taxes and other revenues have to borrow. The more they borrow, the harder it is for them to service their loans, raising fears of a default, which decreases the market price of their bonds. This hurts the balance sheets of firms that invest in government bonds and may lead to an exchange rate crisis as investors sell assets denominated in the local currency in a flight to safety. Precipitous declines in the value of local currency cause enormous difficulties for firms that have borrowed in foreign currencies, such as dollars, sterling, euro, or yen, because they have to pay more units of local currency than expected for each unit of foreign currency. Many are unable to do so and they default, increasing uncertainty and asymmetric information.
Balance sheet deterioration. Whenever a firm’s balance sheet deteriorates, which is to say, whenever its net worth falls because the value of its assets decreases and/or the value of its liabilities increases, or because stock market participants value the firm less highly, the Cerberus of asymmetric information rears its trio of ugly, fang-infested faces. The company now has less at stake, so it might engage in riskier activities, exacerbating adverse selection. As its net worth declines, moral hazard increases because it grows more likely to default on existing obligations, in turn because it has less at stake. Finally, agency problems become more prevalent as employee bonuses shrink and stock options become valueless. As employees begin to shirk, steal, and look for other work on company time, productivity plummets, and further declines in profitability cannot be far behind. The same negative cycle can also be jump-started by an unanticipated deflation, a decrease in the aggregate price level, because that will make the firm’s liabilities (debts) more onerous in real terms (i.e., adjusted for lower prices).
Banking problems and panics. If anything hurts banks’ balance sheets (like higher than expected default rates on loans they have made), banks will reduce their lending to avoid going bankrupt and/or incurring the wrath of regulators. As we have seen, banks are the most important source of external finance in most countries, so their decision to curtail will negatively affect the economy by reducing the flow of funds between investors and entrepreneurs. If bank balance sheets are hurt badly enough, some may fail. That may trigger the failure of yet more banks for two reasons. First, banks often owe each other considerable sums. If a big bank that owes much too many smaller banks were to fail, it could endanger the solvency of the creditor banks. Second, the failure of a few banks may induce the holders of banks’ monetary liabilities (today mostly deposits, but in the past, as we’ve seen, also bank notes) to run on the bank, to pull their funds out en masse because they can’t tell if their bank is a good one or not. The tragic thing about this is that, because all banks engage in fractional reserve banking (which is to say that no bank keeps enough cash on hand to meet all of its monetary liabilities), runs often become self-fulfilling prophecies, destroying even solvent institutions in a matter of days or even hours. Banking panics and the dead banks they leave in their wake cause uncertainty, higher interest rates, and balance sheet deterioration, all of which, as we’ve seen, hurt aggregate economic activity.
A downward spiral often ensues. Interest rate increases, stock market declines, uncertainty, balance sheet deterioration, and fiscal imbalances all tend to increase asymmetric information. That, in turn, causes economic activity to decline, triggering more crises, including bank panics and/or foreign exchange crises, which increase asymmetric information yet further. Economic activity again declines, perhaps triggering more crises or an unanticipated decline in the price level. That is the point, traditionally, where recessions turn into depressions, unusually long and steep economic downturns.
Stop and Think Box
In early 1792, U.S. banks curtailed their lending. This caused a securities speculator and shyster by the name of William Duer to go bankrupt, owing large sums of money to hundreds of investors. The uncertainty caused by Duer’s sudden failure caused people to panic, inducing them to sell securities, even government bonds, for cash. By midsummer, though, the economy was again humming along nicely. In 1819, banks again curtailed lending, leading to a rash of mercantile failures. People again panicked, this time running on banks (but clutching their government bonds for dear life). Many banks failed and unemployment soared. Economic activity shrank, and it took years to recover. Why did the economy right itself quickly in 1792 but only slowly in 1819?
In 1792, America’s central bank (then the Secretary of the Treasury, Alexander Hamilton, working in conjunction with the Bank of the United States) acted as a lender of last resort. By adding liquidity to the economy, the central bank calmed fears, reduced uncertainty and asymmetric information, and kept interest rates from spiking and balance sheets from deteriorating further. In 1819, the central bank (with a new Treasury secretary and a new bank, the Second Bank of the United States) crawled under a rock, allowing the initial crisis to increase asymmetric information, reduce aggregate output, and ultimately cause an unexpected debt deflation. Since 1819, the United States has suffered from financial crises on numerous occasions. Sometimes they have ended quickly and quietly, as when Alan Greenspan stymied the stock market crash of 1987. Other times, like after the stock market crash of 1929, the economy did not fare well at all.www.amatecon.com/gd/gdcandc.html
Assuming their vital human capital and market infrastructure have not been destroyed by the depression, economies will eventually reverse themselves after many companies have gone bankrupt, the balance sheets of surviving firms improve, and uncertainty, asymmetric information, and interest rates decrease. It is better for everyone, however, if financial crises can be nipped in the bud before they turn ugly. This is one of the major functions of central banks like the European Central Bank (ECB) and the Fed. Generally, all that the central bank needs to do at the outset of a crisis is to restore confidence, reduce uncertainty, and keep interest rates in line by adding liquidity (cash) to the economy by acting as a lender of last resort, helping out banks and other financial intermediaries with loans and buying government bonds in the open market. Sometimes a bailout, a transfer of wealth from taxpayers to the financial system, becomes necessary. Figure 13.1 summarizes this discussion of the ill consequences of financial shocks.
But in case you didn’t get the memo, nothing is ever really free. (Well, except for free goods.)en.Wikipedia.org/wiki/Free_good When central banks stop financial panics, especially when they do so by bailing out failed companies, they risk creating moral hazard by teaching market participants that they will shield them from risks. That is why some economists, like Allan Meltzer, said “Let ’Em Fail,” in the op-ed pages of the Wall Street JournalJuly 21, 2007. online.wsj.com/article/SB118498744630073854.html when some hedge funds ran into trouble due to the unexpected deterioration of the subprime mortgage market in 2007. Hamilton’s Law (née Bagehot’s Law, which urges lenders of last resort to lend freely at a penalty rate on good security) is powerful precisely because it minimizes moral hazard by providing relief only to the more prudent and solvent firms while allowing the riskiest ones to go under.
Stop and Think Box
“While we ridicule ancient superstition we have an implicit faith in the bubbles of banking, and yet it is difficult to discover a greater absurdity, in ascribing omnipotence to bulls, cats and onions, than for a man to carry about a thousand acres of land…in his pocket book.…This gross bubble is practiced every day, even upon the infidelity of avarice itself.…So we see wise and honest Americans, of the nineteenth century, embracing phantoms for realities, and running mad in schemes of refinement, tastes, pleasures, wealth and power, by the soul [sic] aid of this hocus pocus.”—Cause of, and Cure for, Hard Times.books.google.com/books When were these words penned? How do you know?
This was undoubtedly penned during one of the nineteenth century U.S. financial crises mentioned above. Note the negative tone, the allusion to Americans, and the reference to the nineteenth century. In fact, the pamphlet appeared in 1818. For a kick, compare/contrast it to blogs bemoaning the crisis that began in 2007:
http://cartledged.blogspot.com/2007/09/greedy-bastards-club.html
http://www.washingtonmonthly.com/archives/individual/2008_03/013339.php
http://thedefenestrators.blogspot.com/2008/10/death-to-bankers.html
Both systemic and nonsystemic crises damage the real economy by preventing the normal flow of credit from savers to entrepreneurs and other businesses and by making it more difficult or expensive to spread risks. Given the damage financial crises can cause, scholars and policymakers are keenly interested in their causes and consequences. You should be, too.
KEY TAKEAWAYS
• Throughout history, systemic (widespread) and nonsystemic (confined to a few industries) financial crises have damaged the real economy by disrupting the normal flow of credit and insurance.
• Understanding the causes and consequences of financial crises is therefore important.
• Financial shocks and crises affect the real economy by increasing asymmetric information.
• Increased asymmetric information, in turn, reduces the amount of funds channeled from investors to entrepreneurs.
• Starved of external finance, businesses cut back production, decreasing aggregate economic activity.
• The conduits include rapidly rising interest rates, foreign exchange crises, and bank panics. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.01%3A_Financial_Crisis_Taxonomies.txt |
Learning Objectives
• What are asset bubbles and what role does leverage play in their creation?
Asset bubbles are increases in the value of some assets, like bonds, commodities (cotton, gold, oil, tulips), equities, or real estate, above their rational or fundamental level. Some combination of low interest rates, new technology, unprecedented increases in demand for the asset, and leverage typically create bubbles.
Low interest rates can cause bubbles by lowering the total cost of asset ownership. Recall that interest rates and bond prices are inversely related. Algebraically, the i term is in the denominator of the PV formula—PV = FV/(1 + i)n—so as it gets smaller, PV must get larger (holding FV constant, of course).
Stop and Think Box
In colonial New York in the 1740s and 1750s, interest rates on mortgages were generally 8 percent. In the late 1750s and early 1760s, they fell to about 4 percent, and expected revenues from land ownership increased by about 50 percent. What happened to real estate prices? Why?
They rose significantly because it was cheaper to borrow money, thus lowering the total cost of real estate ownership, and because the land was expected to create higher revenues. Thinking of the land as a perpetuity and FV as the expected revenues arising from it:
P V = F V / i
P V = £ 100 / .08 = £ 1,250
P V = £ 100 / .04 = £ 2,500
And that is just the real estate effect. Increasing FV by £50 leads to the following:
P V = £ 150 / .04 = £ 3,750 , or a tripling of prices .
In 1762, Benjamin Franklin reported that the “Rent of old Houses, and Value of Lands,…are trebled in the last Six Years.”For more on the crisis, see Tim Arango, “The Housing-Bubble Revolution,” New York Times (30 November 2008), WK 5. www.nytimes.com/2008/11/30 /weekinreview/30arango.html?_r=2&pagewanted=1&ref=weekinreview Unfortunately for the colonists, increases in FV proved transient, and interest rates soon soared past 8 percent.
The effect of new technology can be thought of as increasing FV, leading, of course, to a higher PV. Or, in the case of equities, low interest rates decrease k (required return) and new inventions increase g (constant growth rate) in the Gordon growth model—P = E × (1 + g)/(k – g)—both of which lead to a higher price. During bubbles, investors overestimate the likely effects of new technology and place unreasonably high estimates on FV and g.
Large increases in the demand for an asset occur for a variety of reasons. Demand can be increased merely by investors’ expectations of higher prices in the future, as in the one period valuation model—P = E/(1 + k) + P1/(1 + k). If many investors believe that P1 must be greater than P a year (or any other period) hence, demand for the asset will increase and the expectation of a higher P1 will be vindicated. That sometimes leads investors to believe that P2 will be higher than P1, leading to a self-fulfilling cycle that repeats through P3 to Px. At some point, the value of the asset becomes detached from fundamental reality, driven solely by expectations of yet higher future prices. In fact, some scholars verify the existence of an asset bubble when news about the price of an asset affects the economy, rather than the economy affecting the price of the asset.
To increase their returns, investors often employ leverage, or borrowing. Compare three investors, one who buys asset X entirely with his own money, one who borrows half of the price of asset X, and one who borrows 90 percent of the price of asset X. Their returns (not including the cost of borrowing, which as noted above is usually low during bubbles) will be equal to those calculated in Figure 13.2.
The figures were calculated using the rate of return formula: R = (C + Pt1 – Pt0)/Pt0. Here, coupons are zero and hence drop out so that R = (Pt1 – Pt0)/Pt0.
In this example, returns for the unleveraged investor are great:
110 - 100 / 100 = .1 (rendered as 10% in the figure)
120 - 100 / 100 = .2
130-100/100=.3
But the returns are not as high as the investor who borrowed half the cash, in essence paying only \$50 of his own money for the \$100 asset at the outset:
110 - 50 / 100 = .6
120 - 50 / 100 = .7
130 - 50 / 100 = .8
But even he looks like a chump compared to the investor who borrowed most of the money to finance the original purchase, putting up only \$10 of his own money:
110 - 10 / 100 = 1
120 - 10 = 1.1
130 - 10 = 1.2
If you are thinking the most highly leveraged investor is the smart one, recall that a trade-off between risk and return exists before continuing.
KEY TAKEAWAYS
• Asset bubbles occur when the prices of some asset, like stocks or real estate, increase rapidly due to some combination of low interest rates, high leverage, new technology, and large, often self-fulfilling shifts in demand.
• The expectation of higher prices in the future, combined with high levels of borrowing, allow asset prices to detach from their underlying economic fundamentals. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.02%3A_Asset_Bubbles.txt |
Learning Objectives
• What are financial panics and what causes them?
A financial panic occurs when leveraged financial intermediaries and other investors must sell assets quickly in order to meet lenders’ calls. Lenders call loans, or ask for repayment, when interest rates increase and/or when the value of collateral pledged to repay the loan sinks below the amount the borrower owes. Calls are a normal part of everyday business, but during a panic, they all come en masse due to some shock, often the bursting of an asset bubble. Bubbles, like people, are bound to die but nobody knows in advance when they will do so. A burst is sometimes triggered by an obvious shock, like a natural catastrophe or the failure of an important company, but sometimes something as seemingly innocuous as a large sell order can touch them off.
During a panic, almost everybody must sell and few can or want to buy, so prices plummet, triggering additional calls, and yet more selling. Invariably, some investors, usually the most highly leveraged ones, cannot sell assets quickly enough, or for a high enough price, to “meet the call” and repay their loans. Banks and other lenders begin to suffer defaults. Their lenders (other banks, depositors, holders of commercial paper), in turn, begin to wonder if they are still credit-worthy. Asymmetric information and uncertainty reign supreme, inducing lenders to restrict credit. At some point, investors’ emotions take over, and they literally go into a panic, one that makes Tony Soprano’s panic attacks seem like a stroll in the park.www.menshealth.com/health/when-panic-attacks
Panics often cause the rapid de-leveragingof the financial system, a period when interest rates for riskier types of loans and securities increase and/or when a credit crunch, or a large decrease in the volume of lending, takes place. Such conditions often usher in a negative bubble, a period when high interest rates, tight credit, and expectations of lower asset prices in the future cause asset values to trend downward, sometimes well below the values indicated by underlying economic fundamentals. During de-leveraging, the forces that drove asset prices up now conspire to drag them lower.
Stop and Think Box
In New York in 1764, interest rates spiked from 6 to 12 percent and expected revenues from land plummeted by about 25 percent. What happened to real estate prices and why?
They dropped significantly because it was more expensive to borrow money, thus increasing the total cost of real estate ownership, and because the land was expected to yield lower revenues. Thinking of the land as a perpetuity and FV as the expected revenues arising from it:
P V = F V / i
P V = £ 100 / .06 = £ 1,666.66
P V = £ 100 / .12 = £ 833.33
And that is just the real estate effect. Decreasing FV by £25 leads to the following:
P V = £ 75 / .12 = £ 625 , or a decrease of about two-thirds .
“I know of sundry Estates [farms and other landed property] that has been taken by Execution [foreclosed upon],” a New York merchant reported late in 1766, “and sold for not more than one third of their value owing to the scarcity of money.”
As shown in Figure 13.3, the most highly leveraged investor suffers most of all.
Again, I used the rate of return formula, but coupons are zero so that R = (Pt1 – Pt0)/Pt0. As the price of the asset falls, the unleveraged investor suffers negative returns:
90 - 100 / 100 = - .1
80 - 100 / 100 = - .2
70 - 100 / 100 = - .3
The leveraged investors lose the same percentage and must now pay a high interest rate for their loans, or put up the equity themselves, at a time when the opportunity cost of doing so is substantial:
( 90 - 50 + 50 ) / 100 = - .1 + interest on \$ 50
(80 - 50 + 50)/100 = - .2 + interest on \$50
( 70 - 50 + 50 ) / 100 = - .3 + interest on \$ 50
The higher the leverage, the larger the sum that must be borrowed at high rates.
( 90 - 90 + 90 ) / 100 = - .1 + interest on \$ 90
( 80 - 90 + 90 ) / 100 = - .2 + interest on \$ 90
( 70 - 90 + 90 ) / 100 = - .3 + interest on \$ 90
Also, the higher the leverage, the smaller the price change needs to be to trigger a call. At 50 percent leverage, a \$100 asset could drop to \$50 before the lender must call. At 90 percent leverage, a \$100 asset need lose only \$10 to induce a call.
KEY TAKEAWAYS
• The bursting of an asset bubble, or the rapidly declining prices of an asset class, usually leads to a financial panic, reductions in the quantity of available credit, and the de-leveraging of the financial system.
• The most highly leveraged investors suffer most. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.03%3A_Financial_Panics.txt |
Learning Objectives
• What is a lender of last resort and what does it do?
As noted above, financial panics and the de-leveraging that often occur after them can wreak havoc on the real economy by decreasing the volume of loans, insurance contracts, and other beneficial financial products. That, in turn, can cause firms to reduce output and employment. Lenders of last resort try to stop panics and de-leveraging by adding liquidity to the financial system and/or attempting to restore investor confidence. They add liquidity by increasing the money supply, reducing interest rates, and making loans to worthy borrowers who find themselves shut off from their normal sources of external finance. They try to restore investor confidence by making upbeat statements about the overall health of the economy and/or financial system and by implementing policies that investors are likely to find beneficial. After a stock market crash in 1987, for example, the Federal Reserve stopped a panic merely by promising to loan liberally to temporarily strapped banks.
Stop and Think Box
In a single day, October 19, 1987, the S&P fell by 20 percent. What caused such a rapid decline? Why did the panic not result in de-leveraging or recession?
According to a short history of the event by Mark Carlson (“A Brief History of the 1987 Stock Market Crash with a Discussion of the Federal Reserve Response”),www.federalreserve.gov/Pubs/feds/2007/200713/200713pap.pdf “During the years prior to the crash, equity markets had been posting strong gains.…There had been an influx of new investors.…Equities were also boosted by some favorable tax treatments given to the financing of corporate buyouts.…The macroeconomic outlook during the months leading up to the crash had become somewhat less certain.…Interest rates were rising globally.…A growing U.S. trade deficit and decline in the value of the dollar were leading to concerns about inflation and the need for higher interest rates in the United States as well.” On the day of the crash, investors learned that deficits were higher than expected and that the favorable tax rules might change. As prices dropped, “record margin calls” were made, fueling further selling. The panic did not proceed further because Federal Reserve Chairman Alan Greenspan restored confidence in the stock market by promising to make large loans to banks exposed to brokers hurt by the steep decline in stock prices. Specifically, the Fed made it known that “The Federal Reserve, consistent with its responsibilities as the Nation’s central bank, affirmed today its readiness to serve as a source of liquidity to support the economic and financial system.”
Lenders of last resort partially emulate three rules first promulgated by U.S. Treasury Secretary Alexander Hamilton (1789–1795) but popularized by Economist editor Walter Bagehot in his 1873 book Lombard Street. As Bagehot put it, during a banking panic an LLR should make loans:
at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who do not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible. Secondly. That at this rate these advances should be made on all good banking securities, and as largely as the public ask for them. The reason is plain. The object is to stay alarm, and nothing therefore should be done to cause alarm. But the way to cause alarm is to refuse some one who has good security to offer…No advances indeed need be made by which the Bank will ultimately lose. The amount of bad business in commercial countries is an infinitesimally small fraction of the whole business…The great majority, the majority to be protected, are the ‘sound’ people, the people who have good security to offer. If it is known that the Bank of England [the LLR in Bagehot’s time and country] is freely advancing on what in ordinary times is reckoned a good security—on what is then commonly pledged and easily convertible—the alarm of the solvent merchants and bankers will be stayed. But if securities, really good and usually convertible, are refused by the Bank, the alarm will not abate, the other loans made will fail in obtaining their end, and the panic will become worse and worse.
This is usually translated as LLRs lending freely on good security at a penalty rate. Today, central banks acting as LLR usually lend freely on good collateral but only to banks, not the public. Moreover, they typically reduce interest rates in order to stimulate the economy. The unfortunate result of the latter change is to increase moral hazard, or risk taking on the part of banks that “bank on” cheap loans from the LLR should they run into difficulties.
The most common form of lender of last resort today is the government central bank, like the European Central Bank (ECB) or the Federal Reserve. The International Monetary Fund (IMF) sometimes tries to act as a sort of international lender of last resort, but it has been largely unsuccessful in that role. In the past, wealthy individuals like J. P. Morgan and private entities like bank clearinghouses tried to act as lenders of last resort, with mixed success. Most individuals did not have enough wealth or influence to thwart a panic, and bank clearinghouses were at most regional in nature.
KEY TAKEAWAY
• A lender of last resort is an individual, a private institution, or, more commonly, a government central bank that attempts to stop a financial panic and/or postpanic de-leveraging by increasing the money supply, decreasing interest rates, making loans, and/or restoring investor confidence. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.04%3A_Lender_of_Last_Resort_%28LLR%29.txt |
Learning Objectives
• What is a bailout and how does it differ from the actions of a lender of last resort?
• What is a resolution, and how does it differ from a bailout?
As noted above, lenders of last resort provide liquidity, loans, and confidence. They make loans to solvent institutions facing temporary solvency problems due to the crisis, not inevitable bankruptcy.Doug Arner, Financial Stability, Economic Growth, and the Role of Law (New York: Cambridge University Press, 2007), 139–140. Bailouts, by contrast, restore the losses suffered by one or more economic agents, usually with taxpayer money. The restoration can come in the form of outright grants or the purchase of equity but often takes the form of subsidized or government-guaranteed loans. Unsurprisingly, bailouts are often politically controversial because they can appear to be unfair and because they increase moral hazard, or risk-taking on the part of entities that expect to be bailed out if they encounter difficulties. Nevertheless, if the lender of last resort cannot stop the formation of a negative bubble or massive de-leveraging, bailouts can be an effective way of mitigating further declines in economic activity.
During the Great Depression, for example, the federal government used \$500 million of taxpayer money to capitalize the Reconstruction Finance Corporation (RFC). In its initial phase, the RFC made some \$2 billion in low-interest loans to troubled banks, railroads, and other businesses. Though at first deprecated as welfare for the rich, the RFC, most observers now concede, helped the economy to recover by keeping important companies afloat. Also during the depression, the Home Owners Loan Corporation (HOLC), seeded with \$200 million of taxpayer dollars, bailed out homeowners, many of whom had negative equity in their homes, by refinancing mortgages on terms favorable to the borrowers.
In a resolution, by contrast, a government agency, like the Federal Deposit Insurance Corporation (FDIC), disposes of a failed bank’s assets (one at a time or in bulk to an acquiring institution) and uses the proceeds to repay the bank’s creditors and owners according to their seniority, a predetermined order depending on their class (depositor, bondholder, stockholder). The line between resolutions and bailouts sometimes blurs. In the aftermath of the Savings and Loan Crisis, for example, the Resolution Trust Corporation (RTC) closed 747 thrifts with total assets of almost \$400 billion. The RTC cost taxpayers only \$125 billion while staving off a more severe systemic crisis.
Stop and Think Box
The 1979 bailout of automaker Chrysler, which entailed a government guarantee of its debt, saved the troubled corporation from bankruptcy. It quickly paid off its debt, and the U.S. Treasury, and hence taxpayers, were actually the richer for it. Was this bailout successful?
At the time, many observers thought so. Chrysler creditors, who received 30 cents for every dollar the troubled automaker owed them, did not think so, however, arguing that they had been fleeced to protect Chrysler stockholders. Workers who lost their jobs or were forced to accept reductions in pay and benefits were also skeptical. Now that Chrysler and the other U.S. carmakers are again in serious financial trouble, some scholars are suggesting that the bailout was a disaster in the long term because it fooled Detroit execs into thinking they could continue business as usual. In retrospect, it may have been better to allow Chrysler to fail and a new, leaner, meaner company to emerge like a Phoenix from its ashes.
KEY TAKEAWAYS
• Bailouts usually occur after the actions of a lender of last resort, such as a central bank, have proven inadequate to stop negative effects on the real economy.
• Unlike resolutions, where assets are sold off to compensate creditors and owners according to their seniority, bailouts usually entail restoring losses to one or more economic agents using taxpayer funds.
• Although politically controversial, bailouts can stop negative bubbles from leading to excessive de-leveraging, debt deflation, and economic depression. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.05%3A_Bailouts_and_Resolutions.txt |
Learning Objectives
• What factors led to the present financial crisis?
The most recent financial crisis began in 2007 as a nonsystemic crisis linked to subprime mortgages, or risky loans to homeowners. In 2008, the failure of several major financial services companies turned it into the most severe systemic crisis in the United States since the Great Depression.
The troubles began with a major housing asset bubble. As shown in Figure 13.4, between January 2000 and 2006, a major index of housing prices in the United States more than doubled. (Prices went up more in some areas than in others because real estate is a local asset.) Home prices rose rapidly for several reasons. As shown in Figure 13.5, mortgage rates were quite low, to a large extent because the Federal Reserve kept the federal funds rate, the rate at which banks lend to each other overnight, very low.
Mortgages also became much easier to obtain. Traditionally, mortgage lenders held mortgage loans on their own balance sheets. If a homeowner defaulted, the lender, usually a bank or life insurance company, suffered the loss. They were therefore understandably cautious about whom they lent to and on what terms. To shield themselves from loss, lenders insisted that borrowers contribute a substantial percentage of the home’s value as a down payment. The down payment ensured that the borrower had some equity at stake, some reason to work hard and not to default. It also provided lenders with a buffer if housing prices declined. Traditionally, lenders also verified that borrowers were employed or had other means of income from investments or other sources.
All that changed with the widespread advent of securitization, the practice of bundling and selling mortgages to institutional investors. Banks also began to “financial engineer” those bundles, called mortgage-backed securities (MBSs), into more complex derivative instruments like collateralized mortgage obligations (CMOs). MBSs afforded investors the portfolio diversification benefits of holding a large number of mortgages; CMOs allowed investors to pick the risk-return profile they desired. They did so by slicing a group of MBSs into derivative securities (aka tranches) with credit ratings ranging from AAA, which would be the last to suffer losses, to BBB, which would suffer from the first defaults. The AAA tranches, of course, enjoyed a higher price (lower yield) than the lower-rated tranches. The holders of the lowest-rated tranches, those who took on the most risks, suffered most during the subprime maelstrom.
Securitization allowed mortgage lenders to specialize in making loans, turning them more into originators than lenders. Origination was much easier than lending because it required little or no capital. Unsurprisingly, a large number of new mortgage originators, most mere brokers, appeared on the scene. Paid a commission at closing, originators had little incentive to screen good borrowers from bad and much more incentive to sign up anyone with a pulse. A race to the bottom occurred as originators competed for business by reducing screening and other credit standards. At the height of the bubble, loans to no income, no job or assets (NINJA) borrowers were common. So-called liars’ loans for hundreds of thousands of dollars were made to borrowers without documenting their income or assets. Instead of insisting on a substantial down payment, many originators cajoled homeowners into borrowing 125 percent of the value of the home because it increased their commissions. They also aggressively pushed adjustable rate mortgages (ARMs) that offered low initial teaser rates and later were reset at much higher levels.
Regulators allowed, and even condoned, such practices in the name of affordable housing, even though six earlier U.S. mortgage securitization schemes had ended badly.Kenneth Snowden, “Mortgage Securitization in the United States: Twentieth Century Developments in Historical Perspective,” in Michael Bordo and Richard Sylla, eds., Anglo-American Financial Systems: Institutions and Markets in the Twentieth Century (Burr Ridge, IL: Irwin Professional Publishing, 1995), 261–298. Regulators also allowed Fannie Mae and Freddie Mac, two giant stockholder-owned mortgage securitization companies whose debt was effectively guaranteed by the federal government, to take on excessive risks and leverage themselves to the hilt. They also allowed credit-rating agencies to give investment-grade ratings to complicated mortgage-backed securities of dubious quality.
Observers, including Yale’s Robert Shillerwww.econ.yale.edu/~shiller and Stern’s Nouriel Roubini,pages.stern.nyu.edu/~nroubini warned about the impending crisis, but few listened. As long as housing prices kept rising, shoddy underwriting, weak regulatory oversight, and overrated securities were not problems because borrowers who got into trouble could easily refinance or sell the house for a profit. Indeed, many people began to purchase houses with the intention of “flipping” them a month later for a quick buck.
In June 2006, however, housing prices peaked, and by the end of that year it was clear that the bubble had gone bye-bye. By summer 2007, prices were falling quickly. Defaults mounted as the sale/refinance option disappeared, and borrowers wondered why they should continue paying a \$300,000 mortgage on a house worth only \$250,000, especially at a time when a nasty increase in fuel costs and a minor bout of inflation strained personal budgets. Highly leveraged subprime mortgage lenders, like Countrywide and Indymac, suffered large enough losses to erode their narrow base of equity capital, necessitating their bankruptcy or sale to stronger entities. By early 2008, investment bank Bear Stearns, which was deeply involved in subprime securitization products, teetered on the edge of bankruptcy before being purchased by J. P. Morgan for a mere \$10 per share.
As the crisis worsened, becoming more systemic in nature as asymmetric information intensified, the Federal Reserve responded as a lender of last resort by cutting its federal funds target from about 5 to less than 2 percent between August 2007 and August 2008. It also made massive loans directly to distressed financial institutions. Mortgage rates decreased from a high of 6.7 percent in July 2007 to 5.76 percent in January 2008, but later rebounded to almost 6.5 percent in August 2008. Moreover, housing prices continued to slide, from an index score of 216 in July 2007 to just 178 a year later. Defaults on subprime mortgages continued to climb, endangering the solvency of other highly leveraged financial institutions, including Fannie Mae and Freddie Mac, which the government had to nationalize (take over and run). The government also arranged for the purchase of Merrill Lynch by Bank of America for \$50 billion in stock. But it decided, probably due to criticism that its actions were creating moral hazard, to allow Lehman Brothers to go bankrupt. That policy quickly backfired, however, because Lehman dragged one of its major counterparties, AIG, down with it. Once bitten, twice shy, the government stepped in with a massive bailout for AIG to keep it from bankrupting yet other large institutions as it toppled.
The damage, however, had been done and panic overtook both the credit and stock markets in September and October 2008. With each passing day, asymmetric information grew more intense. With Treasury bonds the only clear safe haven, investors fled other markets thereby causing significant disruptions and failures. The entire asset-backed commercial paper market shut down, money market withdrawals soared after one of the largest of those staid institutions reported losses (“broke the buck,” a very rare event indeed), and mortgage and bond insurers dropped like flies hit with a can of Raid. Figure 13.7 and Figure 13.8 graphically portray the resulting carnage in the stock and bond markets.
Stop and Think Box
What is happening in Figure 13.8?
Investors sold corporate bonds, especially the riskier Baa ones, forcing their prices down and yields up. In a classic flight to quality, they bought Treasuries, especially short-dated ones, the yields of which dropped from 1.69 percent on September 1 to .03 percent on the September 17.
With an economic recession and major elections looming, politicians worked feverishly to develop a bailout plan. The Bush administration’s plan, which offered some \$700 billion to large financial institutions, initially met defeat in the House of Representatives. After various amendments, including the addition of a large sum of pork barrel sweeteners, the bill passed the Senate and the House. The plan empowered the Treasury to purchase distressed assets and to inject capital directly into banks. Combined with the \$300 billion Hope for Homeowners plan, a bailout for some distressed subprime borrowers, and the direct bailout of AIG, the government’s bailout effort became the largest, in percentage of GDP terms, since the Great Depression. The Treasury later decided that buying so-called toxic assets, assets of uncertain and possibly no value, was not economically or politically prudent. Instead, it purchased preferred shares in most major banks, even those that did not desire any assistance. That raised fear of government ownership of banks, which has a dubious history because many governments have found the temptation to direct loans to political favorites, instead of the best borrowers, irresistible.“Leaving Las Vegas: No Dire Mistakes so Far, but Governments Will Find Exiting Banks Far Harder Than Entering Them,” The Economist (22 November 2008), 22.
Economists and policymakers are now busy trying to prevent a repeat performance, or at least mitigate the scale of the next bubble. One approach is to educate people about bubbles in the hope that they will be more cautious investors. Another is to encourage bank regulators to use their powers to keep leverage to a minimum. A third approach is to use monetary policy—higher interest rates or tighter money supply growth—to deflate bubbles before they grow large enough to endanger the entire financial system. Each approach has its strengths and weaknesses. Education might make investors afraid to take on any risk. Tighter regulation and monetary policy might squelch legitimate, wealth-creating industries and sectors. A combination of better education, more watchful regulators, and less accommodative monetary policy may serve us best.
Dodd-Frank, a regulatory reform passed in July 2010 in direct response to the crisis, may be a step in that direction, but critics note that the legislation is complex, unwieldy, and “does not incorporate a clear or consistent approach to the problem of regulating the financial sector.”Viral Acharya, Thomas Cooley, Matthew Richardson, and Ingo Walter, Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance (Hoboken: John Wiley and Sons, 2011), 45. Like other regulations passed in the wake of panics, it may stop an exact repeat of the 2008 crisis but probably will not prevent a different set of institutions, instruments, derivatives, and bubbles from causing another crisis in the future. Instead of creating new approaches to regulation, like a proposed tax on banks that pose systemic risks, the Dodd-Frank Act establishes new tools like resolution plans as well as new agencies like the Financial Stability Oversight Council, which is charged with monitoring and reducing systemic risk. The act also simultaneously increases and decreases the powers of others, including the Federal Reserve, which must now enforce stiffer capital, liquidity, leverage, and risk management requirements.
KEY TAKEAWAYS
• Low interest rates, indifferent regulators, unrealistic credit ratings for complex mortgage derivatives, and poor incentives for mortgage originators led to a housing bubble that burst in 2006.
• As housing prices fell, homeowners with dubious credit and negative equity began to default in unexpectedly high numbers.
• Highly leveraged financial institutions could not absorb the losses and had to shut down or be absorbed by stronger institutions.
• Despite the Fed’s efforts as lender of last resort, the nonsystemic crisis became systemic in September 2008 following the failure of Lehman Brothers and AIG.
• The government responded with huge bailouts of subprime mortgage holders and major financial institutions.
13.07: Suggested Reading
Acharya, Viral, Thomas Cooley, Matthew Richardson, and Ingo Walter. Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance. Hoboken, NJ: John Wiley and Sons, 2011.
Ben-Shahard, Danny, Charles Ka Yui Leung, and Seow Eng Ong. Mortgage Markets Worldwide. Hoboken, NJ: John Wiley and Sons, 2007.
Kindleberger, Charles, and Robert Aliber. Manias, Panics, and Crashes: A History of Financial Crises, 5th ed. Hoboken, NJ: John Wiley and Sons, 2005.
Mishkin, Frederic. “How Should We Respond to Asset Price Bubbles?” in Banque de France, Financial Stability Review. October 2008, 65–74.
Reinhart, Carmen, and Kenneth Rogoff. This Time Is Different: Eight Centuries of Financial Folly. Princeton: Princeton University Press, 2009.
Roubini, Nouriel, and Brad Stetser. Bailouts or Bail-ins: Responding to Financial Crises in Emerging Markets. New York: Peterson Institute, 2004.
Shiller, Robert. Irrational Exuberance. New York: Doubleday, 2006.
The Subprime Solution: How Today’s Global Financial Crisis Happened, and What to Do About It. Princeton, NJ: Princeton University Press, 2008.
Sprague, Irvine. Bailout: An Insider’s Account of Bank Failures and Rescues. New York: Beard Books, 2000.
Wright, Robert E., ed. Bailouts: Public Money, Private Profit. New York: Columbia University Press, 2010. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/13%3A_Financial_Crises-_Causes_and_Consequences/13.06%3A_The_Crisis_of_2007-2009.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Define central bank and explain the importance of central banking.
• Briefly sketch the history of U.S. central banking.
• Explain when and how a country can do without a central bank.
• Briefly sketch the structure of the Federal Reserve System.
• Explain how other central banks compare to the Fed.
• Define central bank independence and explain its importance.
• Explain why independent central bankers prefer lower inflation rates than government officials do.
Thumbnail: Image by U.S. Government via Wikimedia Commons (Public Domain)
14: Central Bank Form and Function
Learning Objectives
• What is a central bank?
• Why is central banking important?
• How can a country manage without a central bank?
• What is the history of central banking in the United States?
A central bank is a bank under some degree of government control that is generally charged with
• controlling the money supply (to a greater or lesser degree);
• providing price stability (influencing the price level);
• attaining economic output and employment goals;
• regulating commercial banks (and perhaps other depository and nondepository financial institutions);
• stabilizing the macroeconomy (proactively and/or by acting as a lender of last resort during financial crises);
• providing a payments system (check clearing and long-distance payments).
Central banks also often act as the national government’s banker by holding its deposits and making payments on its behalf. During its 200-plus-year existence, the United States has had three different central banks and two periods, one short and one extremely long, with no central bank.
Chartered by the federal government in 1791, the Bank of the United States (BUS) worked in conjunction with the U.S. Treasury secretary to act as a lender of last resort and a regulator of commercial banks. Specifically, it helped Alexander Hamilton, America’s first Secretary of the Treasury,www.treasury.gov/about/history/Pages/ahamilton.aspx to stymie the Panic of 1792. It also returned the notes of commercial banks for redemption into gold and silver (the era’s base money), thereby regulating commercial banks’ reserve ratios and hence the money supply. Owned by private shareholders, the BUS was quite independent, a good trait for a central bank to have, as we’ll see. Its very independence and power to regulate commercial banks, however, made it unpopular in some influential political circles. Its charter was not renewed when it expired in 1811. The government’s difficulties financing the War of 1812 (aka the Second War for Independence) convinced many that the country needed a new central bank. As a result, the government chartered the Bank of the United States (informally called the Second Bank or SBUS) in 1816. Insufficiently independent of the government at first, the SBUS, which like the BUS was headquartered in Philadelphia but had more numerous branches, stumbled by allowing commercial banks to increase their lending too much. It also suffered from internal agency problems, particularly at its branch in Baltimore. When a financial panic struck in late 1818 and early 1819, it failed to prevent a recession and debt deflation. Private stockholders reasserted control over the bank, placing it under the able direction of Nicholas Biddle, who successfully prevented the British economic meltdown of 1825 from spreading to America. Under Biddle, the SBUS also became an effective regulator of the nation’s commercial banks, which by the 1820s numbered in the hundreds. Like the BUS before it, the SBUS paid for its diligence with its life. Aided by many commercial bankers, particularly those in Philadelphia’s financial rival Manhattan, and America’s traditional distaste for powerful institutions, Andrew Jackson vetoed the act rechartering it. (The SBUS continued its corporate life under a Pennsylvania charter, but it no longer had nationwide branches and was no longer the nation’s central bank. It went bankrupt a few years later.)
From 1837 until late 1914, the United States had no central bank. Private institutions cropped up to clear checks and transfer funds over long distances. The Treasury kept its funds in commercial banks and in the hands of its tax collectors and left bank regulation to the market (deposit and note holders and stockholders) and state governments. The monetary base (gold and silver) it left largely to the whims of international trade. It could do so because the United States and most of the world’s other major economies were on a gold and/or silver standard, meaning that their respective units of account were fixed in terms of so many grains of the precious stuff and hence fixed against each other. This does not mean that the exchange rate didn’t change, merely that it stayed within a narrow band of transaction costs. The system was self-equilibrating. In other words, discretionary monetary policy was unnecessary because gold and silver flowed into or out of economies automatically, as needed. (The price level could move up or down in the short-term but eventually reverted to the long-term mean because deflation [inflation] created incentives [disincentives] to bring more gold and silver to market.) Nations today that maintain fixed exchange rates also find no need for a central bank, but instead use a simpler institution called a currency board. Countries that use a foreign currency as their own, a process called dollarization, need nothing at all because they essentially outsource their monetary policy to the central bank of the nation whose currency they use. (That is often the United States, hence the term dollarization.) Other central banking functions, like clearing checks and regulating financial institutions, can be performed by other entities, public and private. The function of lender of last resort typically cannot be fulfilled, however, by anything other than a central bank.
Indeed, the biggest problem with the U.S. arrangement was that there was no official systemwide lender of last resort, nobody to increase the money supply or lower interest rates in the face of a shock. As a result, the United States suffered from banking crises and financial panics of increasing ferocity beginning soon after the Second Bank’s demise: 1837, 1839, 1857, 1873, 1884, 1893, and 1907. Most of those panics were followed by recessions and debt deflation because there was no institution wealthy enough to stop the death spiral (a shock, increased asymmetric information, decline in economic activity, bank panic, increased asymmetric information, decline in economic activity, unanticipated decline in the price level). In 1907, J. P. Morgan (the man, with help from his bank and web of business associates) mitigated, but did not prevent, a serious recession by acting as a lender of last resort. The episode convinced many Americans that the time had come to create a new central bank lest private financiers come to wield too much power. Anyone with the power to stop a panic, they reasoned, had the power to start one. Americans still feared powerful government institutions too, however, so it took another six years (1913) to agree on the new bank’s structure, which was highly decentralized geographically and chock full of checks and balances. It took another year (1914) to get the bank, often called simply the Fed or the Federal Reserve, into operation.
KEY TAKEAWAYS
• A central bank is a bank under some degree of government control that is responsible for influencing the money supply, interest rates, inflation, and other macroeconomic outcomes like output and employment. A central bank is usually the lender of last resort, the institution that can (and should) add liquidity and confidence to the financial system at the outbreak of panics and crises. On a quotidian basis, central banks also may clear checks, regulate banks and/or other financial institutions, and serve as the national government’s bank.
• Early in its history, the United States was home to two privately owned central banks, the Bank of the United States and the Second Bank, that acted as a lender of last resort and regulated commercial banks by returning their notes to them for redemption in base money (then gold and silver). Although economically effective, both were politically unpopular so when their twenty-year charters expired, they were not renewed. From 1837 until the end of 1914, the United States had no central bank, but the Treasury Department fulfilled some of its functions.
• A country can do without a central bank if it is on fixed exchange rates, such as the gold standard, or otherwise gives up discretionary monetary policy, as when countries dollarize or adopt a foreign currency as their own. In such cases, other institutions fulfill central banking functions: government departments regulate financial institutions, commercial banks safeguard the government’s deposits, a currency board administers the fixed exchange rate mechanism, clearinghouses established by banks clear checks, and so forth.
• The Treasury Department did not act as a lender of last resort, however, so recurrent banking crises and financial panics plagued the economy. When J. P. Morgan acted as a lender of last resort during the Panic of 1907, political sentiments shifted and the Federal Reserve system emerged out of a series of political compromises six years later. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/14%3A_Central_Bank_Form_and_Function/14.01%3A_Americas_Central_Banks.txt |
Learning Objectives
• What is the structure of the Federal Reserve system?
The Federal Reserve is composed of twelve numbered districts, each with its own Federal Reserve Bank: Boston (1), New York (2), Philadelphia (3), Cleveland (4), Richmond (5), Atlanta (6), Chicago (7), St. Louis (8), Minneapolis (9), Kansas City (10), Dallas (11), and San Francisco (12). Except for regions 1 and 3, each of those district banks also operates one or more branches. For example, the Federal Reserve Bank of New York (FRBNY) maintains a branch in Buffalo; the Atlanta Fed has branches in Nashville, Birmingham, New Orleans, Jacksonville, and Miami. The Fed’s headquarters is located in Washington, DC.For an interactive map of the system, browse www.federalreserve.gov/otherfrb.htm.
Missouri is the only state with two federal reserve district banks. This was thought necessary to secure the votes of Missouri congressional representatives for the bill. (So much for public interest!) The districts don’t seem to be evenly balanced economically. They were, more or less, when the legislation was passed before World War I, but since then, the West Coast, Southwest, and Southeast (Sunbelt) have grown in economic importance relative to the Northeast and old Midwest (Rustbelt). (District 3 encompasses only southern New Jersey and eastern Pennsylvania, an area that is no longer the economic powerhouse it once was.) Rather than redistrict, the Fed has simply shifted resources over the years toward the larger and economically more potent districts.
Each Federal Reserve bank is owned (but not entirely controlled) by the commercial banks in its district, and they are members of the system. Those banks, which include all nationally chartered banks and any state banks that choose to join, own restrictedThe Fed’s stock is not traded in public markets and pays an annual dividend no higher than 6 percent. shares in the Fed, which they use to elect six district bank directors, three of whom have to be professional bankers and three of whom have to be nonbank business leaders. The Board of Governors in Washington selects another three directors, who are supposed to represent the public interest and are not allowed to work for or own stock in any bank. The nine directors, with the consent of the board, then appoint a president.
The twelve district banks do mostly grunt work:
• Issue new Federal Reserve notes (FRNs) in place of worn currency
• Clear checks
• Lend to banks within their districts
• Act as a liaison between the Fed and the business community
• Collect data on regional business and economic conditions
• Conduct monetary policy research
• Evaluate bank merger and new activities applications
• Examine bank holding companies and state-chartered member banks.The Comptroller of the Currency is the primary regulator of federally chartered banks. State regulators and the FDIC regulate state banks that are not members of the Federal Reserve system.
The FRBNY is the most important of the district banks because, in addition to the tasks listed above, it also conducts so-called open market operations, buying and selling government bonds (and occasionally other assets) on behalf of the Federal Reserve system and at the behest of headquarters in Washington. Moreover, the FRBNY is a member of the Bank for International Settlements (BIS) www.bis.org and safeguards over \$100 billion in gold owned by the world’s major central banks. Finally, the FRBNY’s president is the only permanent member of the Federal Open Market Committee (FOMC).
The FOMC is composed of the seven members of the Board of Governors, the president of the FRBNY, and the presidents of the other district banks, though only four of the last-mentioned group can vote (on a rotating basis). The FOMC meets every six weeks or so to decide on monetary policy, specifically on the rate of growth of the money supply or the federal funds target rate, an important interest rate, both of which are controlled via so-called open market operations. Until recently, the Fed had only two other tools for implementing monetary policy, the discount rate at which district banks lend directly to member banks and reserve requirements. Prior to the crisis of 2007–2008, neither was an effective tool for a long time, so the market and the media naturally concentrated on the FOMC and have even taken to calling it “the Fed,” although technically it is only one part of the central bank. The head of the Fed is the Board of Governors, which is composed of a chairperson, currently Ben Bernanke, and six governors. www.federalreserve.gov/aboutthefed/bios/board/bernanke.htm All seven are appointed by the president of the United States and confirmed by the U.S. Senate. The governors must come from different Federal Reserve districts and serve a single fourteen-year term. The chairperson is selected from among the governors and serves a four-year, renewable term. The chairperson is the most powerful member of the Fed because he or she controls the board, which controls the FOMC, which controls the FRBNY’s open market operations, which influences the money supply or a key interest rate. The chairperson also effectively controls reserve requirements and the discount rate. He (so far no women) is also the Fed’s public face and its major liaison to the national government. Although de jure power within the Fed is diffused by the checks and balances discussed above, today de facto power is concentrated in the chairperson. That allows the Fed to be effective but ensures that a rogue chairperson cannot abuse his power.
Historically, some chairpersons have made nebbishes look effective, while others, including most recently Alan Greenspan, have been considered, if not infallible demigods, then at least erudite gurus. Neither extreme view is accurate because all chairpersons have relied heavily on the advice and consent of the other governors, the district banks’ presidents, and the Fed’s research staff of economists, which is the world’s largest. The researchers provide the chairperson and the entire FOMC with new data, qualitative assessments of economic trends, and quantitative output from the latest and greatest macroeconomic models. They also examine the global economy and analyze the foreign exchange market, on the lookout for possible shocks from abroad. Fed economists also help the district banks to do their jobs by investigating market and competition conditions and engaging in educational and other public outreach programs.
KEY TAKEAWAYS
• The Fed is composed of a Washington-based headquarters and twelve district banks and their branches.
• The district banks, which are owned by the member banks, fulfill the Fed’s quotidian duties like clearing checks and conducting economic research.
• The most important of the district banks is the Federal Reserve Bank of New York (FRBNY), which conducts open market operations, the buying and selling of bonds that influences the money supply and interest rates.
• It also safeguards much of the world’s gold and has a permanent seat on the Federal Open Market Committee (FOMC), the Fed’s most important policymaking body.
• Composed of the Board of Governors and the presidents of the district banks, the FOMC meets every six weeks or so to decide whether monetary policy should be tightened (interest rates increased), loosened (interest rates decreased), or maintained.
• The Fed is full of checks and balances, but is clearly led by the chairperson of the Board of Governors.
• The chairperson often personifies the Fed as he (to date it’s been a male) is the bank’s public face.
• Nevertheless, a large number of people, from common businesspeople to the Fed’s research economists, influence his decisions through the data, opinions, and analysis they present. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/14%3A_Central_Bank_Form_and_Function/14.02%3A_The_Federal_Reserve_Systems_Structure.txt |
Learning Objectives
• How do other central banks compare to the Fed?
The Fed is the world’s most important central bank because the United States has been the world’s most important economy since at least World War II. But the Maastricht Treaty created a contender: Figure 14.1 ).
The ECB is part of a larger system, the European System of Central Banks (ESCB), some of the countries of which (Bulgaria, Czech Republic, Denmark, Estonia, Cyprus, Latvia, Lithuania, Hungary, Malta, Poland, Romania, Slovakia, Sweden, and the United Kingdom) are part of the European Union but have opted out of the currency union. Other countries in the ESCB, including Bulgaria, Denmark, Latvia, and Lithuania, currently link their national currencies to the euro.
The ECB or Eurosystem was consciously modeled on the Fed, so it is not surprising that their structures are similar. Each nation is like a Federal Reserve district headed by its national central bank (NCB). At its headquarters in Frankfurt sits the ECB’s Executive Board, the structural equivalent of the Fed’s Board of Governors, and the Governing Council, which like the Fed’s FOMC makes monetary policy decisions. The ECB is more decentralized than the Fed, however, because the NCBs control their own budgets and conduct their own open market operations. Also unlike the Fed, the ECB does not regulate financial institutions, a task left to each individual country’s government. The two central banks, of course, also differ in many matters of detail. The ECB was led by Frenchman Jean-Claude Trichet from 2003 until November 2011, when he was replaced by Italian economist and central banker Mario Draghi. en.Wikipedia.org/wiki/President_of_the_European_Central_Bank#Trichet Unless he resigns, like the ECB’s first president, Dutchman Wim Duisenberg did (1998–2003), Draghi will serve a single 8-year term. Like the other presidents, he was appointed by the European Council, which is comprised of the heads of state of the EU member states, the president of the European Commission, and the president of the European Council.
Three other important central banks, the Bank of England, the Bank of Japan, and the Bank of Canada, look nothing like the Fed or the ECB because they are unitary institutions with no districts. Although they are more independent from their respective governments than in the past, most are not as independent as the Fed or the ECB. Despite their structural differences and relative dearth of independence, unit central banks like the Bank of Japan implement monetary policy in ways very similar to the Fed and ECB.Dieter Gerdesmeier, Francesco Mongelli, and Barbara Roffia, “The Eurosystem, the US Federal Reserve and the Bank of Japan: Similarities and Differences,” ECB Working Paper Series No. 742 (March 2007).
KEY TAKEAWAY
The European Central Bank (ECB), the central bank of the nations that have adopted the euro, and the larger European System of Central Banks (ECSB), of which it is a part, are modeled after the Fed. Nevertheless, numerous differences of detail can be detected. The ECB’s national central banks (NCBs), for example, are much more powerful than the Fed’s district banks because they control their own budgets and conduct open market operations. Most of the world’s other central banks are structured differently than the ECB and the Fed because they are unit banks without districts or branches. Most are less independent than the Fed and ECB but conduct monetary policy in the same ways. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/14%3A_Central_Bank_Form_and_Function/14.03%3A_Other_Important_Central_Banks.txt |
Learning Objectives
• What is central bank independence, why is it important, and why do independent central bankers prefer lower inflation rates than government officials usually do?
What exactly is central bank independence (sometimes referred to as autonomy) and why is it important? Independence means just that, independence from the dictates of government, the freedom to conduct monetary policy as central bankers (and not politicians) wish. Why does it matter whether a central bank is independent or not? Figure 14.2, the results of a classic study, reveals all.
Note that as a country’s central bank becomes more independent (as its independence score increases from 1 to 4), its average inflation rate drops. The negative relationship is quite pronounced, producing a correlation coefficient of −.7976. The correlation is so strong, in fact, that many believe that independence causes low inflation. (Correlation alone cannot establish causation, but a strong correlation coefficient is a necessary first step in establishing causation.) Some scholars have argued, however, that the results were rigged, that researchers simply assigned central banks with a good record on inflation with a high independence score. (If this is true, it would destroy the causal implications of the study.) While it is true that rating a central bank’s independence is something of an art, there are clear rules to follow. Where there is no rule of law, as in dictatorships, there can be no independence. The central banker must do as he or she is instructed or be sacked or possibly shot. Little wonder, then, that many Latin American and African countries had very high rates of inflation when they were ruled by dictators.
In nations with rule of law, like those in Figure 14.2, it’s best to follow the purse. If a central bank has control of its own budget, as the Fed and ECB (and some of its predecessors, like the Bundesbank of Germany) do, then the bank is quite independent because it is beholden to no one. The Fed is slightly less independent than the ECB, however, because its existence is not constitutionally guaranteed. (Indeed, as we learned above, the United States had a nasty habit of dispatching its early central banks.) Congress could change or abolish the Fed simply by passing a law and getting the president to sign it or it could override his veto. The ECB, by contrast, was formed by an international treaty, changes to which must be ratified by all the signatories, a chore and a half to achieve, to be sure! Finally, central banks led by people who are appointed are more independent than those led by popularly elected officials. Long, nonrenewable terms are better for independence than short, renewable ones, which tend to induce bankers to curry the favor of whoever decides their fate when their term expires.
None of this is to say, however, that determining a central bank’s independence is easy, particularly when de jure and de facto realities differ. The Bank of Canada’s independence is limited by the fact that the Bank Act of 1967 made the government ultimately responsible for Canada’s monetary policy. But, in fact, the Canadian government has allowed its central bank to run the money show. The same could be said of the Bank of England. The Bank of Japan’s independence was strengthened in 1998 but the Ministry of Finance, a government agency, still controls part of its budget and can request delays in monetary policy decisions. The current de facto independence of those banks could be undermined and quite quickly at that.
Stop and Think Box
“Bank of Japan Faces Test of Independence,” Wall Street Journal, August 10, 2000.“The political storm over a possible interest rate increase by the Bank of Japan is shaping up to be the biggest challenge to the central bank’s independence since it gained autonomy two years ago. Members of the ruling Liberal Democratic Party stepped up pressure on the bank to leave the country’s interest rates where they are now.” Why does the Liberal Democratic Party (LDP) want to influence the Bank of Japan’s (BoJ’s) interest rate policy? Why was the issue important enough to warrant a major article in a major business newspaper?
The LDP wanted to influence the BoJ’s interest rate policy for political reasons, namely, to keep the economy from slowing, a potential threat to its rule. This was an important story because the de facto “independence” of the BoJ was at stake and hence the market’s perception of the Japanese central bank’s ability to raise interest rates to stop inflation in the face of political pressure.
Why, when left to their own devices, are central bankers tougher on inflation than governments, politicians, or the general populace? Partly because they represent bank, business, and creditor interests, all of which are hurt if prices rise quickly and unexpectedly. Banks are naturally uncomfortable in rising interest rate environments, and inflation invariably brings with it higher rates. Net creditors—economic entities that are owed more than they owe—also dislike inflation because it erodes the real value of the money owed them. Finally, businesses tend to dislike inflation because it increases uncertainty and makes long-term planning difficult. Central bankers also know the damage that inflation can do to an economy, so a public interest motivation drives them as well.
People and the politicians they elect to office, on the other hand, sometimes desire inflation. Many households are net debtors, meaning that they owe more money than is owed to them. Inflation, they know, will decrease the real burden of their debts. In addition, most members of the public do not want the higher interest rates that are sometimes necessary to combat inflation because it will cost them money and perhaps even their jobs. They would rather suffer from some inflation, in other words, rather than deal with the pain of keeping prices in check.
Politicians know voter preferences, so they, too, tend to err on the side of higher rather than lower inflation. Politicians also know that monetary stimulus—increasing the money supply at a faster rate than usual or lowering the interest rate—can stimulate a short burst of economic growth that will make people happy with the status quo and ready to return incumbents to office. If inflation ensues and the economy turns sour for awhile after the election, that is okay because matters will likely sort out before the next election, when politicians will be again inclined to pump out money. Some evidence of just such a political business cycle in the postwar United States has been found.See, for example, Jac Heckelman, “Historical Political Business Cycles in the United States,” EH.Net Encyclopedia (2001). eh.net/encyclopedia/article/heckelman .political.business.cycles. The clearest evidence implicates Richard Nixon. See Burton Abrams and James Butkiewicz, “The Political Business cycle: New Evidence from the Nixon Tapes,” University of Delaware Working Paper Series No. 2011-05 (2011). www.lerner.udel.edu/sites/default/files/imce/economics/Working Papers/2011/UDWP 2011-05.pdf Politicians might also want to print money simply to avoid raising direct taxes. The resultant inflation acts like a tax on cash balances (which lose value each day) and blame can be cast on the central bankers.
All in all, then, it is a good idea to have a central bank with a good deal of independence, though some liberals complain that independent central banks aren’t sufficiently “democratic.” But who says everything should be democratic? Would you want the armed forces run by majority vote? Your company? Your household? Have you heard about the tyranny of the majority?xroads.virginia.edu/~hyper/detoc/1_ch15.htm That’s when two wolves and a sheep vote on what’s for dinner. Central bank independence is not just about inflation but about how well the overall economy performs. There is no indication that the inflation fighting done by independent central banks in any way harms economic growth or employment in the long run. Keeping the lid on inflation, which can seriously injure national economies, is therefore a very good policy indeed.
Another knock against independent central banks is that they are not very transparent. The Fed, for example, has long been infamous for its secrecy. When forced by law to disclose more information about its actions sooner, it turned to obfuscation. To this day, decoding the FOMC’s press releases is an interesting game of semantics. For all its unclear language, the Fed is more open than the ECB, which will not make the minutes of its policy meetings public until twenty years after they take place. It is less transparent, however, than many central banks that publish their economic forecasts and inflation rate targets. Theory suggests that central banks should be transparent when trying to stop inflation but opaque when trying to stimulate the economy.
KEY TAKEAWAYS
• Central bank independence is a measure of how free from government influence central bankers are. Independence increases as a central bank controls its own budget; it cannot be destroyed or modified by mere legislation (or, worse, executive fiat), and it is enhanced when central banks are composed of people serving long, nonrenewable terms. Independence is important because researchers have found that the more independent a central bank is, the lower the inflation it allows without injuring growth and employment goals.
• When unanticipated, inflation redistributes resources from net creditors to net debtors, creates uncertainty, and raises nominal interest rates, hurting economic growth.
• Independent central bankers represent bank, business, and net creditor interests that are hurt by high levels of inflation. Elected officials represent voters, many of whom are net debtors, and hence beneficiaries of debt-eroding inflationary measures.
• They also know that well-timed monetary stimulus can help them obtain re-election by inducing economic growth in the months leading up to the election. The inflation that follows will bring some pain, but there will be time for correction before the next election. Governments where officials are not elected, as in dictatorships, often have difficulty collecting taxes, so they use the central bank as a source of revenue, simply printing money (creating bank deposits) to make payments. High levels of inflation act as a sort of currency tax, a tax on cash balances that lose some of their purchasing power each day.
14.05: Suggested Reading
Bremner, Robert. Chairman of the Fed: William McChesney Martin Jr. and the Creation of the American Financial System. New Haven, CT: Yale University Press, 2004.
Bruner, Robert, and Sean Carr. The Panic of 1907: Lessons Learned from the Market’s Perfect Storm. Hoboken, NJ: John Wiley and Sons, 2007.
Clark, William Roberts. Capitalism, Not Globalismml: Capital Mobility, Central Bank Independence, and the Political Control of the Economy. Ann Arbor, MI: University of Michigan Press, 2005.
Meltzer, Allan. A History of the Federal Reserve, Volume 1: 1913–1951. Chicago, IL: University of Chicago Press, 2003.
Timberlake, Richard. Monetary Policy in the United States: An Intellectual and Institutional History. Chicago, IL: University of Chicago Press, 1993. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/14%3A_Central_Bank_Form_and_Function/14.04%3A_Central_Bank_Independence.txt |
Learning Objectives
By the end of this chapter, students should be able to:
• Describe who determines the money supply.
• Explain how the central bank’s balance sheet differs from the balance sheets of commercial banks and other depository institutions.
• Define the monetary base and explain its importance.
• Define open market operations and explain how they affect the monetary base.
• Describe the multiple deposit creation process.
• Define the simple deposit multiplier and explain its information content.
• List and explain the two major limitations or assumptions of the simple deposit multiplier.
• Compare and contrast the simple money multiplier and the m1 and m2 multipliers.
• Write the equation that helps us to understand how changes in the monetary base affect the money supply.
• Explain why the M2 multiplier is almost always larger than the m1 multiplier.
• Explain why the required reserve ratio, the excess reserve ratio, and the currency ratio are in the denominator of the m1 and m2 money multipliers.
• Explain why the currency, time deposit, and money market mutual fund ratios are in the numerator of the M2 money multiplier.
• Describe how central banks influence the money supply.
• Describe how banks, borrowers, and depositors influence the money supply.
Thumbnail: Image by Pepi Stojanovski from Unsplash
15: The Money Supply Process and the Money Multipliers
Learning Objectives
• Who determines the money supply?
• How does the central bank’s balance sheet differ from the balance sheets of other banks?
• What is the monetary base?
In most countries today, a central bank or other monetary authority is charged with issuing domestic currency. That is an important charge because the supply of money greatly influences interest and inflation rates and, ultimately, aggregate output. If the central bank’s monetary policy is good, if it creates just the right amount of money, the economy will hum, and interest and inflation rates will be low. If it creates too much money too quickly, prices will increase rapidly and wipe out people’s savings until even the poorest people are nominal billionaires (as in Zimbabwe recently). funkydowntown.com/poor-people-in-zimbabwe-are-millionaires-and-billionaires; www.hoax-slayer.com/zimbabwe-hyperinflation.shtml If it creates too little money too slowly, prices will fall, wiping out debtors and making it nearly impossible to earn profits in business (as in the Great Depression). But even less extreme errors can have serious negative consequences for the economy and hence your wallets, careers, and dreams. This chapter is a little involved, but it is worth thoroughly understanding the money supply process and money multipliers if you want you and yours to be healthy and happy.
Ultimately, the money supply is determined by the interaction of four groups: commercial banks and other depositories, depositors, borrowers, and the central bank. Like any bank, the central bank’s balance sheet is composed of assets and liabilities. Its assets are similar to those of common banks and include government securitiesStudents sometimes become confused about this because they think the central bank is the government. At most, it is part of the government, and not the part that issues the bonds. Sometimes, as in the case of the BUS and SBUS, it is not part of the government at all. and discount loans. The former provide the central bank with income and a liquid asset that it can easily and cheaply buy and sell to alter its balance sheet. The latter are generally loans made to commercial banks. So far, so good. The central bank’s liabilities, however, differ fundamentally from those of common banks. Its most important liabilities are currency in circulation and reserves.
It may seem strange to see currency and reserves listed as liabilities of the central bank because those things are the assets of commercial banks. In fact, for everyone but the central bank, the central bank’s notes, Federal Reserve notes (FRN) in the United States, are assets or things owned. But for the central bank, its notes are things owed (liabilities). Every financial asset is somebody else’s liability, of course. A promissory note (IOU) that you signed would be your liability, but it would be an asset for the note’s holder or owner. Similarly, a bank deposit is a liability for the bank but an asset for the depositor. In like fashion, commercial banks own their deposits in the Fed (reserves), so they count them as assets. The Fed owes that money to commercial banks, so it must count them as liabilities. The same goes for FRN: the public owns them, but the Fed, as their issuer, owes them. (Don’t be confused by the fact that what the Fed owes to holders is nothing more than the right to use the notes to pay sums the holders owe to the government for taxes and the like.)
Currency in circulation (C) and reserves (R) compose the monetary base(MB, aka high-powered money), the most basic building blocks of the money supply. Basically, MB = C + R, an equation you’ll want to internalize. In the United States, C includes FRN and coins issued by the U.S. Treasury. We can ignore the latter because it is a relatively small percentage of the MB, and the Treasury cannot legally manage the volume of coinage in circulation in an active fashion, but rather only meets the demand for each denomination: .01, .05, .10, .25, .50, and 1.00 coins. (The Fed also supplies the \$1.00 unit, and for some reason Americans prefer \$1 notes to coins. In most countries, coins fill demand for the single currency unit denomination.) C includes only FRN and coins in the hands of nonbanks. Any FRN in banks is called vault cash and is included in R, which also includes bank deposits with the Fed. Reserves are of two types: those required or mandated by the central bank (RR), and any additional or excess reserves (ER) that banks wish to hold. The latter are usually small, but they can grow substantially during panics like that of September–October 2008.
Central banks, of course, are highly profitable institutions because their assets earn interest but their liabilities are costless, or nearly so. Printing money en masse with modern technology is pretty cheap, and reserves are nothing more than accounting entries. Many central banks, including the Federal Reserve, now pay interest on reserves, but of course any interest paid is composed of cheap notes or, more likely, even cheaper accounting entries. Central banks, therefore, have no gap problems, and liquidity management is a snap because they can always print more notes or create more reserves. Central banks anachronistically own prodigious quantities of gold, but some have begun to sell off their holdings because they no longer convert their notes into gold or anything else for that matter. news.goldseek.com/GoldSeek/1177619058.php Gold is no longer part of the MB but is rather just a commodity with unusually good monetary characteristics (high value-to-weight ratio, divisible, easily authenticated, and so forth).
KEY TAKEAWAYS
• It is important to understand the money supply process because having too much or too little money will lead to negative economic outcomes including high(er) inflation and low(er) total output.
• The central bank, depository institutions of every stripe, borrowers, and depositors all help to determine the money supply.
• The central bank helps to determine the money supply by controlling the monetary base (MB), aka high-powered money or its monetary liabilities.
• The central bank’s balance sheet differs from those of other banks because its monetary liabilities, currency in circulation (C) and reserves (R), are everyone else’s assets.
• The monetary base or MB = C + R, where C = currency in circulation (not in the central bank or any bank); R = reserves = bank vault cash and deposits with the central bank. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.01%3A_The_Central_Banks_Balance_Sheet.txt |
Learning Objectives
• What are open market operations and how do they affect the monetary base?
We are now ready to understand how the central bank influences the money supply (MS) with the aid of the T-accounts—accounts that show only the changes in balance sheets. Like regular balance sheets, however, T-accounts must balance (asset changes must equal liability changes). Central banks like the Fed influence the MS via the MB. They control their monetary liabilities, MB, by buying and selling securities, a process called open market operations. If a central bank wants to increase the MB, it need only buy a security. (Any asset will do, but securities, especially government bonds, are generally best because there is little default risk, liquidity is high, and they pay interest.) If a central bank bought a \$10,000 bond from a bank, the following would occur:
Banking System
Assets Liabilities
Securities −\$10,000
Reserves +\$10,000
The banking system would lose \$10,000 worth of securities but gain \$10,000 of reserves (probably a credit in its account with the central bank but, as noted above, FRN or other forms of cash also count as reserves).
Central Bank
Assets Liabilities
Securities +\$10,000 Reserves +\$10,000
The central bank would gain \$10,000 of securities essentially by creating \$10,000 of reserves. Notice that the item transferred, securities, has opposite signs, negative for the banking system and positive for the central bank. That makes good sense if you think about it because one party is selling (giving up) and the other is buying (receiving). Note also that the central bank’s liability has the same sign as the banking system’s asset. That too makes sense because, as noted above, the central bank’s liabilities are everyone else’s assets. So if the central bank’s liabilities increase or decrease, everyone else’s assets should do likewise.
If the central bank happens to buy a bond from the public (any nonbank), and that entity deposits the proceeds in its bank, precisely the same outcome would occur, though via a slightly more circuitous route:
Some Dude
Assets Liabilities
Securities −\$10,000
Checkable deposits +\$10,000
Banking System
Assets Liabilities
Reserves +\$10,000 Checkable deposits +\$10,000
Central Bank
Assets Liabilities
Securities +\$10,000 Reserves +\$10,000
If the nonbank seller of the security keeps the proceeds as cash (FRN), however, the outcome is slightly different:
Some Dude
Assets Liabilities
Securities −\$10,000
Currency +\$10,000
Central Bank
Assets Liabilities
Securities +\$10,000 Currency in circulation +\$10,000
Note that in either case, however, the MB increases by the amount of the purchase because either C or R increases by the amount of the purchase. Keep in mind that currency in circulation means cash (like FRN) no longer in the central bank. An IOU in the hands of its maker is no liability; cash in the hands of its issuer is not a liability. So although the money existed physically before Some Dude sold his bond, it did not exist economically as money until it left its papa (mama?), the central bank. If the transaction were reversed and Some Dude bought a bond from the central bank with currency, the notes he paid would cease to be money, and currency in circulation would decrease by \$10,000.
In fact, whenever the central bank sells an asset, the exact opposite of the above T-accounts occurs: the MB shrinks because C (and/or R) decreases along with the central bank’s securities holdings, and banks or the nonbank public own more securities but less C or R.
The nonbank public can influence the relative share of C and R but not the MB. Say that you had \$55.50 in your bank account but wanted \$30 in cash to take your significant other to the carnival. Your T-account would look like the following because you turned \$30 of deposits into \$30 of FRN:
Your T-Account
Assets Liabilities
Checkable deposits −\$30.00
Currency +\$30.00
Your bank’s T-account would look like the following because it lost \$30 of deposits and \$30 of reserves, the \$30 you walked off with:
Your Bank
Assets Liabilities
Reserves −\$30.00 Checkable deposits −\$30.00
The central bank’s T-account would look like the following because the nonbank public (you!) would hold \$30 and your bank’s reserves would decrease accordingly (as noted above):
Central Bank
Assets Liabilities
Currency in circulation \$30.00
Reserves −\$30.00
The central bank can also control the monetary base by making loans to banks and receiving their loan repayments. A loan increases the MB and a repayment decreases it. A \$1 million loan and repayment a week later looks like this:
Central Bank
Assets Liabilities Date
Loans +\$1,000,000 Reserves +\$1,000,000 January 1, 2010
Loans −\$1,000,000 Reserves −\$1,000,000 January 8, 2010
Banking System
Assets Liabilities Date
Reserves +\$1,000,000 Borrowings +\$1,000,000 January 1, 2010
Reserves −\$1,000,000 Borrowings −\$1,000,000 January 8, 2010
Take time now to practice deciphering the effects of open market operations and central bank loans and repayments via T-accounts in Exercise 1. You’ll be glad you did.
EXERCISES
Use T-accounts to describe what happens in the following instances:
1. The Bank of Japan sells ¥10 billion of securities to banks.
2. The Bank of England buys £97 million of securities from banks.
3. Banks borrow €897 million from the ECB.
4. Banks repay \$C80 million of loans to the Bank of Canada.
5. The Fed buys \$75 billion of securities from the nonbank public, which deposits \$70 billion and keeps \$5 billion in cash.
KEY TAKEAWAYS
• MB is important because an increase (decrease) in it will increase (decrease) the money supply (M1—currency plus checkable deposits, M2—M1 plus time deposits and retail money market deposit accounts, etc.) by some multiple (hence the “high-powered” nickname).
• Open market operations occur whenever a central bank buys or sells assets, usually government bonds.
• By purchasing bonds (or anything else for that matter), the central bank increases the monetary base and hence, by some multiple, the money supply. (Picture the central bank giving up some money to acquire the bond, thereby putting FRN or reserves into circulation.)
• By selling bonds, the central bank decreases the monetary base and hence the money supply by some multiple. (Picture the central bank giving up a bond and receiving money for it, removing FRN or reserves from circulation.)
• Similarly, the MB and MS increase whenever the Fed makes a loan, and they decrease whenever a borrower repays the Fed. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.02%3A_Open_Market_Operations.txt |
Learning Objectives
• What is the multiple deposit creation process?
• What is the money multiplier?
• What are the major limitations of the simple deposit multiplier?
The central bank pretty much controls the size of the monetary base. (The check clearing process and the government’s banking activities can cause some short-term flutter, but generally the central bank can anticipate such fluctuations and respond accordingly.) That does not mean, however, that the central bank controls the money supply, which consists of more than just MB. (M1, for example, also includes checkable deposits.) The reason is that each \$1 (or €1, etc.) of additional MB creates some multiple > 1 of new deposits in a process called multiple deposit creation.
Suppose Some Bank wants to decrease its holding of securities and increase its lending. It could sell \$1 million of its securities to the central bank. The T-accounts would be:
Some Bank
Assets Liabilities
Securities −\$1 million
Reserves +\$1 million
Central Bank
Assets Liabilities
Securities +\$1 million Reserves +\$1 million
Some Bank suddenly has \$1 million in excess reserves. (Its deposits are unchanged, but it has \$1 million more in cash.) The bank can now make more loans. So its T-account will be the following:
Some Bank
Assets Liabilities
Loans +\$1 million Deposits +\$1 million
Deposits are created in the process of making the loan, so the bank has effectively increased M1 by \$1 million. The borrower will not leave the proceeds of the loan in the bank for long but instead will use it, within the guidelines set by the loan’s covenants, to make payments. As the deposits flow out of Some Bank, its excess reserves decline until finally Some Bank has essentially swapped securities for loans:
Some Bank
Assets Liabilities
Securities ?\$1 million
Loans +\$1 million
But now there is another \$1 million of checkable deposits out there and they rarely rest. Suppose, for simplicity’s sake, they all end up at Another Bank. Its T-account would be the following:
Another Bank
Assets Bank Liabilities
Reserves +\$1 million Checkable deposits +\$1 million
If the required reserve ratio (rr) is 10 percent, Another Bank can, and likely will, use those deposits to fund a loan, making its T-account:
Another Bank
Assets Liabilities
Reserves +\$.1 million Checkable Deposits +\$1 million
Loans +\$.9 million
That loan will also eventually be paid out to others and deposited into other banks, which in turn will lend 90 percent of them (1 ? rr) to other borrowers. Even if a bank decides to invest in securities instead of loans, as long as it buys the bonds from anyone but the central bank, the multiple deposit creation expansion will continue, as in Figure 15.1.
Notice that the increase in deposits is the same as the increase in loans from the previous bank. The increase in reserves is the increase in deposits times the required reserve ratio of .10, and the increase in loans is the increase in deposits times the remainder, .90. Rather than working through this rather clunky process every time, you can calculate the effects of increasing reserves with the so-called simple deposit multiplier formula:
△D = ( 1 / r r ) × △R
where:
△D = change in deposits
△R = change in reserves
Rr = required reserve ratio
1/.1 × 1 million = 10 million, just as in Figure 15.1
Practice calculating the simple deposit multiplier in Exercise 2.
EXERCISE
1. Use the simple deposit multiplier △D = (1/rr) × △R to calculate the change in deposits given the following conditions:
Required Reserve Ratio Change in Reserves Answer: Change in Deposits
.1 10 100
.5 10 20
1 10 10
.1 −10 −100
.1 100 1,000
0 43.5 ERROR—cannot divide by 0
Stop and Think Box
Suppose the Federal Reserve wants to increase the amount of checkable deposits by \$1,000,000 by conducting open market operations. Using the simple model of multiple deposit creation, determine what value of securities the Fed should purchase, assuming a required reserve ratio of 5 percent. What two major assumptions does the simple model of multiple deposit creation make? Show the appropriate equation and work.
The Fed should purchase \$50,000 worth of securities. The simple model of multiple deposit creation is △D = (1/rr) × △R, which of course is the same as △R = △D/(1/rr). So for this problem 1,000,000/(1/.05) = \$50,000 worth of securities should be purchased. This model assumes that money is not held as cash and that banks do not hold excess reserves.
Pretty easy, eh? Too bad the simple deposit multiplier isn’t very accurate. It provides an upper bound to the deposit creation process. The model simply isn’t very realistic. Sometimes banks hold excess reserves, and people sometimes prefer to hold cash instead of deposits, thereby stopping the multiple deposit creation process cold. If the original borrower, for example, had taken cash and paid it out to people who also preferred cash over deposits no expansion of the money supply would have occurred. Ditto if Some Bank had decided that it was too risky to make new loans and had simply exchanged its securities for reserves. Or if no one was willing to borrow. Those are extreme examples, but anywhere along the process leaks into cash or excess reserves sap the deposit multiplier. That is why, at the beginning of the chapter, we said that depositors, borrowers, and banks were also important players in the money supply determination process. In the next section, we’ll take their decisions into account.
KEY TAKEAWAYS
• The multiple deposit creation process works like this: say that the central bank buys \$100 of securities from Bank 1, which lends the \$100 in cash it receives to some borrower. Said borrower writes checks against the \$100 in deposits created by the loan until all the money rests in Bank 2. Its deposits and reserves increased by \$100, Bank 2 lends as much as it can, say (1 − rr = .9) or \$90, to another borrower, who writes checks against it until it winds up in Bank 3, which also lends 90 percent of it. Bank 4 lends 90 percent of that, Bank 5 lends 90 percent of that, and so on, until a \$100 initial increase in reserves has led to a \$1,000 increase in deposits (and loans).
• The simple deposit multiplier is △D = (1/rr) × △R, where △D = change in deposits; △R = change in reserves; rr = required reserve ratio.
• The simple deposit multiplier assumes that banks hold no excess reserves and that the public holds no currency. We all know what happens when we assume or ass|u|me. These assumptions mean that the simple deposit multiplier overestimates the multiple deposit creation process, providing us with an upper-bound estimate. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.03%3A_A_Simple_Model_of_Multiple_Deposit_Creation.txt |
Learning Objectives
• How do the simple money multiplier and the more sophisticated one developed here contrast and compare?
• What equation helps us to understand how changes in the monetary base affect the money supply?
To review, an increase (decrease) in the monetary base (MB, which = C + R) leads to an even greater increase (decrease) in the money supply (MS, such as M1 or M2) due to the multiple deposit creation process. In the previous section, you also learned a simple but unrealistic upper-bound formula for estimating the change that assumed that banks hold no excess reserves and that the public holds no currency.
Stop and Think Box
You are a research associate for Moody’s subsidiary, High Frequency Economics, in West Chester, Pennsylvania. A client wants you to project changes in M1 given likely increases in the monetary base. Because of a glitch in the Federal Reserve’s computer systems, currency, deposit, and excess reserve figures will not be available for at least one week. A private firm, however, can provide you with good estimates of changes in banking system reserves, and of course the required reserve ratio is well known. What equation can you use to help your client? What are the equation’s assumptions and limitations?
You cannot use the more complex M1 money multiplier this week because of the Fed’s computer glitch, so you should use the simple deposit multiplier from Chapter 15: ΔD = (1/rr) × ΔR. The equation provides an upper-bound estimate for changes in deposits. It assumes that the public will hold no more currency and that banks will hold no increased excess reserves.
To get a more realistic estimate, we’ll have to do a little more work. We start with the observation that we can consider the money supply to be a function of the monetary base times some money multiplier (m):
△ M S = m × △ M B
This is basically a broader version of the simple multiplier formula discussed in the previous section, except that instead of calculating the change in deposits (ΔD) brought about by the change in reserves (ΔR), we will now calculate the change in the money supply (ΔMS) brought about by the change in the monetary base (ΔMB). Furthermore, instead of using the reciprocal of the required reserve ratio (1/rr) as the multiplier, we will use a more sophisticated one (m1, and later m2) that doesn’t assume away cash and excess reserves.
We can add currency and excess reserves to the equation by algebraically describing their relationship to checkable deposits in the form of a ratio:
C/D = currency ratio
ER/D = excess reserves ratio
Recall that required reserves are equal to checkable deposits (D) times the required reserve ratio (rr). Total reserves equal required reserves plus excess reserves:
R = r r D + E R
So we can render MB = C + R as MB = C + rrD + ER. Note that we have successfully removed C and ER from the multiple deposit expansion process by separating them from rrD. After further algebraic manipulations of the above equation and the reciprocal of the reserve ratio (1/rr) concept embedded in the simple deposit multiplier, we’re left with a more sophisticated, more realistic money multiplier:
m 1 = 1 + ( C / D ) / [ r r + ( E R / D ) + ( C / D ) ]
So if
Required reserve ratio (rr) = .2
Currency in circulation = \$100 billion
Deposits = \$400 billion
Excess reserves = \$10 billion
m 1 = 1 + ( 100 / 400 ) / ( .2 + ( 10 / 400 ) + ( 100 / 400 ) )
m 1 = 1.25 / ( .2 + .025 + .25 )
m 1 = 1.25 / .475 = 2.6316
Practice calculating the money multiplier in Exercise 1.
EXERCISES
1. Given the following, calculate the M1 money multiplier using the formula m1 = 1 + (C/D)/[rr + (ER/D) + (C/D)].
Currency Deposits Excess Reserves Required Reserve Ratio Answer: m1
100 100 10 .1 1.67
100 100 10 .2 1.54
100 1,000 10 .2 3.55
1,000 100 10 .2 1.07
1,000 100 50 .2 1.02
100 1,000 50 .2 3.14
100 1,000 0 1 1
Once you have m, plug it into the formula ΔMS = m × ΔMB. So if m1 = 2.6316 and the monetary base increases by \$100,000, the money supply will increase by \$263,160. If m1 = 4.5 and MB decreases by \$1 million, the money supply will decrease by \$4.5 million, and so forth. Practice this in Exercise 2.
2. Calculate the change in the money supply given the following:
Change in MB m1 Answer: Change in MS
100 2 200
100 4 400
−100 2 −200
−100 4 −400
1,000 2 2,000
−1,000 2 −2,000
10,000 1 10,000
−10,000 1 −10,000
Stop and Think Box
Explain Figure 15.2, Figure 15.3, and Figure 15.4.
KEY TAKEAWAYS
• The more sophisticated money multipliers are similar to the simple deposit multiplier in that they equate changes in the money supply to changes in the monetary base times some multiplier.
• The money multipliers differ because the simple multiplier is merely the reciprocal of the required reserve ratio, while the other multipliers account for cash and excess reserve leakages.
• Therefore, m1 and m2 are always smaller than 1/rr (except in the rare case where C and ER both = 0).
• ΔMS = m × ΔMB, where ΔMS = change in the money supply; m = the money multiplier; ΔMB = change in the monetary base. A positive sign means an increase in the MS; a negative sign means a decrease. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.04%3A_A_More_Sophisticated_Money_Multiplier_for_M1.txt |
Learning Objectives
• Why is the M2 multiplier almost always larger than the M1 multiplier?
• Why are the required reserve ratio, the excess reserve ratio, and the currency ratio in the denominator of the m1 and m2 money multipliers?
• Why are the currency, time deposit, and money market mutual fund ratios in the numerator of the m2 money multiplier?
Note that m1 is the M1 money multiplier. With a little bit more work, one can also calculate the M2 money multiplier (m2). We want to do this because M2 is a more accurate measure of the money supply than M1, as it is usually a better indicator of changes in prices, interest rates, inflation, and, ultimately, aggregate output. (And hence whether you and your family live in a nice place with a 3D HDTV, three big refrigerators, etc., or if you live in “a van down by the river.”)www.youtube.com/watch?v=3nhgfjrKi0o; www.facebook.com/pages/Living-in-a-van-down-by-the -river/120550394658234
Recall from Chapter 3 that M2 = C + D + T + MMF, where T = time and savings deposits and MMF = money market funds, money market deposit accounts, and overnight loans. We account for the extra types of deposits in the same way as we accounted for currency and excess reserves, by expressing them as ratios against checkable deposits:
(T/D) = time deposit ratio
(MMF/D) = money market ratio
which leads to the following equation:
m 2 = 1 + ( C / D ) + ( T / D ) + ( M M F / D ) / [ r r + ( E R / D ) + ( C / D ) ]
Once you calculate m2, multiply it by the change in MB to calculate the change in the MS, specifically in M2, just as you did in Exercise 2. Notice that the denominator of the m2 equation is the same as the m1 equation but that we have added the time and money market ratios to the numerator. So M2 is alwaysM2 would equal m1 iff T = 0 and MMF = 0, which is highly unlikely. Note: if means if and only if. > m1, ceteris paribus, which makes sense when you recall that M2 is composed of M1 plus other forms of money. To verify this, recall that we calculated m1 as 2.6316 when
Required reserves (rr) = .2
Currency in circulation = \$100 million
Deposits = \$400 million
Excess reserves = \$10 million
We’ll now add time deposits of \$900 million and money market funds of \$800 million and calculate M2:
m 2 = 1 + ( C / D ) + ( T / D ) + ( M M F / D ) / [ r r + ( E R / D ) + ( C / D ) ]
m 2 = 1 + ( 100 / 400 ) + ( 900 / 400 ) + ( 800 / 400 ) / [ .2 + ( 10 / 400 ) + ( 100 / 400 ) ]
m 2 = 1 + .25 + 2.25 + 2 / ( .2 + .005 + .25 )
m 2 = 5.5 / .455 = 12.0879
This is quite a bit higher than m1 because time deposits and money market funds are not subject to reserve requirements, so they can expand more than checkable deposits because there is less drag on them during the multiple expansion process.
Practice calculating the M2 money multiplier on your own in the exercise.
EXERCISE
1. Calculate the M2 money multiplier using the following formula: M2 = 1 + (C/D) + (T/D) + (MMF/D)/[rr + (ER/D) + (C/D)].
Currency Deposits Excess Reserves Required Reserve Ratio Time Deposits Money Market Funds Answer: M2
100 100 10 0.1 1,000 1,000 18.33
100 100 10 0.2 1,000 100 10
100 100 10 0.2 100 1,000 10
1,000 100 10 0.2 1,000 1,000 3.01
1,000 100 50 0.2 1,000 1,000 2.90
100 1,000 50 0.2 1,000 1,000 8.86
100 1,000 0 1 1,000 1,000 2.82
100 1 10 0.1 1,000 1,000 19.08
KEY TAKEAWAYS
• Because M1 is part of M2, M2 is always > M1 (except in the rare case where time deposits and money market funds = 0, in which case M1 = M2).
• That fact is reflected in the inclusion of the time deposit and money market fund ratios in the numerator of the M2 multiplier equation.
• Moreover, no reserves are required for time and money market funds, so they will have more multiple expansion than checkable deposits will.
• The required reserve ratio, the excess reserve ratio, and the currency ratio appear in the denominator of the m1 and M2 money multipliers because all three slow the multiple deposit creation process. The higher the reserve ratios (required and excess), the smaller the sum available to make loans from a given deposit. The more cash, the smaller the deposit.
• The currency, time deposit, and money market mutual fund ratios are in the numerator of the M2 money multiplier because M2 is composed of currency, checkable deposits, time deposits, and money market mutual funds. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.05%3A_The_M2_Money_Multiplier.txt |
Learning Objectives
• How do central banks, banks, depositors, and borrowers influence the money supply?
By way of summary, Figure 15.6 explains why each of the major variables influences m1 and m2 in the ways implied by the equations presented above.
As we saw at the beginning of this chapter, currency holdings, excess reserves, and required reserves slow down the multiple deposit creation process by removing funds from it. The bigger rr and ER/D are, the less each bank lends of the new deposits it receives. The bigger C/D is, the less money is deposited in the first place. For those reasons, we place those variables in the denominator. The larger the denominator, holding the numerator constant, the smaller m1 or m2 will be, of course. The appropriate money supply components compose the numerator-currency, and checkable deposits for m1, and currency, checkable deposits, time deposits, and money market mutual funds compose the numerator for m2.
This leaves us to consider why C/D, rr, and ER/D change over time. Short term, the currency ratio varies directly with the interest rate and the stability of the banking system. As the interest rate increases, the opportunity cost of keeping cash increases, so people are less anxious to hold it. People are also less anxious to hold currency if the banking system is stable because their money is safer in a checking deposit. If interest rates are extremely low or people believe the banks might be shaky, they naturally want to hold more physical cash. Longer term, C/D may be influenced by technology and loophole mining, encouraging bankers and depositors to eschew traditional checkable deposits in favor of sweep accounts.
The required reserve ratio is mandated by the central bank but, as noted in Chapter 10, loophole mining and technology have rendered it less important in recent years because sweep accounts allow banks to minimize the de jure level of their checkable deposits. In many places, rr is no longer a binding constraint on banks so, as we’ll see, most central banks no longer consider changing it as an effective monetary policy tool. (This in no way affects the money multiplier, which would provide the same figure for m1 or M2 whether we calculate them as above or replace rr and ER/D with R/D, where R = total reserves.)
Stop and Think Box
Prove the assertion made above: “This in no way affects the money multiplier, which would provide the same figure for m1 or M2 whether we calculate them as above or replace rr and ER/D with R/D, where R = total reserves.” Suppose that C = 100, R = 200, and D = 500 and that R is composed of required reserves of 100 and excess reserves of 100. That means that rr must equal .2(100/500).
Under the formula provided in the text,
m 1 = 1 + ( C / D ) / [ r r + ( E R / D ) + ( C / D ) ]
m 1 = 1 + .2 / .2 + .2 + .2 = 1.2 / .6 = 2.0
Under the formula suggested above,
m 1 = 1 + ( C / D ) / [ ( R / D ) + ( C / D ) ]
m 1 = 1.2 / .4 + 2 = 2.0
Excess reserves (or just reserves in a system without required reserves) are inversely related to the interest rate. In the early 1960s and early 2000s, when the interest rate was well less than 5 percent, ER/D was high, at .003 to .004. In the 1970s and 1980s, when interest rates were 10 percent and higher, ER/D dropped to .001 to .002. As we learned in Chapter 9, expected deposit outflows directly affect excess reserve levels as banks stock up on reserves to meet the outflows. When uncertainty is high or a banking crisis is in progress or appears imminent, bankers will increase ER to protect their banks.
In summary, the central bank influences the money supply by controlling the monetary base and, to a far lesser extent, the required reserve ratio. Depositors, banks, and borrowers influence the money supply by influencing m1 and M2, specifically by determining the money multiplier, with depositors largely in control of C/D; depositors and banks interacting via deposit outflow expectations to determine E/R; and borrowers, depositors, banks, and the central bank interacting to determine interest rates and hence to some extent both C/D and E/R.
KEY TAKEAWAYS
• Central banks control MB and rr, and affect interest rates, which in turn affect C/D and ER/D.
• Depositors determine C/D by deciding how much cash versus deposits to hold. They also influence interest rates.
• Banks influence interest rates and determine ER/D by deciding how many excess reserves to hold in the face of expected deposit outflows and interest rates.
• Borrowers influence the interest rate and hence to some extent C/D and ER/D. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/15%3A_The_Money_Supply_Process_and_the_Money_Multipliers/15.06%3A_Summary_and_Explanation.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. List and assess the strengths and weaknesses of the three primary monetary policy tools that central banks have at their disposal.
2. Describe the federal funds market and explain its importance.
3. Explain how the Fed influences the equilibrium fed funds rate to move toward its target rate.
4. Explain the purpose of the Fed’s discount window and other lending facilities.
5. Compare and contrast the monetary policy tools of central banks worldwide to those of the Fed.
Thumbnail: Image by Burak K from Pexels
16: Monetary Policy Tools
Learning Objectives
1. What three monetary policy tools do central banks have at their disposal?
2. What are the strengths and weaknesses of each? What is the federal funds market and why is it important?
Central banks have three primary tools for influencing the money supply: the reserve requirement, discount loans, and open market operations. The first works through the money multiplier, constraining multiple deposit expansion the larger it becomes. Central banks today rarely use it because most banks work around reserve requirements. (That is not to say that reserve requirements are not enforced, merely that they are not adjusted to influence MS. Currently, the reserve requirement is 10 percent on transaction account deposits [demand, ATS, NOW, and share draft] greater than \$58.8 million.www.federalreserve.gov/monetarypolicy/reservereq.htm#table1) The second and third tools influence the monetary base (MB = C + R). Discount loans depend on banks (or nonbank borrowers, where applicable) first borrowing from, then repaying loans to, the central bank, which therefore does not have precise control over MB. Open market operations (OMO) are generally preferred as a policy tool because the central bank can easily expand or contract MB to a precise level. Using OMO, central banks can also reverse mistakes quickly.
In the United States, under typical conditions, the Fed conducts monetary policy primarily through the federal funds (fed funds) market, an overnight market where banks that need reserves can borrow them from banks that hold reserves they don’t need. Banks can also borrow their reserves directly from the Fed, but, except during crises, most prefer not to because the Fed’s discount rate is generally higher than the federal funds rate. Also, borrowing too much, too often from the Fed can induce increased regulatory scrutiny. So usually banks get their overnight funds from the fed funds market, which, as Figure 16.1 shows, pretty much works like any other market.
The downward slope of the demand curve for reserves is easily explained. Like anything else, as the price of reserves (in this case, the interest rate paid for them) increases, the quantity demanded decreases. As reserves get cheaper, banks will want more of them because the opportunity cost of that added protection, of that added liquidity, is lower. But what is the deal with that weird S-looking reserve supply curve? Note that the curve takes a hard right (becomes infinitely elastic) at the discount rate. That’s because, if the federal funds rate ever exceeded the discount rate, banks’ thirst for Fed discount loans would be unquenchable because a clear arbitrage opportunity would exist: borrow at the discount rate and relend at the higher market rate. Below that point, the reserve supply curve is vertical (perfectly inelastic) down to the rate at which the Fed pays interest on reserves (it currently pays .25% on both required and excess reserves, a practice begun in October 2008).www.federalreserve.gov/monetarypolicy/reqresbalances.htm Banks are, of course, unwilling to lend in the federal funds market at a rate below what the Fed will pay it, so the curve again becomes flat (infinitely elastic).
The intersection of the supply and demand curves is the equilibrium or market rate, the actual federal funds rate, ff*. When the Fed makes open market purchases, the supply of reserves shifts right, lowering ff* (ceteris paribus). When it sells, it moves the reserve supply curve left, increasing ff*, all else constant. In most circumstances, the discount and reserve rates effectively channel the market federal funds rate into a range.
Theoretically, the Fed could also directly affect the demand for reserves by changing the reserve requirement. If it increased (decreased) rr, demand for reserves would shift up (down), increasing (decreasing) ff*. As noted above, however, banks these days can so easily sidestep required reserves that the Fed’s ability to influence the demand for reserves is extremely limited. Demand for reserves (excess reserves that is) can also shift right or left due to bank liquidity management activities, increasing (decreasing) as expectations of net deposit outflows increase (decrease). The Fed tries to anticipate such shifts and generally has done a good job of counteracting changes in excess reserves through OMO. Going into holidays, for example, banks often hold a little extra vault cash (a form of reserves). Knowing this, the Fed counteracts the rightward shift in demand (which would increase ff*) by shifting the reserve supply curve to the right by buying bonds (thereby decreasing ff* by an offsetting amount). Although there have been days when ff* differed from the target by several percentage points (several hundred basis points), between 1982 and 2007, the fed funds target was, on average, only .0340 of a percent lower than ff*. Between 2000 and the subprime mortgage uproar in the summer of 2007, the Fed did an even better job of moving ff* to its target, as Figure 16.2 shows. During the crises of 2007 and 2008, however, the Fed often missed its target by a long way, as shown in Figure 16.3 . So in December 2008, it stopped publishing a feds fund target and instead began to publish the upper limit it was willing to tolerate.
Stop and Think Box
America’s first central banks, the BUS and SBUS, controlled commercial bank reserve levels by varying the speed and intensity by which it redeemed convertible bank liabilities (notes and deposits) for reserves (gold and silver). Can you model that system?
Kudos if you can! I’d plot quantity of reserves along the horizontal axis and interest rate along the vertical axis. The reserve supply curve was probably highly but not perfectly inelastic and the reserve demand curve sloped downward, of course. When the BUS or SBUS wanted to tighten monetary policy, it would return commercial bank monetary liabilities in a great rush, pushing the reserve demand curve to the right, thereby raising the interest rate. When it wanted to soften, it would dawdle before redeeming notes for gold and so forth, allowing the demand for reserves to move left, thereby decreasing the interest rate.
KEY TAKEAWAYS
• Central banks can influence the money multiplier (simple, m1, m2, etc.) via reserve requirements.
• That tool is somewhat limited these days given the introduction of sweep accounts and other reserve requirement loopholes.
• Central banks can also influence MB via loans to banks and open market operations.
• For day-to-day policy implementation, open market operations are preferable because they are more precise and immediate and almost completely under the control of the central bank, which means it can reverse mistakes quickly.
• Discount loans depend on banks borrowing and repaying loans, so the central bank has less control over MB if it relies on loans alone.
• Discount loans are therefore used now primarily to set a ceiling on the overnight interbank rate and to provide liquidity during crises.
• The federal funds market is the name of the overnight interbank lending market, basically the market where banks borrow and lend bank reserves, in the United States.
• It is important because the Fed uses open market operations (OMO) to move the equilibrium rate ff* toward the target established by the Federal Open Market Committee (FOMC). | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/16%3A_Monetary_Policy_Tools/16.01%3A_The_Federal_Funds_Market_and_Reserves.txt |
learning objectives
1. How does the Fed influence the equilibrium fed funds rate to move toward its target rate?
2. What purpose does the Fed’s discount window now serve?
In practical terms, the Fed engages in two types of OMO, dynamic and defensive. As those names imply, it uses dynamic OMO to change the level of the MB, and defensive OMO to offset movements in other factors affecting MB, with an eye toward maintaining the federal funds target rate determined by the Federal Open Market Committee (FOMC) at its most recent meeting. If it wanted to increase the money supply, for example, it would buy bonds “dynamically.” If it wanted to keep the money supply stable but knew that a bank was going to repay a large discount loan (which has the effect of decreasing the MB), it would buy bonds “defensively.”
The responsibility for actually buying and selling government bonds devolves upon the Federal Reserve Bank of New York (FRBNY). Each trading day, FRBNY staff members look at the level of reserves, the fed funds target, the actual market fed funds rate, expectations regarding float, and Treasury activities. They also garner information about Treasury market conditions through conversations with so-called primary dealers, specialized firms and banks that make a market in Treasuries. With the input and consent of the Monetary Affairs Division of the Board of Governors, the FRBNY determines how much to buy or sell and places the appropriate order on the Trading Room Automated Processing System (TRAPS) computer system that links all the primary dealers. The FRBNY then selects the best offers up to the amount it wants to buy or sell. It enters into two types of trades, so-called outright ones, where the bonds permanently join or leave the Fed’s balance sheet, and temporary ones, called repos and reverse repos. In a repo (aka a repurchase agreement), the Fed purchases government bonds with the guarantee that the sellers will repurchase them from the Fed, generally one to fifteen days hence. In a reverse repo (aka a matched sale-purchase transaction), the Fed sells securities and the buyer agrees to sell them to the Fed again in the near future. The availability of such self-reversing contracts and the liquidity of the government bond market render open market operations a precise tool for implementing the Fed’s monetary policy.
The so-called discount window, where banks come to borrow reserves from the Federal district banks, is today primarily a backup facility used during crises, when the federal funds market might not function effectively. As noted above, the discount rate puts an effective cap on ff* by providing banks with an alternative source of reserves (see Figure 16.4 ). Note that no matter how far the reserve demand curve shifts to the right, once it reaches the discount rate, it merely slides along it.
As lender of last resort, the Fed has a responsibility to ensure that banks can obtain as much as they want to borrow provided they can post what in normal times would be considered good collateral security. So that banks do not rely too heavily on the discount window, the discount rate is usually set a full percentage point above ff*, a “penalty” of 100 basis points. (This policy is usually known as Bagehot’s Law, but the insight actually originated with Alexander Hamilton, America’s first Treasury secretary, so I like to call it Hamilton’s Law.) On several occasions (including the 1984 failure of Continental Illinois, a large commercial bank; the stock market crash of 1987; and the subprime mortgage debacle of 2007), the discount window added the liquidity (reserves) and confidence necessary to stave off more serious disruptions to the economy.
Only depository institutions can borrow from the Fed’s discount window. During the financial crisis of 2008, however, many other types of financial institutions, including broker-dealers and money market funds, also encountered significant difficulties due to the breakdown of many credit markets. The Federal Reserve responded by invoking its emergency powers to create additional lending powers and programs, including the following:www.federalreserve.gov/monetarypolicy
1. Term Auction Facility (TAF), a “credit facility” that allows depository institutions to bid for short term funds at a rate established by auction.
2. Primary Dealer Credit Facility (PDCF), which provides overnight loans to primary dealers at the discount rate.
3. Term Securities Lending Facility (TSLF), which also helps primary dealers by exchanging Treasuries for riskier collateral for twenty-eight-day periods.
4. Asset-Backed Commercial Paper Money Market Mutual Liquidity Facility, which helps money market mutual funds to meet redemptions without having to sell their assets into distressed markets.
5. Commercial Paper Funding Facility (CPFF), which allows the FRBNY, through a special-purpose vehicle (SPV), to purchase commercial paper (short-term bonds) issued by nonfinancial corporations.
6. Money Market Investor Funding Facility (MMIFF), which is another lending program designed to help the money markets (markets for short-term bonds) return to normal.
Most of these programsblogs.wsj.com/economics/2011/08/09/a-look-inside-the-feds-balance-sheet-12/tab/interactive phased out as credit conditions returned to normal. (The Bank of England and other central banks have implemented similar programs.“Credit Markets: A Lifeline for Banks. The Bank of England’s Bold Initiative Should Calm Frayed Financial Nerves,” The Economist, April 26, 2008, 74–75.)
The financial crisis also induced the Fed to engage in several rounds of “quantitative easing” or Large Scale Asset Purchases (LSAP), the goals of which appear to be to increase the prices of (decrease the yields of) Treasury bonds and the other financial assets purchased and to influence the money supply directly. Due to LSAP, the Fed’s balance sheet swelled from less than a trillion dollars in early 2008 to almost 3 trillion by August 2011.
Stop and Think Box
What in Sam Hill happened in Figure 16.5 ? (Hint: The dates are important.)
Terrorists attacked New York City and Washington, DC, with hijacked airplanes, shutting down the nation and parts of the financial system for the better part of a week. Some primary dealers were destroyed in the attacks, which also brought on widespread fears of bankruptcies and bank runs. Banks beefed up reserves by selling bonds to the Fed and by borrowing from its discount window. (Excess reserves jumped from a long-term average of around \$1 billion to \$19 billion.) This is an excellent example of the discount window providing lender-of-last-resort services to the economy.
The discount window is also used to provide moderately shaky banks a longer-term source of credit at an even higher penalty rate .5 percentage (50 basis) points above the regular discount rate. Finally, the Fed will also lend to a small number of banks in vacation and agricultural areas that experience large deposit fluctuations over the course of a year. Increasingly, however, such banks are becoming part of larger banks with more stable deposit profiles, or they handle their liquidity management using the market for negotiable certificates of deposit NCDs or other market borrowings.
key takeaways
• The Fed can move the equilibrium fed funds rate toward its target by changing the demand for reserves by changing the required reserve ratio. However, it rarely does so anymore.
• It can also shift the supply curve to the right (add reserves to the system) by buying assets (almost always Treasury bonds) or shift it to the left (remove reserves from the system) by selling assets.
• The discount window caps ff* because if ff* were to rise above the Fed’s discount rate, banks would borrow reserves from the Fed (technically its district banks) instead of borrowing them from other banks in the fed funds market.
• Because the Fed typically sets the discount rate a full percentage point (100 basis) points above its feds fund target, ff* rises above the discount rate only in a crisis, as in the aftermath of the 1987 stock market crash and the 2007 subprime mortgage debacle. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/16%3A_Monetary_Policy_Tools/16.02%3A_Open_Market_Operations_and_the_Discount_Window.txt |
learning objective
1. In what ways are the monetary policy tools of central banks worldwide similar to those of the Fed? In what ways do they differ?
The European Central Bank (ECB) also uses open market operations to move the market for overnight interbank lending toward its target. It too uses repos and reverse repos for reversible, defensive OMO and outright purchases for permanent additions to MB. Unlike the Fed, however, the ECB spreads the love around, conducting OMO in multiple cities throughout the European Union. The ECB’s national central banks (NCBs,) like the Fed’s district banks, also lend to banks at a so-called marginal lending rate, which is generally set 100 basis points above the overnight cash rate. The ECB pays interest on reserves, a central bank best practice the Fed took up only recently.
Canada, New Zealand, and Australia do likewise and have eliminated reserve requirements, relying instead on what is called the channel, or corridor, system. As Figure 16.6 depicts, the supply curve in the corridor system looks like a weird S. The vertical part of the supply curve represents the area in which the central bank engages in OMO to influence the market rate, i*, to meet its target rate, it. The top horizontal part of the supply curve, il for the Lombard rate, is the functional equivalent of the discount rate in the American system. The ECB and other central banks using this system, like the Fed, will lend at this rate whatever amount banks with good collateral desire to borrow. Under normal circumstances, that quantity is nil because it (and i*) will be 25, 50, or more basis points lower, depending on the country. The big innovation in the channel system is the lower horizontal part of the supply curve, ir, or the rate at which the central bank pays banks to hold reserves. That sets a floor on i* because no bank would lend in the relatively risky overnight market if it could earn a safer, higher return by depositing its excess funds with the central bank. Using the corridor system, a central bank can keep the overnight rate within the bands set by il and ir and use OMO to keep i* near it.
key takeaways
• Most central banks now use OMO instead of discount loans or reserve requirement adjustments for conducting day-to-day monetary policy.
• Some central banks, including those of the euro zone and the British Commonwealth (Canada, Australia, and New Zealand) have developed an ingenious new method called the channel or corridor system.
• Under that system, which is rapidly becoming a best practice, the central bank conducts OMO to get the overnight interbank lending rate near the central bank’s target, as the Fed now does in the United States.
• That market rate is capped at both ends: on the upper end by the discount (aka Lombard) rate, and at the lower end by the reserve rate, the interest rate the central bank pays to banks for holding reserves.
• The market overnight rate can never dip below that rate because banks would simply invest their extra funds in the central bank rather than lend them to other banks at a lower rate.
16.04: Suggested Reading
Axilrod, Stephen H. Inside the Fed: Monetary Policy and Its Management, Martin Through Greenspan to Bernanke. Cambridge, MA: MIT Press, 2009.
Hetzel, Robert L. The Monetary Policy of the Federal Reserve: A History. New York: Cambridge University Press, 2008.
Mishkin, Frederic S. Monetary Policy Strategy. Cambridge, MA: MIT Press, 2007. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/16%3A_Monetary_Policy_Tools/16.03%3A_The_Monetary_Policy_Tools_of_Other_Central_Banks.txt |
chapter objectives
By the end of this chapter, students should be able to:
1. Explain why the Fed was generally so ineffective before the late 1980s.
2. Explain why macroeconomic volatility declined from the late 1980s until 2008.
3. List the trade-offs that central banks face and describe how they confront them.
4. Define monetary targeting and explain why it succeeded in some countries and failed in others.
5. Define inflation targeting and explain its importance.
6. Provide and use the Taylor Rule and explain its importance.
Thumbnail: Image by Mudassar Iqbal from Pixabay
17: Monetary Policy Targets and Goals
learning objectives
1. Why was the Fed generally so ineffective before the late 1980s?
2. Why has macroeconomic volatility declined since the late 1980s?
The long and at first seemingly salutary reign of Greenspan the Great (1987–2006)wohlstetter.typepad.com/letterfromthecapitol/2006/02/greenspan_the_g.html and the auspicious beginning of the rule of Bernanke the Bald (2006–present)www.princeton.edu/pr/pictures/a-f/bernanke/bernanke-03-high.jpg temporarily provided the Fed with something it has rarely enjoyed in its nearly century-long existence, the halo of success and widespread approbation. While it would be an exaggeration to call Federal Reserve Board members the Keystone Kops of monetary policy, the Fed’s history is more sour than sweet.
Central bankers use tools like open market operations, the buying and selling of assets in the open market, to influence the money supply and interest rates. If they decrease rates, businesses and people will want to borrow more to build factories and offices, buy automobiles, and so forth, thus stimulating the economy. If they increase rates, the opposite will occur as businesses and people find it too costly to purchase big ticket items like houses, boats, and cars. Unlike communist central planners, central bankers do not try to directly run the economy or the various economic entities that compose it, but they do try to steer aggregate behavior toward higher levels of output. In that sense, central banks are the last bastions of central planning in otherwise free market economies. And central planning,en.Wikipedia.org/wiki/Planned_economy as the Communists and the Austrian economists who critiqued them discovered, is darn difficult.en.Wikipedia.org/wiki/Austrian_School
This is not a history textbook, but the past can often shed light on the present. History warns us to beware of claims of infallibility. In this case, however, it also provides us with a clear reason to be optimistic. Between 1985 or so and 2007, the U.S. macroeconomy, particularly output, was much less volatile than previously. That was a happy development for the Fed because it, like most other central banks, is charged with stabilizing the macroeconomy, among other things. The Fed in particular owes its genesis to the desire of Americans to be shielded from financial panics and economic crises.
The Fed itself took credit for almost 60 percent of the reduction in volatility. (Is anyone surprised by this? Don’t we all embrace responsibility for good outcomes, but eschew it when things turn ugly?) Skeptics point to other causes for the Great Calm, including dumb luck; less volatile oil prices (the 1970s were a difficult time in this regard);www.imf.org/external/pubs/ft/fandd/2001/12/davis.htmless volatile total factor productivity growth;en.Wikipedia.org/wiki/Total_factor_productivity and improvements in management, especially just-in-time inventory techniques, which has helped to reduce the inventory gluts of yore.http://en.Wikipedia.org/wiki/Just-in-time_(business) Those factors all played roles, but it also appears that the Fed’s monetary policies actually improved. Before Paul Volcker (1979–1987), the Fed engaged in pro-cyclical monetary policies. Since then, it has tried to engage in anti-cyclical policies. And that, as poet Robert Frost wrote in “The Road Not Taken,” has made all the difference.www.bartleby.com/119/1.html
For reasons that are still not clearly understood, economies have a tendency to cycle through periods of boom and bust, of expansion and contraction. The Fed used to exacerbate this cycle by making the highs of the business cycle higher and the lows lower than they would otherwise have been. Yes, that ran directly counter to one of its major missions. Debates rage whether it was simply ineffective or if it purposely made mistakes. It was probably a mixture of both that changed over time. In any event, we needn’t “go there” because a simple narrative will suffice.
The Fed was conceived in peace but born in war. As William SilberIn the interest of full disclosure, Silber was once my colleague, but he is also the co-author of a competing, and storied, money and banking textbook. points out in his book When Washington Shut Down Wall Street, the Federal Reserve was rushed into operation to help the U.S. financial system, which had been terribly shocked, economically as well as politically, by the outbreak of the Great War (1914–1918) in Europe.www.pbs.org/greatwar At first, the Fed influenced the monetary base (MB) through its rediscounts—it literally discounted again business commercial paper already discounted by commercial banks. A wholesaler would take a bill owed by one of its customers, say, a department store like Wanamaker’s, to its bank. The bank might give \$9,950 for a \$10,000 bill due in sixty days. If, say, thirty days later the bank needed to boost its reserves, it would take the bill to the Fed, which would rediscount it by giving the bank, say, \$9,975 in cash for it. The Fed would then collect the \$10,000 when it fell due. In the context of World War I, this policy was inflationary, leading to double-digit price increases in 1919 and 1920. The Fed responded by raising the discount rate from 4.75 to 7 percent, setting off a sharp recession.
The postwar recession hurt the Fed’s revenues because the volume of rediscounts shrank precipitously. It responded by investing in securities and, in so doing, accidentally stumbled upon open market operations. The Fed fed the speculative asset bubble of the late 1920s, then sat on its hands while the economy crashed and burned in the early 1930s. Here’s another tidbit: it also exacerbated the so-called Roosevelt Recession of 1937–1938 by playing with fire, by raising the reserve requirement, a new policy placed in its hands by FDR and his New Dealers in the Banking Act of 1935.
During World War II, the Fed became the Treasury’s lapdog. Okay, that is an exaggeration, but not much of one. The Treasury said thou shalt purchase our bonds to keep the prices up (and yields down) and the Fed did, basically monetizing the national debt. In short, the Fed wasn’t very independent in this period. Increases in the supply of some items, coupled with price controls and quantity rationing, kept the lid on inflation during the titanic conflict against Fascism, but after the war the floodgates of inflation opened. Over the course of just three years, 1946, 1947, and 1948, the price level jumped some 30 percent. There was no net change in prices in 1949 and 1950, but the start of the Korean War sent prices up another almost 8 percent in 1951, and the Fed finally got some backbone and stopped pegging interest rates. As the analysis of central bank independence suggests, inflation dropped big time, to 2.19 percent in 1952, and to less than 1 percent in 1953 and 1954. In 1955, prices actually dropped slightly, on average.
This is not to say, however, that the Fed was a fully competent central bank because it continued to exacerbate the business cycle instead of ameliorating it. Basically, in booms (recessions) business borrowing and the supply of bonds would increase (decrease), driving rates up (down). (For a review of this, see Chapter 5.) The Fed, hoping to keep interest rates at a specific rate, would respond by buying (selling) bonds in order to drive interest rates back down (up), thus increasing (decreasing) MB and the money supply (MS). So when the economy was naturally expanding, the Fed stoked its fires and when it was contracting, the Fed put its foot on its head. Worse, if interest rates rose (bond prices declined) due to an increase in inflation (think Fisher Equation), the Fed would also buy bonds to support their prices, thereby increasing the MS and causing yet further inflation. This, as much as oil price hikes, caused the Great Inflation of the 1970s. Throughout the crises of the 1970s and 1980s, the Fed toyed around with various targets (M1, M2, fed funds rate), but none of it mattered much because its pro-cyclical bias remained.
Stop and Think Box
Another blunder made by the Fed was Reg Q, which capped the interest rates that banks could pay on deposits. When the Great Inflation began in the late 1960s, nominal interest rates rose (think Fisher Equation) above those set by the Fed. What horror directly resulted? What Fed goal was thereby impeded?
Shortages known as credit crunches resulted. Whenever p* > preg, shortages result because the quantity demanded exceeds the quantity supplied by the market. Banks couldn’t make loans because they couldn’t attract the deposits they needed to fund them. That created much the same effect as high interest rates—entrepreneurs couldn’t obtain financing for good business ideas, so they wallowed, decreasing economic activity. In response, banks engaged in loophole mining.
By the late 1980s, the Fed, under Alan Greenspan, finally began to engage in anti-cyclical policies, to “lean into the wind” by raising the federal funds rate before inflation became a problem and by lowering the federal funds rate at the first sign of recession. Since the implementation of this crucial insight, the natural swings of the macroeconomy have been much more docile than hitherto, until the crisis of 2007–2008, that is. The United States experienced two recessions (July 1990–March 1991 and March 2001–November 2001)www.nber.org/cycles/cyclesmain.html but they were so-called soft landings, that is, short and shallow. Expansions have been longer than usual and not so intense. Again, some of this might be due to dumb luck (no major wars, low real oil prices [until summer 2008 that is]) and better technology, but there is little doubt the Fed played an important role in the stabilization.
Of course, past performance is no guarantee of future performance. (Just look at the New York Knicks.) As the crisis of 2007–2008 approached, the Fed resembled a fawn trapped in the headlights of an oncoming eighteen-wheeler, too afraid to continue on its path of raising interest rates and equally frightened of reversing course. The result was an economy that looked like road kill. Being a central banker is a bit like being Goldilocks. It’s important to get monetary policy just right, lest we wake up staring down the gullets of three hungry bears. (I don’t mean Stephen Colbert’s bearswww.youtube.com/watch?v=KsTVK9Cv9U8 here, but rather bear markets.)
key takeaways
• The Fed was generally ineffective before the late 1980s because it engaged in pro-cyclical monetary policies, expanding the MS and lowering interest rates during expansions and constricting the MS and raising interest rates during recessions, the exact opposite of what it should have done.
• The Fed was also ineffective because it did not know about open market operations (OMO) at first, because it did not realize the damage its toying with rr could cause after New Dealers gave it control of reserve requirements, and because it gave up its independence to the Treasury during World War II.
• The Fed’s switch from pro-cyclical to anti-cyclical monetary policy, where it leans into the wind rather than running with it, played an important role in decreased macroeconomic volatility, although it perhaps cannot take all of the credit because changes in technology, particularly inventory control, and other lucky events conspired to help improve macro stability over the same period.
• Future events will reveal if central banking has truly and permanently improved. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/17%3A_Monetary_Policy_Targets_and_Goals/17.01%3A_A_Short_History_of_Fed_Blunders.txt |
learning objective
1. What trade-offs do central banks face and how do they confront them?
Central banks worldwide often find themselves between a rock and a hard place. The rock is price stability (inflation control) and the hard place is economic growth and employment. Although in the long run the two goals are perfectly compatible, in the short run, they sometimes are not. In those instances, the central bank has a difficult decision to make. Should it raise interest rates or slow or even stop MS growth to stave off inflation, or should it decrease interest rates or speed up MS growth to induce companies and consumers to borrow, thereby stoking employment and growth? In some places, like the European Union, the central bank is instructed by its charter to stop inflation. “The primary objective of the European System of Central Banks,” the Maastricht Treaty clearly states, “shall be to maintain price stability. Without prejudice to the objective of price stability, the ESCB shall support the general economic policies in the Community” including high employment and economic growth. The Fed’s charter and the Dodd-Frank Act of 2010, by contrast, instruct the Fed to ensure price stability, maximum employment, and financial stability. Little wonder that the Fed has not held the line on inflation as well as the European Central Bank (ECB), but unemployment rates in the United States are generally well below those of most European nations. (There are additional reasons for that difference that are not germane to the discussion here.)
Do note that almost nobody wants 100 percent employment, when everyone who wants a job has one. A little unemployment, called frictional unemployment, is a good thing because it allows the labor market to function more smoothly. So-called structural unemployment, when workers’ skills do not match job requirements, is not such a good thing, but is probably inevitable in a dynamic economy saddled with a weak educational system. (As structural unemployment increased in the United States, education improved somewhat, but not enough to ensure that all new jobs the economy created could be filled with domestic laborers.) So the Fed shoots for what is called the natural rate of unemployment. Nobody is quite sure what that rate is, but it is thought to be around 5 percent, give or take.
key takeaways
• The main trade-off that central banks face is a short-term one between inflation, which calls for tighter policy (higher interest rates, slower money growth), and employment and output, which call for looser policy (lower interest rates, faster money growth).
• Some central banks confront trade-offs by explicitly stating that one goal, usually price stability (controlling inflation), is of paramount concern.
• Others, including the Fed, confront the trade-off on an ad hoc, case-by-case basis.
17.03: Central Bank Targets
learning objectives
1. What is monetary targeting and why did it succeed in some countries and fail in others?
2. What is inflation targeting and why is it important?
Once a central bank has decided whether it wants to hold the line (no change [Δ]), tighten (increase i, decrease or slow the growth of MS), or ease (lower i, increase MS), it has to figure out how best to do so. Quite a gulf exists between the central bank’s goals (low inflation, high employment) and its tools or instruments (OMO, discount loans, changing rr). So it sometimes creates a target between the two, some intermediate goal that it shoots for with its tools, with the expectation that hitting the target’s bull’s-eye would lead to goal satisfaction:
TOOLS→TARGET→GOAL
In the past, many central banks targeted monetary aggregates like M1 or M2. Some, like Germany’s Bundesbank and Switzerland’s central bank, did so successfully. Others, like the Fed, the Bank of Japan, and the Bank of England, failed miserably. Their failure is partly explained by what economists call the time inconsistency problem, the inability over time to follow a good plan consistently. (Weight-loss diets suffer from the time inconsistency problem, too, and every form of procrastination is essentially time inconsistent.) Basically, like a wayward dieter or a lazy student (rare animals to be sure), they overshot their targets time and time again, preferring pleasure now at the cost of pain later.
Another major problem was that monetary targets did not always equate to the central banks’ goals in any clear way. Long lags between policy implementation and real-world effects made it difficult to know to what degree a policy was working—or not. Worse, the importance of specific aggregates as a determinant of interest rates and the price level waxed and waned over time in ways that proved difficult to predict. Finally, many central banks experienced a disjoint between their tools or operating instruments, which were often interest rates like the federal funds, and their monetary targets. It turns out that one can’t control both an interest rate and a monetary aggregate at the same time. To see why, study Figure 17.1. Note that if the central bank leaves the supply of money fixed, changes in the demand for money will make the interest rate jiggle up and down. It can only keep i fixed by changing the money supply. Because open market operations are the easiest way to conduct monetary policy, most central banks, as we’ve seen, eventually changed reserves to maintain an interest rate target. With the monetary supply moving round and round, up and down, it became difficult to hit monetary targets.
Central banks can control i or MS, but not both.
In response to all this, several leading central banks, beginning with New Zealand in 1990, have adopted explicit inflation targets. The result everywhere has been more or less the same: lower employment and output in the short run as inflation expectations are wrung out of the economy, followed by an extended period of prosperity and high employment. As long as it remains somewhat flexible, inflation targeting frees central bankers to do whatever it takes to keep prices in check, to use all available information and not just monetary statistics. Inflation targeting makes them more accountable because the public can easily monitor their success or failure. (New Zealand took this concept a step further, enacting legislation that tied the central banker’s job to keeping inflation within the target range.)
Stop and Think Box
What do you think of New Zealand’s law that allows the legislature to oust a central banker who allows too much inflation?
Well, it makes the central bank less independent. Of course, independence is valuable to the public only as a means of keeping inflation in check. The policy is only as good as the legislature. If it uses the punishment only to oust incompetent or corrupt central bankers, it should be salutary. If it ousts good central bankers caught in a tough situation (for example, an oil supply shock or war), the law may serve only to keep good people from taking the job. If the central banker’s salary is very high, the law might also induce him or her to try to distort the official inflation figures on which his or her job depends.
The Fed has not yet adopted explicit inflation targeting, though a debate currently rages about whether it should. And under Ben Bernanke, it moved to what some have called inflation targeting-lite, with a new policy of communicating with the public more frequently about its forecasts, which now run to three years instead of the traditional two.“The Federal Reserve: Letting Light In,” The Economist (17 November 2007), 88–89. As noted above, the Fed is not very transparent, and that has the effect of roiling the financial markets when expectations about its monetary policy turn out to be incorrect. It also induces people to waste a lot of time engaging in “Fed watching,” looking for clues about monetary policy. Reporters actually used to comment on the thickness of Greenspan’s briefcase when he went into Federal Open Market Committee (FOMC) meetings. No joke!www.amazon.com/Inside-Greenspans-Briefcase-Investment-Strategies/dp/007138913X
Why doesn’t the Fed, which is charged with maintaining financial market and price stability, adopt explicit targets? It may be that it does not want to be held accountable for its performance. It probably wants to protect its independence, but maybe more for its private interest (power) rather than for the public interest (low inflation). It may also be that the Fed has found the holy grail of monetary policy, a flexible rule that helps it to determine the appropriate federal funds target.
key takeaways
• Monetary targeting entails setting and attempting to meet growth rates of monetary aggregates such as M1 or M2.
• It succeeded in countries like Germany and Switzerland, where the central bank was committed to keeping inflation in check.
• In other countries, like the United States and the United Kingdom, where price stability was not the paramount goal of the central bank, the time inconsistency problem eroded the effectiveness of the targets.
• In short, like a dieter who can’t resist that extra helping at dinner and two desserts, the central banks could not stick to a good long-term plan day to day.
• Also, the connection between increases in particular aggregates and the price level broke down, but it took a long time for central bankers to realize it because the lag between policy implementation and real-world outcome was often many months and sometimes years.
• Inflation targeting entails keeping increases in the price level within a predetermined range, e.g., 1 and 2 percent per year.
• Countries whose central banks embraced inflation targeting often suffered a recession and high unemployment at first, but in the long run were able to achieve both price level stability and economic expansion and high employment.
• Inflation targeting makes use of all available information, not just monetary aggregates, and increases the accountability of central banks and bankers. That reduces their independence but not at the expense of higher inflation because inflation targeting, in a sense, is a substitute for independence. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/17%3A_Monetary_Policy_Targets_and_Goals/17.02%3A_Central_Bank_Goal_Trade-offs.txt |
learning objective
1. What is the Taylor Rule and why is it important?
Many observers suspect that the Fed under Greenspan and Bernanke has followed the so-called Taylor Rule, named after the Stanford University economist, John Taylor, who developed it. The rulestates that
fft = π + ff*r + ½(π gap) + ½(Y gap)
where
fft = federal funds target
π = inflation
ff*r = the real equilibrium fed funds rate
π gap = inflation gap (π – π target)
Y gap = output gap (actual output [e.g. GDP] − output potential)
So if the inflation target was 2 percent, actual inflation was 3 percent, output was at its potential, and the real federal funds rate was 2 percent, the Taylor Rule suggests that the fed funds target should be
fft = π + ff*r + ½(π gap) + ½(Y gap)
fft = 3 + 2 + ½(1) + ½(0)
fft = 5.5
If the economy began running a percentage point below its potential, the Taylor Rule would suggest easing monetary policy by lowering the fed funds target to 5 percent:
fft = 3 + 2 + ½(1) + ½(−1)
fft = 3 + 2 + .5 + −.5 = 5
If inflation started to heat up to 4 percent, the Fed should respond by raising the fed funds target to 6.5:
fft = 4 + 2 + ½(2) + ½(−1) = 6.5
Practice calculating the fed funds target on your own in Exercise 1.
exercise
1. Use the Taylor Rule—fft = π + ff*r + ½(π gap) + ½(Y gap)—to determine what the federal funds target should be if:
Inflation Equilibrium Real Fed Funds Rate Inflation Target Output Output Potential Answer: Fed Funds Target
0 2 1 3 3 1.5
1 2 1 3 3 3
2 2 1 3 3 4.5
3 2 1 3 3 6
1 2 1 2 3 2.5
1 2 1 1 3 2
1 2 1 4 3 3.5
1 2 1 5 3 4
1 2 1 6 3 4.5
7 2 1 7 3 14
Notice that as actual inflation exceeds the target, the Taylor Rule suggests raising the fed funds rate (tightening monetary policy). Notice too that as output falls relative to its potential, the rule suggests decreasing the fed funds rate (easier monetary policy). As output exceeds its potential, however, the rule suggests putting on the brakes by raising rates. Finally, if inflation and output are both screaming, the rule requires that the fed funds target soar quite high indeed, as it did in the early 1980s. In short, the Taylor Rule is countercyclical and accounts for two important Federal Reserve goals: price stability and employment/output.
The Taylor Rule nicely explains U.S. macroeconomic history since 1960. In the early 1960s, the two were matched: inflation was low, and growth was strong. In the latter part of the 1960s, the 1970s, and the early 1980s, actual ff* was generally well below what the Taylor Rule said it should be. In that period, inflation was so high we refer to the period as the Great Inflation. In the latter part of the 1980s, ff* was higher than what the Taylor Rule suggested. That was a period of weak growth but decreasing inflation. From 1990 or so until the early 2000s, a period of low inflation and high growth, the Taylor Rule and ff* were very closely matched. In the middle years of the first decade of the new millennium, however, the Fed kept ff* well below the Rule and thereby fueled the housing bubble that led to the 2007–8 crisis. Since then, the economy has been weak and little wonder: the Fed lowered rates to zero, but that was still well above the negative 7 percent or so called for by the rule. Figure 17.2 graphs the latter portion of the story.
Source: St. Louis Federal Reserve Economic Data (http://research.stlouisfed.org/fred2) and T. Pettinger (http://econ.economicshelp.org/2009/05/taylor-rule-and-interest-rates.html).
Stop and Think Box
Examine Figure 17.3 carefully. Assuming the Fed uses the Taylor Rule, what happened to inflation and output from mid-2003 until mid-2006. Then what happened?
Assuming that the Fed’s inflation target, the real equilibrium federal funds rate, and the economy’s output potential were unchanged in this period (not bad assumptions), increases in actual inflation and increases in actual output would induce the Fed, via the Taylor Rule, to increase its feds fund target. Both were at play but were moderating by the end of 2006, freezing the funds target at 5.25 percent, as shown in Figure 17.4 . Then the subprime mortgage crisis, recession, and Panic of 2008 struck, inducing the Fed quickly to lower its target to 3, then 2, then 1, then almost to zero.
None of this means, however, that the Fed will continue to use the Taylor Rule, if indeed it does so.www.frbsf.org/education/activities/drecon/9803.html Nor does it mean that the Taylor Rule will provide the right policy prescriptions in the future. Richard Fisher and W. Michael Cox, the president and chief economist of the Dallas Fed, respectively, believe that globalization makes it increasingly important for the Fed and other central banks to look at world inflation and output levels in order to get domestic monetary policy right.See Richard W. Fisher and W. Michael Cox, “The New Inflation Equation,” Wall Street Journal, April 6, 2007, A11.
Stop and Think Box
Foreign exchange rates can also flummox central bankers and their policies. Specifically, increasing (decreasing) interest rates will, ceteris paribus, cause a currency to appreciate (depreciate) in world currency markets. Why is that important?
The value of a currency directly affects foreign trade. When a currency is strong relative to other currencies (when each unit of it can purchase many units of foreign currencies), imports will be stimulated because foreign goods will be cheap. Exports will be hurt, however, because domestic goods will look expensive to foreigners, who will have to give up many units of their local currency. Countries with economies heavily dependent on foreign trade must be extremely careful about the value of their currencies; almost every country is becoming more dependent on foreign trade, making exchange rate policy an increasingly important one for central banks worldwide to consider.
key takeaways
• The Taylor Rule is a simple equation—fft = π + ff*r + ½( π gap) + ½(Y gap)—that allows central bankers to determine what their overnight interbank lending rate target ought to be given actual inflation, an inflation target, actual output, the economy’s potential output, and an estimate of the equilibrium real fed funds rate.
• When the Fed has maintained the fed funds rate near that prescribed by the Taylor Rule, the economy has thrived; when it has not, the economy has been plagued by inflation (when the fed funds rate was set below the Taylor rate) or low output (when the fed funds rate was set above the Taylor rate).
17.05: Suggested Reading
Blinder, Alan. Central Banking in Theory and Practice. Cambridge, MA: MIT Press, 1999.
Silber, William. When Washington Shut Down Wall Street: The Great Financial Crisis of 1914 and the Origins of America’s Monetary Supremacy. Princeton, NJ: Princeton University Press, 2007.
Taylor, John B. Monetary Policy Rules. Chicago, IL: University of Chicago Press, 2001. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/17%3A_Monetary_Policy_Targets_and_Goals/17.04%3A_The_Taylor_Rule.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Define foreign exchange and explain its importance.
2. Describe the market for foreign exchange.
3. Explain why countries shouldn’t be proud that it takes many units of foreign currencies to purchase a single unit of their currency.
4. Define purchasing power parity and explain its importance.
5. List and explain the long-run determinants of exchange rates.
6. List and explain the short-run determinants of exchange rates.
7. Define the interest parity condition and explain when and why it holds.
Thumbnail: Image by Clker-Free-Vector-Images from Pixabay
18: Foreign Exchange
Learning Objective
1. What is foreign exchange and why is it important?
Before we turn to monetary theory (gulp!), there is one more real-world financial market we need to investigate in this and the next chapter, the market for foreign currencies or foreign exchange, where the relative prices of national units of account or exchange rates are determined. Why should you care how many U.S. dollars (USD) it takes to buy a euro or a yen, a pound (sterling) or a dollar (of Canada or Australia, respectively)? If you plan to travel to any of those places, you’ll want to know so you can evaluate prices. Is €1,000 a good price for a hotel room? How about ¥1,000?The symbol for the euro, the currency of the European Union, is €. The symbol for the Japanese yen is ¥. But even if you remain your entire life in a small village in Alaska, one of Hawaii’s outer islands, Michigan’s Upper Peninsula, or the northern reaches of Maine, the value of USD will affect your life deeply, whether you know it or not. Come again? How could that possibly be?
Every nation in the world trades with other nations. Some trade more than others (little islands like Iceland, Mauritius, and Ireland lead the way, in percentage of gross domestic product [GDP] terms anyway) but all do it, even illicitly, when the United Nations says that they can’t because they’ve been bad.www.entemp.ie/trade/export/sanctions.htm#overview Conducting trade via barter isn’t practical in most circumstances. So we use money. But what happens when people who want to trade use different types of money, when their units of account are not the same? There are several solutions to that problem. The most frequent solution today is for one party, usually the buyer, to exchange the money of his or her country for the money of the seller’s country, then to consummate the transaction.
How does this affect you? Well, when the unit of account of your country, say, U.S. dollars (USD or plain \$), is strong, when it can buy many units of a foreign currency, say, Canadian dollars (C\$), Canadian goods look cheap to you. And we all know what happens when goods are cheap. So you stop drinking Bud and start drinking Moosehead. Instead of going to Manhattan to shop, you go to Toronto, and check out some Maple Leafs, Raptors, and Blue Jays games while you’re at it. (You go in April, that magical month for sports fans.) When the Blue Jays game gets snowed out, you go instead to the Canadian ballet. (Do you have any sense of humor at all?) You might even consider buying a Canadian computer or automobile. (Okay, let’s not get crazy.) The point is you and your fellow Americans import more from Canada.
The Canadians are very happy about this, but they are not so thrilled with American goods, which look dreadfully expensive to them because they have to give up many of their dear loonies to buy USD. So they too eschew Manhattan for Toronto and drink Moosehead rather than Bud. In other words, U.S. exports to Canada fall. And because Canada is a major U.S. trading partner, that does not bode well for the U.S. economy overall, or U.S. residents, even those in remote villages. If USD were to continue to appreciate (strengthen, buy yet more C\$), the situation would grow increasingly worse. Were the dollar to depreciate (weaken, buy fewer C\$), the situation would ameliorate and eventually reverse, and you’d go back to Bud, Manhattan shopping sprees, and the Yankees, Mets, Knicks, Nets, Islanders, and Rangers.
Stop and Think Box
A chain of pizza parlors in the southwestern part of the United States accepts Mexican pesos in payment for its pizzas. Many U.S. retail stores located near the Canadian border accept Canadian currency. (Many Canadian businesses accept U.S. dollars, too.) Why do these businesses accept payment in a foreign currency?
Well, maybe they are good folks who want to help out others and maybe some of them need foreign currencies to purchase supplies. But those are at best ulterior motives in most instances because the exchange rate offered usually heavily favors the retailer. For example, the pizza parlor’s exchange rate was 12 pesos to the dollar when the market exchange rate was closer to 11. So a \$10 pizza costs 120 pesos (10 × 12) instead of 110 pesos (10 × 11). In short, it makes a tidy and largely riskless profit from the offer.
Or imagine you don’t have many assets or a high income, but you need an automobile. You see a commercial that says that there are three V-dubs (German-made Volkswagen automobile models) under \$17,000. You think you can afford that and begin to make arrangements to buy a Rabbit. But look in Figure 18.1 at what happens to the dollar price of a Rabbit when the exchange rate changes. Say that the Rabbit of your dreams costs €17,000. When the dollar and the euro are at parity (1 to 1), the Rabbit costs \$17,000. If the dollar depreciates (buys fewer euro, and more USD are needed to buy €1), the Rabbit grows increasingly costly to you. If the dollar appreciates (buys more euro, and fewer USD are needed to buy €1), that cool automotive bunny gets very cheap indeed!
Now imagine that in your remote little town you make fans for French computers that you can sell profitably for \$10.00. The dollar’s movements will affect you as a producer, but in precisely the opposite way as it affected you as a consumer. When the dollar appreciates against the euro, your computer fans grow more expensive in France (and indeed the entire euro zone), which will undoubtedly cut into sales and maybe your salary or your job. When the dollar depreciates, the euro price of your fans plummet, sales become increasingly brisk, and you think about buying a Cadillac (a more expensive American car).
KEY TAKEAWAYS
• Foreign exchange is the trading of different national currencies or units of account.
• It is important because the exchange rate, the price of one currency in terms of another, helps to determine a nation’s economic health and hence the well-being of all the people residing in it.
• The exchange rate is also important because it can help or hurt specific interests within a country: exporters tend to be helped (hurt) by a weak (strong) domestic currency because they will sell more (less) abroad, while consumers are hurt (helped) by a strong currency because imported goods will be more (less) expensive for them. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/18%3A_Foreign_Exchange/18.01%3A_The_Economic_Importance_of_Currency_Markets.txt |
Learning Objectives
1. What is the structure of the foreign exchange market?
2. Why shouldn’t countries be proud that it takes many units of foreign currencies to purchase a single unit of their currency?
We can’t teach you how to predict future exchange rates because the markets are highly efficient (free floating exchange rates follow a random walk) and because many exchange rates are more or less heavily influenced by monetary authorities. Some countries try to maintain fixed exchange rates by pegging their respective currencies to gold or some other currency, like the U.S. dollar, euro, or Swiss franc. Many others allow exchange rates to float within a range or band, some of which are broader than others. Other countries allow the value of their currencies to freely float, determined solely by supply and demand. Nations that fix their exchange rates or engage in a so-called dirty float (within bands) find it necessary to make periodic adjustments to both the width and range of the bands over time. So trying to make a living predicting exchange rate changes is difficult indeed. That said, you should be able to post-dict why floating exchange rates changed or, in other words, to narrate plausible reasons why past changes, like those depicted in Figure 18.2 and Figure 18.3 , may have occurred. (This is similar to what we did with interest rates.)
The figures, like the exchange rates in Figure 18.1 , are mathematical reciprocals of each other. Both express the exchange rate but from different perspectives. Figure 18.2 asks how many USD it took to buy \$C1, or mathematically USD/C\$. Figure 18.3 asks how many \$C it took to buy 1 USD, or C\$/USD. In Figure 18.2 , USD weakens as the line moves up the chart because it takes more USD to buy \$C1. The dollar strengthens as it moves down the chart because it takes fewer USD to buy \$C1. Everything is reversed in Figure 18.3 , where upward movements indicate a strengthening of USD (a weakening of \$C) because it takes more \$C to buy 1 USD, and downward movements indicate a weakening of USD (a strengthening of \$C) because it takes fewer \$C to buy 1 USD. Again, the figures tell the same story: USD strengthened vis-à-vis the Canadian dollar from 2000 to early 2003, then weakened considerably, experiencing many ups and downs along the way due to relative differences in inflation, interest, and productivity rates in each country. USD appreciated during the financial crisis in an apparent “flight to quality” but weakened again during the 2010 recovery, bringing it back to parity with the Looney. We could do the same exercise ad nauseam (Latin for “until we vomit”) with every pair of currencies in the world. But we won’t because the mode of analysis would be precisely the same.
We’ll concentrate on the spot exchange rate, the price of one currency in terms of another today, and currencies that are allowed to float freely or at least within wide bands. The forward exchange rate, the price today of future exchanges of foreign currencies, is also important but follows the same general principles as the spot market. Both types of trading are conducted on a wholesale (large-scale) basis by a few score-big international banks in an over-the-counter (OTC) market. Investors and travelers can buy foreign currencies in a variety of ways, via everything from brokerage accounts to airport kiosks, to their credit cards. Retail purchasers give up more of their domestic currency to receive a given number of units of a foreign currency than the wholesale banks do. (To put the same idea another way, they receive fewer units of the foreign currency for each unit of their domestic currency.) That’s partly why the big banks are in the business. The big boys also try to earn profits via speculation, buying (selling) a currency when it is low (high), and selling (buying) it when it is high (low). (They also seek out arbitrage opportunities, but those are rare and fleeting.) Each day, over \$1 trillion of wholesale-level (\$1 million plus per transaction) foreign exchange transactions take place.
Before we go any further, a few words of caution. Students sometimes think that a strong currency is always better than a weak one. That undoubtedly stems from the fact that strong sounds good and weak sounds bad. As noted above, however, a strong (weak) currency is neither good nor bad but rather advantageous (disadvantageous) for imports/consumers and disadvantageous (advantageous) for exports/producers of exportable goods and services. Another thing: no need to thump your chest patriotically because it takes many units of foreign currencies to buy 1 USD. That would be like proclaiming that you are “hot” because your temperature is 98.6 degrees Fahrenheit instead of 37 degrees Centigrade (that’s the same temperature, measured two different ways) or that you are 175 centimeters tall instead of 68.9 inches (another equivalent). Most countries have a very small unit of account compared to the United States, that is all. Other countries, like Great Britain, have units of account that are larger than the USD, so it takes more than 1 USD to buy a unit of those currencies. The nominal level of the exchange rate in no way means that one country or economy is better than another. Changes in exchange rates, by contrast, have profound consequences, as we have seen. They also have profound causes.
KEY TAKEAWAYS
• At the wholesale level, the market for foreign exchange is conducted by a few score large international players in huge (> \$1 trillion per day) over-the-counter spot and forward markets.
• Those markets appear to be efficient in the sense that exchange rates follow a random walk and arbitrage opportunities, which appear infrequently, are quickly eliminated.
• In the retail segment of the market, tourists, business travelers, and small-scale investors buy and sell foreign currencies, including physical media of exchange (paper notes and coins), where appropriate.
• Compared to the wholesale (\$1 million plus per transaction) players, retail purchasers of a foreign currency obtain fewer units of the foreign currency, and retail sellers of a foreign currency receive fewer units of their domestic currency.
• The nominal level of exchange rates is essentially arbitrary. Some countries simply chose a smaller unit of account, a smaller amount of value. That’s why it often takes over ¥100 to buy 1 USD. But if the United States had chosen a smaller unit of account, like a cent, or if Japan had chosen a larger one (like ¥100 = ¥1), the yen and USD (and the euro, as it turns out) would be roughly at parity.
• A strong currency is not necessarily a good thing because it promotes imports over exports (because it makes foreign goods look so cheap and domestic goods look so expensive to foreigners).
• A weak currency, despite the loser-sound to it, means strong exports because domestic goods now look cheap both at home and abroad. Imports will decrease, too, because foreign goods will look more expensive to domestic consumers and businesses. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/18%3A_Foreign_Exchange/18.02%3A_Determining_the_Exchange_Rate.txt |
Learning Objectives
1. What is purchasing power parity?
2. What are the other long-run determinants of exchange rates?
If transaction costs are zero, identical goods should have the same price no matter what unit of account that price is expressed in. Or so says the law of one price. The reason is clear: if they did not, arbitrageurs would buy where the good was cheapest and sell where it was highest until the prices were equalized. Where transaction costs are nontrivial or goods are similar but not identical, we don’t expect a single price, but rather a band or range of prices. So if product X cost \$100 in Country Y and \$110 in Country Z, and it costs \$10 to transport X from Y to Z, there would be no arbitrage opportunity and the price differential could persist. If the price of X rose in Z to \$120, we’d expect it to increase in Y to at least \$110, or arbitrageurs would start buying it in Y and selling it in Z until the prices were within \$10 of each other. Similarly, Japanese-style beer is not the same as U.S.-style beer. But it is close enough that we would not expect the prices to vary widely or otherwise consumers would dump Bud, Miller, and Coors in favor of Kirin and Sapporo (or vice versa, as the case may be).
This sort of analysis has led economists to apply the law of one price to entire economies in what they call the theory of purchasing power parity (PPP), which predicts that, in the long run, exchange rates will reflect price level changes. In other words, higher rates of inflation in Country A compared to Country B will cause Country A’s currency to depreciate vis-à-vis Country B’s currency in the long run. In the short run, however, matters are quite different, as Figure 18.4 shows. If PPP held in the short run, USD should have appreciated against the pound (the blue line should be above zero) every year in which inflation in the United Kingdom exceeded inflation in the United States (the red line is above zero), and vice versa. Clearly, that was not the case. But PPP has the long-run right, in sign but not quite in magnitude. Between 1975 and 2005, prices rose in Great Britain a shade under 205 percent all told. In that same period, they rose just under 142 percent in the United States. In other words, prices rose about 44 percent ([205 − 142]/142) more in Britain than in the United States. Over that same period, the pound sterling depreciated 22 percent against USD (from £.4505 to £.5495 per USD or from \$2.22 to \$1.82 per £1), just as PPP theory predicts it should have. But why did the pound weaken only 22 percent against the dollar?
For starters, not all goods and services are traded internationally. Land and haircuts come immediately to mind, but many other things as well when you think about it hard enough. There is no reason for prices of those goods to be the same or even similar in different countries. Arbitrageurs cannot buy low in one place and sell high in another because transaction costs are simply too high. (For example, you could get a great haircut in Malaysia for fifty cents but it would cost several thousand dollars and several days to get there and back.)
In addition, three other factors affect exchange rates in the long run: relative trade barriers, differential preferences for domestic and foreign goods, and differences in productivity. Tariffs (taxes on imported goods), quotas (caps on the quantity of imported goods), and sundry nontariff barriers (NTBs) to trade Figure 18.5 summarizes the discussion.
KEY TAKEAWAYS
• Purchasing power parity (PPP) is the application of the law of one price to entire economies.
• It predicts that exchange rates will adjust to relative price level changes, to differential inflation rates between two countries. They indeed do, but only in the long run and not to precisely the same degree.
• In the long run, exchange rates are determined by PPP (as described above) and relative differences in productivity, trade barriers, and import and export demand.
• As Country A’s price level and import demand increase, and as Country A’s productivity, trade barriers, and export demand decrease vis-à-vis another Country B, Country A’s currency depreciates and Country B’s appreciates.
• Basically, anything that lowers demand for Country A’s goods, services, and currency induces the currency to depreciate; anything that increases demand for Country A’s stuff induces the currency to appreciate in response.
• Higher inflation relative to Country B makes Country A’s stuff look more expensive, lowering demand and inducing depreciation.
• If economic actors in Country A take a fancy to Country B’s stuff, they will import it even if Country A’s currency weakens, making Country B’s stuff more expensive. Reductions in trade barriers (lower tariffs, higher quotas, fewer NTBs) will exacerbate that.
• If, for whatever reason, economic actors in Country B don’t like Country A’s stuff as much as they used to, they’ll buy less of it unless Country A’s currency depreciates, making it cheaper.
• Finally, if Country A’s productivity slips relative to Country B’s, Country A’s goods and services will get more expensive than Country B’s so it will sell in Country B only if its currency depreciates. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/18%3A_Foreign_Exchange/18.03%3A_Long-Run_Determinants_of_Exchange_Rates.txt |
Learning Objectives
1. What are the short-run determinants of exchange rates?
2. What is the interest parity condition and when and why does it hold?
As Figure 18.6 shows, exchange rates can be very volatile. In a single month (June 2006), the South African rand depreciated from about 6.6 to 7.4 rand to 1 USD, with various ups and downs along the way. The rand then reversed course and appreciated toward 7.1 rand/USD. Such fluctuations are by no means unusual. Why do exchange rates undergo such gyrations? Figure 18.7 summarizes the major factors affecting exchange rates in the short run. Note that it looks very much like Figure 18.5 but with three key differences. First, instead of actual relative price levels, trade barriers, exports, imports, and productivity driving changes, expectations of their future direction drive changes. This should not be surprising given the basic rationality of most financial markets. Second, two additional variables have entered the equation: foreign and domestic interest rates. The intuition behind the first variables is the same as those discussed above, but in the short run, the mere expectation of a change in a variable moves the market. The intuition behind the interest rates is also straightforward. If something increases demand for the domestic currency, like domestic interest rates increasing or foreign interest rates decreasing, it will appreciate. If something reduces demand for the domestic currency, like domestic interest rates decreasing or foreign interest rates increasing, it will depreciate. Because expectations and interest rates change frequently, so, too, do exchange rates under the current floating rate regime.
Stop and Think Box
There is an important distinction between real and nominal interest rates. Through the Fisher Equation, we know that the nominal interest rate equals the real interest rate plus inflation expectations. Is that distinction important when considering foreign exchange markets?
Absolutely, and here is why. An increase in nominal interest rates caused by a rise in the real interest rate would leave expectations about future exchange rates unchanged and hence would cause the domestic currency to appreciate. An increase in nominal interest rates caused solely by an increase in inflation expectations, by contrast, would cause the expected future exchange rate to decrease through the expected and actual price level effects. So the domestic currency would depreciate instead.
The third difference between the long and short terms is that, in the short term, the expectation of the future direction of the exchange rate plays an important role. The easiest way to see this is to compare two investments with a one-year time horizon: a domestic (say, USD-denominated) bank account that pays 5 percent per year and a foreign (say, pound-sterling-denominated) account paying 6 percent per year. Before you jump for the sterling (6 > 5), you need to consider that, in a year, you’re going to want dollars again because you reside in the United States and need USD to buy lunch, pay the rent, and so forth. If the dollar appreciates more than 1 percent over the course of the year, you’d be better off with the dollar deposit. Say that you invest \$10,000 in sterling when the exchange rate is \$1.50/£1 or, in other words, £.6667/\$1. Your investment today would buy 10,000 × .6667 = £6,667. Multiply that by the interest on the sterling deposit (1.06) and you get £7,067.02 in a year. If the exchange rate is unchanged, you’re cool because you’ll have 7,067.02 × 1.50 = \$10,600.53, which is greater than \$10,000 invested at 5 percent, which equals 10,000 × 1.05 = \$10,500.00. But what if, over the course of that year, the dollar appreciated strongly, to \$1.25 per pound? Then your £7,067.02 would buy you only 7,067.02 × 1.25 = \$8,833.78. You just took a bath, and not the good kind, because you should have invested in the dollar deposit! Of course, if the dollar depreciated to, say, \$1.75, you’ll be pheeling phat at 7,067.02 × 1.75 = \$12,367.29.
Stop and Think Box
Increases in the growth rate of the money supply will eventually cause the price level to increase, but its effect on nominal interest rates in the short term can vary: rates can dip strongly, then rebound but remain permanently lower than the previous level, decrease temporarily before increasing permanently, or increase immediately. What does this mean for the market for foreign exchange?
The fact that a major short-run determinant of the exchange rate, foreign and domestic interest rates, moves around a lot helps to explain why the foreign exchange market is volatile. That market is also volatile because expectations of many things, including future differential price levels, productivity, and trading levels, will affect it via the expected future exchange rate (the Eefvariable in the equation introduced below).
As noted above, the markets for foreign exchange and bonds/deposits are highly competitive and efficient, so we wouldn’t expect discrepancies in returns to last long. The law of one price, of course, applies most stringently to financial markets in which international capital mobility is allowed because huge sums of money (deposits) can be sent hither and thither almost immediately and cost-free, ideal conditions for the law of one price to prevail. So what economists call the interest parity condition often holds (is true). More formally,
\[i^D = i^F - \dfrac{E^{ef} - E^t}}{E^t}\]
where:
• iD = domestic interest rate
• iF = foreign interest rate
• Eef = expected future exchange rate
• Et = exchange rate today
(Note: express all variables as decimals, e.g. 6% = .06; 5 = 500%.)
In plain English, if the so-called interest parity condition holds, the domestic interest rate should equal the foreign interest rate minus the expected appreciation of the domestic currency. If iF is > iD, the domestic currency must be expected to appreciate; otherwise, everyone would sell their domestic deposits to buy the foreign ones. If iF is < iD, the domestic currency must be expected to depreciate (have a negative sign, two of which make a positive, augmenting iF); otherwise, everyone would sell the foreign deposits and buy the domestic ones. If you find this confusing, there is another, more intuitive way of stating it: the domestic interest rate must equal the foreign interest rate plus the expected appreciation of the foreign currency. If iF is < iD, the expected appreciation of the foreign currency compensates for the lower interest rate, allowing equilibrium. You can practice calculating interest parity in the following Exercise.
EXERCISE
1. Use the interest parity formula (iD = iF − (Eef − Et)/Et) to calculate the following:
Foreign Interest Rate Expected Future Exchange Rate Exchange Rate Today Answer: Domestic Interest Rate
0.05 1 1 0.05
0.05 1.01 1 0.04
0.05 1.02 1 0.03
0.05 1.03 1 0.02
0.05 0.9 1 0.15
0.05 0.8 1 0.25
0.05 0.7 1 0.35
0.06 1 1 0.06
0.06 1 1.1 0.15
0.06 1 1.2 0.23
0.06 1 1.3 0.29
0.06 1 0.99 0.05
0.06 1 0.95 0.01
0.1 1 0.95 0.05
0.15 1 1 0.15
0.15 1.1 1 0.05
0.15 1 10 1.05
Expected Future Exchange Rate Exchange Rate Today Domestic Interest Rate Answer: Foreign Interest Rate
1 1 0.02 0.02
1.1 1 0.02 0.12
1.2 1 0.02 0.22
1.3 1 0.02 0.32
0.9 1 0.11 0.01
0.8 1 0.21 0.01
0.7 1 0.31 0.01
1 1 0.1 0.10
1 1.1 0.1 0.01
1 1.2 0.2 0.03
1 1.3 0.25 0.02
1 0.9 0.1 0.21
1 0.8 0.1 0.35
1 0.7 0.1 0.53
1 1 0 0.00
10 1 0 9.00
1 5 1 0.20
KEY TAKEAWAYS
• Because foreign exchange markets are efficient, in the short run, the mere expectation of changes in relative inflation, exports, imports, trade barriers, and productivity moves the markets.
• Also in the short run, differences in interest rates and expectations of the future exchange rate play key roles in exchange rate determination.
• The interest parity condition equates the domestic interest rate to the foreign interest rate minus the appreciation of the domestic currency. (Or, by rearranging the terms, it equates the foreign interest rate to the domestic interest rate plus the expected appreciation of the domestic currency.)
• The interest parity condition holds whenever there is capital mobility, whenever deposits (units of account) can move freely and cheaply from one country to another.
• It holds under those conditions because if it didn’t, an arbitrage condition would exist, inducing arbitrageurs to sell the overvalued deposit (side of the equation) and buy the undervalued one until the equation held. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/18%3A_Foreign_Exchange/18.04%3A_Short-Run_Determinants_of_Exchange_Rates.txt |
Learning Objective
1. How can the market for foreign exchange be modeled?
Like other markets, the market for foreign exchange can be graphically modeled to help us visualize the action, as in Figure 18.8 . There are a number of ways to do this, but perhaps the easiest is to plot the quantity of dollars on the horizontal and the exchange rate, stated in terms of foreign divided by domestic (say, yen or ¥/USD) on the vertical. The supply of dollar assets will be perfectly vertical, unchanged at every exchange rate. The demand for dollars, by contrast, will have the usual downward slope because, at higher exchange rates, fewer dollar assets will be demanded than at lower exchange rates. So at ¥120 to 1 USD, relatively few dollar-denominated assets will be demanded compared to only ¥100 or ¥80 per dollar. The intersection of the supply and demand curves will determine E*, which in this case is ¥100/\$, and q*, which in this case is \$100 billion.
We can immediately see that, holding all else constant, anything that increases demand for dollar-denominated assets (shifts the demand curve to the right), including an increase in the domestic interest rate, a decrease in the foreign interest rate, or an increase in Eef (for any reason, including the variables in Figure 18.5 ), will cause the dollar to appreciate (E* to increase when stated in terms of foreign/domestic or in this case ¥/\$). Anything that causes demand for dollar-denominated assets, including a decrease in the domestic interest rate, an increase in the foreign interest rate, or a decrease in Eef, to decrease (shift the demand curve to the left) will cause the dollar to depreciate (E* to decrease when stated in terms of foreign/domestic).
Stop and Think Box
Post-dict Figure 18.9 using Figure 18.10 and Figure 18.11 .
From the beginning of 2000 until early 2002, the dollar appreciated against the euro, moving from rough parity (1 to 1) to €1.10 to €1.20 per USD. This isn’t surprising given that U.S. interest rates (proxied here by the fed funds rate ff*) were higher than euro zone interest rates (proxied here by EONIA, the ECB’s fed funds equivalent). Moreover, except for the spike in early 2001, the price level in the United States did not rise appreciably faster than prices in the euro zone did. Since mid-2002, prices in the United States have risen faster than prices in the euro zone. (There are more periods when the consumer price index [CPI] in the United States was > the CPI in the euro zone, for example, when the red line is above zero.) Since mid-2004, interest rates have risen more quickly in the United States than in the euro zone, but not enough to offset the higher U.S. inflation rate. Fears of a recession in the United States and slowing U.S. productivity also dragged on the dollar.
KEY TAKEAWAYS
• The market for foreign exchange can be modeled in many different ways.
• The easiest way, perhaps, is to think of the price of a domestic currency, say, USD.
• There is a given quantity of USD that is insensitive to the exchange rate.
• Demand for the domestic currency slopes downward for the usual reasons that economic actors demand more of an asset when it is cheaper.
• The intersection of the two lines determines the exchange rate.
18.06: Suggested Reading
Galant, Mark, and Brian Dolan. Currency Trading for Dummies. Hoboken, NJ: John Wiley and Sons, 2007.
Shamah, Shani. A Foreign Exchange Primer. Hoboken, NJ: John Wiley and Sons, 2009. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/18%3A_Foreign_Exchange/18.05%3A_Modeling_the_Market_for_Foreign_Exchange.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Define the impossible trinity, or trilemma, and explain its importance.
2. Identify the four major types of international monetary regimes and describe how they differ.
3. Explain how central banks manage the foreign exchange (FX) rate.
4. Explain the benefits of fixing the FX rate, or keeping it within a narrow band.
5. Explain the costs of fixing the FX rate, or keeping it in a narrow band.
Thumbnail: Photo by Ethan McArthur on Unsplash
19: International Monetary Regimes
learning objectives
1. What is the impossible trinity, or trilemma, and why is it important?
2. What are the four major types of international monetary regimes and how do they differ?
The foreign exchange (foreign exchange rate (FX or forex)) market described in Figure 19.1 .
Note that those were the prevailing regimes. Because nations determine their monetary relationship with the rest of the world individually, some countries have always remained outside the prevailing system, often for strategic reasons. In the nineteenth century, for example, some countries chose a silver rather than a gold standard. Some allowed their currencies to float in wartime. Today, some countries maintain fixed exchange rates (usually against USD) or manage their currencies so their exchange rates stay within a band or range. But just as no country can do away with scarcity or asymmetric information, none can escape the trilemma (a dilemma with three components), also known as the impossible trinity.
In an ideal world, nations would like to have fixed exchange rates, capital mobility, and monetary policy discretion at the same time in order to reap their respective benefits: exchange rate stability for importers and exporters, liquid securities markets that allocate resources to their best uses globally, and the ability to change interest rates in response to foreign and domestic shocks. In the real world, however, trade-offs exist. If a nation lowers its domestic interest rate to stave off a recession, for example, its currency (ceteris paribus) will depreciate and hence exchange rate stability will be lost. If the government firmly fixes the exchange rate, capital will emigrate to places where it can earn a higher return unless capital flows are restricted/capital mobility is sacrificed.
As Figure 19.1 shows, only two of the three holy grails of international monetary policy, fixed exchange rates, international financial capital mobility, and domestic monetary policy discretion, have been simultaneously satisfied. Countries can adroitly change regimes when it suits them, but they cannot enjoy capital mobility, fixed exchange rates, and discretionary monetary policy all at once. That is because, to maintain a fixed exchange rate, a monetary authority (like a central bank) has to make that rate its sole consideration (thus giving up on domestic goals like inflation or employment/gross domestic product [GDP]), or it has to seal off the nation from the international financial system by cutting off capital flows. Each component of the trilemma comes laden with costs and benefits, so each major international policy regime has strengths and weaknesses, as outlined in Figure 19.2 .
Stop and Think Box
From 1797 until 1820 or so, Great Britain abandoned the specie standard it had maintained for as long as anyone could remember and allowed the pound sterling to float quite freely. That was a period of almost nonstop warfare known as the Napoleonic Wars. The United States also abandoned its specie standard from 1775 until 1781, from 1814 until 1817, and from 1862 until essentially 1873. Why?
Those were also periods of warfare and their immediate aftermath in the United States—the Revolution, War of 1812, and Civil War, respectively. Apparently during wartime, both countries found the specie standard costly and preferred instead to float with free mobility of financial capital. That allowed them to borrow abroad while simultaneously gaining discretion over domestic monetary policy, essentially allowing them to fund part of the cost of the wars with a currency tax, which is to say, inflation.
key takeaways
• The impossible trinity, or trilemma, is one of those aspects of the nature of things, like scarcity and asymmetric information, that makes life difficult.
• Specifically, the trilemma means that a country can follow only two of three policies at once: international capital mobility, fixed exchange rates, and discretionary domestic monetary policy.
• To keep exchange rates fixed, the central bank must either restrict capital flows or give up its control over the domestic money supply, interest rates, and price level.
• This means that a country must make difficult decisions about which variables it wants to control and which it wants to give up to outside forces.
• The four major types of international monetary regime are specie standard, managed fixed exchange rate, free float, and managed float.
• They differ in their solution, so to speak, of the impossible trinity.
• Specie standards, like the classical GS, maintained fixed exchange rates and allowed the free flow of financial capital internationally, rendering it impossible to alter domestic money supplies, interest rates, or inflation rates.
• Managed fixed exchange rate regimes like BWS allowed central banks discretion and fixed exchange rates at the cost of restricting international capital flows.
• Under a free float, free capital flows are again allowed, as is domestic discretionary monetary policy, but at the expense of the security and stability of fixed exchange rates.
• With a managed float, that same solution prevails until the FX rate moves to the top or bottom of the desired band, at which point the central bank gives up its domestic discretion so it can concentrate on appreciating or depreciating its currency. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/19%3A_International_Monetary_Regimes/19.01%3A_The_Trilemma_or_Impossible_Trinity.txt |
learning objective
1. What were the two major types of fixed exchange rate regimes and how did they differ?
Under the gold standard, nations defined their respective domestic units of account in terms of so much gold (by weight and fineness or purity) and allowed gold and international checks (known as bills of exchange) to flow between nations unfettered. Thanks to arbitrageurs, the spot exchange rate, the market price of bills of exchange, could not stray very far from the exchange rate implied by the definition of each nation’s unit of account. For example, the United States and Great Britain defined their units of account roughly as follows: 1 oz. gold = \$20.00; 1 oz. gold = £4. Thus, the implied exchange rate was roughly \$5 = £1 (or £.20 = \$1). It was not costless to send gold across the Atlantic, so Americans who had payments to make in Britain were willing to buy sterling-denominated bills of exchange for something more than \$5 per pound and Americans who owned sterling bills would accept something less than \$5 per pound, as the supply and demand conditions in the sterling bills market dictated. If the dollar depreciated too far, however, people would stop buying bills of exchange and would ship gold to Britain instead. That would decrease the U.S. money supply and appreciate the dollar. If the dollar appreciated too much, people would stop selling bills of exchange and would order gold shipped from Britain instead. That increased the U.S. money supply and depreciated the dollar. The GS system was self-equilibrating, functioning without government intervention (after their initial definition of the domestic unit of account).
As noted in Figure 19.2 and shown in Figure 19.3 , the great strength of the GS was exchange rate stability. One weakness of the system was that the United States had so little control of its domestic monetary policy that it did not need, or indeed have, a central bank. Other GS countries, too, suffered from their inability to adjust to domestic shocks. Another weakness of the GS was the annoying fact that gold supplies were rarely in synch with the world economy, sometimes lagging it, thereby causing deflation, and sometimes exceeding it, hence inducing inflation.
Stop and Think Box
Why did the United States find it prudent to have a central bank (the B.U.S. [1791–1811] and the S.B.U.S. [1816–1836]) during the late eighteenth and early nineteenth centuries, when it was on a specie standard, but not later in the nineteenth century? (Hint: Transatlantic transportation technology improved dramatically beginning in the 1810s.)
As discussed in earlier chapters, the B.U.S. and S.B.U.S. had some control over the domestic money supply by regulating commercial bank reserves via the alacrity of its note and deposit redemption policy. Although the United States was on a de facto specie standard (legally bimetallic but de facto silver, then gold) at the time, the exchange rate bands were quite wide because transportation costs (insurance, freight, interest lost in transit) were so large compared to later in the century that the U.S. monetary regime was more akin to a modern managed float. In other words, the central bank had discretion to change the money supply and exchange rates within the wide band that the costly state of technology created.
The Bretton Woods System adopted by the first world countries in the final stages of World War II was designed to overcome the flaws of the GS while maintaining the stability of fixed exchange rates. By making the dollar the free world’s reserve currency (basically substituting USD for gold), it ensured a more elastic supply of international reserves and also allowed the United States to earn seigniorage to help offset the costs it incurred fighting World War II, the Korean War, and the Cold War. The U.S. government promised to convert USD into gold at a fixed rate (\$35 per oz.), essentially rendering the United States the banker to more than half of the world’s economy. The other countries in the system maintained fixed exchange rates with the dollar and allowed for domestic monetary policy discretion, so the BWS had to restrict international capital flows, which it did via taxes and restrictions on international financial instrument transactions.For additional details, see Christopher Neely, “An Introduction to Capital Controls,” Federal Reserve Bank of St. Louis Review (Nov./Dec. 1999): 13–30. research.stlouisfed.org/publications/review/99/11/9911cn.pdf Little wonder that the period after World War II witnessed a massive shrinkage of the international financial system.
Under the BWS, if a country could no longer defend its fixed rate with the dollar, it was allowed to devalue its currency, or in other words, to set a newer, weaker exchange rate. As Figure 19.4 reveals, Great Britain devalued several times, as did other members of the BWS. But what ultimately destroyed the system was the fact that the banker, the United States, kept issuing more USD without increasing its reserve of gold. The international equivalent of a bank run ensued because major countries, led by France, exchanged their USD for gold. Attempts to maintain the BWS in the early 1970s failed. Thereafter, Europe created its own fixed exchange rate system called the exchange rate mechanism (ERM), with the German mark as the reserve currency. That system morphed into the European currency union and adopted a common currency called the euro.
Most countries today allow their currencies to float freely or employ a managed float strategy. With international capital mobility restored in many places after the demise of the BWS, the international financial system has waxed ever stronger since the early 1970s.
key takeaways
• The two major types of fixed exchange rate regimes were the gold standard and Bretton Woods.
• The gold standard relied on retail convertibility of gold, while the BWS relied on central bank management where the USD stood as a sort of substitute for gold. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/19%3A_International_Monetary_Regimes/19.02%3A_Two_Systems_of_Fixed_Exchange_Rates.txt |
learning objective
1. How can central banks manage the FX rate?
The so-called managed float (aka dirty float) is perhaps the most interesting attempt to, if not eliminate the impossible trinity, at least to blunt its most pernicious characteristic, that of locking countries into the disadvantages outlined in Figure 19.2 . Under a managed float, the central bank allows market forces to determine second-to-second (day-to-day) fluctuations in exchange rates but intervenes if the currency grows too weak or too strong. In other words, it tries to keep the exchange rate range bound, ostensibly to protect domestic economic interests (exporters, consumers) who would be hurt by rapid exchange rate movements. Those ranges or bands can vary in size from very wide to very narrow and can change levels over time.
Central banks intervene in the foreign exchange markets by exchanging international reserves, assets denominated in foreign currencies, gold, and special drawing rights (SDRs), for domestic currency. Consider the case of Central Bank selling \$10 billion of international reserves, thereby soaking up \$10 billion of MB (the monetary base, or currency in circulation and/or reserves). The T-account would be:
Central Bank
Assets Liabilities
International reserves −\$10 billion Currency in circulation or reserves −\$10 billion
If it were to buy \$100 million of international reserves, both MB and its holdings of foreign assets would increase:
Central Bank
Assets Liabilities
International reserves +\$100 million Monetary base +\$100 million
Such transactions are known in the biz as unsterilized foreign exchange interventions and they influence the FX rate via changes in MB. Recall that increasing the money supply (MS) causes the domestic currency to depreciate, while decreasing the MS causes it to appreciate. It does so by influencing both the domestic interest rate (nominal) and expectations about Eef, the future exchange rate, via price level (inflation) expectations. (There is also a direct effect on the MS, but it is too small in most instances to be detectable and so it can be safely ignored. Intuitively, however, increasing the money supply leaves each unit of currency less valuable, while decreasing it renders each unit more valuable.)
Central banks also sometimes engage in so-called sterilized foreign exchange interventions when they offset the purchase or sale of international reserves with a domestic sale or purchase. For example, a central bank might offset or sterilize the purchase of \$100 million of international reserves by selling \$100 million of domestic government bonds, or vice versa. In terms of a T-account:
Central Bank
Assets Liabilities
International reserves +\$100 million Monetary base +\$100 million
Government bonds −\$100 million Monetary base −\$100 million
Because there is no net change in MB, a sterilized intervention should have no long-term impact on the exchange rate. Apparently, central bankers engage in sterilized interventions as a short-term ruse (where central banks are not transparent, considerable asymmetric information exists between them and the markets) or to signal their desire to the market. Neither go very far, so for the most part central banks that wish to manage their nation’s exchange rate must do so via unsterilized interventions, buying international reserves with domestic currency when they want to depreciate the domestic currency, and selling international reserves for domestic currency when they want the domestic currency to appreciate.
The degree of float management can range from a hard peg, where a country tries to keep its currency fixed to another, so-called anchor currency, to such wide bands that intervention is rarely undertaken. Figure 19.5 clearly shows that Thailand used to maintain a hard peg against the dollar but gave it up during the Southeast Asian financial crisis of 1997. That big spike was not pleasant for Thailand, especially for economic agents within it that had debts denominated in foreign currencies, which suddenly became much more difficult to repay. (In June 1997, it took only about 25 baht to purchase a dollar. By the end of that year, it took over 50 baht to do so.) Clearly, a major downside of maintaining a hard peg or even a tight band is that it simply is not always possible for the central bank to maintain or defend the peg or band. It can run out of international reserves in a fruitless attempt to prevent a depreciation (cause an appreciation). Or maintenance of the peg might require increasing or decreasing the MB counter to the needs of the domestic economy.
A graph, like the one in Figure 19.6 , might be useful here. When the market exchange rate (E1) is equal to the fixed, pegged, or desired central bank rate (Epeg) everything is hunky dory. When a currency is overvalued (by the central bank), which is to say that E1 is less than Epeg (measuring E as foreign currency/domestic currency), the central bank must soak up domestic currency by selling international reserves (foreign assets). When a currency is undervalued (by the central bank), which is to say that when E1 is higher than Epeg, the central bank must sell domestic currency, thereby gaining international reserves.
Stop and Think Box
In 1990, interest rates rose in Germany due to West Germany’s reunification with formerly communist East Germany. (When exchange rates are fixed, the interest parity condition collapses to iD = iF because Eef = Et.) Therefore, interest rates also rose in the other countries in the ERM, including France, leading to a slowing of economic growth there. The same problem could recur in the new European currency union or euro zone if part of the zone needs a high interest rate to stave off inflation while another needs a low interest rate to stoke employment and growth. What does this analysis mean for the likelihood of creating a single world currency?
It means that the creation of a world currency is not likely anytime soon. As the European Union has discovered, a common currency has certain advantages, like the savings from not having to convert one currency into another or worry about the current or future exchange rate (because there is none). At the same time, however, the currency union has reminded the world that there is no such thing as a free lunch, that every benefit comes with a cost. The cost in this case is that the larger the common currency area becomes, the more difficult it is for the central bank to implement policies beneficial to the entire currency union. It was for that very reason that Great Britain opted out of the euro.
key takeaways
• Central banks influence the FX rate via unsterilized foreign exchange interventions or, more specifically, by buying or selling international reserves (foreign assets) with domestic currency.
• When central banks buy international reserves, they increase MB and hence depreciate their respective currencies by increasing inflation expectations.
• When central banks sell international reserves, they decrease MB and hence appreciate their respective currencies by decreasing inflation expectations. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/19%3A_International_Monetary_Regimes/19.03%3A_The_Managed_or_Dirty_Float.txt |
learning objective
1. What are the costs and benefits of fixing the FX rate or keeping it within a narrow band?
Problems ensue when the central bank runs out of reserves, as it did in Thailand in 1997. The International Monetary Fund (IMF) often provides loans to countries attempting to defend the value of their currencies. It doesn’t really act as an international lender of last resort, however, because it doesn’t follow Hamilton’s née Bagehot’s Law. It simply has no mechanism for adding liquidity quickly, and the longer one waits, the bigger the eventual bill. Moreover, the IMF often forces borrowers to undergo fiscal austerity programs (high government taxes, decreased expenditures, high domestic interest rates, and so forth) that can create as much economic pain as a rapid depreciation would. Finally, it has created a major moral hazard problem, repeatedly lending to the same few countries, which quickly learned that they need not engage in responsible policies in the long run because the IMF would be sure to help out if they got into trouble. Sometimes the medicine is indeed worse than the disease!
Trouble can also arise when a central bank no longer wants to accumulate international reserves (or indeed any assets) because it wants to squelch domestic inflation, as it did in Germany in 1990–1992. Many fear that China, which currently owns over \$1 trillion in international reserves (mostly USD), will find itself in this conundrum soon. The Chinese government accumulated such a huge amount of reserves by fixing its currency (which confusingly goes by two names, the yuan and the renminbi, but one symbol, CNY) at the rate of CNY8.28 per USD. Due to the growth of the Chinese economy relative to the U.S. economy, E* exceeded Epeg, inducing the Chinese, per the analysis above, to sell CNY for international reserves to keep the yuan permanently weak, or undervalued relative to the value the market would have assigned it.
Recall that undervaluing the yuan helps Chinese exports by making them appear cheap to foreigners. (If you don’t believe me, walk into any Wal-Mart, Target, or other discount store.) Many people think that China’s peg is unfair, a monetary form of dirty pool. Such folks need to realize that there is no such thing as a free lunch. To maintain its peg, the Chinese government has severely restricted international capital mobility via currency controls, thereby injuring the efficiency of Chinese financial markets, limiting foreign direct investment, and encouraging mass loophole mining. It is also stuck with a trillion bucks of relatively low-yielding international reserves that will decline in value when the yuan floats (and probably appreciates strongly), as it eventually must. In other words, China is setting itself up for the exact opposite of the Southeast Asian Crisis of 1997–1998, where the value of its assets will plummet instead of the value of its liabilities skyrocketing.
In China’s defense, many developing countries find it advantageous to peg their exchange rates to the dollar, the yen, the euro, the pound sterling, or a basket of such important currencies. The peg, which can be thought of as a monetary policy target similar to an inflation or money supply target, allows the developing nation’s central bank to figure out whether to increase or decrease MB and by how much. A hard peg or narrow band effectively ties the domestic inflation rate to that of the anchor country, As noted in Chapter 18 "Foreign Exchange", however, not all goods and services are traded internationally, so the rates will not be exactly equal. instilling confidence in the developing country’s macroeconomic performance.
Indeed, in extreme cases, some countries have given up their central bank altogether and have dollarized, adopting USD or other currencies (though the process is still called dollarization) as their own. No international law prevents this, and indeed the country whose currency is adopted earns seigniorage and hence has little grounds for complaint. Countries that want to completely outsource their monetary policy but maintain seigniorage revenue (the profits from the issuance of money) adopt a currency board that issues domestic currency but backs it 100 percent with assets denominated in the anchor currency. (The board invests the reserves in interest-bearing assets, the source of the seigniorage.) Argentina benefited from just such a board during the 1990s, when it pegged its peso one-to-one with the dollar, because it finally got inflation, which often ran over 100 percent per year, under control.
Fixed exchange rates not based on commodities like gold or silver are notoriously fragile, however, because relative macroeconomic changes in interest rates, trade, and productivity can create persistent imbalances over time between the developing and the anchor currencies. Moreover, speculators can force countries to devalue (move Epeg down) or revalue (move Epeg up) when they hit the bottom or top of a band. They do so by using the derivatives markets to place big bets on the future exchange rate. Unlike most bets, these are one-sided because the speculators lose little money if the central bank successfully defends the peg, but they win a lot if it fails to. Speculator George Soros, for example, is reported to have made \$1 billion speculating against the pound sterling during the ERM balance of payments crisis in September 1992. Such crises can cause tremendous economic pain, as when Argentina found it necessary to abandon its currency board and one-to-one peg with the dollar in 2001–2002 due to speculative pressures and fundamental macroeconomic misalignment between the Argentine and U.S. economies. (Basically, the United States was booming and Argentina was in a recession. The former needed higher interest rates/slower money growth and the latter needed lower interest rates/higher money growth.)
Developing countries may be best off maintaining what is called a crawling target or crawling peg. Generally, this entails the developing country’s central bank allowing its domestic currency to depreciate or appreciate over time, as general macroeconomic conditions (the variables discussed in Chapter 18 "Foreign Exchange") dictate. A similar strategy is to recognize imbalances as they occur and change the peg on an ad hoc basis accordingly, perhaps first by allowing the band to widen before permanently moving it. In those ways, developing countries can maintain some FX rate stability, keep inflation in check (though perhaps higher than in the anchor country), and hopefully avoid exchange rate crises.
Stop and Think Box
What sort of international monetary regimes are consistent with Figure 19.7 and Figure 19.8 ?
Figure 19.7 certainly is not a fixed exchange rate regime, or a managed float with a tight band. It could be consistent with a fully free float, but it might also represent a managed float with wide bands between about ¥100 to ¥145 per dollar.
It appears highly likely from Figure 19.8 that Hong Kong’s monetary authority for most of the period from 1984 to 2007 engaged in a managed float within fairly tight bands bounded by about HK7.725 and HK7.80 to the dollar. Also, for three years early in the new millennium, it pegged the dollar at HK7.80 before returning to a looser but still tight band in 2004.
key takeaways
• A country with weak institutions (e.g., a dependent central bank that allows rampant inflation) can essentially free-ride on the monetary policy of a developed country by fixing or pegging its currency to the dollar, euro, yen, pound sterling, or other anchoring currency to a greater or lesser degree.
• In fact, in the limit, a country can simply adopt another country’s currency as its own in a process called dollarization.
• If it wants to continue earning seigniorage (profits from the issuance of money), it can create a currency board, the function of which is to maintain 100 percent reserves and full convertibility between the domestic currency and the anchor currency.
• At the other extreme, it can create a crawling peg with wide bands, allowing its currency to appreciate or depreciate day to day according to the interaction of supply and demand, slowly adjusting the band and peg in the long term as macroeconomic conditions dictate.
• When a currency is overvalued, which is to say, when the central bank sets Epeg higher than E* (when E is expressed as foreign currency/domestic currency), the central bank must appreciate the currency by selling international reserves for its domestic currency.
• It may run out of reserves before doing so, however, sparking a rapid depreciation that could trigger a financial crisis by rapidly increasing the real value of debts owed by domestic residents but denominated in foreign currencies.
• When a currency is undervalued, which is to say, when the central bank sets Epeg below E*, the central bank must depreciate its domestic currency by exchanging it for international reserves. It may accumulate too many such reserves, which often have low yields and which could quickly lose value if the domestic currency suddenly appreciates, perhaps with the aid of a good push by currency speculators making big one-sided bets.
19.05: Suggested Reading
Bordon, Michael, and Barry Eichengreen. A Retrospective on the Bretton Woods Systemml: Lessons for International Monetary Reform. Chicago, IL: University of Chicago Press, 1993.
Eichengreen, Barry. Globalizing Capital: A History of the International Monetary System. Princeton, NJ: Princeton University Press, 2008.
Gallorotti, Giulio. The Anatomy of an International Monetary Regime: The Classical Gold Standard, 1880–1914. New York: Oxford University Press, 1995.
Moosa, Imad. Exchange Rate Regimes: Fixed, Flexible or Something in Between. New York: Palgrave Macmillan, 2005.
Rosenberg, Michael. Exchange Rate Determination: Models and Strategies for Exchange Rate Forecasting. New York: McGraw-Hill, 2003. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/19%3A_International_Monetary_Regimes/19.04%3A_The_Choice_of_International_Policy_Regime.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Describe Friedman’s modern quantity theory of money.
2. Describe the classical quantity theory.
3. Describe Keynes’s liquidity preference theory and its improvements.
4. Contrast the modern quantity theory with the liquidity preference theory.
Thumbnail: Photo by cottonbro from Pexels
20: Money Demand
learning objective
1. What is the liquidity preference theory, and how has it been improved?
The rest of this book is about monetary theory, a daunting-sounding term. It’s not the easiest aspect of money and banking, but it isn’t terribly taxing either so there is no need to freak out. We’re going to take it nice and slow. And here’s a big hint: you already know most of the outcomes because we’ve discussed them already in more intuitive terms. In the chapters that follow, we’re simply going to provide you with more formal ways of thinking about how the money supply determines output (Y*) and the price level (P*).
Intuitively, people want to hold a certain amount of cash because it is by definition the most liquid asset in the economy. It can be exchanged for goods at no cost other than the opportunity cost of holding a less liquid income–generating asset instead. When interest rates are low (high), so is the opportunity cost, so people hold more (less) cash. Similarly, when inflation is low (high), people are more (less) likely to hold assets, like cash, that lose purchasing power. Think about it: would you be more likely to keep \$100 in your pocket if you believed that prices were constant and your bank pays you .00005% interest, or if you thought that the prices of the things you buy (like gasoline and food) were going up soon and your bank pays depositors 20% interest? (I would hope the former. If the latter, I have some derivative bridge securities to sell you.)
We’ll start our theorizing with the demand for money, specifically the simple quantity theory of money, then discuss John Maynard Keynes’s improvement on it, called the liquidity preference theory, and end with Milton Friedman’s improvement on Keynes’ theory, the modern quantity theory of money.
John Maynard Keynes (to distinguish him from his father, economist John Neville Keynes) developed the liquidity preference theory in response to the pre-Friedman quantity theory of money, which was simply an assumption-laden identity called the equation of exchange:
M V = P Y
where
M = money supply
V = velocity
P = price level
Y = output
Nobody doubted the equation itself, which, as an identity (like x = x), is undeniable. But many doubted the way that classical quantity theorists used the equation of exchange as the causal statement: increases in the money supply lead to proportional increases in the price level, although in the long term it was highly predictive. The classical quantity theory also suffered by assuming that money velocity, the number of times per year a unit of currency was spent, was constant. Although a good first approximation of reality, the classical quantity theory, which critics derided as the “naïve quantity theory of money,” was hardly the entire story. In particular, it could not explain why velocity was pro-cyclical, i.e., why it increased during business expansions and decreased during recessions.
To find a better theory, Keynes took a different point of departure, asking in effect, “Why do economic agents hold money?” He came up with three reasons:
1. Transactions: Economic agents need money to make payments. As their incomes rise, so, too, do the number and value of those payments, so this part of money demand is proportional to income.
2. Precautions: S—t happens was a catch phrase of the 1980s, recalled perhaps most famously in the hit movie Forrest Gump. Way back in the 1930s, Keynes already knew that bad stuff happens—and that one defense against it was to keep some spare cash lying around as a precaution. It, too, is directly proportional to income, Keynes believed.
3. Speculations: People will hold more bonds than money when interest rates are high for two reasons. The opportunity cost of holding money (which Keynes assumed has zero return) is higher, and the expectation is that interest rates will fall, raising the price of bonds. When interest rates are low, the opportunity cost of holding money is low, and the expectation is that rates will rise, decreasing the price of bonds. So people hold larger money balances when rates are low. Overall, then, money demand and interest rates are inversely related.
More formally, Keynes’s ideas can be stated as
M d / P = f ( i <−> , Y <+> )
where
Md/P = demand for real money balances
f means “function of” (this simplifies the mathematics)
i = interest rate
Y = output (income)
<+> = increases in
<−> = decreases in
An increase in interest rates induces people to decrease real money balances for a given income level, implying that velocity must be higher. So Keynes’s view was superior to the classical quantity theory of money because he showed that velocity is not constant but rather is positively related to interest rates, thereby explaining its pro-cyclical nature. (Interest rates rise during expansions and fall during recessions.) Keynes’s theory was also fruitful because it induced other scholars to elaborate on it further.
In the early 1950s, for example, a young Will Baumolpages.stern.nyu.edu/~wbaumol and James Tobinnobelprize.org/nobel_prizes/economics/laureates/1981/tobin-autobio.html independently showed that money balances, held for transaction purposes (not just speculative ones), were sensitive to interest rates, even if the return on money was zero. That is because people can hold bonds or other interest-bearing securities until they need to make a payment. When interest rates are high, people will hold as little money for transaction purposes as possible because it will be worth the time and trouble of investing in bonds and then liquidating them when needed. When rates are low, by contrast, people will hold more money for transaction purposes because it isn’t worth the hassle and brokerage fees to play with bonds very often. So transaction demand for money is negatively related to interest rates. A similar trade-off applies also to precautionary balances. The lure of high interest rates offsets the fear of bad events occurring. When rates are low, better to play it safe and hold more dough. So the precautionary demand for money is also negatively related to interest rates. And both transaction and precautionary demand are closely linked to technology: the faster, cheaper, and more easily bonds and money can be exchanged for each other, the more money-like bonds will be and the lower the demand for cash instruments will be, ceteris paribus.
key takeaways
• Before Friedman, the quantity theory of money was a much simpler affair based on the so-called equation of exchange—money times velocity equals the price level times output (MV = PY)—plus the assumptions that changes in the money supply cause changes in output and prices and that velocity changes so slowly it can be safely treated as a constant. Note that the interest rate is not considered at all in this so-called naïve version.
• Keynes and his followers knew that interest rates were important to money demand and that velocity wasn’t a constant, so they created a theory whereby economic actors demand money to engage in transactions (buy and sell goods), as a precaution against unexpected negative shocks, and as a speculation.
• Due to the first two motivations, real money balances increase directly with output.
• Due to the speculative motive, real money balances and interest rates are inversely related. When interest rates are high, so is the opportunity cost of holding money.
• Throw in the expectation that rates will likely fall, causing bond prices to rise, and people are induced to hold less money and more bonds.
• When interest rates are low, by contrast, people expect them to rise, which will hurt bond prices. Moreover, the opportunity cost of holding money to make transactions or as a precaution against shocks is low when interest rates are low, so people will hold more money and fewer bonds when interest rates are low. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/20%3A_Money_Demand/20.01%3A_The_Simple_Quantity_Theory_and_the_Liquidity_Preference_Theory_of_Keynes.txt |
learning objective
1. What is the quantity theory of money, and how was it improved by Milton Friedman?
Building on the work of earlier scholars, including Irving Fisher of Fisher Equation fame, Milton Friedman improved on Keynes’s liquidity preference theory by treating money like any other asset. He concluded that economic agents (individuals, firms, governments) want to hold a certain quantity of real, as opposed to nominal, money balances. If inflation erodes the purchasing power of the unit of account, economic agents will want to hold higher nominal balances to compensate, to keep their real money balances constant. The level of those real balances, Friedman argued, was a function of permanent income (the present discounted value of all expected future income), the relative expected return on bonds and stocks versus money, and expected inflation.
More formally,
M d / P : f ( Y p <+> , r b − r m <−> , r s − r m <−> , π e − r m <−> )
where
Md/P = demand for real money balances (Md = money demand; P = price level)
f means “function of” (not equal to)
Yp = permanent income
rb − rm = the expected return on bonds minus the expected return on money
rs − rm = the expected return on stocks (equities) minus the expected return on money
πe − rm = expected inflation minus the expected return on money
<+> = increases in
<−> = decreases in
So the demand for real money balances, according to Friedman, increases when permanent income increases and declines when the expected returns on bonds, stocks, or goods increases versus the expected returns on money, which includes both the interest paid on deposits and the services banks provide to depositors.
Stop and Think Box
As noted in the text, money demand is where the action is these days because, as we learned in previous chapters, the central bank determines what the money supply will be, so we can model it as a vertical line. Earlier monetary theorists, however, had no such luxury because, under a specie standard, money was supplied exogenously. What did the supply curve look like before the rise of modern central banking in the twentieth century?
The supply curve sloped upward, as most do. You can think of this in two ways, first, by thinking of interest on the vertical axis. Interest is literally the price of money. When interest is high, more people want to supply money to the system because seigniorage is higher. So more people want to form banks or find other ways of issuing money, extant bankers want to issue more money (notes and/or deposits), and so forth. You can also think of this in terms of the price of gold. When its price is low, there is not much incentive to go out and find more of it because you can earn just as much making cheesecake or whatever. When the price of gold is high, however, everybody wants to go out and prospect for new veins or for new ways of extracting gold atoms from what looks like plain old dirt. The point is that early monetary theorists did not have the luxury of concentrating on the nature of money demand; they also had to worry about the nature of money supply.
This all makes perfectly good sense when you think about it. If people suspect they are permanently more wealthy, they are going to want to hold more money, in real terms, so they can buy caviar and fancy golf clubs and what not. If the return on financial investments decreases vis-à-vis money, they will want to hold more money because its opportunity cost is lower. If inflation expectations increase, but the return on money doesn’t, people will want to hold less money, ceteris paribus, because the relative return on goods (land, gold, turnips) will increase. (In other words, expected inflation here proxies the expected return on nonfinancial goods.)
The modern quantity theory is generally thought superior to Keynes’s liquidity preference theory because it is more complex, specifying three types of assets (bonds, equities, goods) instead of just one (bonds). It also does not assume that the return on money is zero, or even a constant. In Friedman’s theory, velocity is no longer a constant; instead, it is highly predictable and, as in reality and Keynes’s formulation, pro-cyclical, rising during expansions and falling during recessions. Finally, unlike the liquidity preference theory, Friedman’s modern quantity theory predicts that interest rate changes should have little effect on money demand. The reason for this is that Friedman believed that the return on bonds, stocks, goods, and money would be positively correlated, leading to little change in rb − rm, rs − rm, or πe − rm because both sides would rise or fall about the same amount. That insight essentially reduces the modern quantity theory to Md/P = f(Yp <+>).
key takeaways
• According to Milton Friedman, demand for real money balances (Md/P) is directly related to permanent income (Yp)—the discounted present value of expected future income—and indirectly related to the expected differential returns from bonds, stocks (equities), and goods vis-à-vis money (rb − rm, rs − rm, πe − rm ), where inflation (π) proxies the return on goods.
• Because he believed that the return on money would increase (decrease) as returns on bonds, stocks, and goods increased (decreased), Friedman did not think that interest rate changes mattered much.
• Friedman’s modern quantity theory proved itself superior to Keynes’s liquidity preference theory because it was more complex, accounting for equities and goods as well as bonds.
• Friedman allowed the return on money to vary and to increase above zero, making it more realistic than Keynes’s assumption of zero return. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/20%3A_Money_Demand/20.02%3A_Friedmans_Modern_Quantity_Theory_of_Money.txt |
learning objective
1. When, how, and why did Friedman’s modern quantity theory of money prove an inadequate guide to policy?
Until the 1970s, Friedman was more or less correct. Interest rates did not strongly affect the demand for money, so velocity was predictable and the quantity of money was closely linked to aggregate output. Except when nominal interest rates hit zero (as in Japan), the demand for money was somewhat sensitive to interest rates, so there was no so-called liquidity trap (where money demand is perfectly horizontal, leaving central bankers impotent). During the 1970s, however, money demand became more sensitive to interest rate changes, and velocity, output, and inflation became harder to predict. That’s one reason why central banks in the 1970s found that targeting monetary aggregates did not help them to meet their inflation or output goals.
Stop and Think Box
Stare at Figure 20.1 for a spell. How is it related to the discussion in this chapter? Then take a gander at Figure 20.2 . In addition to giving us a new perspective on Figure 20.1 , it shows that the velocity of money (velocity = GDP/M1 because MV = PY can be solved for V: V = PY/M) has increased considerably since the late 1950s. Why might that be?
The chapter makes the point that velocity became much less stable and much less predictable in the 1970s and thereafter. Figure 20.1 shows that by measuring the quarterly change in velocity. Before 1970, velocity went up and down between −1 and 3 percent in pretty regular cycles. Thereafter, the variance increased to between almost −4 and 4 percent, and the pattern has become much less regular. This is important because it shows why Friedman’s modern quantity theory of money lost much of its explanatory power in the 1970s, leading to changes in central bank targeting and monetary theory.
Figure 20.2 suggests that velocity likely increased in the latter half of the twentieth century due to technological improvements that allowed each unit of currency to be used in more transactions over the course of a year. More efficient payment systems (electronic funds transfer), increased use of credit, lower transaction costs, and financial innovations like cash management accounts have all helped to increase V, to help each dollar move through more hands or the same number of hands in less time.
The breakdown of the quantity theory had severe repercussions for central banking, central bankers, and monetary theorists. That was bad news for them (and for people like myself who grew up in that awful decade), and it is bad news for us because our exploration of monetary theory must continue. Monetary economists have learned a lot over the last few decades by constantly testing, critiquing, and improving models like those of Keynes and Friedman, and we’re all going to follow along so you’ll know precisely where monetary theory and policy stand at present.
Stop and Think Box
Examine Figure 20.3 , Figure 20.4 , and Figure 20.5 carefully. Why might velocity have trended upward to approximately 1815 and then fallen? Hint: Alexander Hamilton argued in the early 1790s that “in countries in which the national debt is properly funded, and an object of established confidence, it answers most of the purposes of money. Transfers of stock or public debt are there equivalent to payments in specie; or in other words, stock, in the principal transactions of business, passes current as specie. The same thing would, in all probability happen here, under the like circumstances”—if his funding plan was adopted. It was, and interest rates fell dramatically as a result and thereafter remained at around 6 percent in peacetime.
Velocity rises when there are money substitutes, highly liquid assets that allow economic agents to earn interest. Apparently Hamilton was right—the national debt answered most of the purposes of money. Ergo, not as much M1 was needed to support the gross domestic product (GDP) and price level, so velocity rose during the period that the debt was large. It then dropped as the government paid off the debt, requiring the use of more M1.
key takeaways
• Money demand was indeed somewhat sensitive to interest rates but velocity, while not constant, was predictable, making the link between money and prices that Friedman predicted a close one.
• Friedman’s reformulation of the quantity theory held up well only until the 1970s, when it cracked asunder because money demand became more sensitive to interest rate changes, thus causing velocity to vacillate unpredictably and breaking the close link between the quantity of money and output and inflation.
20.04: Suggested Reading
Friedman, Milton. Money Mischief: Episodes in Monetary History. New York: Harvest, 1994.
Friedman, Milton, and Anna Jacobson. A Monetary History of the United States, 1867–1960. Princeton, NJ: Princeton University Press, 1971.
Kindleberger, Charles. Keynesianism vs. Monetarism and Other Essays in Financial History. London: George Allen & Unwin, 1985.
Minsky, Hyman. John Maynard Keynes. New York: McGraw-Hill, 2008.
Serletis, Apostolos. The Demand for Money: Theoretical and Empirical Approaches. New York: Springer, 2007. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/20%3A_Money_Demand/20.03%3A_The_Policy_Failure_of_the_Modern_Quantity_Theory_of_Money.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Explain this equation: Y = Yad = C + I + G + NX.
2. Provide the equation for C and explain its importance.
3. Describe the Keynesian cross diagram and explain its use.
4. Describe the investment-savings (IS) curve and its characteristics.
5. Describe the liquidity preference–money (LM) curve and its characteristics.
6. Explain why equilibrium is achieved in the markets for goods and money.
7. Explain the IS-LM model’s biggest drawback.
Thumbnail: Image by krzysztof-m from Pixabay
21: IS-LM
learning objectives
1. What does this equation mean: Y = Yad = C + I + G + NX?
2. Why is this equation important?
3. What is the equation for C and why is it important?
4. What is the Keynesian cross diagram and what does it help us to do?
Developed in 1937 by economist and Keynes disciple John Hicks, the IS-LM model is still used today to model aggregate output (gross domestic product [GDP], gross national product [GNP], etc.) and interest rates in the short run.en.Wikipedia.org/wiki/John_Hicks It begins with John Maynard Keynes’s recognition that
Y = Y a d = C + I + G + N X
where:
Y = aggregate output (supplied)
Yad = aggregate demand
C = consumer expenditure
I = investment (on new physical capital like computers and factories, and planned inventory)
G = government spending
NX = net exports (exports minus imports)
Keynes further explained that C = a + (mpc × Yd)
where:
Yd = disposable income, all that income above a
a = autonomous consumer expenditure (food, clothing, shelter, and other necessaries)
mpc = marginal propensity to consume (change in consumer expenditure from an extra dollar of income or “disposable income;” it is a constant bounded by 0 and 1)
Practice calculating C in Exercise 1.
exercise
1. Calculate consumer expenditure using the formula C = a + (mpc × Yd).
Autonomous Consumer Expenditure Marginal Propensity to Consume Disposable Income Answer: C
200 0.5 0 200
400 0.5 0 400
200 0.5 200 300
200 0.5 300 350
300 0.5 300 450
300 0.75 300 525
300 0.25 300 375
300 0.01 300 303
300 1 300 600
100 0.5 1000 600
100 0.75 1000 850
You can plot a consumption function by drawing a graph, as in Figure 21.1 , with consumer expenditure on the vertical axis and disposable income on the horizontal. (Autonomous consumer expenditure a will be the intercept and mpc × Yd will be the slope.)
Investment is composed of so-called fixed investment on equipment and structures and planned inventory investment in raw materials, parts, or finished goods.
For the present, we will ignore G and NX and, following Keynes, changes in the price level. (Remember, we are talking about the short term here. Remember, too, that Keynes wrote in the context of the gold standard, not an inflationary free floating regime, so he was not concerned with price level changes.) The simple model that results, called a Keynesian cross diagram, looks like the diagram in Figure 21.2 .
The 45-degree line simply represents the equilibrium Y = Yad. The other line, the aggregate demand function, is the consumption function line plus planned investment spending I. Equilibrium is reached via inventories (part of I). If Y > Yad, inventory levels will be higher than firms want, so they’ll cut production. If Y < Yad, inventories will shrink below desired levels and firms will increase production. We can now predict changes in aggregate output given changes in the level of I and C and the marginal propensity to consume (the slope of the C component of Yad).
Suppose I increases. Due to the upward slope of Yad, aggregate output will increase more than the increase in I. This is called the expenditure multiplier and it is summed up by the following equation:
Y = ( a + I ) × 1 / ( 1 - m p c )
So if a is 200 billion, I is 400 billion, and mpc is .5, Y will be
Y = 600 × 1 / .5 = 600 × 2 = \$ 1,200 billion
If I increases to 600 billion, Y = 800 × 2 = \$1,600 billion.
If the marginal propensity to consume were to increase to .75, Y would increase to
Y = 800 × 1/.25 = 800 × 4 = \$3,200 billion because Yad would have a much steeper slope. A decline in mpc to .25, by contrast, would flatten Yad and lead to a lower equilibrium:
Y = 800 × 1 / .75 = 800 × 1.333 = \$ 1,066.67 billion
Practice calculating aggregate output in Exercise 2.
exercise
1. Calculate aggregate output with the formula: Y = (a + I) × 1/(1 ? mpc)
Autonomous Spending Marginal Propensity to Consume Investment Answer: Aggregate Output
200 0.5 500 1400
300 0.5 500 1600
400 0.5 500 1800
500 0.5 500 2000
500 0.6 500 2500
200 0.7 500 2333.33
200 0.8 500 3500
200 0.4 500 1166.67
200 0.3 500 1000
200 0.5 600 1600
200 0.5 700 1800
200 0.5 800 2000
200 0.5 400 1200
200 0.5 300 1000
200 0.5 200 800
Stop and Think Box
During the Great Depression, investment (I) fell from \$232 billion to \$38 billion (in 2000 USD). What happened to aggregate output? How do you know?
Aggregate output fell by more than \$232 billion − \$38 billion = \$194 billion. We know that because investment fell and the marginal propensity to consume was > 0, so the fall was more than \$194 billion, as expressed by the equation Y = (a + I) × 1/(1 − mpc).
To make the model more realistic, we can easily add NX to the equation. An increase in exports over imports will increase aggregate output Y by the increase in NX times the expenditure multiplier. Likewise, an increase in imports over exports (a decrease in NX) will decrease Y by the decrease in NX times the multiplier.
Government spending (G) also increases Y. We must realize, however, that some government spending comes from taxes, which consumers view as a reduction in income. With taxation, the consumption function becomes the following:
C = a + m p c × ( Y d - T )
T means taxes. The effect of G is always larger than that of T because G expands by the multiplier, which is always > 1, while T is multiplied by MPC, which never exceeds 1. So increasing G, even if it is totally funded by T, will increase Y. (Remember, this is a short-run analysis.) Nevertheless, Keynes argued that, to help a country out of recession, government should cut taxes because that will cause Yd to rise, ceteris paribus. Or, in more extreme cases, it should borrow and spend (rather than tax and spend) so that it can increase G without increasing T and thus decreasing C.
Stop and Think Box
Many governments, including that of the United States, responded to the Great Depression by increasing tariffs in what was called a beggar-thy-neighbor policy. Today we know that such policies beggared everyone. What were policymakers thinking?
They were thinking that tariffs would decrease imports and thereby increase NX (exports minus imports) and Y. That would make their trading partner’s NX decrease, thus beggaring them by decreasing their Y. It was a simple idea on paper, but in reality it was dead wrong. For starters, other countries retaliated with tariffs of their own. But even if they did not, it was a losing strategy because by making neighbors (trading partners) poorer, the policy limited their ability to import (i.e., decreased the first country’s exports) and thus led to no significant long-term change in NX.
Figure 21.3 sums up the discussion of aggregate demand.
key takeaways
• The equation Y = Yad = C + I + G + NX tells us that aggregate output (or aggregate income) is equal to aggregate demand, which in turn is equal to consumer expenditure plus investment (planned, physical stuff) plus government spending plus net exports (exports – imports).
• It is important because it allows economists to model aggregate output (to discern why, for example, GDP changes).
• In a taxless Eden, like the Gulf Cooperation Council countries, consumer expenditure equals autonomous consumer expenditure (spending on necessaries) (a) plus the marginal propensity to consume (mpc) times disposable income (Yd), income above a.
• In the rest of the world, C = a + mpc × (Yd − T), where T = taxes.
• C, particularly the marginal propensity to consume variable, is important because it gives the aggregate demand curve in a Keynesian cross diagram its upward slope.
• A Keynesian cross diagram is a graph with aggregate demand (Yad) on the vertical axis and aggregate output (Y) on the horizontal.
• It consists of a 45-degree line where Y = Yad and a Yad curve, which plots C + I + G + NX with the slope given by the expenditure multiplier, which is the reciprocal of 1 minus the marginal propensity to consume: Y = (a + I + NX + G) × 1/(1 − mpc).
• The diagram helps us to see that aggregate output is directly related to a, I, exports, G, and mpc and indirectly related to T and imports. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/21%3A_IS-LM/21.01%3A_Aggregate_Output_and_Keynesian_Cross_Diagrams.txt |
learning objectives
1. What are the IS and LM curves?
2. What are their characteristics?
3. What do we learn when we combine the IS and the LM curves on one graph?
4. Why is equilibrium achieved?
5. What is the IS-LM model’s biggest drawback?
The Keynesian cross diagram framework is great, as far as it goes. Note that it has nothing to say about interest rates or money, a major shortcoming for us students of money, banking, and monetary policy! It does, however, help us to build a more powerful model that examines equilibrium in the markets for goods and money, the IS (investment-savings) and the LM (liquidity preference–money) curves, respectively (hence the name of the model).
Interest rates are negatively related to I and to NX. The reasoning here is straightforward. When interest rates (i) are high, companies would rather invest in bonds than in physical plant (because fewer projects are positive net present value or +NPV) or inventory (because it has a high opportunity cost), so I (investment) is low. When rates are low, new physical plant and inventories look cheap and many more projects are +NPV (i has come down in the denominator of the present value formula), so I is high. Similarly, when i is low the domestic currency will be weak, all else equal. Exports will be facilitated and imports will decline because foreign goods will look expensive. Thus, NX will be high (exports > imports). When i is high, by contrast, the domestic currency will be in demand and hence strong. That will hurt exports and increase imports, so NX will drop and perhaps become negative (exports < imports).
Now think of Yad on a Keynesian cross diagram. As we saw above, aggregate output will rise as I and NX do. So we know that as i increases, Yad decreases, ceteris paribus. Plotting the interest rate on the vertical axis against aggregate output on the horizontal axis, as below, gives us a downward sloping curve. That’s the IS curve! For each interest rate, it tells us at what point the market for goods (I and NX, get it?) is in equilibrium—holding autonomous consumption, fiscal policy, and other determinants of aggregate demand constant. For all points to the right of the curve, there is an excess supply of goods for that interest rate, which causes firms to decrease inventories, leading to a fall in output toward the curve. For all points to the left of the IS curve, an excess demand for goods persists, which induces firms to increase inventories, leading to increased output toward the curve.
Obviously, the IS curve alone is as insufficient to determine i or Y as demand alone is to determine prices or quantities in the standard supply and demand microeconomic price model. We need another curve, one that slopes the other way, which is to say, upward. That curve is called the LM curve and it represents equilibrium points in the market for money. The demand for money is positively related to income because more income means more transactions and because more income means more assets, and money is one of those assets. So we can immediately plot an upward sloping LM curve, a curve that holds the money supply constant. To the left of the LM curve there is an excess supply of money given the interest rate and the amount of output. That’ll cause people to use their money to buy bonds, thus driving bond prices up, and hence i down to the LM curve. To the right of the LM curve, there is an excess demand for money, inducing people to sell bonds for cash, which drives bond prices down and hence i up to the LM curve.
When we put the IS and LM curves on the graph at the same time, as inFigure21.4 "IS-LM diagram: equilibrium in the markets for money and goods", we immediately see that there is only one point, their intersection, where the markets for both goods and money are in equilibrium. Both the interest rate and aggregate output are determined by that intersection. We can then shift the IS and LM curves around to see how they affect interest rates and output, i* and Y*. In the next chapter, we’ll see how policymakers manipulate those curves to increase output. But we still won’t be done because, as mentioned above, the IS-LM model has one major drawback: it works only in the short term or when the price level is otherwise fixed.
Stop and Think Box
Does Figure 21.5 make sense? Why or why not? What does Figure 21.6 mean? Why is Figure 21.7 not a good representation of G?
Source: U.S. Department of Commerce, Bureua of Economic Analysis
Source: U.S. Department of Commerce, Bureua of Economic Analysis
Source: U.S. Department of Commerce, Bureua of Economic Analysis
Figure 21.5 makes perfectly good sense because it depicts I in the equation Y = Yad = C + I + G + NX, and the shaded areas represent recessions, that is, decreases in Y. Note that before almost every recession in the twentieth century, I dropped.
Figure 21.6 means that NX in the United States is considerably negative, that exports < imports by a large margin, creating a significant drain on Y (GDP). Note that NX improved (became less negative) during the crisis and resulting recession but dipped downward again during the 2010 recovery.
Figure 21.7 is not a good representation of G because it ignores state and local government expenditures, which are significant in the United States, as Figure 21.8 shows.
Source: U.S. Department of Commerce, Bureua of Economic Analysis
key takeaways
• The IS curve shows the points at which the quantity of goods supplied equals those demanded.
• On a graph with interest (i) on the vertical axis and aggregate output (Y) on the horizontal axis, the IS curve slopes downward because, as the interest rate increases, key components of Y, I and NX, decrease. That is because as i increases, the opportunity cost of holding inventory increases, so inventory levels fall and +NPV projects involving new physical plant become rarer, and I decreases.
• Also, high i means a strong domestic currency, all else constant, which is bad news for exports and good news for imports, which means NX also falls.
• The LM curve traces the equilibrium points for different interest rates where the quantity of money demanded equals the quantity of money supplied.
• It slopes upward because as Y increases, people want to hold more money, thus driving i up.
• The intersection of the IS and LM curves indicates the macroeconomy’s equilibrium interest rate (i*) and output (Y*), the point where the market for goods and the market for money are both in equilibrium.
• At all points to the left of the LM curve, an excess supply of money exists, inducing people to give up money for bonds (to buy bonds), thus driving bond prices up and interest rates down toward equilibrium.
• At all points to the right of the LM curve, an excess demand for money exists, inducing people to give up bonds for money (to sell bonds), thus driving bond prices down and interest rates up toward equilibrium.
• At all points to the left of the IS curve, there is an excess demand for goods, causing inventory levels to fall and inducing companies to increase production, thus leading to an increase in output.
• At all points to the right of the IS curve, there is an excess supply of goods, creating an inventory glut that induces firms to cut back on production, thus decreasing Y toward the equilibrium.
• The IS-LM model’s biggest drawback is that it doesn’t consider changes in the price level, so in most modern situations, it’s applicable in the short run only.
21.03: Suggested Reading
Dimand, Robert, Edward Nelson, Robert Lucas, Mauro Boianovsky, David Colander, Warren Young, et al. The IS-LM Model: Its Rise, Fall, and Strange Persistence. Raleigh, NC: Duke University Press, 2005.
Young, Warren, and Ben-Zion Zilbefarb. IS-LM and Modern Macroeconomics. New York: Springer, 2001. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/21%3A_IS-LM/21.02%3A_21.2_The_IS-LM_Model.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Explain what causes the liquidity preference–money (LM) curve to shift and why.
2. Explain what causes the investment-savings (IS) curve to shift and why.
3. Explain the difference between monetary and fiscal stimulus in the short term and why the difference is important.
4. Explain what happens when the IS-LM model is used to tackle the long term by taking changes in the price level into account.
5. Describe the aggregate demand curve and explain what causes it to shift.
Thumbnail: Image by krzysztof-m from Pixabay
22: IS-LM in Action
learning objective
1. What causes the LM and IS curves to shift and why?
Policymakers can use the IS-LM model developed in Chapter 21to help them decide between two major types of policy responses, fiscal (or government expenditure and tax) or monetary (interest rates and money). As you probably noticed when playing around with the IS and LM curves at the end of the previous chapter, their relative positions matter quite a bit for interest rates and aggregate output. Time to investigate this matter further.
The LM curve, the equilibrium points in the market for money, shifts for two reasons: changes in money demand and changes in the money supply. If the money supply increases (decreases), ceteris paribus, the interest rate is lower (higher) at each level of Y, or in other words, the LM curve shifts right (left). That is because at any given level of output Y, more money (less money) means a lower (higher) interest rate. (Remember, the price level doesn’t change in this model.) To see this, look at Figure 22.1 .
An autonomous change in money demand (that is, a change not related to the price level, aggregate output, or i) will also affect the LM curve. Say that stocks get riskier or the transaction costs of trading bonds increases. The theory of asset demand tells us that the demand for money will increase (shift right), thus increasing i. Interest rates could also decrease if money demand shifted left because stock returns increased or bonds became less risky. To see this, examine Figure 22.2 . An increase in autonomous money demand will shift the LM curve left, with higher interest rates at each Y; a decrease will shift it right, with lower interest rates at each Y.
An autonomous change in money demand (that is, a change not related to the price level, aggregate output, or i) will also affect the LM curve. Say that stocks get riskier or the transaction costs of trading bonds increases. The theory of asset demand tells us that the demand for money will increase (shift right), thus increasing i. Interest rates could also decrease if money demand shifted left because stock returns increased or bonds became less risky. To see this, examine Figure 22.2 . An increase in autonomous money demand will shift the LM curve left, with higher interest rates at each Y; a decrease will shift it right, with lower interest rates at each Y.
The IS curve, by contrast, shifts whenever an autonomous (unrelated to Y or i) change occurs in C, I, G, T, or NX. Following the discussion of Keynesian cross diagrams in Chapter 21, when C, I, G, or NX increases (decreases), the IS curve shifts right (left). When T increases (decreases), all else constant, the IS curve shifts left (right) because taxes effectively decrease consumption. Again, these are changes that are not related to output or interest rates, which merely indicate movements alongthe IS curve. The discovery of new caches of natural resources (which will increase I), changes in consumer preferences (at home or abroad, which will affect NX), and numerous other “shocks,” positive and negative, will change output at each interest rate, or in other words shift the entire IS curve.
We can now see how government policies can affect output. As noted above, in the short run, an increase in the money supply will shift the LM curve to the right, thereby lowering interest rates and increasing output. Decreasing the MS would have precisely the opposite effect. Fiscal stimulus, that is, decreasing taxes (T) or increasing government expenditures (G), will also increase output but, unlike monetary stimulus (increasing MS), will increase the interest rate. That is because it works by shifting the IS curve upward rather than shifting the LM curve. Of course, if T increases, the IS curve will shift left, decreasing interest rates but also aggregate output. This is part of the reason why people get hot under the collar about taxes.See, for example, www.nypost.com/p/news/opinion/opedcolumnists /soaking_the_rich_AW6hrJYHjtRd0Jgai5Fx1O (Of course, individual considerations are paramount!)www.politicususa.com/en/polls-taxes-deficit. Note that the people supporting tax increases typically support raising other people’s taxes: “The poll also found wide support for increasing taxes, as 67% said the more high earners income should be subject to being taxed for Social Security, and 66% support raising taxes on incomes over \$250,000, and 62% support closing corporate tax loopholes.”
Stop and Think Box
During financial panics, economic agents complain of high interest rates and declining economic output. Use the IS-LM model to describe why panics have those effects.
The LM curve will shift left during panics, raising interest rates and decreasing output, because demand for money increases as economic agents scramble to get liquid in the face of the declining and volatile prices of other assets, particularly financial securities with positive default risk.
Figure 22.3 summarizes.
Stop and Think Box
Describe Hamilton’s Law (née Bagehot’s Law) in terms of the IS-LM model. Hint: Hamilton and Bagehot argued that, during a financial panic, the lender of last resort needs to increase the money supply by lending to all comers who present what would be considered adequate collateral in normal times.
During financial panics, the LM curve shifts left as people flee risky assets for money, thereby inducing the interest rate to climb and output to fall. Hamilton and Bagehot argued that monetary authorities should respond by nipping the problem in the bud, so to speak, by increasing MS directly, shifting the LM curve back to somewhere near its pre-panic position.
key takeaways
• The LM curve shifts right (left) when the money supply (real money balances) increases (decreases).
• It also shifts left (right) when money demand increases (decreases).
• The easiest way to see this is to first imagine a graph where money demand is fixed and the money supply increases (shifts right), leading to a lower interest rate, and vice versa.
• Then imagine a fixed MS and a shift upward in money demand, leading to a higher interest rate, and vice versa.
• The IS curve shifts right (left) when C, I, G, or NX increase (decrease) or T decreases (increases).
• This relates directly to the Keynesian cross diagrams and the equation Y = C + I + G + NX discussed in Chapter 21, and also to the analysis of taxes as a decrease in consumption expenditure C. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/22%3A_IS-LM_in_Action/22.01%3A_Shifting_Curves-_Causes_and_Effects.txt |
learning objectives
1. In the short term, what is the difference between monetary and fiscal stimulus and why is it important?
2. What happens when the IS-LM model is used to tackle the long term by taking changes in the price level into account?
The IS-LM model has a major implication for monetary policy: when the IS curve is unstable, a money supply target will lead to greater output stability, and when the LM curve is unstable, an interest rate target will produce greater macro stability. To see this, look at Figure 22.4 and Figure 22.5 . Note that when LM is fixed and IS moves left and right, an interest rate target will cause Y to vary more than a money supply target will. Note too that when IS is fixed and LM moves left and right, an interest rate target keeps Y stable but a money supply target (shifts in the LM curve) will cause Y to swing wildly. This helps to explain why many central banks abandoned money supply targeting in favor of interest rate targeting in the 1970s and 1980s, a period when autonomous shocks to LM were pervasive due to financial innovation, deregulation, and loophole mining. An important implication of this is that central banks might find it prudent to shift back to targeting monetary aggregates if the IS curve ever again becomes more unstable than the LM curve.
As noted in Chapter 21, the policy power of the IS-LM is severely limited by its short-run assumption that the price level doesn’t change. Attempts to tweak the IS-LM model to accommodate price level changes led to the creation of an entirely new model called aggregate demand and supply. The key is the addition of a new concept, called the natural rate level of output, Ynrl, the rate of output at which the price level is stable in the long run. When actual output (Y*) is below the natural rate, prices will fall; when it is above the natural rate, prices will rise.
The IS curve is stated in real terms because it represents equilibrium in the goods market, the real part of the economy. Changes in the price level therefore do not affect C, I, G, T, or NX or the IS curve. The LM curve, however, is affected by changes in the price level, shifting to the left when prices rise and to the right when they fall. This is because, holding the nominal MS constant, rising prices decrease real money balances, which we know shifts the LM curve to the left.
So suppose an economy is in equilibrium at Ynrl, when some monetary stimulus in the form of an increased MS shifts the LM curve to the right. As noted above, in the short term, interest rates will come down and output will increase. But because Y* is greater than Ynrl, prices will rise, shifting the LM curve back to where it started, give or take. So output and the interest rate are the same but prices are higher. Economists call this long-run monetary neutrality.
Fiscal stimulus, as we saw above, shifts the IS curve to the right, increasing output but also the interest rate. Because Y* is greater than Ynrl, prices will rise and the LM curve will shift left, reducing output, increasing the interest rate higher still, and raising the price level! You just can’t win in the long run, in the sense that policymakers cannot make Y* exceed Ynrl. Rendering policymakers impotent did not win the IS-LM model many friends, so researchers began to develop a new model that relates the price level to aggregate output.
Stop and Think Box
Under the gold standard (GS), money flows in and out of countries automatically, in response to changes in the price of international bills of exchange. From the standpoint of the IS-LM model, what is the problem with that aspect of the GS?
As noted above, decreases in MS lead to a leftward shift of the LM curve, leading to higher interest rates and lower output. Higher interest rates, in turn, could lead to a financial panic or a decrease in C or I, causing a shift left in the IS curve, further reducing output but relieving some of the pressure on i. (Note that NX would not be affected under the GS because the exchange rate was fixed, moving only within very tight bands, so a higher i would not cause the domestic currency to strengthen.)
key takeaways
• Monetary stimulus, that is, increasing the money supply, causes the LM curve to shift right, resulting in higher output and lower interest rates.
• Fiscal stimulus, that is, increasing government spending and/or decreasing taxes, shifts the IS curve to the right, raising interest rates while increasing output.
• The higher interest rates are problematic because they can crowd out C, I, and NX, moving the IS curve left and reducing output.
• The IS-LM model predicts that, in the long run, policymakers are impotent.
• Policymakers can raise the price level but they can’t get Y* permanently above Ynrl or the natural rate level of output.
• That is because whenever Y* exceeds Ynrl, prices rise, shifting the LM curve to the left by reducing real money balances (which happens when there is a higher price level coupled with an unchanged MS).
• That, in turn, eradicates any gains from monetary or fiscal stimulus.
22.03: Aggregate Demand Curve
learning objective
1. What is the aggregate demand (AD) curve and what causes it to shift?
Imagine a fixed IS curve and an LM curve shifting hard left due to increases in the price level, as in Figure 22.6 . As prices increase, Y falls and i rises. Now plot that outcome on a new graph, where aggregate output Y remains on the horizontal axis but the vertical axis is replaced by the price level P. The resulting curve, called the aggregate demand (AD) curve, will slope downward, as below. The AD curve is a very powerful tool because it indicates the points at which equilibrium is achieved in the markets for goods and money at a given price level. It slopes downward because a high price level, ceteris paribus, means a small real money supply, high interest rates, and a low level of output, while a low price level, all else constant, is consistent with a larger real money supply, low interest rates, and kickin’ output.
Because the AD curve is essentially just another way of stating the IS-LM model, anything that would change the IS or LM curves will also shift the AD curve. More specifically, the AD curve shifts in the same direction as the IS curve, so it shifts right (left) with autonomous increases (decreases) in C, I, G, and NX and decreases (increases) in T. The AD curve also shifts in the same direction as the LM curve. So if MS increases (decreases), it shifts right (left), and if Md increases (decreases) it shifts left (right), as in Figure 22.3 .
key takeaways
• The aggregate demand curve is a downward sloping curve plotted on a graph with Y on the horizontal axis and the price level on the vertical axis.
• The AD curve represents IS-LM equilibrium points, that is, equilibrium in the market for both goods and money.
• It slopes downward because, as the price level increases, the LM curve shifts left as real money balances fall.
• AD shifts in the same direction as the IS or LM curves, so anything that shifts those curves shifts AD in precisely the same direction and for the same reasons.
22.04: Suggested Reading
Dimand, Robert, Edward Nelson, Robert Lucas, Mauro Boianovsky, David Colander, Warren Young, et al. The IS-LM Model: Its Rise, Fall, and Strange Persistence. Raleigh, NC: Duke University Press, 2005.
Young, Warren, and Ben-Zion Zilbefarb. IS-LM and Modern Macroeconomics. New York: Springer, 2001. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/22%3A_IS-LM_in_Action/22.02%3A_Implications_for_Monetary_Policy.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Describe the aggregate demand (AD) curve and explain why it slopes downward.
2. Describe what shifts the AD curve and explain why.
3. Describe the short-run aggregate supply (AS) curve and explain why it slopes upward.
4. Describe what shifts the short-run AS curve and explain why.
5. Describe the long-run aggregate supply (ASL) curve, and explain why it is vertical and what shifts it.
6. Explain the term long term and its importance for policymakers.
7. Describe the growth diamond model of economic growth and its importance.
Thumbnail: Image by Dhruv from Unsplash
23: Aggregate Supply and Demand and the Growth Diamond
learning objectives
1. What is the AD curve and why does it slope downward?
2. What shifts the AD curve and why?
The IS-LM model isn’t entirely agreeable to policymakers because it examines only the short term, and when pressed into service for the long-term, or changes in the price level, it suggests that policy initiatives are more likely to mess matters up than to improve them. In response, economists developed a new theory, aggregate demand and supply, that relates the price level to the total final goods and services demanded (aggregate demand [AD]) and the total supplied (aggregate supply [AS]). This new framework is attractive for several reasons: (1) it can be used to examine both the short and the long run; (2) it takes a form similar to the microeconomic price theory model of supply and demand, so it is familiar; and (3) it gives policymakers some grounds for implementing activist economic policies. To understand aggregate demand and supply theory, we need to understand how each of the curves is derived.
The aggregate demand curve can be derived three ways, through the IS-LM model, with help from the quantity theory of money, or directly from its components. Remember that Y = C + I + G + NX. As the price level falls, ceteris paribus, real money balances are higher. That spells a lower interest rate. A lower interest rate, in turn, means an increase in I (and hence Y). A lower interest rate also means a lower exchange rate and hence more exports and fewer imports. So NX also increases. (C might be positively affected by lower i as well.) As the price level increases, the opposite occurs. So the AD curve slopes downward.
The quantity theory of money also shows that the AD curve should slope downward. Remember that the quantity theory ties money to prices and output via velocity, the average number of times annually a unit of currency is spent on final goods and services, in the so-called equation of exchange:
M V = P Y
where
M = money supply
V = velocity of money
P = price level
Y = aggregate output
If M = \$100 billion and V = 3, then PY must be \$300 billion. If we set P, the price level, equal to 1, Y must equal \$300 billion (300/1). If P is 2, then Y is \$150 billion (300/2). If it is .5, then Y is \$600 billion (300/.5). Plot those points and you get a downward sloping curve, as in Figure 23.1 . The AD curve shifts right if the MS increases and left if it decreases. Continuing the example above, if we hold P constant at 1.0 but double M to \$200 billion, then Y will double to \$600 billion (200 × 3). (Recall that the theory suggests that V changes only slowly.) Cut M in half (\$50 billion) and Y will fall by half, to \$150 billion (50 × 3).
For a summary of the factors that shift the AD curve, review Figure 23.2 .
key takeaways
• The aggregate demand (AD) curve is the total quantity of final goods and services demanded at different price levels.
• It slopes downward because a lower price level, holding MS constant, means higher real money balances.
• Higher real money balances, in turn, mean lower interest rates, which means more investment (I) due to more +NPV projects and more net exports (NX) due to a weaker domestic currency (exports increase and imports decrease).
• The AD curve is positively related to changes in MS, C, I, G, and NX, and is negatively related to T.
• Those variables shift AD for the same reasons they shift Yad and the IS curve because all of them except taxes add to output.
• An increase in the MS increases AD (shifts the AD curve to the right) through the quantity theory of money and the equation of exchange MV = PY. Holding velocity and the price level constant, it is clear that increases in M must lead to increases in Y. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/23%3A_Aggregate_Supply_and_Demand_and_the_Growth_Diamond/23.01%3A_Aggregate_Demand.txt |
learning objectives
1. What is the short-run AS curve and why does it slope upward?
2. What shifts the short-run AS curve and why?
The aggregate supply curve is a tad trickier because it is believed to change over time. In the long run, it is thought to be vertical at Ynrl, the natural rate of output concept introduced earlier. In the long run, the economy can produce only so much given the state of technology, the natural rate of unemployment, and the amount of physical capital devoted to productive uses.
In the short run, by contrast, the total value of goods and services supplied to the economy is a function of business profits, meant here simply as the price goods bear in the market minus all the costs of their production, including wages and raw material costs. Prices of final goods and services generally adjust faster than the cost of inputs like labor and raw materials, which are often “sticky” due to long-term contracts fixing their price. So as the price level rises, ceteris paribus, business profits are higher and hence businesses supply a higher quantity to the market. That is why the aggregate supply (AS) curve slopes upward in the short run, as in Figure 23.3 .
The short-run AS curve shifts due to changes in costs and hence profits. When the labor market is tight, the wage bill rises, cutting into profits and shifting the AS curve to the left. Any so-called wage push from any source, like unionization, will have the same effect. If economic agents expect the price level to rise, that will also shift the AS curve left because they are going to demand higher wages or higher prices for their wares. Finally, changes in technology and raw materials supplies will shift the AS curve to the right or left, depending on the nature of the shock. Improved productivity (more output from the same input) is a positive shock that moves the AS curve to the right. A shortage due to bad weather, creation of a successful producer monopoly or cartel, and the like, is a negative shock that shifts the AS curve to the left.
Also, whenever Y exceeds Ynrl, the AS curve shifts left. That is because when Y exceeds Ynrl, the labor market gets tighter and expectations of inflation grow. Reversing that reasoning, the AS curve shifts right whenever Ynrl exceeds Y. Figure 23.4 summarizes the discussion of the short-run AS curve.
key takeaways
• The aggregate supply (AS) curve is the total quantity of final goods and services supplied at different price levels.
• It slopes upward because wages and other costs are sticky in the short run, so higher prices mean more profits (prices minus costs), which means a higher quantity supplied.
• The AS curve shifts left when Y* exceeds Ynrl, and it shifts right when Y* is less than Ynrl.
• In other words, Ynrl is achieved via shifts in the AS curve, particularly through labor market “tightness” and inflation expectations.
• When Y* is > Ynrl, the labor market is tight, pushing wages up and strengthening inflation expectations; when Ynrl is > *Y, the labor market is loose, keeping wages low and inflation expectations weak.
• Supply shocks, both positive and negative, also shift the AS curve.
• Anything (like a so-called wage push or higher raw materials prices) that decreases business profits shifts AS to the left, while anything that increases business profits moves it to the right. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/23%3A_Aggregate_Supply_and_Demand_and_the_Growth_Diamond/23.02%3A_Aggregate_Supply.txt |
learning objectives
1. What is the ASL curve?
2. Why is it vertical, and what shifts it?
3. How long is the long term and why is the answer important for policymakers?
Of course, this is all just a prelude to the main event: slapping these curves—AD, AS, and ASL (the long-run AS curve)—on the same graph at the same time. Let’s start, as in Figure 23.5 , with just the short-run AS and AD curves. Their intersection indicates both the price level P* (not to be confused with the microeconomic price theory model’s p*) and Y* (again not to be confused with q*). Equilibrium is achieved because at any P > P*, there will be a glut (excess supply), so prices (of all goods and services) will fall toward P*. At any P < P*, there will be excess demand, many bidders for each automobile, sandwich, haircut, and what not, who will bid prices up to P*. We can also now examine what happens to P* and Y* in the short run by moving the curves to and fro.
To study long-run changes in the economy, we need to add the vertical long-run aggregate supply curve (ASL) to the graph. As discussed above, if Y* is > or < Ynrl, the AS curve will shift (via the labor market and/or inflation expectations) until it Y* = Ynrl, as in Figure 23.6 . So attempts to increase output above its natural rate will cause inflation and recession. Attempts to keep it below its natural rate will lead to deflation and expansion.
The so-called self-correcting mechanism described above makes many policymakers uneasy, so the most activist among them argue that the long-run analysis holds only over very long periods. In fact, the great granddaddy, intellectually speaking, of today’s activist policymakers, John Maynard Keynes, once remarked, “[The l]ong run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean is flat again.”www.bartleby.com/66/8/32508.html Other economists (nonactivists, including monetarists like Milton Friedman) think that the short run is short indeed and the long run is right around the corner. Figuring out how short and long the short and long runs are is important because if the nonactivists are correct, policymakers are wasting their time trying to increase output by shifting AD to the right: the AS curve will soon shift left, leaving the economy with a higher price level but the same level of output. Similarly, policymakers need do nothing in response to a negative supply shock (which, as noted above, shifts AS to the left) because the AS curve will soon shift back to the right on its own, restoring both the price level and output. If the activists are right, on the other hand, policymakers can improve people’s lives by shifting AD to the right to counter, say, the effects of negative supply shocks by helping the AS curve to return to its original position or beyond.
The holy grail of economic growth theory is to figure out how to shift Ynrl to the right because, if policymakers can do that, it doesn’t matter how short the long term is. Policymakers can make a difference—and for the better. The real business cycle theory of Edward Prescott suggests that real aggregate supply shocks can affect Ynrl.www.minneapolisfed.org/research/prescott This is an active area of research, and not just because Prescott took home the Nobel Prize in 2004 for his contributions to “dynamic macroeconomics: the time consistency of economic policy and the driving forces behind business cycles.”nobelprize.org/nobel_prizes/economics/laureates/2004/prescott-autobio.html Other economists believe that activist policies designed to shift AD to the right can influence Ynrl through a process called hysteresis.economics.about.com/library/glossary/bldef-hysteresis.htm It’s still all very confusing and complicated, so the author of this book and numerous others prefer bringing an institutional analysis to Ynrl, one that concentrates on providing economic actors with incentives to labor, to develop and implement new technologies, and to build new plant and infrastructure.
Stop and Think Box
People often believe that wars induce long-term economic growth; however, they are quite wrong. Use Figure 23.7 and the AS-AD model to explain why people think wars induce growth and why they are wrong.
Y* often increases during wars because AD shifts right because of increases in G (tanks, guns, ships, etc.) and I (new or improved factories to produce tanks, guns, ships, etc.) that exceed decreases in C (wartime rationing) and possibly NX (trade level decreases and/or subsidies provided to or by allies). Due to the right shift in AD, P* also rises, perhaps giving the illusion of wealth. After the war, however, two things occur: AD shifts back left as war production ceases and, to the extent that the long run comes home to roost, AS shifts left. Both lower Y* and the AD leftward shift decreases the price level. Empirically, wars are indeed often followed by recessions and deflation. Figure 23.7 shows what happened to prices and output in the United States during and after the Civil War (1861–1865) and World War I (1914–1918; direct U.S. involvement, 1917–1918), respectively. The last bastion of the warmongers is the claim that, by inducing technological development, wars cause Ynrl to shift right. Wars do indeed speedresearch and development, but getting a few new gizmos a few years sooner is not worth the wartime destruction of great masses of human and physical capital.
key takeaways
• The ASL is the amount of output that is obtainable in the long run given the available labor, technology, and physical capital set.
• It is vertical because it is insensitive to changes in the price level.
• Economists are not entirely certain why ASL shifts. Some point to hysteresis, others to real business cycles, still others to institutional improvements like the growth diamond.
• Nobody knows how long the long term is, but the answer is important for one’s attitude toward economic policymaking.
• Those who favor activist policies think the long term is a long way off indeed, so policymakers can benefit the economy by shifting AD and AS to the right.
• Those who are suspicious of interventionist policies think that the long run will soon be upon us, so interventionist policies cannot help the economy for long because output must soon return to Ynrl. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/23%3A_Aggregate_Supply_and_Demand_and_the_Growth_Diamond/23.03%3A_Equilibrium_Analysis.txt |
learning objective
1. What is the growth diamond and why is it important?
Over the last two decades or so, many scholars, including the author of this textbook, have examined the link between financial development and economic growth. They have found that financial repression, severe underdevelopment of financial intermediaries and markets, can stymie growth and that financial development paves the way for growth. The reason is clear: by reducing asymmetric information and tapping economies of scale (and scope), the financial system efficiently links investors to entrepreneurs, ensuring that society’s scarce resources are allocated to their highest valued uses and that innovative ideas get a fair trial.
The research agenda of some of those scholars, including the author of this textbook, has recently broadened to include more of the institutional factors that enhance or reduce economic growth, sustained rightward movements of Ynrl. A leading model, set forth by two economic historians who teach economics at New York University’s Stern School of Business,w4.stern.nyu.edu/economics/facultystaff.cfm?doc_id=1019 is called the growth diamond or diamond of sustainable growth.w4.stern.nyu.edu/sternbusiness/spring_2007/sustainableGrowth.html Imagine a baseball or softball diamond. At the bottom of the diamond is home plate, the most important base in the game, where the player both begins and, if successful, ends his or her journey. Looking out from home, first base is at the right corner; second base is at the top of the diamond, dead ahead; and third base is at the diamond’s left corner. To score a run, a player must return to home plate after touching first, second, and third base, in that order. Countries are no different than ballplayers in this regard. For a country to get rich, it needs to progress from base to base in the proper order.
In the growth diamond, home plate is represented by government, first base by the financial system, second base by entrepreneurs, and third base by management. To succeed economically, as depicted in Figure 23.8 , a country must first possess a solid home plate, a government that at a minimum protects the lives, liberty, and property of its citizens. Next, it must develop an efficient financial system capable of linking savers/investors to people with good business ideas, the entrepreneurs at second base. The managers at third take over after a product has emerged and matured.
The growth diamond is a powerful model because it can be applied to almost every country on earth. The poorest countries never left home plate because their governments killed and robbed their citizens. Poor but not destitute countries never made it to first base, often because their governments, while not outright predatory, restricted economic liberty to the point that financiers and entrepreneurs could not thrive. In many such countries, the financial system is the tool of the government (indeed many banks in poor countries are owned by the state outright), so they allocate resources to political cronies rather than to the best entrepreneurs. Countries with middling income rounded the bases once or twice but found that managers, entrepreneurs, and financiers co-opted the government and implemented self-serving policies that rendered it difficult to score runs frequently. Meanwhile the rich countries continue to rack up the runs, growing stronger as players circle the bases in a virtuous or self-reinforcing cycle.
Stop and Think Box
In the early nineteenth century, Ontario, Canada (then a colony of Great Britain), and New York State (then part of a fledgling but independent United States) enjoyed (perhaps hated is a better word here!) a very similar climate, soil type, and flora and fauna (plants and animals). Yet the population density in New York was much higher, farms (ceteris paribus) were worth four times more there than on the north side of Lake Ontario, and per capita incomes in New York dwarfed those of Ontario. What explains those differences?
The growth diamond does. By the early 1800s, the United States, of which New York State was a part, had put in place a nonpredatory government and a financial system that, given the technology of the day, was quite efficient at linking investors to entrepreneurs, the activities of whom received governmental sanction and societal support. A nascent management class was even forming. Ontario, by contrast, was a colony ruled by a distant monarch. Canadians had little incentive to work hard or smart, so they didn’t, and the economy languished, largely devoid of banks and other financial intermediaries and securities markets. As late as the 1830s, New York was sometimes “a better market for the sale of Canada exchange on London than Canada itself.”T. R. Preston, Three Years’ Residence in Canada, from 1837 to 1839, 2 vols., (London: Richard Bentley 1840), 185. Only after they shed their imperial overlords and reformed their domestic governments did Canadians develop an effective financial system and rid themselves of anti-entrepreneurial laws and sentiments. The Canadian economy then grew with rapidity, making Canada one of the world’s richest countries.
A narrower and more technical explanation of the higher value of New York farms comparable to Canadian farms in size, soil quality, rainfall, and so forth is that interest rates were much lower in New York. Valuing a farm is like valuing any income-producing asset. All it takes is to discount the farm’s expected future income stream. Holding expected income constant, the key to the equation becomes the interest rate, which was about four times lower in New York (say, 6 percent per year versus 24 percent). Recall that PV = FV/(1 + i). If FV (next year’s income) in both instances is 100, but i = .24 in Canada and .06 in New York, an investor would be willing to lease the New York farm for a year for 100/1.06 = \$94.34, but the Canadian farm for only 100/1.24 = \$80.65. The longer the time frame, the more the higher Canadian interest rate will bite. In the limit, we could price the farms as perpetuities using the equation PV = FV/i. That means the New York farm would be worth PV = 100/.06 = \$1,666.67, while the Canadian farm would be worth a mere PV = 100/.24 = \$416.67 (which, of course, times 4 equals the New York farm price). Canadian land values increased when Canadian interest rates decreased after about 1850.
One important implication of the growth diamond is that emerging (from eons of poverty) or transitioning (from communism) economies that are currently hot, like those of China and India, may begin to falter if they do not strengthen their governance, financial, entrepreneurial, and management systems. Some of today’s basket-case economies, including that of Argentina, were once high fliers that ran into an economic brick wall because they inadequately protected property rights, impeded financial development, and squelched entrepreneurship.
Although currently less analytically rigorous than the AS-AD model, the growth diamond is more historically grounded than the AS-AD model or any other macro model and that is important. As storied economist Will Baumol once put it,
We cannot understand current phenomena…without systematic examination of earlier events which affect the present and will continue to exercise profound effects tomorrow…[T]he long run is important because it is not sensible for economists and policymakers to attempt to discern long-run trends and their outcomes from the flow of short-run developments, which may be dominated by transient conditions.Will Baumol, “Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show,” American Economic Review 76 (December 1986): 1072–1086, as quoted in Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk (New York: John Wiley and Sons, 1996), 181.
key takeaways
• The growth diamond is a model of economic growth (increases in real per capita aggregate output) being developed by economic historians at the Stern School of Business.
• It posits that sustained, long-term economic growth is predicated on the existence of a nonpredatory government (home plate), an efficient financial system (first base), entrepreneurs (second base), and modern management (third base).
• It is important because it explains why some countries are very rich and others are desperately poor.
• It also explains why some countries, like Argentina, grew rich, only to fall back into poverty.
• Finally, it warns investors that the growth trends of current high fliers like China could reverse if they do not continue to strengthen their governance, financial, entrepreneurial, and management systems.
23.05: Suggested Reading
Baumol, William, Robert Litan, and Carl Schramm. Good Capitalism, Bad Capitalism, and the Economics of Growth and Prosperity. New Haven, CT: Yale University Press, 2007.
Haber, Stephen, Douglass North, and Barry Weingast. Political Institutions and Financial Development. Stanford, CA: Stanford University Press, 2008.
Powell, Benjamin. Making Poor Nations Rich: Entrepreneurship and the Process of Economic Development. Stanford, CA: Stanford University Press, 2008.
Wright, Robert E. One Nation Under Debt: Hamilton, Jefferson, and the History of What We Owe. New York: McGraw-Hill, 2008. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/23%3A_Aggregate_Supply_and_Demand_and_the_Growth_Diamond/23.04%3A_The_Growth_Diamond.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Explain why structural models are generally superior to reduced-form models.
2. Describe the types of evidence that can strengthen researchers’ conviction that a reduced-form model has the direction of causation right, say, from money (M) to output (Y).
3. Describe the evidence that money matters.
4. List and explain several important monetary policy transmission mechanisms.
Thumbnail: Image by David Schwarzenberg from Pixabay
24: Monetary Policy Transmission Mechanisms
learning objective
1. Why are structural models generally superior to reduced-form models?
We’ve learned in the last few chapters that monetary policy is not the end-all and be-all of the economy or even of policymakers’ attempts to manipulate it. But we knew that before. The question before us is, Given what we know of IS-LM and AS-AD, just how important is monetary policy? And how do we know? We’ve got theories galore—notions about how changes in sundry variables, like interest rates, create certain outcomes, like changes in prices and aggregate output. But how well do those theories describe reality? To answer those questions, we need empirical evidence, good hard numbers. We also need to know how scientists and social scientists evaluate such evidence.
Structural models explicitly link variables from initial cause all the way to final effect via every intermediate step along the causal chain. Reduced-form evidence makes assertions only about initial causes and ultimate effects, treating the links in between as an impenetrable black box. The quantity theory makes just such a reduced-form claim when it asserts that, as the money supply increases, so too does output. In other words, the quantity theory is not explicit about the transmission mechanisms of monetary policy. On the other hand, the assertion that increasing the money supply decreases interest rates, which spurs investment, which leads to higher output, ceteris paribus, is a structural model. Such a model can be assessed at every link in the chain: MS up, i down, I up, Y up. If the relationship between MS and Y begins to break down, economists with a structural model can try to figure out specifically why. Those touting only a reduced-form model will be flummoxed. Structural models also strengthen our confidence that changes in MS cause changes in Y.
Because they leave so much out, reduced-form models may point only to variables that are correlated, that rise and fall in tandem over time. Correlation, alas, is not causation; the link between variables that are only correlated can be easily broken. All sorts of superstitions are based on mere correlation, as their practitioners eventually discover to their chagrin and loss,www.dallasobserver.com/2005-09-08/dining/tryst-of-fate like those who wear goofy-looking rally caps to win baseball games.en.Wikipedia.org/wiki/Rally_cap Reverse causation is also rampant. People who see a high correlation between X and Y often think that X causes Y when in fact Y causes X. For example, there is a high correlation between fan attendance levels and home team victories. Some superfansen.Wikipedia.org/wiki/Bill_Swerski's_Superfans take this to “prove” that high attendance causes the home team to win by acting as a sixth, tenth, or twelfth player, depending on the sport. Fans have swayed the outcome of a few games, usually by touching baseballs still in play,www.usatoday.com/sports/columnist/lopresti/2003-10-15-lopresti_x.htm but the causation mostly runs in the other direction—teams that win many games tend to attract more fans.
Omitted variables can also cloud the connections made by reduced-form models. “Caffeine drinkers have higher rates of coronary heart disease (CHD) than people who don’t consume caffeine” is a reduced-form model that probably suffers from omitted variables in the form of selection biases. In other words, caffeine drinkers drink caffeine because they don’t get enough sleep; have hectic, stressful lives; and so forth. It may be that those other factors give them heart attacks, not the caffeine per se. Or the caffeine interacts with those other variables in complex ways that are difficult to unravel without growing human beings in test tubes (even more alarming!).
Stop and Think Box
A recent reduced-form study shows a high degree of correlation between smoking marijuana and bad life outcomes: long stints of unemployment, criminal arrests, higher chance of disability, lower lifetime income, and early death. Does that study effectively condemn pot smoking?
Not nearly as much as it would if it presented a structural model that carefully laid out and tested the precise chain by which marijuana smoking causes those bad outcomes. Omitted variables and even reverse causation can be at play in the reduced-form version. For example, some people smoke pot because they have cancer. Some cancer treatments require nasty doses of chemotherapy, the effect of which is to cause pain and reduce appetite. Taking a toke reduces the pain and restores appetite. Needless to say, such people have lower life expectancies than people without cancer. Therefore, they have lower lifetime income and a higher chance of disability and unemployment. Because not all states have medical marijuana exceptions, they are also more liable to criminal arrest. Similarly, unemployed people might be more likely to take a little Mary Jane after lunch or perhaps down a couple of cannabis brownies for dessert, again reversing the direction of causation. A possible omitted variable is selection bias: people who smoke pot might be less educated than those who abstain from the weed, and it is the dearth of education that leads to high unemployment, more arrests, and so forth. Unfortunately, bad science like this study pervades public discourse. Of course, this does not mean that you should go get yourself a blunt. Study instead. Correlation studies show that studying . . . .
key takeaways
• Structural models trace the entire causal chain, step by step, allowing researchers to be pretty confident about the direction of causation and to trace any breakdowns in the model to specific relationships.
• Reduced-form models link initial variables to supposed outcomes via an impenetrable black box.
• The problem is that correlation does not always indicate causation. X may increase and decrease with Y, although X does not cause Y because Y may cause X (reverse causation), or Z (an omitted variable) may cause X and Y.
• Reduced-form models can and have led to all sorts of goofy conclusions, like doctors kill people (they seem to be ubiquitous during plagues, accidents, and the like) and police officers cause crime (the number on the streets goes up during crime waves, and they are always at crime scenes—very suspicious). In case you can’t tell, I’m being sarcastic.
• On the other hand, reduced-form models are inexpensive compared to structural ones. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/24%3A_Monetary_Policy_Transmission_Mechanisms/24.01%3A_Modeling_Reality.txt |
learning objectives
1. What types of evidence can strengthen researchers’ conviction that a reduced-form model has the direction of causation right, say, from M to Y? How?
2. What evidence is there that money matters?
Early Keynesians believed that monetary policy did not matter at all because they could not find any evidence that interest rates affected planned business investment. Milton Friedman and Anna Schwartz, another monetarist, countered with a huge tome called A Monetary History of the United States, 1867–1960 which purported to show that the Keynesians had it all wrong, especially their kooky claim that monetary policy during the Great Depression had been easy (low real interest rates and MS growth). Nominal rates on risky securities had in fact soared in 1930–1933, the depths of the depression. Because the price level was falling, real interest rates, via the Fisher Equation, were much higher than nominal rates. If you borrowed \$100, you’d have to repay only \$102 in a year, but those 102 smackers could buy a heck of a lot more goods and services a year hence. So real rates were more on the order of 8 to 10 percent, which is pretty darn high. The link between interest rates and investment, the monetarists showed, was between investment and real interest rates, not nominal interest rates.
As noted above, the early monetarists relied on MV = PY, a reduced-form model. To strengthen their conviction that causation indeed ran from M to Y instead of Y to M or some unknown variables A…Z to M and Y, the monetarists relied on three types of empirical evidence: timing, statistical, and historical. Timing evidence tries to show that increases in M happen before increases in Y, and not vice versa, relying on the commonplace assumption that causes occur before their effects. Friedman and Schwartz showed that money growth slowed before recessions, but the timing was highly variable. Sometimes slowing money growth occurred sixteen months before output turned south; other times, only a few months passed. That is great stuff, but it is hardly foolproof because, as Steve Miller points out, time keeps on slipping, slipping, slipping, into the future.www.lyricsfreak.com/s/steve+miller/fly+like+an+eagle_20130994.html Maybe a decline in output caused the decline in the money supply by slowing demand for loans (and hence deposits) or by inducing banks to decrease lending (and hence deposits). Changes in M and Y, in other words, could be causing each other in a sort of virtuous or pernicious cycle or chicken-egg problem. Or again maybe there is a mysterious variable Z running the whole show behind the scenes.
Statistical evidence is subject to the same criticisms plus the old adage that there are three types of untruths (besides Stephen Colbert’s truthiness,en.Wikipedia.org/wiki/Truthiness of course): lies, damn lies, and statistics. By changing starting and ending dates, conflating the difference between statistical significance and economic significance,www.deirdremccloskey.com/articles/stats/preface_ziliak.php manipulating the dates of structural breaks, and introducing who knows how many other subtle little fibs, researchers can make mountains out of molehills, and vice versa. It’s kinda funny that when monetarists used statistical tests, the quantity theory won and money mattered, but when the early Keynesians conducted the tests, the quantity theory looked, if not insane, at least inane.
But Friedman and Schwartz had an empirical ace up their sleeves: historical evidence from periods in which declines in the money supply appear to be exogenous, by which economists mean “caused by something outside the model,” thus eliminating doubts about omitted variables and reverse causation. White-lab-coat scientists (you know, physicists, chemists, and so forth—“real” scientists) know that variables change exogenously because they are the ones making the changes. They can do this systematically in dozens, hundreds, even thousands of test tubes, Petri dishes, atomic acceleration experiments, and what not, carefully controlling for each variable (making sure that everything is ceteris paribus), then measuring and comparing the results. As social scientists, economists cannot run such experiments. They can and do turn to history, however, for so-called natural experiments. That’s what the monetarists did, and what they found was that exogenous declines in MS led to recessions (lower Y*) every time. Economic and financial history wins! (Disclaimer: The author of this textbook is a financial historian.) While they did not abandon the view that C, G, I, NX, and T also affect output, Keynesians now accept money’s role in helping to determine Y. (A new group, the real-business-cycle theorists associated with the Minneapolis Fed, has recently challenged the notion that money matters, but those folks haven’t made it into the land of undergraduate textbooks quite yet, except in passing.)
key takeaways
• Timing, statistical, and historical evidence strengthen researchers’ belief in causation.
• Timing evidence attempts to show that changes in M occur before changes in Y.
• Statistical evidence attempts to show that one model’s predictions are closer to reality than another’s.
• The problem with stats, though, is that those running the tests appear to rig them (consciously or not), so the stats often tell us more about the researcher than they do about reality.
• Historical evidence, particularly so-called natural experiments in which variables change exogenously and hence are analogous to controlled scientific experiments, provide the best sort of evidence on the direction of causation.
• The monetarists showed that there is a strong correlation between changes in the MS and changes in Y and also proffered timing, statistical, and historical evidence of a causal link.
• Historical evidence is the most convincing because it shows that the MS sometimes changed exogenously, that is, for reasons clearly unrelated to Y or other plausible causal variables, and that when it did, Y changed with the expected sign (+ if MS increased, − if it decreased). | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/24%3A_Monetary_Policy_Transmission_Mechanisms/24.02%3A_How_Important_Is_Monetary_Policy.txt |
learning objective
1. What are monetary policy transmission mechanisms and why are they important?
Most economists accept the proposition that money matters and have been searching for structural models that delineate the specific transmission mechanisms between MS and Y. The most basic model says the following:
Expansionary monetary policy (EMP), real interest rates down, investment up, aggregate output up
The importance of interest rates for consumer expenditures (especially on durables like autos, refrigerators, and homes) and net exports has also been recognized, leading to the following:
EMP, ir ↓, I ↑, C ↑, NX ↑, Y ↑
Tobin’s q, the market value of companies divided by the replacement cost of physical capital, is clearly analogous to i and related to I. When q is high, firms sell their highly valued stock to raise cash and buy new physical plant and build inventories. When q is low, by contrast, firms don’t get much for their stock compared to the cost of physical capital, so they don’t sell stock to fund increases in I. By increasing stock prices, the MS may be positively related to q. Thus, another monetary policy transmission mechanism may be the following:
EMP, Ps↑, q ↑, I ↑, Y↑
The wealth effect is a transmission mechanism whereby expansionary monetary policy leads to increases in the prices of stocks (Ps), homes, collectibles, and other assets (Pa), in other words, an increase in individual wealth. That increase, in turn, induces people to consume more:
EMP, Pa ↑, wealth ↑, C ↑, Y↑
The credit view posits several straightforward transmission mechanisms, including bank loans, asymmetric information, and balance sheets:
EMP, bank deposits ↑, bank loans ↑, I ↑, Y↑
EMP, net worth ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
EMP, i ↓, cash flow ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
EMP, unanticipated P* ↑, real net worth ↑, asymmetric information ↓, lending ↑, I ↑, Y↑
Asymmetric information is a powerful and important theory, so scholars’ confidence in these transmission mechanisms is high.
Stop and Think Box
The Fed thought that it would quickly squelch the recession that began in March 2001, yet the downturn lasted until November of that year. The terrorist attacks that September worsened matters, but the Fed had hoped to reverse the drop in Y* well before then. Why was the Fed’s forecast overly optimistic? (Hint: Corporate accounting scandals at Enron, Arthur Andersen, and other firms were part of the mix.)
The Fed might not have counted on some major monetary policy transmission mechanisms, including reductions in asymmetric information, being muted by the accounting scandals. In other words,
EMP, net worth ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
EMP, i ↓, cash flow ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
EMP, unanticipated P ↑, real net worth ↑, asymmetric information ↓, lending ↑, I ↑, Y↑
became something more akin to the following:
EMP, net worth ↑, asymmetric information — (flat or no change), lending —, I ↑, C —, Y —
EMP, i ↑, cash flow ↑, asymmetric information —, lending —, I ↑, C —, Y —
EMP, unanticipated P ↑, real net worth ↑, asymmetric information—, lending —, I —, Y — because asymmetric information remained high due to the fact that economic agents felt as though they could no longer count on the truthfulness of corporate financial statements.
The takeaway of all this for monetary policymakers, and those interested in their policies (including you), is that monetary policy needs to take more into account than just short-term interest rates. Policymakers need to worry about real interest rates, including long-term rates; unexpected changes in the price level; the interest rates on risky bonds; the prices of other assets, including corporate equities, homes, and the like; the quantity of bank loans; and the bite of adverse selection, moral hazard, and the principal-agent problem.
Stop and Think Box
Japan’s economy was going gangbusters until about 1990 or so, when it entered a fifteen-year economic funk. To try to get the Japanese economy moving again, the Bank of Japan lowered short-term interest rates all the way to zero for many years on end, to no avail. Why didn’t the Japanese economy revive due to the monetary stimulus? What should the Japanese have done instead?
As it turns out, ir stayed quite high because the Japanese expected, and received, price deflation. Through the Fisher Equation, we know that ir = i − πe, or real interest rates equal nominal interest rates minus inflation expectations. If πe is negative, which it is when prices are expected to fall, ir will be > i. So i can be 0 but ir can be 1, 2, 3…10 percent per year if prices are expected to decline by that much. So instead of EMP, ir ↓, I ↓ C ↓ NX ↑, Y↑ the Japanese experienced ir ↑, I ↓ C ↓ NX ↓, Y↓. Not good. They should have pumped up the MS much faster, driving πe from negative whatever to zero or even positive, and thus making real interest rates low or negative, and hence a stimulant. The Japanese made other mistakes as well, allowing land and equities prices to plummet, thereby nixing the Tobin’s q and wealth effect transmission mechanisms. They also kept some big shaky banks from failing, which kept levels of asymmetric information high and bank loan levels low, squelching the credit channels.
key takeaways
• Monetary policy transmission mechanisms are essentially structural models that predict the precise chains of causation between expansionary monetary policy (EMP) or tight monetary policy (TMP) and Y.
• They are important because they provide central bankers and other monetary policymakers with a detailed view of how changes in the MS affect Y, allowing them to see why some policies don’t work as much or as quickly as anticipated.
• That, in turn, allows them to become better policymakers, to the extent that is possible in a world of rational expectations.
• Transmission mechanisms include:
• EMP, ir↓, I ↑ C ↑, NX ↑, Y↑, EMP, q ↑, I ↑, Y↑
• EMP, Pa ↑, wealth ↑, C ↑, Y↑
• EMP, bank deposits ↑, bank loans ↑, I ↑, Y↑
• EMP, net worth ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
• EMP, i ↓, cash flow ↑, asymmetric information ↓, lending ↑, I ↑, C ↑, Y↑
• EMP, unanticipated P* ↑, real net worth ↑, asymmetric information ↓, lending ↑, I ↑, Y↑
24.04: Suggested Reading
Angeloni, Ignazio, Anil Kashyap, and Benoit Mojon. Monetary Policy Transmission in the Euro Area. New York: Cambridge University Press, 2004.
Friedman, Milton, and Anna Schwartz. A Monetary History of the United States, 1867–1960. Princeton, NJ: Princeton University Press, 1971.
Mahadeva, Lavan, and Peter Sinclair. Monetary Transmission in Diverse Economies. New York: Cambridge University Press, 2002. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/24%3A_Monetary_Policy_Transmission_Mechanisms/24.03%3A_Transmission_Mechanisms.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Describe the strongest evidence for the reduced-form model that links money supply growth to inflation.
2. Explain what the aggregate supply-aggregate demand (AS-AD) model, a structural model, says about money supply growth and the price level.
3. Explain why central bankers allow inflation to occur year after year.
4. Define lags and explain their importance.
Thumbnail: Image by Pete Linforth from Pixabay
25: Inflation and Money
learning objectives
1. What is the strongest evidence for the reduced-form model that links money supply growth to inflation?
2. What does the AS-AD model, a structural model, say about money supply growth and the price level?
Milton Friedman claimed that “inflation is always and everywhere a monetary phenomenon.”A Monetary History of the United States, 1867–1960. We know this isn’t true if one takes a loose view of inflation because negative aggregate supply shocks and increases in aggregate demand due to fiscal stimulus can also cause the price level to increase. Large, sustained increases in the price level, however, are indeed proximately caused by increases in the money supply and only by increases in the money supply. The evidence for this is overwhelming: all periods of hyperinflation from the American and French Revolutions to the German hyperinflation following World War I, to more recent episodes in Latin America and Zimbabwe, have been accompanied by high rates of money supply (MS) growth.In most of those instances, the government printed money in order to finance large budget deficits. The rebel American, French, and Confederate (Southern) governments could not raise enough in taxes or by borrowing to fund their wars, the Germans could not pay off the heavy reparations imposed on them after World War I, and so forth. We know that the deficits themselves did not cause inflation, however, because in some instances governments have dealt with their budget problems in other ways without sparking inflation, and in some instances rapid money creation was not due to seriously unbalanced budgets. So the proximate cause of inflation is rapid money growth, which often, but not always, is caused by budget deficits. Moreover, the MS increases in some circumstances were exogenous, so those episodes were natural experiments that give us confidence that the reduced-form model correctly considers money supply as the causal agent and that reverse causation or omitted variables are unlikely.
Stop and Think Box
During the American Civil War, the Confederate States of America (CSA, or the South) issued more than \$1 billion of fiat paper currency similar to today’s Federal Reserve notes, far more than the economy could support at the prewar price level. Confederate dollars fell in value from 82.7 cents in specie in 1862 to 29.0 cents in 1863, to 1.7 cents in 1865, a level of currency depreciation (inflation) that some economists think was simply too high to be accounted for by Confederate money supply growth alone. What other factors may have been at play? (Hint: Over the course of the war, the Union [the North] imposed a blockade of southern trade that increased in efficiency during the course of the war, especially as major Confederate seaports like New Orleans and Norfolk fell under northern control.)
A negative supply shock, the almost complete cutoff of foreign trade, could well have hit poor Johnny Reb (the South) as well. That would have decreased output and driven prices higher, prices already raised to lofty heights by continual emissions of too much money.
Economists also have a structural model showing a causal link between money supply growth and inflation at their disposal, the AS-AD model. Recall that an increase in MS causes the AD curve to shift right. That, in turn, causes the short-term AS curve to shift left, leading to a return to Ynrl but higher prices. If the MS grows and grows, prices will go up and up, as in Figure 25.1 .
Nothing else, it turns out, can keep prices rising, rising, ever rising like that because other variables are bounded. An increase in government expenditure G will also cause AD to shift right and AS to shift left, leaving the economy with the same output but higher prices in the long run (whatever that is). But if G stops growing, as it must, then P* stops rising and inflation (the change in P*) goes to zero. Ditto with tax cuts, which can’t fall below zero (or even get close to it). So fiscal policy alone can’t create a sustained rise in prices. (Or a sustained decrease either.)
Negative supply shocks are also one-off events, not the stuff of sustained increases in prices. An oil embargo or a wage push will cause the price level to increase (and output to fall, ouch!) and negative shocks may even follow each other in rapid succession. But once the AS curve is done shifting, that’s it—P* stays put. Moreover, if Y* falls below Ynrl, in the long run (again, whatever that is), increased unemployment and other slack in the economy will cause AS to shift back to the right, restoring both output and the former price level!
So, again, Friedman was right: inflation, in the sense of continual increases in prices, is always a monetary phenomenon and only a monetary phenomenon.This is not to say, however, that negative demand shocks might not contribute to a general monetary inflation.
Stop and Think Box
Figure 25.2 compares inflation with M1 growth lagged two years. What does the data tell you? Now look at Figure 25.3 and Figure 25.4 . What caused M1 to grow during the 1960s?
The data clearly show that M1 was growing over the period and likely causing inflation with a two-year lag. M1 grew partly because federal deficits increased faster than the economy, increasing the debt-to-GDP ratio, eventually leading to some debt monetization on the part of the Fed. Also, unemployment rates fell considerably below the natural rate of unemployment, suggesting that demand-pull inflation was taking place as well.
key takeaways
• Throughout history, exogenous increases in MS have led to increases in P*. Every hyperinflation has been preceded by rapid increases in money supply growth.
• The AS-AD model shows that money supply growth is the only thing that can lead to inflation, that is, sustained increases in the price level.
• This happens because monetary stimulus in the short term shifts the AD curve to the right, increasing prices but also rendering Y* > Ynrl.
• Unemployment drops, driving up wages, which shifts the AS curve to the left, Y* back to Ynrl, and P* yet higher.
• Unlike other variables, the MS can continue to grow, initiating round after round of this dynamic.
• Other variables are bounded and produce only one-off changes in P*.
• A negative supply shock or wage push, for instance, increases the price level once, but then price increases stop.
• Similarly, increases in government expenditures can cause P* to rise by shifting AD to the right, but unlike increases in the MS, government expenditures can increase only so far politically and practically (to 100 percent of GDP). | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/25%3A_Inflation_and_Money/25.01%3A_Empirical_Evidence_of_a_Money-Inflation_Link.txt |
learning objectives
1. Given the analysis in this chapter, why do central bankers sometimes allow inflation to occur year after year?
2. What are lags and why are they important?
If the link between money supply growth and inflation is so clear, and if nobody (except perhaps inveterate debtors) has anything but contempt for inflation, why have central bankers allowed it to occur so frequently? Not all central banks are independent of the fiscal authority and may simply print money on its behalf to finance budget deficits, the stuff of hyperinflations. In addition, central bankers might be more privately interested than publicly interested and somehow benefit personally from inflation. (They might score points with politicians for stimulating the economy just before an election or they might take out big loans and repay them after the inflationary period in nearly worthless currency.) Assuming central bankers are publicly interested but far from prescient, what might cause them to err so often? In short, lags and high-employment policies.
A lag is an amount of time that passes between a cause and its eventual effect. Lags in monetary policy, Friedman showed, were “long and variable.” Data lag is the time it takes for policymakers to get important information, like GDP (Y) and unemployment. Recognition lag is the time it takes them to become convinced that the data is accurate and indicative of a trend and not just a random perturbation. Legislative lag is the time it takes legislators to react to economic changes. (This is short for monetary policy, but it can be a year or more for fiscal policy.) Implementation lag refers to the time between policy decision and implementation. (Again, for modern central banks using open market purchases [OMPs], this lag is minimal, but for changes in taxes, it can take a long time indeed.) The most important lag of all is the so-called effectiveness lag, the period between policy implementation and real-world results. Business investments, after all, typically take months or even years to plan, approve, and implement.
All told, lags can add up to years and add considerable complexity to monetary policy analysis because they cloud cause-effect relationships. Lags also put policymakers perpetually behind the eight-ball, constantly playing catch-up. Lags force policymakers to forecast the future with accuracy, something (as we’ve seen) that is not easily done. As noted in earlier chapters, economists don’t even know when the short run becomes the long run!
Consider a case of so-called cost-push inflation brought about by a negative supply shock or wage push. That moves the AS curve to the left, reducing output and raising prices and, in all likelihood, causing unemployment and political angst. Policymakers unable to await the long term (the rightward shift in AS because Y* has fallen below Ynrl, causing unemployment and wages to decline) may well respond with what’s called accommodative monetary policy. In other words, they engage in expansionary monetary policies (EMPs), which shift the AD curve to the right, causing output to increase (with a lag) but prices to rise. Because prices are higher and they’ve been recently rewarded for their wage push with accommodative monetary policy, workers may well initiate another wage push, starting a vicious cycle of wage pushes followed by increases in P* and yet more wage pushes. Monetarists and other nonactivists shake their heads at this dynamic, arguing that if workers’ wage pushes were met by periods of higher unemployment, they would soon learn to stop. (After all, even 2-year-olds and rats eventually learn to stop pushing buttons if they are not rewarded for doing so. They learn even faster to stop pushing if they get a little shock.)
An episode of demand-pull inflation can also touch off accommodative monetary policy and a bout of inflation. If the government sets its full employment target too high, above the natural rate, it will always look like there is too much unemployment. That will eventually tempt policymakers into thinking that Y* is < Ynrl, inducing them to implement an EMP. Output will rise, temporarily, but so too will prices. Prices will go up again when the AS curve shifts left, back to Ynrl, as it will do in a hurry given the low level of unemployment. The shift, however, will again increase unemployment over the government’s unreasonably low target, inducing another round of EMP and price increases.
Another source of inflation is government budget deficits. To cover their expenditures, governments can tax, borrow at interest, or borrow for free by issuing money. (Which would you choose?) Taxation is politically costly. Borrowing at interest can be costly too, especially if the government is a default risk. Therefore, many governments pay their bills by printing money or by issuing bonds that their respective central banks then buy with money. Either way, the monetary base increases, leading to some multiple increases in the MS, which leads to inflation. Effectively a tax on money balances called a currency tax, inflation is easier to disguise and much easier to collect than other forms of taxes. Governments get as addicted to the currency tax as individuals get addicted to crack or meth. This is especially true in developing countries with weak (not independent) central banks.
Stop and Think Box
Why is central bank independence important in keeping inflation at bay?
Independent central banks are better able to withstand political pressures to monetize the debt, to follow accommodative policies, or to respond to (seemingly) “high” levels of unemployment with an EMP. They can also make a more believable or credible commitment to stop inflation, which is an important consideration as well.
key takeaways
• Private-interest scenarios aside, publicly interested central bankers might pursue high employment too vigorously, leading to inflation via cost-push and demand-pull mechanisms.
• If workers make a successful wage push, for example, the AS curve will shift left, increasing P*, decreasing Y*, and increasing unemployment.
• If policymakers are anxious to get out of recession, they might respond with an expansionary monetary policy (EMP).
• That will increase Y* but also P* yet again. Such an accommodative policy might induce workers to try another wage push. The price level is higher after all, and they were rewarded for their last wage push.
• The longer this dynamic occurs, the higher prices will go.
• Policymakers might fall into this trap themselves if they underestimate full employment at, say, 97 percent (3 percent unemployment) when in fact it is 95 percent (5 percent unemployment).
• Therefore, unemployment of 4 percent looks too high and output appears to be < Ynrl, suggesting that an EMP is in order.
• The rightward shift of the AD curve causes prices and output to rise, but the latter rises only temporarily as the already tight labor market gets tighter, leading to higher wages and a leftward shift of the AS curve, with its concomitant increase in P* and decrease in Y*.
• If policymakers’ original and flawed estimate of full employment is maintained, another round of AD is sure to come, as is higher prices.
• Budget deficits can also lead to sustained inflation if the government monetizes its debt directly by printing money (and deposits) or indirectly via central bank open market purchases (OMPs) of government bonds.
• Lags are the amount of time it takes between a change in the economy to take place and policymakers to effectively do something about it.
• That includes lags for gathering data, making sure the data show a trend and are not mere noise, making a legislative decision (if applicable), implementing policy (if applicable), and waiting for the policy to affect the economy.
• Lags are important because they are long and variable, thus complicating monetary policy by making central bankers play constant catch-up and also by clouding cause-effect relationships.
25.03: Suggested Reading
Ball, R. J. Inflation and the Theory of Money. Piscataway, NJ: Aldine Transaction, 2007.
Bresciani-Turroni, Costantino. Economics of Inflation. Auburn, AL: Ludwig von Mises Institute, 2007.
Samuelson, Robert. The Great Inflation and Its Aftermath: The Past and Future of American Affluence. New York: Random House, 2008. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/25%3A_Inflation_and_Money/25.02%3A_Why_Have_Central_Bankers_So_Often_Gotten_It_Wrong.txt |
Chapter Objectives
By the end of this chapter, students should be able to:
1. Describe how the new classical macroeconomic model differs from the standard, pre-Lucas AS-AD model.
2. Explain what the new classical macroeconomic model suggests regarding the efficacy of activist monetary policy.
3. Explain how the new Keynesian model differs from the new classical macroeconomic model.
4. Assess the extent to which policymakers can improve short-run macroeconomic performance.
Thumbnail: Image by Pixabay
26: Rational Expectations Redux- Monetary Policy Implications
learning objectives
1. How does the new classical macroeconomic model differ from the standard, pre-Lucas AS-AD model?
2. What does the new classical macroeconomic model suggest regarding the efficacy of activist monetary policy? Why?
Rational expectations is an economic theory that postulates that market participants input all available relevant information into the best forecasting model available to them. Although individual forecasts can be very wide of the mark, actual economic outcomes do not vary in a predictable way from participants’ aggregate predictions or expectations. Perhaps Abraham Lincoln summed it up best when he asserted that “you can fool some of the people all of the time, and all of the people some of the time, but you cannot fool all of the people all of the time.”www.econlib.org/library/Enc/RationalExpectations.html
That might sound like a trite insight, but the theory of rational expectations has important implications for monetary policy. In a quest to understand why policymakers had such a poor record, especially during the 1970s, Len Mirman (University of Virginia),www.virginia.edu/economics/mirman.htm Robert Lucas (University of Chicago),home.uchicago.edu/~sogrodow Thomas Sargent (New York University),homepages.nyu.edu/~ts43 Bennett McCallum (Carnegie-Mellon),public.tepper.cmu.edu/facultydirectory/FacultyDirectoryProfile.aspx?ID=96 Edward Prescott (Arizona State),www.minneapolisfed.org/research/prescott and other economists of the so-called expectations revolution discovered that expansionary monetary policies cannot be effective if economic agents expect them to be implemented. Conversely, to thwart inflation as quickly and painlessly as possible, the central bank must be able to make a credible commitment to stop it. In other words, it must convince people that it can and will stop prices from rising.
Stop and Think Box
During the American Revolution, the Continental Congress announced that it would stop printing bills of credit, the major form of money in the economy since 1775–1776, when rebel governments (the Continental Congress and state governments) began financing their little revolution by printing money. The Continental Congress implemented no other policy changes, so everyone knew that its large budget deficits would continue. Prices continued upward. Why?
The Continental Congress did not make a credible commitment to end inflation because its announcement did nothing to end its large and chronic budget deficit. It also did nothing to prevent the states from issuing more bills of credit.
Lucas was among the first to highlight the importance of public expectations in macroeconomic forecasting and policymaking. What matters, he argued, was not what policymakers’ models said would happen but what economic agents (people, firms, governments) believed would occur. So in one instance, a rise in the fed funds rate might cause long-term interest rates to barely budge, but in another it might cause them to soar. In short, policymakers can’t be certain of the effects of their policies before implementing them.
Because Keynesian cross diagrams and the IS-LM and AS-AD models did not explicitly take rational expectations into account, Lucas, Sargent, and others had to recast them in what is generally called the new classical macroeconomic model. That new model uses the AS, ASL, and AD curves but reduces the short run of aggregate demand shocks to zero if the policy is expected. So, for example, an anticipated EMP shifts AD right but immediately shifts AS left as workers spontaneously push for higher wages. The price level rises, but output doesn’t budge. An unanticipated EMP, by contrast, has the same effect as described in earlier chapters—a temporary (but who knows how long?) increase in output (and a rise in P followed by another when the AS curve eventually shifts left).
Now get this: Y* can actually decline if an EMP is not as expansionary as expected! If economic actors expect a big shift in AD, the AS curve will shift hard left to keep Y* at Ynrl, as in Figure 26.1 . If the AD curve does not shift as far right as expected, or indeed if it stays put, prices will rise and output will fall, as in the following graph. This helps to explain why financial markets sometimes react badly to small decreases in the Fed’s fed funds target. They expected more!
What this means for policymakers is that they have to know not only how the economy works, which is difficult enough, they also have to know the expectations of economic agents. Figuring out what those expectations are is quite difficult because economic agents are numerous and often have conflicting expectations, and weighting them by their importance is super-duper-tough. And that is at T1. At T2, nanoseconds from now, expectations may be very different.
key takeaways
• The new classical macroeconomic model takes the theory of rational expectations into account, essentially driving the short run to zero when economic actors successfully predict policy implementation.
• The new classical macroeconomic model draws the efficacy of EMP or expansionary fiscal policy (EFP) into serious doubt because if market participants anticipate it, the AS curve will immediately shift left (workers will demand higher wages and suppliers will demand higher prices in anticipation of inflation), keeping output at Ynrl but moving prices significantly higher.
• Stabilization (limiting fluctuations in Y*) is also difficult because policymakers cannot know with certainty what the public’s expectations are at every given moment.
• The good news is that the model suggests that inflation can be ended immediately without putting the economy into recession (decreasing Y*) if policymakers (central bankers and those in charge of the government’s budget) can credibly commit to squelching it.
• That is because workers and others will stop pushing the AS curve to the left as soon as they believe that prices will stay put. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/26%3A_Rational_Expectations_Redux-_Monetary_Policy_Implications/26.01%3A_Rational_Expectations.txt |
learning objective
1. How does the new Keynesian model differ from the new classical macroeconomic model?
The new classical macroeconomic model aids the cause of nonactivists, economists who believe that policymakers should have as little discretion as possible, because it suggests that policymakers are more likely to make things (especially P* and Y*) worse rather than better. The activists could not stand idly by but neither could they ignore the implications of Lucas’s critique of prerational expectations macroeconomic theories. The result was renewed research that led to the development of what is often called the new Keynesian model. That model directly refutes the notion that wages and prices respond immediately and fully to expected changes in P*. Workers in the first year of a three-year labor contract, for example, can’t push their wages higher no matter their expectations. Firms are also reluctant to lower wages even when unemployment is high because doing so may exacerbate the principal-agent problem in the form of labor strife, everything from slacking to theft, to strikes. New hires might be brought in at lower wages, but if turnover is low, that process could take years to play out. Similarly, companies often sign multiyear fixed-price contracts with their suppliers and/or distributors, effectively preventing them from acting on new expectations of P*. In short, wages and prices are “sticky” and hence adjustments are slow, not instantaneous as assumed by Lucas and company.
If that is the case, as Figure 26.2 shows, anticipated policy can and does affect Y*, although not as much as an unanticipated policy move of the same type, timing, and magnitude would. The Takeaway is that an EMP, even if it is anticipated, can have positive economic effects (Y* > Ynrl for some period of time), but it is better if the central bank initiates unanticipated policies. And there is still a chance that policies will backfire if wages and prices are not as sticky as people believe, or if expectations and actual policy implementation differ greatly.
Adherents of the new classical macroeconomic model believe that stabilization policy, the attempt to keep output fluctuations to a minimum, is likely to aggravate changes in Y* as policymakers and economic agents attempt to outguess each other—policymakers by initiating unanticipated policies and economic agents by anticipating them! New Keynesians, by contrast, believe that some stabilization is possible because even anticipated policies have some short-run effects due to wage and price stickiness.
Stop and Think Box
In the early 1980s, U.S. President Ronald Reagan and U.K. Prime Minister Margaret Thatcher announced the same set of policies: tax cuts, more defense spending, and anti-inflationary monetary policy. In both countries, sharp recessions with high unemployment occurred, but the inflation beast was eventually slain. Why did that particular outcome occur?
Tax cuts plus increased defense spending meant larger budget deficits, which spells EFP and a rightward shift in AD. That, of course, ran directly counter to claims about fighting inflation, which were not credible and hence not anticipated. But the Fed and the Bank of England did get tough by raising overnight interest rates to very high levels (about 20 percent!). As a result, the happy conclusions of the new classical macroeconomic model did not hold. The AS curve shifted hard left, while the AD curve did not shift as far right as expected. The result was that prices went up somewhat while output fell. Eventually market participants figured out what was going on and adjusted their expectations, returning Y* to Ynrl and stopping further big increases in P*.
key takeaways
• The new Keynesian model leaves more room for discretionary monetary policy.
• Like the new classical macroeconomic model, it is post-Lucas and hence realizes that expectations are important to policy outcomes.
• Unlike the new classical macroeconomic model, however, it posits significant wage and price stickiness (basically long-term contracts) that prevents the AS curve from shifting immediately and completely, regardless of the expectations of economic actors.
• EMP (and EFP) can therefore increase Y* over Ynrl, although less than if the policy were unanticipated (although, of course, at the cost of higher P*; the long-term analysis of the AS-AD model still holds). Similarly, to the extent that wages and prices are sticky, some stabilization is possible because policymakers can count on some output response to their policies.
• The new Keynesian model is more pessimistic about curbing inflation, however, because the stickiness of the AS curve prevents prices and wages from completely and instantaneously adjusting to a credible commitment.
• Output losses, however, will be smaller than an unanticipated move to squelch inflation. Some economists think it is possible to minimize the output losses further by essentially reducing the stickiness of the AS by credibly committing to slowly reducing inflation. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/26%3A_Rational_Expectations_Redux-_Monetary_Policy_Implications/26.02%3A_New_Keynesians.txt |
learning objective
1. Can policymakers improve short-run macroeconomic performance? If so, how?
Fighting inflation requires the central bank to hold the line on AD, even in the face of a leftward shift in the AS curve that causes a recession (Y* < Ynrl). The question is, How much will fighting inflation “cost” the economy in terms of lost output? According to the pre-Lucas AS-AD model, about 4 percent per year for each 1 percent shaved from inflation! The new classical macroeconomic model, by contrast, is much more optimistic. If the public knows and believes that the central bank will fight inflation, output won’t fall at all because both the AD and the AS curves will stay put. Workers won’t fight for higher wages because they expect P* will stay the same. An unanticipated anti-inflation stance, by contrast, will cause a recession. The moral of the story told by the new classical macroeconomic model appears to be that the central bank should be very transparent about fighting inflation but opaque about EMP!
The new Keynesian model also concludes that an unanticipated anti-inflation policy is worse than an anticipated and credible one, though it suggests that some drop in Y* should be expected due to stickiness. A possible solution to that problem is to slowly ease money supply growth rather than slamming the brakes on. If the slowing is expected and credible (in other words, if economic agents know the slowing is coming and fully expect it to continue until inflation is history), the AS curve can be “destickyfied” to some degree. Maybe contracts indexed to inflation will expire and not be renewed, new contracts will build in no or at least lower inflation expectations, or perhaps contracts (for materials or labor) will become shorter term. If that is the case, when money supply growth finally stops, something akin to the unsticky world of the new classical macroeconomic model will hold; the AS curve won’t shift much, if at all; and inflation will cease without a major drop in output.
How can central bankers increase their credibility? One way is to make their central banks more independent. Another is not to repeatedly announce A but do B. A third is to induce the government to decrease or eliminate budget deficits.
Figure 26.3 summarizes the differences between the pre-Lucas AS-AD model, the new classical macroeconomic model, and the New Keynesian model.
Stop and Think Box
In Bolivia in the first half of 1985, prices rose by 20,000 percent. Within one month, inflation was almost eliminated at the loss of only 5 percent of gross domestic product (GDP). How did the Bolivians manage that? Which theory does the Bolivian case support?
A new Bolivian government came in and announced that it would end inflation. It made the announcement credible by reducing the government’s deficit, the main driver of money expansion, in a very credible way, by balancing its budget every single day! This instance, which is not atypical of countries that end hyperinflation, supports the two rational expectation-based models over the pre-Lucas AS-AD model, which predicts 4 percent losses in GDP for every 1 percent decrease in the inflation rate. The fact that output did decline somewhat may mean that the policy was not credible at first or it may mean that the new Keynesian model has it right and the AS curve was a little bit sticky.
key takeaways
• Whether policymakers can improve short-term macroeconomic performance depends on the degree of wage and price stickiness, that is, how much more realistic the new Keynesian model is than the new classical macroeconomic model.
• If the latter is correct, any attempts at EMP and EFP that are anticipated by economic actors will fail to raise Y* and, in fact, can reduce Y* if the stimulus is less than the public expected. The only hope is to implement unanticipated policies, but that is difficult to do because central bankers can never be absolutely sure what expectations are at the time of policy implementation.
• On the other hand, inflation can be squelched relatively easily by simply announcing the policy and taking steps to ensure its credibility.
• If the new Keynesian model is correct, Y* can be increased over Ynrl (in the short term only, of course) because, regardless of expectations, wages and prices cannot rise due to multiyear contractual commitments like labor union contracts and other sources of stickiness.
• Inflation can also be successfully fought by announcing a credible policy, but due to wage and price stickiness, it will take a little time to take hold and output will dip below Ynrl, though by much less than the pre-Lucas AS-AD model predicts.
26.04: Suggested Reading
Gali, Jordi. Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework. Princeton, NJ: Princeton University Press, 2008.
Lucas, Robert, and Thomas Sargent. Rational Expectations and Econometric Practice. Minneapolis: University of Minnesota Press, 1981.
Scheffrin, Steven. Rational Expectations. New York: Cambridge University Press, 1996. | textbooks/biz/Finance/Book%3A_Finance_Banking_and_Money/26%3A_Rational_Expectations_Redux-_Monetary_Policy_Implications/26.03%3A_Inflation_Busting.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) recognize the six steps included in the management process; (2) apply the management process to better manage the financial resources of the small to medium-size firm; and (3) apply the management process to other activities such as being a successful student.
To achieve your learning goals, you should complete the following objectives:
• Understand the need for a concise firm mission statement.
• Learn how to distinguish between the firm’s strategic (long-term) goals and its tactical (short-term) objectives.
• Learn how to choose goals and objectives that will successfully guide financial managers in the financial management process.
• Learn how to identify a firm’s (internal) strengths and weaknesses.
• Learn how to identify a firm’s (external) opportunities and threats.
• Learn how to develop a strategy to reach the firm’s goals and objectives that take advantage of the firm’s strengths and opportunities and minimize the limitations of its weaknesses and threats.
• Learn how to implement and evaluate outcomes of the firm’s strategy for achieving its goals and objectives.
• Learn how to apply the management process to one’s own efforts to succeed in this class.
Introduction to Management
Financial management is about, above all else, management. The verb manage comes from an Italian verb meaning “to handle” as in how a rider handles a horse. The management process can be applied to a wide variety of organizations and resources. In this book, we apply the management process to managing the financial resources of the small business as opposed to larger corporations.
The Management Process
The management process includes six steps: 1) develop the firm’s mission statement; 2) choose the firm’s strategic (long-term) goals and tactical (short-term) objectives; 3) identify the firm’s strengths, weaknesses, opportunities, and threats; 4) develop the firm’s strategy for accomplishing its strategic goals and tactical objectives; 5) implement the firm’s strategy; and 6) evaluate the firm’s performance.
These six steps are illustrated in Figure 1.1 followed by narrative that describes them in more detail. Note that as one moves from one management step to the other, one moves toward the center of the circle in Figure 1.1. And as one moves toward the center of the circle, each activity is constrained by previous management choices.
Figure 1.1. The Managerial Process in Six Steps
So what have we learned? We learned that the management process includes six steps: 1) develop a mission statement; 2) choose strategic goals and tactical objectives; 3) identify the firm’s strengths, weaknesses, opportunities, and threats; 4) identify strategies, 5) implement strategies; and 6) evaluate performance.
Develop the Firm’s Mission Statement
The management process begins with a mission statement. The firm’s mission statement explains why the firm exists and what it values. The mission statement may also establish criteria for selecting activities in which the firm will participate. Mission statements might also describe the firm’s customers, the markets in which it will participate, and the firm’s social responsibilities. Mission statements are often succinct, short, easy to express and remember, clear, and flexible enough to describe the entire range of the firm’s activities. For example, a mission for a vegetable farm may be: “our mission is to provide wholesome and safe vegetables grown in an environmentally healthy and worker-friendly environment.”
Motives play a critical role in the formulation of the firm’s mission statement. Motives spring from physical and socio-emotional needs and the relative importance of these motives will determine how the firm manages its resources to satisfy its needs. Therefore, the relative importance of the financial manager’s motives should be reflected in the mission statement. To illustrate, motives may reflect the need to increase one’s own consumption, to act in accordance with one’s internalized set of values, to earn the good will of others, to increase one’s sense of belonging in one’s community or other organizations, and to improve the well-being of a disadvantaged group. The mission statement needs to guide the firm’s efforts to manage its resources depending on the relative importance of these competing motives.
One word sometimes associated with management is the word “vision.” Vision is the ability to imagine or picture, in one’s mind, something that has not yet been created physically. Therefore, vision is a necessary condition for any kind of physical creation because we must create an event, outcome, or thing in our mind before we can create it physically. An architect must imagine a building and reflect that vision in plans which the builders will follow to create a building. A football coach imagines an offensive play and reflects it in a drawing before it can be executed in a game. A financial manager must imagine a project that will produce valued outcomes before committing time, energy, and other resources to the project. A vision of what the manager wants the firm to achieve is reflected in the firm’s mission statement. A biblical expression highlights the importance of vision: “where there is no vision, the people perish…” (Proverbs 29:18).
So what have we learned? We learned that the management process begins with a vision that describes what the firm wants to do and become. Without a vision, the firm is unlikely to succeed.
Choose the Firm’s Strategic Goals and Tactical Objectives
Strategic goals set the long-term direction of the firm. Strategic goals are consistent with the firm’s mission statement—what it values, why it exists, and what its purpose is. Strategic goals direct the firm’s efforts toward achieving its mission over the long run. Strategic goals also call for tactical objectives, specific actions needed to achieve strategic goals. For example, a strategic goal may be to increase the firm’s revenues by 10%. The objectives consistent with this goal may be to develop new products, to focus on a particular marketing strategy, or to increase the firm’s sales force. The firm’s objectives transform the firm’s strategic goals into an action plan. Tactical objectives describe what short term actions are required if the firm is to reach its long-term goals.
The importance of goals and objectives
There are at least four reasons management requires the firm to choose goals and objectives:
1. Firm goals and objectives express what the firm believes is possible and desirable to achieve. By choosing the firm’s goals and objectives, the manager is expressing confidence in what the firm can achieve. By declaring the firm’s goals and objectives, the manager is also declaring its commitment of time, energy, and resources to achieve a desired end. Declaring the firm’s confidence and commitments in the form of its goals and objectives is the first reason for setting strategic goals and tactical objectives.
2. As the firm works to achieve its goals and objectives, it faces a multitude of choices, including how best to allocate its limited resources. Goals and objectives guide the firm in its allocation decisions by asking: what choices and resource allocations will best enable the firm to reach its goals and objectives? Therefore, firm goals and objectives provide criteria for making choices, the second reason for setting goals and objectives.
3. Most firms include multiple actors with diverse assignments. Goals and objectives provide a means for rallying firm members to support a common cause. Goals and objectives provide a means for seeing one’s individual efforts in the context of the overall goals and objectives of the firm and to identify opportunities for synergism within the firm. Ideally, the firm’s goals and objectives represent a consensus of firm members’ beliefs in what is possible and desirable and how to best achieve them so that all parts of the firm work cooperatively and enthusiastically together. Providing a framework for firm members to work synergistically is the third reason for setting goals and objectives.
4. Finally, goals and objectives provide a measure against which the firm can evaluate its performance. It allows the firm to ask and answer questions such as: Where are we? How are we doing? Can we get where we want to be from here? Are we closer to reaching our goals than before? Measuring one’s efforts against a standard is the fourth reason for setting goals and objectives.
The characteristics of good goals and objectives.
Some goals are better than others. The four reasons why we choose goals and objectives help us define the characteristics of good goals and objectives.
1. Good goals and objectives are realistic. They identify outcomes that are feasible for the firm to achieve given its environment and resources. It is not helpful to set unrealistic goals and objectives, even if they impress others. Unrealistic goals and objectives may create unrealistic expectations and lead to frustration later because they cannot be achieved. Good goals and objectives can be achieved with the resources available to the firm and the environment in which it exists.
2. Good goals and objectives answer the question: “What must the firm do to achieve its mission?” Goals and objectives that are consistent with the firm’s mission statement provide the criteria for the management of the firm’s energy and resources. If the firm goals and objectives fail to provide such criteria, then other goals and objectives should be selected.
3. Good goals and objectives reflect a consensus among those tasked with achieving them. People work hard for money. But they work harder when they feel they are part of a team—that their contributions are valued. Thus, good goals and objectives are the product of serious discussions intended to produce a consensus among those involved in reaching them. Therefore, at the end of the day, good goals and objectives provide a focus for synergistic efforts.
4. Finally, progress toward the achievement of good goals and objectives can be measured. Thomas S. Monson (1970) taught, “when progress is measured, progress improves. And when progress is measured and reported, the rate of improvement increases.” Measuring the firm’s progress helps guide the firm’s future. If the measures signal that the firm is making adequate progress, then the firm is supported in its efforts to keep doing what it has been doing. If the measures signal that the firm is not making adequate progress, then the firm is supported in its efforts to change directions.
So what have we learned? We learned that to realize the firm’s vision we must choose goals that are realistic, describe what needs to be done, reflect a consensus, and can be measured. We need goals because they reflect what we believe is possible, they provide criteria for choosing between alternatives, they provide a rallying point for firm members to work together, and they provide measures against which performance can be evaluated.
Identify the Firm’s Strengths, Weaknesses, Opportunities, and Threats.
Before developing strategies to accomplish the firm’s goals and objectives, a manager needs to identify and evaluate the internal strengths and weaknesses of the firm. This evaluation should include an assessment of the firm’s ability to survive financially in both the long run and the short run (solvency and liquidity); its profitability; its efficient management of its resources on which its profitability depends; and the risk inherent in its current financial state. External opportunities and threats that impact the firm’s ability to accomplish its objectives also need to be considered. An external opportunity and threat analysis might include evaluating the behavior of close competitors or assessing the condition of the economy and business climate, or the impacts of the business cycle on clients’ incomes and the resulting product demand.
So what have we learned? We learned that strengths, weaknesses, opportunities and threats analysis helps the firm understand the current constraints placed on it by both internal and external forces and enables the firm to take corrective action, when possible, to better position itself to accomplish its mission.
Develop and Evaluate the Firm’s Strategy.
The firm’s strategy is a plan that describes how it intends to achieve its strategic goals and its tactical objectives. Some have claimed that a goal or objective without a plan is only a wish. The firm’s strategy is a plan of action that describes who will do what, when, and how. For each goal or objective, the firm must develop the corresponding strategy to accomplish it. The strategy development process includes collecting data and information about possible choices and likelihoods of possible events. Then, the information must be analyzed to determine the impact of a particular strategy on the firm’s goals and objectives. Based on these analyses, management must select the proper strategy.
So what have we learned? We learned that unless we create a plan to achieve our goals and objectives consistent with our vision statement we have likely engaged only in wishful thinking. Planning who will do what, when, and how moves us in the direction of realizing our mission, goals, and objectives.
Implement the Firm’s Strategy.
Once a strategy is selected, it must be administered throughout the firm. All relevant parts of the business (accounting, purchasing, manufacturing, processing, shipping, sales, administration) must support and take an active role implementing the strategy. There may be changes in the business that are necessary to implement the strategy such as changes in personnel, technology, or financial structure. Implementing the firm’s strategy will require a carefully coordinated effort if the firm’s strategy leads to the firm achieving its goals and objectives.
So what have we learned? We learned that there is often more said than done and more planned than executed. Implementing one’s strategy is the sine qua non—unless the strategy is implemented, nothing else matters.
Evaluate the Firm’s Performance.
Firm managers must continually evaluate the strategies they implemented to reach the firm’s objectives and goals. They must determine if what the firm has achieved is consistent with its mission statement, goals, and objectives within an environment described by the firm’s strengths, weakness, opportunities, and threats. Firm managers must also be prepared to alter strategies in response to changes in technologies, laws, market conditions, and personnel. These changes will make it necessary for the firm to continually reevaluate and make adjustments.
Evaluating the firm’s performance must also include a review of its mission statement, goals, objectives, efforts to implement its strategies, and its strengths, weaknesses, opportunities and threats. Since the firm’s mission statement and strategic goals are oriented toward the long term, they change infrequently. However, the firm’s strategies may change as frequently as its internal strengths and weaknesses and external opportunities and threats change.
So what have we learned? We learned that life is like driving a car. Most of the time we look forward to where we are going. On occasion, however, it is important to look in our rear-view mirror to see where we have been and to learn from our journey.
The Firm Financial Management Process
The firm’s financial management process involves the acquisition and use of funds to accomplish its financial goals and objectives consistent with its financial mission statement. The firm’s financial management process essentially employs the same six management steps described earlier. The six steps of financial management include: 1) develop the financial mission of the firm; 2) choose the financial goals and objectives of the firm; 3) identify and evaluate the firm’s financial strengths, weaknesses, opportunities and threats; 4) develop financial strategies including evaluating and ranking investment opportunities to achieve financial goals and objectives consistent with the firm’s mission; 5) implement investment strategies by matching the liquidity of funding sources with cash flow generated from investments, by forecasting future funding needs, and by assessing the risk facing the firm; and, 6) evaluate the firm’s financial performance relative to the goals and objectives of the firm. These six steps are described next in more detail.
(1) Develop the Firm’s (Financial) Mission Statement.
While financial management usually plays a role in developing the firm’s overall mission statement, there are other considerations shaping the firm’s mission. As a result, the financial mission of the firm is usually nested within the more general mission of the firm. One financial mission of the firm may be to reach certain financial conditions that allow the firm’s owners to pursue other goals and provide firm owners resources in the future. The firm’s mission statement may lead naturally to important financial goals such as to maximize profit, reduce costs and increase efficiency, manage or increase the firm’s market share, limit the firm’s risk, or maximize the owner’s equity in the firm. However, there may be a distinction between a firm’s financial mission and the firm’s overall mission. In other words, the firm’s financial mission included in the strategic financial management process may be an objective in the firm’s overall strategic management process.
(2) Choose the Firm’s (Financial) Strategic Goals and Tactical Objectives.
The part of the firm’s mission related to financial management must lead to the firm selecting financial goals consistent with the firm’s mission statement and objectives likely to lead to the successful achievement of its strategic goals. The financial objectives may direct how the firm organizes itself and how it manages its tax obligations—subjects discussed in Chapters 2 and 3. However, taxes will also influence the development and implementation of investment strategies—subjects discussed in several chapters of this book.
(3) Identify (Financial) Strengths, Weaknesses, Opportunities and Threats.
The use of coordinated financial statements (CFS) discussed in Chapter 4 can be used to evaluate the firm’s internal strengths and weaknesses. We may need to look outside of the firm to identify external opportunities and threats facing the firm. Financial statements are used to formulate ratios that can be compared to other firms to determine how the firm’s financial condition compares to normal—or average—firms, the subject of Chapter 5. Chapter 6 uses financial statements and ratios to demonstrate that the firm is a system with interconnected parts. As a result, each financial measure (e.g. solvency, profitability, efficiency, liquidity, and leverage) are connected to each other, and a change in one measure will change all the others.
(4) Develop and Evaluate the Firm’s (Financial) Strategy.
Financial managers face an almost limitless set of investment opportunities with a wide variety of characteristics. Some investments will be liquid and easily converted to cash, such as inventories or time deposits. Other investments, such as real estate or production facilities, cannot be easily converted to cash and are considered illiquid. There are investments that provide fairly certain, low risk returns while others will provide uncertain, high risk returns. Some investments are depreciable while others increase in value over time. Firm budget resources for capital or long-term investments and evaluate them using present value (PV) tools. Many of the chapters that follow focus on PV models. Indeed, it may be correct to say that the focus of much of this book is on how to use PV models to evaluate a firm’s financial strategy.
• PV models recognize the time value of money; that a dollar today is different than a dollar received in the future (Chapter 7);
• PV models convert future cash flow to their equivalent value in the present (Chapter 8);
• PV models need to be consistent, must be investments of homogeneous size, term, and tax treatments—comparing apples to apples and oranges to oranges (Chapters 9, 10, and 11);
• PV models are similar in construction to accrual income statements (Chapter 12);
• PV models often evaluate incremental changes in a firm’s portfolio of investments and project the future values of exogenous variables (Chapter 13);
• PV models can be used to find the liquidity of investments since investments like firms differ in their degree of liquidity (Chapter 14);
• Risk is ubiquitous and we must account for it in our PV models (Chapter 15).
Equipped with PV models and knowledge of how to conduct proper comparisons of investments using consistent measures, we are prepared to apply our tools to a wide range of investment problems that employ a variety of PV models. Included is a discussion of loan analysis in Chapter 16, land investments in Chapter 17, leasing options in Chapter 18, and investment in financial assets in Chapter 19. Then Chapter 20 introduces yield curves to help us identify outside-of-the-firm external threats and opportunities. Finally, the last chapter in this book, Chapter 21, ends with a cautionary note—there are relational goods that may be more important than money and should not be ignored.
(5) Implement the Firm’s (Financial) Strategy.
Financial managers often play an important role in managing the implementation of an investment strategy. The implementation stage of financial management may include interacting with capital markets to raise funds required to support a strategy. Managers decide whether to acquire funds internally or borrow from other investors, commercial banks, the Farm Credit System, life insurance companies, or, depending on how the firm is organized, by issuing stocks or bonds.
In the process of obtaining and allocating funds, financial managers interact directly or indirectly with financial markets. This interaction could be simply obtaining a savings or checking account at your local bank. Or it could involve more sophisticated interactions such as raising funds by issuing ownership (equity) claims in your firm in the form of shares of stock.
Another part of implementing the financial strategy of the firm is to interact with various parts of the business and the household. For example, setting inventory policy is both a financial and business management decision and requires input from the production and sales departments of the firm as well as the firm’s financial managers. In addition, financial managers must make trade-offs between risks and expected returns. One tool that can be used to evaluate future returns and risk is the term structure of interest rates, the subject of Chapter 20. There are other kinds of trade-offs as well. One important trade-ff is between commodities and relational goods. We will need both because they each satisfy different needs. This book is mostly about managing commodities, but Chapter 21 reminds us that “money can’t buy love” or relational goods. Therefore, one more thing about management is to account for and manage relational goods.
(6) Evaluate the Firm’s (Financial) Performance.
Finally, financial concepts and information are often used to evaluate a strategy’s performance and to signal investment changes the firm needs to adopt in the future. In this effort, PV models will prove to be particularly helpful.
The relative importance of the six steps included in the management process will differ depending on what is being managed. In the case of financial management, the financial goals, the objectives, the strengths, weaknesses, opportunities, and threats analysis, and the strategies adopted and evaluated will differ from personnel management, for example. Similar to both financial management and other management efforts is their shared responsibility for the firm. What follows is really strategic firm management applied to the financial resources available to the firm.
Our focus on firm financial management. While all six firm financial management processes are important and discussed in this book, we focus on two:
1. Assessing the firm’s internal strengths and weakness through the use of coordinated financial statements, ratio analysis, and comparisons with ‘average’ firms; and
2. Developing strategies described by after-tax cash flow and evaluating them using PV models.
Of course the other parts of the management process are important, especially implementing strategic financial investment plans and evaluating the firm’s performance. However, a thorough treatment of these topics which should be pursed in other venues.
Trade-offs between Financial Goals and Objectives
The firm’s financial goals and objectives guide the financial manager. There are, of course, a wide range of possible tactical objectives that a firm may adopt to achieve its strategic goals and its mission. However, one maxim should guide the manager’s choice of objectives: “There is no such thing as a free lunch!” Interpreted, this adage reminds us that nearly always, every objective comes at the cost of another objective
For example, consider the objective of maximizing the firm’s profits. Increases in short-term profits may often reduce long-term profits. If the firm desires to reduce its risk, this may require that the firm reduce its profits by investing in less risky–but lower return–investments.
One often-stated firm financial management objective is to maximize the profits of the firm. However, the measure of profits can differ drastically across different accounting practices. For example, cash versus accrual accounting, different depreciation methods, and different inventory accounting methods all lead to different measures of profit. Maximizing profits using one accounting method may not maximize profits using another accounting practice. Furthermore, profits may be difficult to measure when the firm employs unpaid family labor. The real problem is that profits don’t reflect the actual cash flow of the firm.
In addition, the traditional notion of profit ignores the timing of the cash flow received by a firm. Suppose you are given the choice of receiving \$1,000 either today or one year from today. Which would you choose? Naturally, you would choose to get the money today because you could invest the money for some positive rate of return and earn more than \$1,000 by the end of one year. For instance, suppose you could invest the money in the bank and earn a 5 percent return during the year. At the end of the year you would get back your \$1,000 plus \$1,000 x (.05) = \$50 interest or a total of \$1,050. Clearly, the \$1,000 today is worth more than the \$1,000 one year from today. The notion that dollars at different points in time are not worth the same amounts at a single point in time is known as the time value of money concept. Moreover, it underlies one of the most important financial trade-offs: present profits versus the present value of discounted future after-tax cash flow.
Another trade-off involving the maximize profit objective is that it ignores liquidity. Liquidity can be defined as a firm’s ability to meet unexpected cash demands. These cash demands might be unexpected cash expenses for such things as repairs and overhead expenses, new investment opportunities, or unexpected reductions in revenue. The concept of liquidity is closely related to risk. Liquidity needs are usually met by holding salable assets and/or maintaining the capacity to borrow additional funds. Serious risks may reduce the value of some assets and make liquidation of the assets difficult. Likewise, serious risk may also make it difficult to borrow additional funds.
If you were a firm manager, would your objective be to maximize profits or is some other objective more preferable? In this class, we will argue that traditional profit maximization is not a very desirable objective for a financial manager. We will argue that in most cases, financial decisions should be made so they maximize the value of the firm, which turns out to be the same thing as maximizing the present value of all the future cash generated by the firm. Once again, it is important to note that “cash flow” is much different than “profit.”
This concept of maximizing firm value is easy to defend in large firms where firm ownership is often separate from management. Owners of these firms generally want management to operate the firm in a way that maximizes the value of their investment; however, in smaller firms and households the value maximization principal is often constrained by other considerations such as concerns about quality of life. For example, you would likely be able to increase your personal wealth over time by driving a Chevrolet instead of a Cadillac (you could invest the cost savings), but you may gain enough satisfaction from driving a Cadillac (or a tractor with green paint) that you are willing to accept the lower wealth level. Nevertheless, for most of this course we will assume that financial decisions are made in a manner that is consistent with maximizing value. In cases where a firm does not maximize present value, it is still useful to estimate the present value maximizing decisions as a benchmark in order to understand the cost of alternative decision in terms of wealth loss.
Summary and Conclusions
Like it or not, we are all managers—if not managers of a firm then we are personal managers. We have important management responsibilities for our lives and resources. The management process is a universal process requiring that we first determine our mission and what goals and objectives are consistent with our mission? The goals and objectives we choose must declare what it is that we believe we can and should accomplish and the level of our commitment to reaching our goals and objectives. Finally, we cannot avoid setting goals and objectives because having no goal or objective is a goal or objective—to reach nowhere in particular.
Choosing our goals and objectives is crucial in the management process. We cannot achieve our mission without properly formulated goals and objectives. Goals and objectives lead us to conduct an honest evaluation of our internal strengths and weakness and external threats and opportunities, a process that identifies the resources and constraints likely to contribute to achieving our mission. After formulating our goals and objectives, and after conducting an honest evaluation of our strengths, weaknesses, opportunities and threats, we next decide on a strategy, a plan to follow that will enable us to accomplish our mission. Strategic management requires that we implement our plan, that we take specific actions to ensure we achieve our goal by implementing our strategies. And finally, we evaluate and, if necessary, modify our goals, objectives, and our understanding of our strengths, weaknesses, threats, and opportunities. Then, when we have completed the management process, we repeat it all over again, continually, and not necessarily following the steps in the management process in the same order. We end this chapter by emphasizing this truism: we are all managers, all the time.
Questions
1. What does the word management mean?
2. Discuss the six steps included in the management process. Should these steps be practiced sequentially? In any order? Or does it depend on the management problem? Defend your answer.
3. What features differentiate management and firm financial management?
4. Consider mission statements and strategic goals and tactical objectives. Is the following statement: “I want to obtain a college degree.” a mission statement, a goal, or an objective? If it is a tactical objective, what strategic goals and mission statement are consistent with this tactical objective? If it is a strategic goal, what mission statement and tactical objectives are consistent with this strategic goal? Finally, if it is a mission statement, what strategic goals and tactical objectives are consistent with this mission statement?
5. Mission statements, strategic goals, and tactical objectives reflect motives. Several motives may explain one’s desire to achieve a college degree. One motive for obtaining a college degree is to increase one’s lifetime earnings. But there are other motives. To help you connect motives to your personal mission statement, goal, or objective to obtain a college degree, identify the relative importance of the five motives described below. To complete the questionnaire below, assume you have 10 weights (e.g. pennies) to allocate among the five motives for attending the university. Distribute the 10 weights (pennies) according to the relative importance of each motive. Write your answer in the blank next to each question. There is no right or wrong allocation of weights among the motives except that the sum must add to 10. Each motive reflects the relative importance of one’s need to increase one’s own consumption, to earn internal/external validation, and to have a sense of belonging.
1. I want a college degree so I can increase my lifetime earnings and get a better job.
2. I want a college degree so important people in my life will be pleased with my achievements.
3. I want a college degree to live up to the expectations I have for myself.
4. I want a college degree so I will feel part of groups to which I want to belong.
5. I want a college degree so that in the future, I will be better able to help others.
6. Develop a management plan for this class, this semester. This should include a brief discussion of each of the six steps in the strategic planning process including a mission statement, strategic goals and objectives, your strengths, weaknesses, opportunities, and threats, your strategies, your plan to implement your strategies, and, lastly, your evaluation process. Discuss what role financial management will play in your strategic planning process.
7. Imagine yourself as the financial manager of a small firm. Write a mission statement focused on profit maximization. What other considerations may be ignored if profit maximization were your primary mission? Suppose your mission statement was to “aid the disadvantaged”? Would profit or value maximization be part of your firm’s goals and objectives? Please explain. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/01%3A_Financial_Management_and_the_Firm.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) know the different forms of business organizations; (2) compare the advantages and disadvantages of alternative types of business organizations; and (3) identify how alternative forms of business organizations can influence a firm’s ability to achieve its financial goals and objectives.
To achieve your learning goals, you should complete the following objectives:
• Learn about the advantages and disadvantages of a sole proprietorship.
• Study the characteristics of firms best suited to be organized as sole proprietorships.
• Learn about the advantages and disadvantages of partnerships.
• Study the characteristics of firms best suited to be organized as partnerships.
• Learn about the advantages and disadvantages of C corporations and S corporations.
• Study the characteristics of firms best suited to be organized as C corporations and S corporations.
• Learn about the advantages and disadvantages of a Limited Liability Company (LLC).
• Study the characteristics of firms best suited to be organized as LLCs.
• Learn about the advantages and disadvantages of a cooperative.
• Study the characteristics of firms best suited to be organized as cooperatives.
• Learn about the advantages and disadvantages of a trust.
• Study the characteristics of firms best suited to be organized as trusts.
Introduction
The way a business is organized influences its ability to reach its goals and objectives. This chapter focuses on legal forms of business organizations that are widely used in the U.S. These include sole proprietorships, general and limited partnerships, limited liability corporations (LLCs), S corporations, and C corporations. Partnerships, LLCs, and C corporations are found across a wide spectrum of business types and sizes. LLCs are becoming increasingly important in the production agricultural sector, particularly with multi-generation family businesses. In family businesses, legal business structures which facilitate intergenerational transfer of assets has become particularly important.
Characteristics of businesses organizations that influence the ability of a firm to reach its goals and achieve its mission include: 1) who makes the management decisions; 2) how much flexibility does it have in its production, marketing, consumption, and financing activities; 3) its liability exposure; 4) its opportunities for acquiring capital; 5) how the life of the business is defined; 6) how the death of its owners affects the firm; 7) methods available for transferring the current owners’ interest to others; and 8) Internal Revenue Service definitions of business profits and their taxation. Thus, the way a firm is legally organized provides the framework to make financial management decisions.
Sole Proprietorship
The sole proprietorship is a common organization form especially used by small businesses. A sole proprietorship is a business that is owned and operated by a single individual. Most sole proprietorships are family-owned businesses. The advantages of the sole proprietorship organization include:
1. It is easy and inexpensive to form and operate administratively (simplicity);
2. It offers the maximum managerial control; and
3. Business income is taxed as ordinary (personal) income to the owner.
The disadvantages of the sole proprietorship include:
1. It is difficult to raise large amounts of capital;
2. There is unlimited liability;
3. It is difficult to transfer ownership; and
4. The company has a limited life that is linked to the life of the owner.
Sole proprietorships are typically organized informally and require relatively little paperwork to begin operations. It is the most simple among the alternative business organizations to understand and use. To begin operation, the individual declares himself/herself to be a business. In many cases, a license will be required to operate the business, but often the business begins simply by “opening its door.” The day-to-day operations of the firm are also organized informally and may be administered as the owner desires, subject to legal and tax restrictions. For example, certain taxes must be paid by specific dates. The vast majority of regulations small businesses face are independent of the legal form of the business. Metrics such as business size, number of employees, and location determine which regulations business face.
Since sole proprietorships are owned by a single individual, this form of business organization offers the maximum management control. In small firms, the owner of the business is often involved in all aspects of the business: purchasing, inventory control, production, sales, accounting, personnel and customer relations, as well as financial and general management. While the large amount of owner control can be a strength in small firms, it often turns out to be a disadvantage as firms begin to grow and the owner is no longer able to manage all aspects of the business. The owner must then hire competent staff to manage specific aspects of the business.
Additionally, the business is restricted by the financial resources available to the owner. This can restrict the startup of the business as well as its growth over time. In many cases, substantial cash outlays are required to make the capital purchases (land, facilities, equipment, cars, offices) to start the business and to provide initial overhead expenses (salaries, wages, supplies) until the business gets going. Further, it frequently takes two or three years before the business begins to show a profit. The owner of the business has to obtain these funds using his/her own equity (funds owned by the individual) and/or by borrowing funds, and borrowing requires collateral in the form of owner equity The amount that can be borrowed depends on the level of equity as well as the projected cash flow generated by the business. The lack of available financial capital for starting and expanding the business is a major drawback in the sole proprietorship. The profits from the business are taxed as personal income to the owner.
Sole proprietorships are subject to unlimited liability which means that the liability for business debts extends beyond the owner’s investment in the firm. For example, if the sole proprietorship is unable to cover its debts and obligations, creditors have the right to collect the personal assets that are not part of the business or other businesses of the owner. The owner may be forced to liquidate assets, such as a personal savings account, a vacation home, or other personal assets just to cover the firm’s obligations.
Another disadvantage of a sole proprietorship is that it has a limited life that corresponds to life of the owner. The owner may sell assets from the business to another sole proprietorship or business. However, if the business is not terminated prior to the death of the owner, then after the proprietor’s death, the assets remaining in the firm will be distributed according to the owner’s will or comparable instrument. When the owner dies, the business is terminated.
Partnerships
A general partnership is a business that is owned and operated by two or more individuals. The partners contribute to the business, share in management, and divide any profit. Partnerships are usually created by written contract among the partners, but they can be legally recognized even without a written agreement. If the partnership owns real property, the partnership agreement should be filed in the county where the property is located.
Advantages of partnerships include:
1. They are easy and inexpensive to form and operate administratively;
2. They have the potential for large managerial control;
3. Business income is taxed as ordinary (personal) income to the owner; and
4. A partnership may be able to raise larger amounts of capital than a sole proprietorship.
The disadvantages of a general partnership include:
1. Raising capital can still be a constraint;
2. There is unlimited liability;
3. It is difficult to transfer ownership; and
4. The company has limited life.
The advantages and disadvantages of a general partnership are similar to the sole proprietorship. Partnerships are generally easy and inexpensive to set up and operate administratively. Partnership operating agreements are critical. Like sole proprietorships, profit allocated to the partners is based upon their share in the business.
Managerial control resides with the partners. This feature can be an advantage or disadvantage depending on how well the partners work together and the level of trust in each other. Control by any one partner is naturally diluted as the number of partners increases. Partnerships are separate legal entities that can contract in their own name and hold title to assets
The challenge to partnerships extends beyond possible conflicts with the partners. Divorce and other disputes may threaten the survival of the partnership when a claimant to a portion of the business’s assets demands his/her equity.
Unlimited liability remains a strong disadvantage for a general partnership. All partners are liable for the debts of the firm. Due to this unlimited liability, the risks of the business may be spread according to the owners’ equity rather than according to their interests in the business. This risk becomes an actual obligation whenever the partners are unable to satisfy their shares of the business’s obligations.
Increasing the number of partners can increase the amount of capital that can be accessed by the firm. More partners tends to mean more financial resources and this can be an advantage of a partnership compared to a sole proprietorship. Still, it is generally difficult for partnerships to raise large amounts of capital—particularly when liability is not limited.
Ownership transfer and limited life continues to be a problem in partnerships; however, it may be possible to build provisions into the partnership that will allow it to continue operating if one partner leaves or dies. In some cases, parent-child partnerships can ease the difficulties of ownership transfer.
A limited partnership is another way businesses can organize. Limited partnerships have some partners (limited partners) who possess limited liability; limited partners do not participate in management of the firm. There must be at least one general partner (manager) who has unlimited liability. Because of the limited liability feature for limited partners, this type of business organization makes it easier to raise capital by adding limited partners. These limited partners are investors and make no management decisions in the firm.
One difficulty occurs if the limited partners wish to remove their equity from the firm. In this instance, they must find someone who is willing to buy their share of the partnership. In some cases, this may be difficult to do. Another difficulty is that the Internal Revenue Service (IRS) may tax the limited partnership as a corporation if it believes the characteristics of the business organization are more consistent with the corporate form of business organization.
In production agriculture, family limited partnerships serve a number of objectives. For example, parents contemplating retirement may wish to maintain their investment in a farm business but limit their liability and be free of management concerns. To reduce their liability exposure and be free of managerial responsibilities, parents can be limited partners in a business where younger family members are the general partner.
The joint venture is another variation of the partnership, usually more narrow in function and duration than a partnership. The law of partnership applies to joint ventures. The primary purpose of this form or organization is to share the risks and profits of a specific business undertaking.
Corporations
A corporation is a legal entity separate from the owners and managers of the firm. Three fundamental characteristics distinguish corporations from proprietorships and partnerships: (1) the way they are owned and managed, (2) their perpetual life, and (3) their legal status separate from their owners and managers.
A corporation can own property, sue and be sued, contract to buy and sell, and be fined—all in its own name. The owners usually cannot be made to pay any debts of the corporation. Their liability is limited to the amount of money they have paid or promised to pay into the corporation.
Ownership in the corporation is represented by small claims (shares) on the equity and profit stream of the firm.
The two most common types of claims on the equity of the firm are common and preferred stock. The claims of preferred stockholders takes preference over equity claims of common stockholders in the event of the corporation’s bankruptcy. Preferred stockholders must also receive dividends before other equity claims. The preferred stockholders’ dividends are usually fixed amounts paid at regular intervals that rarely change. In most cases, preferred stock has an accumulated preferred feature. This means that if the firm fails to pay a dividend on preferred stock, at some point in time the corporation must make up the payment to its preferred stockholders holders before it can make payments to other equity claims.
Common stock equity claims are the last ones satisfied in the event of the corporation’s bankruptcy. These are residual claims on the firm’s earnings and assets after all other creditors and equity holders have been satisfied. Although it appears that common stock holders always get the “leftovers,” the good news is that the leftovers can be substantial in some cases because of the nature of the fixed payments to creditors and other equity holders.
Large corporations are usually organized as Subchapter C corporations.
The advantages of a C corporation include:
1. There is limited liability;
2. The corporation has unlimited life;
3. Ownership is easily transferred; and
4. It may be possible to raise large amounts of capital.
The disadvantages of a C corporation include:
1. There is double taxation; and
2. It is expensive and complicated to begin operations and to administer.
Seeing Double
Earnings from the corporation are taxed using a corporate tax rate. When earnings are distributed to the shareholders in the form of dividends, the earnings are taxed again as ordinary income to the shareholder. For example, suppose a corporation, whose ownership is divided among its 3000 shareholders, earns \$1,000,000 in taxable profits for the year and is in a flat 40-percent tax bracket. Profits per share equal \$1,000,000/3000—or \$333.33. The corporation pays 40% of \$1,000,000—or \$400,000—in taxes to the government. Taxes per share equal \$400,000/3000—or \$133.33.
Now suppose the corporation distributes its after-tax profits to its 3,000 shares in the form of dividends. Each shareholder would receive a dividend check of \$600,000/3,000 = \$200. The \$200 dividend income received by each shareholder would then be taxed as ordinary personal income. If all the shareholders were in the 30-percent tax bracket, then each would pay 30% of \$200 or \$60 in taxes, leaving each shareholder with \$140 in after-tax dividend income.
So what is the total tax rate paid on corporate earnings? Dividing the taxes paid by the corporation and the shareholder by the profit per share, the total tax rate is (\$133.33+\$60)/\$333.33 = 58%, a higher rate than would be paid on personal income of the same amount.
One of the primary strengths of the corporate form of business organization is that the most the owners of the firm (shareholders) can lose is what they have invested in the firm. This limited liability feature means that as a shareholder, one’s personal assets beyond the investment in the corporation can’t be taken to satisfy the corporation’s debts or obligations.
Ownership can easily be transferred by selling shares in the corporation. Likewise, the corporation has an unlimited life because when an owner dies, the ownership shares are passed to his/her heirs. The common separation of ownership and management in large corporations helps to ease the ownership transfer as the firm management process never ceases.
The easy transfer of ownership, separation of management and ownership, and limited liability features of a corporation combine to create a business structure that is designed to raise large sums of equity capital. Investors in large corporations don’t have to become involved in management of the firm. Their risk is limited to the amount of funds invested in the firm, and their ownership interest can be transferred by selling their shares in the firm.
Corporations are more expensive and complicated to set up and administer than sole proprietorships or partnerships. Corporations require a charter, must be governed by a board of directors, pay legal fees, and meet certain accounting requirements. Despite the relatively high setup cost, the primary disadvantage of the corporate form of business is that income generated by the corporation is subject to double taxation.
However, there is a limit on corporate earnings that are double-taxed. The corporation may pay reasonable salaries, and these are deducted from the corporation’s profits. Therefore, salaries paid to corporate workers and operators are not taxed at the corporate level. In some cases, the corporation’s entire net profit may be offset by salaries to the owners so that no corporate income tax is due. On the other hand, if the corporation pays dividends to the shareholders, those payments are subject to corporate-level income tax. However, the individual does not have to pay self-employment tax on the dividends. And, qualifying dividends (and most United States Corporation dividends can fit into this definition) are taxed at capital gains rates and not the individual’s top marginal tax rate. Finally, dividends paid to a shareholder that actively participates in the business are not subject to either the 0.9 percent Medicare surtax on earnings or the 3.8 percent tax on net investment income that are levied on higher-income taxpayers.
Another disadvantage of corporations has to do with the fact that the managers do not own the firm. Managers, who control the resources of the firm, may use them for their own benefit. For example, top management may build extravagantly large headquarters and buy fleets of jets and limousines for transportation. If less were spent on perquisites, then the income of the corporation would be higher. Higher income allows higher dividends to be paid to the owners (shareholder).
The (potential) self-serving behavior by management running contrary to the interests of stockholders is an example of a principal-agent problem. Methods of dealing with the principal-agent exist. One way is to hire auditors to monitor the use of firm resources. Further, a corporation has a board of directors responsible for hiring, evaluating, and removing top management. Boards are often ineffective because they meet infrequently and may not have access to the information necessary to fulfill their responsibilities. Additional problems exist if management personnel also sit on the board of directors.
Another way to deal with the principal-agent problem in corporations is to align the interests of management with those of shareholders. This is accomplished by basing the compensation of management on the value of the firm’s stock. A chief executive officer could receive stock options as a part of his/her compensation package. If the stock price rises, the value of the options increase, which benefits the manager financially. The shareholders also benefit when the stock price increases. Such an arrangement may reduce the principal-agent problem. However, very high executive compensation can often trigger criticism from external groups such as consumer or labor activists.
Limitations of linking management’s compensation to the value of its stock have been illustrated by Enron and Tyco corporations. These corporations inflated the value of their stocks and eventually bankrupted themselves and lost the investments of their employees. It seems there is still a lot to be learned about aligning the interests of corporate managers and shareholders.
Many small businesses, including farms, use the C corporation structure and operate much like partnership. This is frequently done for reasons of expensing and intergenerational transfer.
The corporation will need to be “capitalized” by some level of equity funds from the shareholders. It is common practice among lenders to require personal guarantees by the owners of small corporations before providing funds to the business. This essentially eliminates the limited liability features for those shareholders. As one might expect, due to these difficulties, many small corporations are not able to generate large amounts of capital by simply selling ownership shares. As a result, many small corporations do not really receive the full benefits of corporate organization but are still subject to the disadvantages, namely double taxation.
C corporations and S corporations. Any corporation is first formed under the laws of a particular state. From the standpoint of state business law, a corporation is a corporation. However, there are two types of for-profit corporations for federal tax law purposes:
• C corporations: What we normally consider “regular” corporations that are subject to the corporate income tax
• S corporations: Corporations that have filed a special election with the IRS. They are not subject to corporate income tax. Instead, they are treated similarly (but not identically) to partnerships for tax purposes.
There is an alternative form of corporate business organization that is often more desirable from a small business perspective. Subchapter S Corporations have limited liability protection, but the income for the business is only taxed once as ordinary income to the individual (Wolters Kluwer. n.d.).
There are restrictions on what type of firms can be organized as Subchapter S corporations. To do so, it must meet several requirements: (1) cannot have more than 100 shareholders; (2) may have only one class of stock; (3) cannot have partnerships or other corporations as stockholders; and (4) may not receive more than 20 percent of its gross receipts from interest, dividends, rents, royalties, annuities, and gains from sales or exchange of securities. In agriculture, these restrictions usually mean that only family or closely-held farm businesses can achieve Subchapter S status.
Federal income tax rules for Subchapter S corporations are similar to regulations governing partnerships and sole proprietors. However, corporations may provide certain employee benefits that are tax deductible. Accident and health insurance, group life insurance, and certain expenditures for recreation facilities all qualify. However, these benefits may be taxable to the employees and subsequently to the shareholders.
There is greater continuity for businesses organized under Subchapter S than for sole proprietorships or partnerships. Upon the death of shareholders, their shares of the corporations are transferred to the heirs and the Subchapter S election is maintained. Surveys suggest that the major reason farms incorporate is for estate planning. The corporate form allows for the transfer of shares of stock either by sale or gift. This is much easier than transferring assets by deed.
Limited Liability Company
The Limited Liability Company (LLC) is a relatively new form of business organization. An LLC is a separate entity, like a corporation, that can legally conduct business and own assets. The LLC must have an operating agreement which regulates its business activities and the relationship among its owners (referred to as members). There are no restrictions on the number of members or the members’ identities. LLCs are subject to disclosure, record keeping, and reporting requirements that are similar to a corporation.
The attractive feature of the LLC is that all members obtain limited liability, but the entity is taxed as a general partnership. The LLC is similar in most respects to the Subchapter S corporation. The primary differences are: 1) the LLC has less restrictive membership requirements; and 2) the LLC is dissolved in the event of transfer of interest or death unless members vote to continue the LLC. Table 2.1 summarizes the primary characteristics of the business organizations discussed so far.
Table 2.1. Comparison of Business Organizations
Sole Proprietorship Partnership Limited Partnership S Corporation C Corporation Limited Liability Company
ownership
• single
• individual
• two or more individuals
• two or more individuals
• one or more general partners
• legal person
• max 35 shareholders
• individuals
• legal person
• legal person
• two or more members
management decision
• proprietor
• partners
• general partner
• elected directors
• management
• elected directors
• management
• members
• manager
life
• terminates at death
• terminates at death
• agreed term
• terminates at death
• perpetual or fixed
• transfer stock
• perpetual or fixed
• transfer stock
• agreed term
• terminates at death
transfer
• assets
• assets
• assets
• shares
• shares
• assets
income tax
• individual
• individual
• individual
• individual
• corporate
• individual
• individual
liability
• unlimited
• unlimited
• general partners unlimited
• limited partners limited
• limited
• limited
• limited
capital
• personal
• loans
• personal
• loans
• personal
• loans
• shareholders
• bonds
• loans
• shareholders
• bonds
• loans
• members
• loans
Cooperative
A cooperative is a business that is owned and operated by member patrons. Generally, cooperatives are thought to operate at cost, with all profits going to member patrons. The profits are usually redistributed over time in the form of patronage refunds. Cooperatives often appear to operate as profit making organizations much the same as other forms of business organization. Agricultural cooperatives do not face the same anti-trust restrictions as non-cooperative businesses, and they enjoy a different federal income tax status. In most instances, the concepts and analysis techniques covered in this course will be relevant to financial management in cooperatives.
Trusts
A trust transfers legal title of designated assets to a trustee, who is then responsible for managing the assets on the beneficiaries’ behalf. The management objectives can be spelled out in the trust agreement. Beneficiaries retain the right to possess and control the assets of the trust and to receive the income generated by the properties owned by the trust. Beneficiaries hold the trust and personal property, rather than title to the assets. The legal status of certain types of land trusts are unclear in some states.
Farm Business Organization Types in US Agriculture
The USDA defines a farm as a place that generates at least \$1,000 value of agricultural products per year. In 2007, farms generating between \$1,000 and \$10,000 of agricultural products made up 60% of the 2.2 million U.S. farms. Farms producing \$500,000 or more in 2007 dollars generated 96% of the value of U.S. agricultural production.
Table 2.2 shows the percentage of farms by organizational type and their share of aggregate agriculture product sales according to the 2007 Census of Agriculture. Sole proprietorships are the dominant form of business organization measured by farm count (86.5%) but have only 49.6% of the value of agricultural production. Partnerships and family corporations make up 20.8% of farms but have 43% of the value of agricultural production. Non-family corporations, part of the “other organization” category, accounted for 0.4% of farms and 6.5% of the value of agricultural production.
Table 2.2. Farm Business Organization Types (USDA Census of Agriculture, 2007. Farms in US 1,925,300)
Business Type % of Farms % of Cash Receipts
Sole Proprietorships 86.5% 49.6%
Partnerships 7.9% 20.9%
Family Corporations[1] 3.95 22.9%
Other[2] 1.2% 7.3%
More generally, about 80 percent of all businesses (agriculture and non-agriculture) are organized as sole proprietorships while only around 10 percent of businesses are organized as corporations. Conversely, about 80 percent of business sales come from corporations while sole proprietorships account for only about 10 percent of business sales.
So what have we learned? We learned that firms organize differently depending on the size, ability to manage, the need for internal versus external funding, and tax implications. Indeed, the need for different business organizations can be compared to the need for different kinds of transportation—it depends on where you are going.
Summary and Conclusions
Recognizing that we can offer financial management tools that meet a limited set of business organizations, we purposely focus in this text on small to medium-size businesses. As a result, we focus on firms that depend on internal capital and exercise the maximum control of the firm.
Questions
1. Discuss the advantages and disadvantages of organizing a business as a sole proprietorship versus a C corporation.
2. Limited partnerships, limited liability companies, and Subchapter S corporations are also alternative forms of business organization. Discuss the advantages and/or disadvantages these organizations offer relative to sole proprietorships, general partnerships and C corporations.
3. Approximately 85% of all farm businesses in the US are organized as sole proprietorships. Explain why the organization form of farm businesses in the U.S. is dominated by sole proprietorships.
4. Pick an agricultural commodity or product that is produced in the food industry. Describe the different production, processing and marketing steps for the commodity or product and how they are typically coordinated.
5. Can you explain in Table 2.2 why corporations tend to control more land than partnerships and sole proprietorships?
6. What are the advantages or disadvantages of a family corporation compared to a regular corporation?
1. More than 50% of the stock is owned by persons related by blood or marriage.
2. Nonfamily farms, estates or trusts, grazing associations, American Indian Reservations, etc. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/02%3A_Alternative_Forms_of_Business_Organizations.txt |
Learning Objectives
At the end of this chapter, you should be able to: (1) describe the major components of the federal tax system; (2) know how the different forms of business organizations are taxed; (3) recognize the difference between marginal and average tax rates; and (4) understand how depreciation, capital gains, and depreciation recapture affect the amount of taxes a firm pays. To achieve your learning goals, you should complete the following objectives:
• Learn to distinguish between the firm’s gross income, adjusted gross income, and personal deductions.
• Learn how to calculate the firm’s tax liability by finding its taxable income
• Learn how to find the firm’s average tax rate and marginal tax rates.
• Learn how to find a firm’s tax liabilities by using tables of Federal Income Tax Rates.
• Learn how depreciation can reduce the firm’s tax liabilities.
• Learn how to find the amount of taxes paid on interest and dividend income.
• Learn how to distinguish between capital gains and losses and depreciation recapture.
• Learn how taxes are calculated on depreciation recapture and capital gains and losses.
• Learn about the different ways depreciation can be calculated and the advantages and disadvantages of each depreciation method.
Introduction
Chapter 2 proposed that one financial management objective is to organize the firm so that its value is maximized. Of course, “the firm” could mean any business organization ranging from a large corporate firm to a small business or even an individual household. Later, we will see that the firm’s value is determined by its after-tax cash flow, which can differ significantly from the firm’s profits measured by its accounting income. As a result, we need to understand the differences between a firm’s cash flow and its accounting income—this discussion will come later. Fortunately, for the most part, a detailed knowledge of specific accounting differences for the different types of business organizations isn’t essential for our purposes. So we begin by discussing some of the major components of the federal tax system that have a bearing on a firm’s after-tax cash flow.
Due to the influence of taxes on cash flow, it is important to have an understanding of how the tax system works. This chapter intends to present a few of the basic concepts related to taxes that are important from a financial management perspective. Our focus is on the federal tax code, because of its importance in determining after-tax profit and after-tax cash flow. Nevertheless, there are a number of additional taxes (e.g. state and local taxes) that can have a significant impact on a firm’s earnings and cash flow. It is important to consider the impacts of all taxes when making financial decisions. The federal tax laws are written by Congress. The Internal Revenue Service (IRS) is the agency responsible for administering the code and collecting federal income taxes. The IRS issues regulations which are its interpretation of the tax laws. The regulations are effectively the tax laws faced by businesses and individuals. One final word of caution: always remember that tax laws can and do change, and these changes are not always announced in ways that inform small businesses. Nevertheless, ignorance is not an excuse for incorrectly filing one’s taxes.
Individual Taxes
Individual (ordinary) tax liabilities are determined by subtracting certain allowable deductions from one’s total income to obtain taxable income. Taxable income is then used as the basis from which the tax liability is calculated. The general procedure is:
• Gross income – Adjustments to income = Adjusted gross income.
• Adjusted gross income – Personal exemptions and deductions = Taxable income.
• (Taxable income) x (Average tax rate) = Tax liability.
Gross income consists of all income received during the tax year in the form of money, goods and services, and property. Adjustments to income, including some past losses, may include income that is not taxed, such as interest income generated by nontaxable municipal bonds. Adjusted gross income may be reduced by subtracting personal exemptions and deductions regardless of whether you itemize or not and includes such things as business expenses and deductions for some types of Individual Retirement Account (IRA) contributions. A personal exemption is the allowable reduction in the income based on the number of persons supported by that income. You may claim deductions for yourself, your spouse, and other dependents who meet certain criteria. As of 2018, the personal exemption amount is zero until 2025. In addition, you can reduce your taxable income by either claiming a standard deduction or itemizing allowable expenses.
The standard deduction is an amount allowed for all taxpayers who do not itemize, and represents the government’s estimate of the typical tax-deductible expenses that you are likely to have. As of 2018, the standard deduction is \$12,000 for single, \$18,000 for head of household, and \$24,000 for married filing jointly. These are adjusted annually for inflation. If your tax-deductible expenses are greater than the standard deduction, you can list them separately and deduct the total value of the itemized deductions. Itemized deductions include expenses for such things as medical expenses, certain types of taxes, mortgage interest expense, and charitable contributions. After reducing Adjusted gross income by subtracting Personal exemptions and deductions, we obtain our Taxable income, the amount of income that will be used to calculate your Tax liability.
The Federal income tax in the United States is called a progressive tax, meaning that the percentage tax rate increases as taxable income increases. In contrast, regressive taxes have their tax rate remain constant or decrease as taxable income increases. State sales taxes, property taxes, social security taxes, and in some cases, state income taxes are regressive taxes because as a percentage of one’s income paid as taxes they increase with a decline in one’s income.
Two different tax rate measures include the Average tax rate and the Marginal tax rate defined below:
The average tax rate represents the “average” tax rate that is paid on each dollar of taxable income. The marginal tax rate is the tax rate that is paid on the next dollar of taxable income. In a progressive tax system, the marginal tax rate will always be equal to or greater than the average tax rate.
The federal tax rate schedule for 2018 taxable income is shown in Table 3.1.
Table 3.1. Federal Income Tax Rates in 2018
Tax Bracket Married Filing Jointly Single
10% Bracket \$0 – \$19,050 \$0 – \$9,525
12% Bracket \$19,050 – \$77,400 \$9,525 – \$38,700
22% Bracket \$77,400 – \$165,000 \$38,700 – \$82,500
24% Bracket \$165,000 – \$315,000 \$82,500 – \$157,500
32% Bracket \$315,000 – \$400,000 \$157,500 – \$200,000
35% Bracket \$400,000 – \$600,000 \$200,000 – \$500,000
37% Bracket Over \$600,000 Over \$500,000
Because of the progressive nature of the tax, the marginal tax rate increases as your income increases. The first \$19,050 of taxable income for married couples filing a joint return are taxed at a rate of 10%, the next \$58,350 (\$77,400 – \$19,050) of taxable income are taxed at a rate of 12%, and so on. Suppose a married couple had \$120,000 of taxable income in 2018.
Their Federal tax liability would be calculated on each increment of income as follows: The average tax rate paid equals Total tax liability/taxable income = \$18,279/\$120,000 = 15.2% and the marginal tax rate paid on the last dollar earned would be 22%.
10% tax on first \$19,050 (\$19,050 – \$0) = 10% x \$19,050 = \$1,905.00
12% tax on next \$58,350 (\$77,400 – \$19,050) = 12% x \$58,350 =\$7,002.00
22% tax on next \$42,600 (\$120,000 – \$77,400) = 25% x \$44,700 = \$9,372.00
Total Tax Liability on \$120,000 = \$18,279.00
It is important to distinguish between the marginal and average tax rate. The average tax rate is useful because it allows us, with a single number, to characterize the proportion of our total income that is taxed. In many cases, however, we are interested in the amount of tax that will be paid on any additional income that is earned, perhaps as a result of profitable investment. In these situations, the marginal tax rate is the appropriate rate to use. For example, suppose your average tax rate is 18.4 percent and you are in the 22 percent tax bracket, and you receive a \$1,000 raise. The additional income you earn will be taxed at the marginal tax rate of 22 percent, regardless of the average tax rate, so that your increase in after-tax income is only \$1,000(1 – .22) = \$780. The marginal tax rate is also significant when considering the impact of tax deductions. Suppose you are in the 22 percent tax bracket and you contribute \$2,000 to your favorite charity. This reduces your taxable income by \$2,000, saving you \$440 in taxes (22% times \$2,000) so that your after-tax cost of your contribution is only \$2,000(1 – .22) = \$1,560.
Total Marginal Tax Rates
As we pointed out earlier, because of the progressive nature of the federal tax code, the effective marginal rate that individuals pay is nearly always greater than the federal marginal tax rate. However, there are more levels of government collecting tax revenues than just the federal government. In addition to the federal tax, most personal income is also subject to state taxes, Social Security taxes, Medicare taxes, and perhaps city taxes. State taxes vary but often run in the 4 – 6 percent range. Social Security (6.2 percent) and Medicare (1.45 percent) taxes are split between employer and employee, and the rate for most employees is 7.65 percent (self-employed pay both the employer and employee half, usually 15.3 percent). In 2018, the social security tax is imposed only on individual income up to \$128,400. There is no maximum income limit on the Medicare tax. City taxes can run 3 – 4 percent. Therefore, the effective marginal tax rate for someone in the 24 percent federal tax bracket who pays social security tax will generally be over 37 percent. If the same person were self-employed they would be subject to an additional 7.65 percent, and a marginal tax rate that could exceed 50 percent of taxable income in some cases. It should be noted that one-half of “self-employment tax” is deductible from income subject to federal tax, so the effective marginal tax rate increases by only 7.65(1 – .24) = 5.81 percent for someone in the 24 percent tax bracket. As you can see, it is extremely important to understand what the effective marginal tax rate is when making financial management decisions.
Bracket Creep
Progressive tax systems are subject to an undesirable feature, often termed “bracket creep.” Bracket creep is an inflation-induced increase in taxes that results in a loss in purchasing power in a progressive tax system. The idea is that inflation increases tend to cause roughly equal increases in both nominal income and the prices of goods and services. Inflation induced increases in income push taxpayers into higher marginal tax brackets, which reduces real after tax income. Consider an example of how inflation reduces real after-tax income and therefore purchasing power.
For the couple in our previous example with a taxable income of \$120,000, their real after-tax income, their purchasing power in today’s dollars, is equal to their Gross income less any Tax liabilities which in their case is: \$120,000 – \$18,279 = \$101,721. Another way to calculate their purchasing power is to multiply (1 – average tax rate T) times their gross income: (1 – 15.2325%)\$120,000 = \$101,721.
Inflation is a general increase in price. Suppose that, as a result of inflation, that next year inflation will increase your salary 10%. However, suppose that inflation will also increase the cost of things you buy by 10%. As a result, to purchase the same amount of goods next year that were purchased this year will require a 10% increase in this year’s expenditures. For the couple described in our earlier example, this will require expenditures of \$101,721 times 110% = \$111,893.10.
Now let’s see what happens to our couple’s after-tax income. A 10% increase in taxable income means they will have \$120,000 times 110% = \$132,000 in taxable income next year. Recalculating the couple’s tax liabilities on their new income of \$130,000:
The average tax rate paid equals Total tax liability/taxable income = \$20,919/\$132,000 = 15.85% while the marginal tax rate paid on the last dollar earned would be 22%. Subtracting couple’s tax liabilities from their income leaves them \$111,051, less than \$111,893.10 which is the amount required to maintain the same purchasing power before inflation. In other words, as a result of the combination of inflation and bracket creep with increases on the average tax rate, the couple’s purchasing power is reduced
The IRS recognizes the impacts of bracket creep, and periodically adjusts the tax schedules and/or deductions in an attempt to smooth or eliminate purchasing power losses due to bracket creep.
10% tax on first \$19,050 (\$19,050 – \$0) = 10% x \$19,050 = \$1,905.00
12% tax on next \$58,350 (\$77,400 – \$19,050) = 12% x \$58,350 = \$7,002.00
22% tax on next \$54,600 (\$132,000 – \$77,400) = 25% x \$54,700 = \$12,012.00
Total Tax Liability on \$132,000 = \$20,919.00
Interest and Dividend Income
Interest and ordinary dividends earned by individuals are generally taxed as ordinary income. One exception is interest income earned on municipal bonds issued by state and local governments (bonds are promissory notes issued by a business or government when it borrows money). Municipal bonds are exempt from federal taxes, which makes them attractive to investors in high marginal tax brackets.
Suppose you are in a 25% marginal tax bracket and are considering investing \$1,000 in either a corporate bond that yields 10% per year, (yield means the rate of return the investment provides) or a municipal bond yielding 8% each year. You can calculate your after-tax cash flow from each investment by subtracting the tax liability from the before-tax cash flow from each investment.
The corporate bond provides a \$100 cash flow before taxes but only \$75 is left after paying taxes. Meanwhile, the municipal bond is exempt from federal taxes and provides an \$80 before and after-tax cash flow. This example illustrates the importance of considering after-tax cash flow as opposed to before-tax cash flow when considering investment opportunities.
Asset Before-tax cash flow return – Taxes = After-tax cash flow
Corporate bond \$1,000(.10) = \$100 \$100(25%) \$75.00
Municipal bond \$1,000(.08) = \$80 \$0 \$80.00
We can also measure an investment’s return using percentages. Percentage measures standardize return measures so investments of different sizes can be compared. We calculate the percentage return during a period as the cash flow received during the period divided by the total amount invested. For example, the percentage rate of return on the corporate bond was \$75/\$1000=7.5%, while the percentage rate of return on the municipal bond was \$80/\$1000=8.0%.
When the returns on the bonds are expressed as rates of return, it is clear that the municipal bond is the preferred investment.
Suppose you wanted to find the before-tax rate of return on a corporate bond (rcb), a pre-tax equivalent rate of return that would provide the same after-tax rate of return as a tax free municipal bond (rmb ). To find rcb , equate the after-tax rates of returns on the corporate and municipal bonds, rcb (1 – T ) = rmb , and solve for the following:
(3.1)
In our example municipal bond rate is 8% so that for an investor in the 25% marginal tax bracket, the pre-tax equivalent rate of return is:
(3.2)
In other words, a corporate bond yielding 10.67% would produce the same after-tax return as the municipal bond yielding 8% for an investor in the 25% tax bracket.
Interest Paid by Individuals
Interest paid by individuals is generally not tax deductible for personal expenditures, such as interest on a loan for a car used solely for personal travel. One primary, and important, exception to this is that interest on a home mortgage is usually deductible from taxable income if filing using itemized deductions. There is also a limited deduction available for student loan interest payments.
Capital Gains and Losses
From an accounting standpoint, we define book value (or basis) as acquisition cost less accumulated depreciation, which is determined by tax codes. (Book value may also be altered by improvements to depreciable assets.) For a variety of reasons, an asset’s market value is usually different from its book value. When an asset is liquidated at a market value greater than its book value we say it has appreciated in value. If the appreciation is equal to or less than its original acquisition cost, we refer to the appreciation value as depreciation recapture. Appreciated value in excess of its acquisition value is referred to as capital gains.
Likewise, when an asset’s liquidation value is less than its book value, we say that the asset has experienced capital losses and define: capital losses = book value – market value (if book value > market value). The tax rate for individuals on “long-term capital gains”, which are gains on assets that have been held for over one year before being sold, depends on the ordinary income tax bracket. For taxpayers in the 10% or 15% bracket, the rate is 0%. For taxpayers in the 22%, 24%, 32%, or 35% bracket, it is 15%. For those in the 37% bracket, the rate is 20%. Other rates also exist under certain situations. The tax rate paid on depreciation recapture is the taxpayer’s income tax rate since depreciation was used to shield income from income tax payments.
Suppose you are in the 24% tax bracket. You have just sold some land (a non-depreciable asset) for \$50,000. The land was purchased 5 years ago for \$30,000. Since you sold the land for more than its book value (the purchase price in this case) you will realize a capital gain of \$50,000 – \$30,000 = \$20,000. Your tax liability on the sale will then be the capital gain times the capital gains tax rate or in this case \$20,000(15%) = \$3,000.
Capital losses must first be used to offset any capital gains realized that year; however, if you have any capital losses remaining after offsetting capital gains, you may offset ordinary income. If you still have capital losses remaining, you may carry the losses forward to offset future capital gains and income. This can be a powerful tool. Suppose the land in the above example brought a selling price of \$20,000. Now you have realized a capital loss of \$30,000 – \$20,000 = \$10,000. If you have not realized capital gains for the year, you can use the loss to offset your ordinary income, which in this example is being taxed at 24%. Your tax savings from the capital loss would be \$10,000(24%) = \$2,400. In other words, you can use the loss to reduce the level of taxable income by \$10,000, which saves you \$2,400 in taxes you would have been required to pay without the loss. If you had realized at least \$10,000 in capital gains on assets held over 12 months during the year, your capital loss would have only saved you \$10,000(.15%) = \$1,500. It is clear that the current capital laws require some careful planning to capture the full benefits. (Note: some capital losses are limited to \$3,000 per year to be taken against regular income. Anything left over can be carried forward to future years.)
Tax Credits
Tax deductions are subtracted from Adjusted Gross income and reduce the level of Taxable income. This results in a tax savings that is equal to the marginal tax rate for each dollar of allowable deduction. Tax credits, on the other hand, are direct deductions from one’s Tax liability. Tax credits, therefore, result in a tax savings of one dollar for each dollar of tax credit. For example, consider the tax savings of a \$1,000 deduction versus a \$1,000 tax credit for an individual facing a 24% marginal percent tax rate:
tax deduction: tax savings = \$1,000(24%) = \$240; and
tax credit: tax savings = \$1,000(100%) = \$1,000.
Clearly, you would prefer one dollar of tax credits more than one dollar of tax-deductible expense. Tax credits come and go sporadically in the tax laws. They have been used in the past to stimulate investment in some types of assets. There are still some tax credits available today. For example, certain college tuition and child care expenses may be eligible for tax credits. Also, for each dependent child under age 17, up to \$2,000 credit may be available.
Business Taxation
Remember that Subchapter S corporations, partnerships, and sole proprietorships are taxed according to the individual tax rate schedule the owner faces. Many Subchapter S corporations, partnerships, and sole proprietorships may get a 20% reduction of their Qualified Business Income, which might be their net business income. C corporations, on the other hand, are taxed according to corporate income tax rates. The corporate tax ate schedule for 2018 is now 21%.
Not all the income generated by a business’s operations is subject to taxes. Most expenses incurred in order to generate the business income are deductible. In addition, there are a number of other adjustments to business income which deserve mention. Also be aware that many, but not all, states impose an additional tax on corporate income.
Depreciation
When a business purchases assets that can be used in the business for more than one year (often called capital expenditures), the business is generally not allowed to deduct the entire cost of the asset in the year in which it was purchased. Depreciation is an accounting expense that allocates the purchase cost of a depreciable asset over its projected economic life. This deduction acts as an expense for both accounting and tax purposes; so increases in depreciation expense result in decreased profit measures for a business. Nevertheless, depreciation expense is a noncash expense; that is, you aren’t sending a check to anyone for the amount of the depreciation expense. This allows depreciation expense to act as a tax shield, which lowers taxable income, resulting in lower tax obligations and consequently higher after-tax cash flow. Accordingly, higher depreciation expenses result in lower profits but higher after-tax cash flow.
For tax purposes, there are rules that determine how you depreciate an asset. You can only depreciate an asset that has been placed in service, which means that it is available for use during the accounting period. There are also conventions that determine the point in time during the accounting period you must assume the asset was placed into service. Most depreciable assets are assumed to be placed into service at the mid-point of the year, regardless of the actual date they are placed in service. This is known as the half-year convention. There are also rules about the recovery period over which an asset can be depreciated. Table 3.2. shows the allowable recovery periods for different classes of farm property.
Table 3.2. Farm Property Recovery Periods[1]
Assets
Recovery Period in Years
Gen. Dep. System Alter. Dep. System
Agricultural structures (single purpose) 10 15
Automobiles 5 5
Calculators and copiers 5 6
Cattle (dairy or breeding) 5 7
Communication equipment 7 10
Computers and peripheral equipment 5 5
Cotton ginning assets
Drainage facilities 15 20
Farm buildings 20 25
Farm machinery and equipment 7 10
Fences (agricultural) 7 10
Goats and sheep (breeding) 5 5
Grain bin 7 10
Hogs (breeding) 3 3
Horses (age when placed in service)
Breeding and working (12 yrs or less)
7 10
Breeding and working (more than 12 yrs)
3 10
Racing horses (more than 2 yrs)
3 12
Horticultural structures (single purpose) 10 15
Logging machinery and equipment 5 6
Nonresidential real property 39 40
Office furniture, fixtures and equipment (not calculators, copiers, or typewriters) 7 10
Paved lots 15 20
Residential rental property 27.5 40
Tractor units (over-the-road) 3 4
Trees or vines bearing fruit or nuts 10 20
Truck (heavy duty, unloaded weight 13,000 lbs. or more) 5 6
Truck (weight less than 13,000 lbs.) 5 5
Water wells 15 20
There are two depreciation methods that can be used for tax reporting purposes: straight line (SL) and modified accelerated cost recovery system (MACRS). Straight line allocates the depreciation expense uniformly each period. The amount of depreciation is found by multiplying the straight line recovery rate for each year times the asset’s unadjusted basis (original cost). The SL recovery rate is simply the inverse of the number of years in the asset’s recovery period adjusted by the required half-year placed in service convention. The straight recovery rates for 3-year, 5-year, and 7-year assets are shown in Table 3.3.
Table 3.3. Straight Line Recovery Rates for 3, 5, 7 Year Assets
Year 3-Year 5-Year 7-Year
1 16.67% 10% 7.14%
2 33.33% 20% 14.29%
3 33.33% 20% 14.29%
4 16.67% 20% 14.28%
5 20% 14.29%
6 10% 14.28%
7 14.29%
8 7.14%
As you might guess from its name, MACRS produces larger depreciation expenses in early years than the SL method of depreciation and lower depreciation expenses in the later years than the SL method of depreciation. The federal government specifies the allowable rates of MACRS depreciation. These rates are determined by using a combination of the declining balance (either 150% or 200%) and straight-line depreciation methods. Prior to 2018, farmers were not permitted to use 200% declining balance. The MACRS depreciation expense for each year is calculated by multiplying the unadjusted basis (acquisition cost) of the asset by the appropriate recovery rate for that year. The MACRS (200% method) recovery rates for the 3-year, 5-year, and 7-year asset classes are shown in Table 3.4.
Table 3.4. MACRS Recovery Rates for 3, 5, and 7-Year Assets
Year 3-Year 5-Year 7-Year
1 33.0% 20.00% 14.29%
2 44.45% 32.00% 24.49%
3 14.81% 19.20% 17.49%
4 7.41% 11.52% 12.49%
5 11.52% 8.93%
6 5.76% 8.93%
7 8.93%
8 4.46%
Suppose your business just purchased a \$100,000 asset that has a 3-year useful life, and falls into 3-year class of assets. Using the SL method, the depreciation expense each year for the next 3 years would be:
Year Recovery Rate Unadjusted Basis Depreciation Expense Accumulated Depreciation
1 .1667 \$100,000 \$16,670 \$16,670
2 .3333 \$100,000 \$33,330 \$50,000
3 .3333 \$100,000 \$33,330 \$88,330
4 .1667 \$100,000 \$16,670 \$100,000
Note that the book value or basis of the asset (acquisition cost – accumulated depreciation) would be \$0 after it has been fully depreciated at the end of 4 years. Because of the half-year convention, it takes 4 years to depreciate the asset, even though it falls into the 3-year classification.
Depreciation expense for the same asset using the MACRS method would be calculated as:
Year Recovery Rate Unadjusted Basis Depreciation Expense Accumulated Depreciation
1 .3333 \$100,000 \$33,333 \$33,333
2 .4445 \$100,000 \$44,450 \$77,780
3 .1481 \$100,000 \$14,810 \$92,950
4 .741 \$100,000 \$7,410 \$100,000
Note again that the depreciation expense using MACRS is higher in the early years and lower in later years than with the SL method and that the book value after 4 years is again zero. Businesses often use MACRS for tax purposes and SL for profit reporting. Can you think of any reasons why?
Some businesses that invest small amounts in capital assets are allowed to deduct up to \$1,000,000 of the cost of acquired depreciable property as a current expenditure instead of a capital expenditure. This is known as direct expensing, and is available only to businesses that don’t make large capital purchases each year. The allowable expensing amount is reduced by one dollar for each dollar of capital investment expenditure over \$2,500,000 during the year. Other restrictions also apply.
Bonus or Additional Depreciation
Property purchased with a recovery period of 20 years or less may be eligible for 100% additional depreciation the year it is purchased. It is required unless the taxpayer elects out of it by class or recovery period (3, 5, 7, 10, 15, 20 year classes). It can be used on either new or used property but has limitations if purchased from a relative. Passenger automobiles may be limited to an extra \$8,000 additional depreciation rather than 100%. The 100% depreciation decreases to 80% in 2024 and reduces by 20% each year after that until 2028 when it disappears.
Interest and Dividends Received
Interest and ordinary dividend income received by sole proprietorships and partnerships is taxed as ordinary income. Interest income received by corporations is taxed as corporate income. However, dividend income received by corporations is allowed eighty percent tax exclusion (only 20 percent is taxed) before being taxed as corporate income. The reason for the exclusion is that corporate income is already subject to double taxation, and taxing dividends as corporate income would result in triple (or more) taxation. Can you explain why?
Which is better for a corporation in a 21% marginal tax bracket: \$1,000 of interest income or \$1,000 of dividend income? Remember what we care about is after-tax cash flow (ATCF) so let’s evaluate both investments:
Investment Income – Taxes = ATCF
Interest income \$1,000 – \$1,000(.21) = \$790
Dividend income \$1,000 – \$1,000(.20)(.21) = \$958
The ATCF from the dividends of \$958 would be preferred to the \$790 from the interest income. The dividends are effectively taxed at a lower rate than interest income. We can find the effective rate on each dollar of dividend income received by multiplying the two marginal tax rates by the proportion of income subject to tax: that is \$1(.20)(T) = \$1(.20)(.21) = 0.042 or 4.2%. Accordingly, the effective tax rate T for dividends in this case is 4.2% as opposed to 21% for interest income at this marginal tax rate. What incentives do federal tax laws give regarding the type of investments that corporate businesses make?
Interest and Dividends Paid
Interest expenses paid by businesses are tax deductible. Dividends or withdrawals paid by businesses are not tax deductible. Consider a firm in a 21 percent tax bracket that pays \$1,000 in interest expense and \$1,000 in dividends or withdrawals. What is the after-tax cost of each expense?
Expense Type Expense – Tax-savings = After-tax expense
Interest expense \$1,000 – \$100(.21) = \$790
Dividend expense \$1,000 – \$0 = \$1000
Dividends and withdrawals cost the firm \$1 of after-tax income for each \$1of dividend paid. Interest expense, on the other hand, costs the firm \$1(1 – T) = \$1(1 – .21) = \$0.79 of after-tax income for each \$1 of interest expense paid. Another way to think about it is to find out how much before-tax income it takes to pay \$1 of both interest and dividend expenses. Using the formula discussed earlier:
Before-tax dividend expense = \$1.00/(1 – .21) = \$1.266
Before-tax interest expense = \$0.79/(1 – .21) = \$1.00
It takes \$1.27 of before-tax income to pay \$1 in dividend or withdrawal expense, while it takes only \$1 in before-tax income to pay \$1 in interest expense. The two ways for a firm to finance its assets are to use debt or equity financing. Which method of financing do the federal tax loans favor?
So what have we learned? It’s not what you earn but what you get to keep that matters. And that’s where tax management plays an important role. Taxes are an important difference between what you earn and what you get to keep. Thus, an important part of strategic financial management is managing one’s tax obligations.
Summary and Conclusions
The main lesson for managing taxes is to look at investments and cash flow on an after-tax basis, and this requires that all tax obligations are accounted for in the tax management process. Management of the firm’s taxes also requires managers to understand how different business organizations can create different tax obligations, the difference between average and marginal tax rates, the different tax obligations associated with interest versus dividend income, capital gains and capital losses, depreciation schedules, book value and market value of assets, tax deductions, and tax credits. Understanding these and other tax-related concepts will help financial managers manage the difference between what you earn and what you get to keep.
Questions
1. Tiptop Farms, a sole proprietorship, had a gross income of \$600,000 in 2018. Tiptop Farms expenses were equal to \$320,000. Tiptop had interest expenses of \$80,000 and depreciation expenses of \$75,000 during the year. Tiptop’s owner withdrew \$25,000 from the business during the year to help pay college expenses for the owners’ children. The tax schedule for 2018 is:
Income Tax Rate
\$0 – 40,000 15%
\$40,001 – 100,000 28%
\$100,000 – 150,000 31%
\$150,001 + 35%
1. What was Tiptop’s taxable income during 2018?
2. What is Tiptop’s tax liability for 2018?
3. What is Tiptop’s average and marginal tax rate for the year?
4. If Tiptop is considering the purchase of a new investment, what tax rate should they use?
2. Consider a couple filing jointly, whose taxable income last year was \$130,000. Assume that state taxes on their taxable earnings were 5%. The couple pays social security at the rate of 6.2%, and Medicare taxes at the rate of 1.45%. Half of the couple’s social security and Medicare taxes are paid by their employer. Also recognize that social security was only charged on the first \$128,400. Find the couples tax liability, its average tax rate, and its marginal tax rate. What is higher, the couple’s average tax rate or their marginal tax rate? Explain your answer.
3. Suppose that last year, inflation was 8%, meaning that the price of every- thing you buy has increased by 8%. If your before-tax income increased by 8% would you be just as well off as before? If not, how much more than 8% would you need to increase to buy as much as you did before inflation?
4. A corporate bond is providing a yield of 12% per year, while at the same time, a municipal bond (which is tax exempt) is yielding 9% per year. Each bond only pays interest each year until the bond matures, at which time the principal investment will be returned. Each bond is equally risky, and your marginal tax bracket is 30%. You have \$1,000 to invest.
1. What is the after-tax cash flow from each bond? Which bond would you invest in?
2. What is the percentage after-tax return on each bond?
3. What before-tax equivalent on the corporate bond would make you choose it as an investment?
4. Suppose that you are also subject to a 5% state tax from which neither the corporate or municipal bond is tax exempt. What is the after-tax return on each bond?
5. Suppose you invest in a new tractor during the tax year that costs you \$78,000, plus \$2,000 for delivery and set up. Your marginal tax rate is 40%. Note: new farm machinery has a class life of 5 years.
1. What is the depreciation expense each year using the straight line method of depreciation?
2. What is the depreciation expense each year using the MACRS 200% declining balance method of depreciation?
3. What is the tax shield each year from each method?
4. Which method would you use for tax purposes? How about profit reporting? Explain.
6. Businesses often use MACRS for tax purposes and SL for profit reporting. Can you think of any reasons why?
1. Most assets use the General Depreciation System for recovery periods. See IRS guidelines for more information. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/03%3A_The_Federal_Tax_System.txt |
Learning Objectives
After completing this chapter, you should be able to (1) construct consistent and accurate coordinated financial statements (CFS) (2) describe the differences and connections among balance sheets, accrual income statements (AIS), and statements of cash flows; and (3) distinguish between endogenous and exogenous variables and how they influence the construction of CFS.
To achieve your learning goals, you should complete the following objectives:
• Learn how to construct the financial statements included in the CFS.
• Learn how the fundamental accounting equation organizes the firm’s balance sheet entries.
• Learn how to organize a firm’s cash flow data into a Sources and Uses of Funds (SAUF) statement.
• Learn how to distinguish between a firm’s cash income statement and its accrual income statements (AIS).
• Learn how to compute a firm’s cash income statement using cash flow and depreciation data.
• Learn how to distinguish between exogenous and endogenous variables.
• Learn how to compute a firm’s statement of cash flow using data from its checkbook and other cash flow records.
• Learn the consistency requirements that connect data from the firm’s balance sheets, AIS and statement of cash flow.
• Learn the distinction between consistency of financial statements and accuracy of financial statements.
• Learn how to organize firm financial data into a consistent and (as far as possible) accurate set of CFS.
Introduction
Financial statements include balance sheets, the cash income statement, an accrual income statement (AIS), the statement of cash flow (SCF), and the sources and uses of funds (SAUF) statement. Coordinated financial statements (CFS) include beginning and ending period balance sheets, an AIS, and a SCF. We are particularly interested in the financial statements included in CFS because they are interdependent and when constructed consistently can help us identify inaccuracies in our data.
The purpose of financial statements is to provide the firm the information it needs to identify its strengths and weaknesses, to evaluate its performance, to assess its alternative futures, and to guide its choices between alternative futures to the one most consistent with its mission, goals, and objectives.
Financial managers are expected to conduct financial analysis. To be effective in this role, financial managers need to have a basic understanding of financial statements—how to construct them and how to analyze them. The material that follows provides a basic understanding of financial statements and how to construct them. Later chapters will focus on how to analyze them.
There are, of course, other reasons why familiarity with financial statements may be important. We may have an interest in learning about successful firms, and one way to do this is to examine their financial statements. We may be interested in investing in a firm and want to evaluate its financial condition. We may be employed in a job that requires an understanding of financial statements. Or, we may simply want to make informed decisions that influence the financial conditions of firms in which we have an interest.
Ideally, firms maintain properly constructed financial statements which financial managers can use to conduct financial analysis. But the reality is that many firms, especially small firms, do not maintain a properly constructed set of financial statements. Furthermore, many firms do not record all the data necessary to construct an accurate set of financial statements. On the other hand, nearly all firms maintain cash receipts and cash expense records needed to construct income tax liabilities. And these same tax record lists the book value of long-term assets necessary to construct balance sheets. Fortunately, with balance sheet data and a cash income statement computed from tax records, we can construct a set of financial statements including an AIS.
Financial Statements
Financial statements may vary by type of firm. For example, financial statements prepared for corporations must satisfy generally accepted accounting practices (GAAP) in which ownership claims are represented by shares of stock. Financial statements prepared for sole proprietorships and partnerships are not subjected to GAAP requirements. In addition, some financial statements are based on accrual methods that record transactions when they occur, while others record transactions only when cash is exchanged.
Different financial statements may report the value of assets differently. Some financial statements represent the value of assets at the price at which they could be sold in the current accounting period. These values are referred to as market values. Other financial statements represent the value of assets at the price at which they were purchased less depreciation. In these statements, allowable depreciation is usually described in tax codes. These values are referred to as book values.
So what have we learned? We learned that financial managers need access to identify the following financial statements: book value balance sheets, accrual and cash income statements, sources and uses of funds (SAUF) statement, and statement of cash flow. Of these statements we make particular mention of the book value balance sheets, the accrual income statement (AIS) and the statement of cash flow. We refer to these as coordinated financial statements (CFS) because they are interdependent and their proper connections to each other—their consistency—can be easily checked. In addition, consistently constructed CFS can help us identify inaccuracies in our data. In what follows we describe firm financial statements.
The Balance Sheet
The balance sheet describes the firm’s assets—what the firm owns or controls. It also lists the claims on the firm’s assets from outside the firm called liabilities. The difference between assets and liabilities equals net worth and represents the firm’s equity. The balance sheet is constructed at a point in time, e.g. the last day of the year, leading some to describe it as a snapshot of the firm’s financial condition.
In the balance sheets presented in this class, the value of assets and liabilities is a combination of current and book values. Long-term assets are recorded at their book value—their purchase prices less accumulated depreciation determined by tax codes. Most liabilities and current assets are valued at their current values.
The underlying principal for constructing any balance sheet is the fundamental accounting equation: Assets = Liabilities + Equity. The fundamental accounting equation declares that each of the firm’s assets must be financed either by liabilities (funds supplied by those outside the firm) or equity (funds supplied by the firm’s owners). Moreover, the fundamental accounting equation separates the firm’s assets from its liabilities and equity on the balance sheet. We can check the fundamental accounting equation by noting that the total value of assets equals the total value of liabilities and equity for each year the balance sheet is calculated.
Table 4.1 reports 2016, 2017 and 2018 year-end balance sheets for the hypothetical proprietary firm called HiQuality Nursery. Since we will repeatedly use data associated with this hypothetical firm and refer to the firm frequently, we will refer to it in the future using the acronym HQN. When reporting balance sheets for multiple years, the balance sheets in this text will appear in increasing time periods from least current to most current: 2016, 2017, and 2018 in the case of HQN.
Table 4.1. Year End Balance Sheet for HQN (all numbers in 000s)
Open HQN Coordinated Financial Statement in MS Excel
Balance Sheet
Year
12/31/16
12/31/17
12/31/18
Cash and Marketable Securities
\$1,200
\$930
\$600
Accounts Receivable
\$1,560
\$1,640
\$1,200
Inventory
\$3,150
\$3,750
\$5,200
Notes Receivable
\$0
\$0
\$0
CURRENT ASSETS
\$5,910
\$6,320
\$7,000
Depreciable Long-term Assets
\$3,270
\$2,990
\$2,710
Non-depreciable Long-term Assets
\$710
\$690
\$690
LONG-TERM ASSETS
\$3,980
\$3,680
\$3,400
TOTAL ASSETS
\$9,890
\$10,000
\$10,400
Notes Payable
\$1,400
\$1,500
\$1,270
Current Portion LTD
\$700
\$500
\$450
Accounts Payable
\$2,400
\$3,000
\$4,000
Accrued Liabilities
\$870
\$958
\$880
CURRENT LIABILITIES
\$5,370
\$5,958
\$6,600
NONCURRENT LONG-TERM DEBT
\$2,560
\$2,042
\$1,985
TOTAL LIABILITIES
\$7,930
\$8,000
\$8,585
Contributed capital
\$1900
\$1900
\$1,900
Retained earnings
\$60
\$100
(\$85)
TOTAL EQUITY
\$1,960
\$2,000
\$1,815
TOTAL LIABILITIES AND EQUITY
\$9,890
\$10,000
\$10,400
Assets
Assets represent everything of value that the firm controls. Assets have value to the firm, mostly because they represent what can be used to generate earnings. The firm’s assets are typically listed in order of liquidity, or nearness to cash. In most cases asset liquidity depends on the ease or cost of converting them to cash.
Current Assets. Current assets are cash and near-cash assets that are expected to be liquidated or converted to cash during the next year. Current assets are typically assets whose liquidation will not significantly disrupt the operation of the firm. We describe current assets next in their order of liquidity, or their nearness to cash.
• Cash balances are the firm’s most liquid assets.
• Marketable securities are interest-bearing deposits with low risk of losing principal and can easily be converted to cash if needed.
• Accounts receivable include completed sales, for which payment has not been received.
• Notes receivable represent short-term loans the firm has made to others that are expected to be repaid during the coming year. Notes receivables are important for firms for whom lending money and earning interest on their loans is a significant source of income.
• Finally, inventories may be of two kinds. One kind of inventory represents the value of inputs on hand that can be used in future production or manufacturing of goods. A second kind of inventory are products available for sale. Inventories are often the least liquid of the firm’s current assets, and their value is often not known until they are sold.
Long-term assets. Long-term assets yield services over several time periods. Liquidation of long-term assets would typically disrupt the operations of the firm and would occur only if the firm were facing a solvency crisis or replacing long-term assets with more productive ones.
Some balance sheets distinguish long-term assets by the length of time they will be held by the firm before being liquidated, referring to them as intermediate versus long-term assets. We prefer to distinguish between long-term assets by whether or not they depreciate. Depreciable long-term assets include machinery, equipment, breeding stock, contracts, long-term notes receivable, building and improvements. Non depreciable long-term assets are mostly land.
Book value versus market value of long-term assets. The book value of long-term assets is equal to their purchase price less accumulated depreciation: book value = acquisition cost – accumulated depreciation.
Accumulated depreciation is intended to reflect the loss in value of long-term assets due to use or the passage of time. As a practical matter, the depreciation rate is usually determined by tax codes.
While long-term assets are valued at their book value in the balance sheet, firms are also interested in the market value of their long-term assets. An asset’s market value is the price at which it could be sold in the current market. An asset’s book value is almost always different than its market value, the price at which the asset could be sold in the current period. Two reasons why an asset’s book value and market value differ are because an asset’s book value ignores appreciation and its depreciation is set by predetermined rates (rather than market forces), most often reflected in tax codes.
Tax consequences created by depreciable assets are complicated. Consider an example. Suppose a firm purchased a depreciable asset for \$1,000 and then depreciated its value by \$100 for four years and then sells the asset for \$1,300. The difference between the realized market value of \$1,300 and its book value of \$600 consists of recaptured depreciation of \$400 and capital gains of \$300. The \$300 of capital gains are taxed at the capital gains tax rate. Because the depreciation shielded the firm’s income from income tax, the tax savings from \$400 of depreciation is recaptured at the firm’s income tax rate.
To better understand why book value is not equal to market value, think about what determines market value. As will be demonstrated later, the market value of an asset generally depends on the discounted value of future cash flow the asset is expected to generate. The cash flow characteristics that are important in establishing the market value of an asset include:
• the size and/or number of expected future cash flow;
• the timing of expected future cash flow; and
• the risk and variability of future cash flow.
In general, the larger the size and/or number of expected future cash flow, the larger will be the market value of the asset. Likewise, the sooner the asset is expected to generate cash flow, the higher will be the asset’s market value, because a dollar today is generally preferred to a dollar later. Finally, as the risk or variability of an asset’s future cash flow increase, the lower will be the asset’s market value. To account for the influence of the size, timing, and risk of an asset’s cash flow on an asset’s value, later chapters will introduce the concepts of the time value of money and certainty equivalent measures (see Chapters 7 and 14).
So what have we learned? We learned that with so many variables affecting the market value of an asset, we cannot expect that any predetermined depreciation schedule will accurately predict a depreciable asset’s market value. Therefore, depreciable assets are valued at their book value in our balance sheets.
Liabilities
Liabilities are obligations to repay debt and accrued interest charges. They are listed according to the date they become due. Current liabilities are debt and interest payments due during the current period and pose the greatest liquidity demands on the firm’s resources. Long-term liabilities are debts that will come due after the current year. Equity, which represents residual ownership of the firm’s assets, has no fixed due date and is consequently listed after current and fixed liabilities.
Current liabilities. Current liabilities include the following:
• Notes payable are short-term debt (written promises) the firm is obligated to pay during the current year.
• The current portion of long-term debt (LTD) is the portion of LTD that is due during the upcoming year.
• Accounts payable equal the value of purchases made for inputs but not paid.
• Accrued liabilities are expenses that have been incurred through the operation of the firm and the passage of time, but have not been paid. Examples of accrued expenses include taxes payable, interest payable, and salary and wages payable.
Non-current long-term debt is the final category of liabilities, a long-term liability. Non-current long-term debt is that portion of the firm’s debt due after the current period. These are usually long-term notes payable, mortgages, or bond obligations.
Equity: Equity, or net worth, is the difference between assets and liabilities, the difference between what one owns and what one owes. The firm’s equity is an estimate of what owners of the firm would have left if they sold all their assets at their book value and paid all their liabilities valued at their market value. Therefore, equity is an important indicator of a firm’s financial health.
The actual difference between what one owns and what one owes, if required to sell all of one’s assets and repay one’s liabilities, depends not only on the difference between the market value and book value of assets but also on the liquidity of the firm. Therefore, some caution is called for when interpreting the equity appearing on the firm’s balance sheet as an indicator of its financial well-being.
Equity consists of accumulated retained earnings reported in the AIS and contributed capital by the firm’s owners. One practical note is that when reconciling assets and liabilities, contributed capital is sometimes treated as a residual endogenous variable.
Checkbooks and Sources and Uses of Funds (SAUF) Statement
Most small firms record cash flow data in checkbooks, credit card statements, or other financial worksheets. These data are central to the construction of financial statements. They also supply the information needed to construct the firm’s income tax returns. Consider HQN’s cash flow data recorded in its checkbook reported in Table 4.2. To simplify the reporting of cash flow data, individual entries of the same kind have been combined into general categories.
Checkbooks
Beginning cash balance. Beginning cash balance is the cash the firm had on hand at the end of the previous period. It also appears on the first line of the firm’s checkbook.
Cash receipts. Cash receipts may include cash received from the sale of tangible products like grain and livestock. Cash receipts may also include cash received from services the firm sells to other firms such as tiling, harvesting, and veterinary services. Cash receipts may include government payments from sponsored activities and insurance payments. Finally, cash receipts include reductions in accounts receivables and inventories that represent previous sales and production converted to cash in the present period.
Cash costs of goods sold (COGS). Cash COGS reflect the direct cost of materials and labor used to produce the goods that were sold to generate the firm’s revenue. Cash COGS vary with the production levels and are usually the largest expense in most businesses. Cash COGS may also include payments on accounts payable. Finally, cash COGS include reductions in accounts payable that represent expenses incurred in the previous periods paid for in the present period.
Cash overhead expenses (OE). Cash OE represent the costs of operating and administrating the business beyond those expenses included in COGS. These expenses typically include such things as administrative expenses, general office expenses, rents, salaries, and utilities. OE are difficult to assign to a particular production activity because they contribute to more than one project. Moreover, they tend not to vary with changes in production levels. Cash OE may also include payments on accrued liabilities. Finally, cash OE include reductions in accrued liabilities incurred in previous periods paid for in the present period.
Taxes. Taxes include all compulsory contributions to and determined by governmental units. Taxes may be imposed on property, profits, and some goods used in production and sales.
Interest. Interest is the cost paid to use money provided by others during the current period. We sometimes distinguish between interest paid on long-term and short-term debt obligations.
Cash purchases or sales of long-term assets. Depreciable and non-depreciable long-term assets provide services for more than one period providing the firm a measure of control over its capital service flow not afforded by rental agreements.
Loan payments and account and note payments. Loan payments and account and note payments reflect payments on the amount of financial resources owed others. Sometimes referred to as principal payments, in the case of loans, note payment reflect reductions in the financial obligations of the firm as opposed to interest payments charged for the use of the financial resources of others.
Owner draw. Owner draw represents funds withdrawn from proprietary firms by its owners. These payments may be in exchange for services rendered by the firm’s owner. In other cases, owner draws are funds withdrawn from the firm to meet financial needs of the firm’s owner.
Table 4.2. HQN’s 2018 Checkbook
Date Item Withdrawal Deposit Balance
12/31/17 Beginning cash balance \$930
Cash receipts \$38,990 \$39,920
Cash cost of goods sold (COGS) \$27,000 \$12,920
Cash overhead expenses (OE) \$11,078 \$1,842
Interest paid \$480 \$1,362
Taxes paid \$68 \$1,294
Purchase of long-term assets \$100 \$1,194
Sale of long-term assets \$30 \$1,224
Current portion of long-term debt paid \$157 \$1,067
Long-term borrowings \$50 \$1,117
Notes payable \$230 \$887
Owners’ draw \$287 \$600
12/31/18 Ending cash balance \$600
The Sources and Uses of Funds (SAUF) statement.
The data recorded in the firm’s checkbook and other cash flow records can be organized as an SAUF statement that identifies sources of cash for the firm (cash inflows) and uses of funds (cash outflows). The SAUF statement is consistent with the cash flow data reported in HQN’s checkbook in Table 4.2. HQN’s SAUF statement is reported in Table 4.3.
At the beginning of the period, firm managers make cash flow projections recorded in the SAUF statement. These projections allow the firm to plan in advance for cash flow shortages or for investment and savings opportunities. Obviously, a negative ending cash balance is not possible; therefore, the firm adjusts its cash expenses or cash receipts so that the firm remains solvent. In the last column of HQN’s SAUF, ending period cash balances were projected to equal \$51.
Table 4.3. HQN’s 2018 SAUF Statement
Date Sources of Cash Actual Projected
12/31/17 Beginning cash balance \$930 \$930
Cash receipts \$38,990 \$39,000
Sale of long-term assets \$30 \$50
Long-term borrowing \$50 \$25
12/31/18 Total sources of funds \$40,000 \$40,005
Uses of Cash
Cash COGS \$27,000 \$25,000
Cash OE \$11,078 \$12,000
Interest paid \$480 \$480
Taxes paid \$68 \$70
Cash purchases of long-term assets \$100 \$150
Pay current portion of long-term debt payment \$157 \$1,067
Notes payable \$230 \$887
Owners’ draw \$287 \$300
12/31/18 Total uses of funds \$39,400 \$39,954
12/31/18 Ending cash balance (Total sources – total uses of funds) \$600 \$51
Notice that the entries in the Checkbook reported in Table 4.2 match those in the SAUF statement reported in Table 4.3, except that they are organized as sources of funds coming into the firm and uses of funds representing funds flowing out of the firm. Consistency between the firm’s SAUF statement and its checkbook requires cash at the ending periods in the balance sheet and the SAUF are equal.
So what have we learned? We learned that records of cash flow whether recorded in checkbooks or similar records is one of the most important data sources for constructing CFS for the firm. This data can be used to construct SAUF statements and statements of cash flow.
Statement of Cash Flow (SCF)
The firm’s balance sheet describes its financial position at a point in time while the firm’s statement of cash flow (SCF) describes the firm’s cash flow over a period of time between the firm’s beginning and ending balance sheets. The main purpose of the SCF is to find the change in the firm’s cash position during the accounting year.
Three major cash flow activities. The firm’s SCF is similar to its SAUF statement except that it separates cash flow into the three categories: (1) cash flow from operations, (2) cash flow from investments, and (3) and cash flow from its financing activities.
The cash flow from operations reflect the cash flow generated by the firm in producing and delivering its goods and services. Cash flow from operations reflect the firm’s management of its production and marketing activities.
The cash flow from investment activities result from the firm’s sale and purchase of long-term assets. Sales of long-term assets whose market value exceeds its book value create realized capital gains and depreciation recapture. Cash flow from investment activities reflect the firm’s investment management strategies.
The cash flow from financing activities result from borrowing new debt, repaying old debt, raising new equity capital, and returning capital to owners. Cash flow from financing reflect the firm’s management of its debt and equity.
Cash flow for the firm during the accounting period are summarized by its change in cash position. By adding cash on hand at the end of the previous period to the change in cash position reported in the statement of cash flow, we obtain cash on hand at the end of the period. As a result, the change in cash position links the beginning and ending cash on hand reported in the balance sheet.
The SAUF statement derived from the checkbook contains all the data required to construct a statement of cash flow (SCF) for the firm. While cash flow can occur in any order in real life, we have arranged them in the SAUF statement by categories: cash flow associated with operations, cash flow associated with investment, and cash flow associated with financing.
Net cash flow from operations. The first entry in HQN’s checkbook is cash receipts of \$38,990. This represents a source of cash, and is therefore entered in the “credit” or “deposit” column of the checkbook. The next items that appear in the checkbook are cash COGS of \$27,000, cash OE of \$11,078, interest paid of \$480, and taxes paid equal to \$68. We find net operating cash flow by subtracting from cash receipts, cash expenditures or COGS, cash OE, interest and taxes.
+ Cash receipts \$38,990
Cash COGS \$27,000
Cash OE \$11,078
Interest paid \$480
Taxes paid \$68
= Net Cash Flow from Operations \$364
Net cash flow from investments. Net cash flow from investment activity is calculated from checkbook entries equal to \$70 which corresponds to net cash flow from investment. It is calculated as the difference between purchases of long-term assets (\$100) less sales of long investments assets equal to \$30. These calculations for HQN in 2018 are recorded below.
+ Realized capital gains + depreciation recapture \$0
+ Sales of non-depreciable assets \$0
Purchases of non-depreciable assets \$0
+ Sales of long-term assets \$100
Purchases of long-term assets \$30
= Net Cash Flow from Investments (\$70)
It is important to recognize that some purchases may be paid for with borrowed funds. In this case the borrowed funds would be entered in the SAUF as a source of funds while the purchase reflects own plus borrowed funds expended to acquire the long-term asset.
Net cash flow from financing. Cash flow from financing activities recorded in the checkbook reflect the difference between borrowing and repayment of long-term debt and payments of notes payable. Interest paid on long-term debt and notes payable is included in net cash flow from operations. Finally, dividends paid and owner draw are subtracted and the difference between new equity contributed and purchased is reflected in the net cash flow from financing. HQN’s 2018 net cash flow from financing are recorded below.
Long-term debt payments \$157
+ Long-term borrowings \$50
Payments on notes payable \$230
Owner draw \$287
= Net Cash Flow from Financing (\$624)
An alternative to calculating net cash flow from financing is to use the difference between the ending and beginning balance sheet to the find the change in long-term debt and current long-term debt plus the change in notes payable. Finally, we subtract payment of dividends and owner draw. Net cash flow calculated using the balance sheet rather than the checkbook is reported next.
+ Change in non-current LTD (\$57)
+ Change in current portion of LTD (\$50)
+ Change in notes payable (borrowing less payments) (\$230)
Payment of dividends and owner draw \$287
= Net Cash Flow from Financing (\$624)
We demonstrate that cash flow associated with borrowing LTD, repaying current and noncurrent portions of LTD, and converting noncurrent LTD to current LTD are properly accounted for by adding changes in current and noncurrent LTD. To this end, consider the following. We assume transactions occur at the end of each period. Current and noncurrent LTD at the end of the previous period are designated and respectively. Current and noncurrent LTD at the end of the current period are designated and respectively. Assume that at the end of the current period: (1) the firm reduces its outstanding LTD by paying amounts and on noncurrent and current LTD balances respectively ; (2) it increases its LTD by borrowing amount ; and (3) some noncurrent LTD becomes current LTD—an amount equal to . We can now write the identity:
(4.1)
In words, current LTD at the end of the period equals current LTD at the beginning of the period plus noncurrent LTD converted to current LTD less current LTD payments made at the end of the period. Then we find the difference between current LTD at the end of the previous and current periods as:
(4.2)
Similarly, we write the identity
(4.3)
In words, noncurrent LTD at the end of period one is equal to noncurrent LTD at the beginning of the period plus additional LTD borrowings, less noncurrent LTD converted to current LTD minus noncurrent LTD payments. Then we find the difference between noncurrent LTD at the end of the previous and current periods as:
(4.4)
Finally we add to find:
(4.5)
Since cancels when the two equation are added together, we prove that including the difference in current and noncurrent LTD in the financing cash flow section of the statement of cash flow properly accounts for borrowing and payment of LTD and transferring funds from noncurrent to current LTD.
We are now prepared to calculate the change in the net cash position of the firm by combining HQN’s cash flow from operations, investing, and financing.
Table 4.4a. HQN’s 2018 Statement of Cash Flow
+ Cash receipts \$38,990
Cash COGS \$27,000
Cash OE \$11,078
Interest paid \$480
Taxes paid \$68
= Net Cash Flow from Operations \$364
+ Realized capital gains / depreciation recapture \$0
Purchases of long-term assets \$100
+ Sales of long-term assets \$30
= Net Cash Flow from Investments (\$70)
+ Long-term borrowing \$50
Long-term debt payments \$157
Note payments \$230
Dividends and owner’s draw \$287
= Net Cash Flow from Financing (\$624)
Change in Cash Position of the Firm (\$330)
An alternative statement of cash flow calculates Net Cash Flows from financing, logically equivalent to Table 4.4a, using changes in Current and Non-current LTD and Changes in notes payable, including as before dividends and owner’s draw. The alternative to Table 4.4a, especially useful when data on borrowings and payment data is not available, is reported below:
Table 4.4b. HQN’s 2018 Statement of Cash Flow
Open HQN Coordinated Financial Statement in MS Excel
+ Cash receipts \$38,990
Cash COGS \$27,000
Cash OE \$11,078
Interest paid \$480
Taxes paid \$68
= Net Cash Flow from Operations \$364
+ Realized capital gains / depreciation recapture \$0
Change in non-depreciable long-term assets \$0
Change in depreciable long-term assets + depreciation \$70
= Net Cash Flow from Investments (\$70)
+ Change in noncurrent LTD (\$57)
+ Change in current portion of LTD (\$50)
+ Change in notes payable (\$230)
Payment of dividends and owner’s draw \$287
= Net Cash Flow from Financing (\$624)
Change in Cash Position of the Firm (\$330)
Since the ending cash position of the firm in the previous period was \$930, a change in the cash position associated with the firm’s cash flow implies that the ending cash position of the firm is: \$930 – \$330 = \$600. This amount, \$600, corresponds to the cash balance appearing at the end of the current period’s balance sheet. Indeed, a check on the consistency of the calculation that uses a checkbook to construct a statement of cash flow is that the change in cash position reconciles the cash balances appearing in the end of period balance sheets. Furthermore, the beginning and ending cash balances in the checkbook must equal the ending cash balances in the end of period balance sheets. In this case, the beginning and ending cash balances in the checkbook are \$930 and \$600, respectively, which matches the ending cash balances in the previous and current end of period balance sheets.
So what have we learned? We learned that it is essential to understand that the individual financial statements included in CFS are interdependent and all are important for describing the financial condition of the firm. Their interdependence can be verified with the following consistency checks. The fundamental accounting identity requires that total assets equal liabilities plus net worth. The change in cash position calculated in the SCF equals the difference in cash and marketable securities in the beginning and ending period balance sheets. And finally, the change in retained earnings calculated in the AIS must equal the change in retained earnings in the ending and beginning period balance sheets.
Cash Income Statements
Unlike the balance sheet—which is a picture of the firm’s assets, liabilities, and net worth at a point in time—the firm’s income statement is a record of the firm’s income and expenses incurred between two points in time. Profits (losses) reported in the firm’s income statement are reflected in the firm’s balance sheet as an increase (decrease) in the firm’s equity. Therefore, the firm’s income statement provides the details that explain changes in the firm’s equity. To complicate matters, there are two distinct income statements, cash and accrual. We first discuss the firm’s cash income statement.
Cash income statements record the firm’s income and expenses when they generate a cash flow. One of the most important uses of a cash income statement is to determine the firm’s tax obligations. The cash income statement is also an important tool for determining the liquidity of the firm—to determine if its cash receipts are sufficient to meet its cash expenses.
HQN’s 2018 Cash income statement. Using data from the firm’s checkbook or its SAUF statement plus the ending balance sheets, we are prepared to complete a cash income statement. Sometimes the cash income statement is referred to as a modified cash income statement because it includes depreciation which is not a cash flow event but which is an expense allowed when computing taxable income. The 2018 HQN cash income statement constructed using data from HQN’s checkbook plus book value asset data from ending balance sheets used to calculate depreciation is reported below:
Table 4.5. HQN’s 2018 Cash Income Statement (all number in \$000s)
Cash receipts \$38,990
+ Realized Cap. Gains and Depreciation Recapture 0
Cash COGS \$27,000
Cash Overhead Expenses \$11,078
Depreciation \$350
= Cash Earnings Before Interest and Taxes (CEBIT) \$562
Interest paid \$480
= Cash Earnings Before Taxes (CEBT) \$82
Taxes paid \$68
= Cash Net Earnings After Taxes (CNIAT) \$14
Dividends and Owner Draws \$287
= Cash Additions to Retained Earnings (\$273)
Notice that all of the entries in the cash income statement are entries in the firm’s checkbook and SAUF statement except for realized capital gains and depreciation recapture and depreciation. Depreciation is listed as an expense even though it may not reflect a cash flow event because it represents a loss in value to the firm of assets previously purchased. To find the depreciation for HQN we begin with a fundamental relationship that applies to all depreciable long-term assets (DLTA):
Beginning DLTA + purchases of DLTA – sales of DLTA (book value) – depreciation = Ending (book value) DLTA
Notice that the sale of DLTA is listed at their book value. This is necessary to maintain the value of DLTA at their book value in the balance sheets. Solving for depreciation in the identity above and substituting data from the checkbook and balance sheets we find:
Depreciation = Beginning DLTA + purchases of DLTA – sales of DLTA (book value) – Ending DLTA
Depreciation = \$2990 + \$100 – \$30 – \$2710 = \$350.
Finally, depreciation recapture is treated a separate category of cash receipts to the firm because it represents a value that was previously deducted as an expense included in depreciation and is now received as an unexpected income (or loss). Depreciation recapture plus capital gains is equal to the market value of DLTA sold less the book value of DLTA sold provided the sale price is not greater than the original purchase price.
Realized capital gains (losses) + depreciation recapture = Sale of DLTA (market value) – sale of DLTA (book value)
= \$30 – \$0 = \$30.
In this example, we assume that DLTA were sold at their book value so realized capital gains plus depreciation recapture are zero.
Accrual Income Statement (AIS)
HQN’s 2018 accrual income statement (AIS) is reported in Table 4.6. Because the accrued income statement is the more common of the two income statements, we sometimes drop the word accrual and refer to it as the firm’s income statement. We create HQN’s income statement by adding to cash transactions non cash exchanges affecting the financial condition of the firm.
Table 4.6. HQN’s 2018 Accrual Income Statement
(all numbers in \$000s)
+ Cash receipts \$38,990
+ Δ Accounts Receivable (\$440)
+ Δ Inventories \$1450
+ Realized Capital Gains / Depreciation Recapture \$0
= Total Revenue \$40,000
+ Cash COGS \$27,000
+ Δ Accounts Payable \$1,000
+ Cash OE \$11,078
+ Δ Accrued Liabilities (\$78)
+ Depreciation \$350
= Total Expenses \$39,350
Earnings Before Interest and Taxes (EBIT) \$650
Interest \$480
= Earnings Before Taxes (EBT) \$170
Taxes \$68
= Net Income After Taxes (NIAT) \$102
Dividends and owner draws \$287
= Additions To Retained Earnings (\$185)
An important check on the consistency of HQN’s balance sheets and its AIS is that additions to retained earning of (\$185) should equal the difference between beginning and ending retained earning in the balance sheet.
We now explain in more detail the calculation of the individual entries in the AIS. In addition, by rearranging the numbers used to find AIS entries, we can find cash income statement entries.
Finding accrued income. We first want to calculate accrued income. Our first checkbook entry records cash receipts of \$38,990. So, what is the difference between cash receipts and accrued income? Accrued income includes cash receipts from the sale of products, insurance, and government payments plus credit sales—creating accounts receivable. In addition, accrued income includes inventory increases—production essentially sold into inventory. Both increases in accounts receivable and inventory increase accrued income. While cash receipts are recorded in the checkbook, changes in accounts receivable and changes in inventories are found as the differences between accounts receivable and inventory entries in the two ending period balance sheets. Since we can find changes in accounts receivable and changes in inventories, we can now calculate accrued income equals the following:
Accrued Income = Cash Receipts + Δ Accounts Receivables + Δ Inventories
\$40,000 = \$38990 + (\$440) + \$1450
Notice that cash receipts understate actual income in this example.
Total revenue. Adding cash receipts, realized capital gains / depreciation recapture, changes in inventory, and changes in accounts receivable provides a measure of the firm’s total accrued income.
Finding accrued COGS. The checkbook records cash COGS of \$27,000. But accrued COGS must add to cash COGS the COGS that the firm purchased on credit which increased the firm’s accounts payable. The amount of goods the firm purchased on credit can be calculated as the difference between accounts payable at the beginning and at the end of the year recorded in the firm’s balance sheets. For HQN, changes in accounts payable equal \$1,000, allowing us to find accrued COGS as:
Accrued COGS = Cash COGS + Δ Accounts Payable
\$28,000 = \$27,000 + \$1000
Note that cash COGS understate actual COGS.
Finding accrued OE. The checkbook records cash OE of \$11,078. But accrued OE must add to cash OE the overhead expenses that were purchased on credit increasing the firm’s accrued liabilities. In general, changes in accrued liabilities equal the difference between accrued and cash overhead expenses, and can be found as the difference between accrued liabilities recorded in the ending period balance sheets. The difference between ending period accrued liabilities equals (\$78), meaning that the firm actually paid off some accrued liabilities incurred in earlier periods in addition to paying for overhead expenses incurred during the current period. We express accrued overhead expenses as:
Accrued OE = Cash OE + Δ Accrued Liabilities
\$11,000 = \$11,078 + (\$78)
Note that cash OE overstate actual overhead expenses.
Calculating depreciation in the accrual income statement. We previously calculated depreciation in the cash income statement and found it to equal to \$350. The calculation of depreciation is the same in both the accrual and cash income statement.
Earnings Before Interest and Taxes (EBIT). After subtracting from the firm’s total revenue, its cash COGS, change in accounts payable, cash OE, changes in accrued liabilities and depreciation, we obtain a measure of the firm’s profits (total revenue minus total expenses). But the profit measure obtained is before subtracting interest costs and taxes. Therefore, we call this profit measure Earnings Before Interest and Taxes are paid (EBIT).
Earnings Before Taxes (EBT). Subtracting interest expenses from EBIT gives the firm’s earnings before taxes (EBT), which are the firm’s profits after paying all expenses except taxes.
Net Income After Taxes (NIAT). Subtracting the firm’s tax liabilities from EBT gives the firm’s net income after taxes (NIAT), generally referred to as the firm’s profits. NIAT is also what is available to be reinvested in the firm or withdrawn by the owners.
Interest costs, taxes, and withdrawals. The checkbook records interest costs of \$480, taxes equal to \$68, and withdrawals of \$287. These are paid in cash and can be entered directly in the AIS.
Dividends and owner draw. Dividends and owner draw represent payments make to owners of the firms from the firm’s profits. In the case of dividends, these reflect payments made to compensate owners of the firm for their investments in the firm. In the case of owner draw, these may include payments to owners for services rendered or to meet the financial needs of the firm’s owners.
Finding Cash Receipts, Cash COGS, and Cash OE from accrual statement entries. Usually, firms have access to cash receipts, cash COGS, and cash OE from which it can find accrued income, accrued COGS, and accrued OE. This was our approach in the previous section. However, we could reverse the calculations and beginning with accrued income, accrued COGS, and accrued OE solve for cash receipts, cash COGS, and cash OE. These calculations are described next and are essential in order to complete the firm’s statement of Cash Flow when we begin with accrual data rather than cash flow data.
Suppose that we knew that accrued income were equal to \$40,000. We could find cash receipts by subtracting from accrued income, change in accounts receivable and change in inventory:
\$38,990 = \$40,000 – (\$440) – \$1450
Finding cash COGS. Suppose that we knew that accrued COGS were equal to \$28,000. We could find cash COGS by subtracting accrued COGS change in Accounts Payable:
\$27,000 = \$28,000 – \$1,000
Finding accrued OE. Suppose that we knew that accrued OE were equal to \$11,078. We could find cash OE by subtracting from accrued OE, change in accrued liabilities.
\$11,078 = \$11,000 – (\$78)
More Complicated Financial Statements
Compared to HQN’s balance sheets, income statements, and SCF described in this chapter, balance sheets, income statemetns, and SCF for an actual firm are often much more complicated. In what follows, we highlight the main differences between HQN’s financial statements and financial statements of actual firms.
Level of detail. One of the main differences between HQN’s financial statements and financial statements of actual firms is the level of detail. For example, the income statement may separate total sales into sales of livestock and livestock products, crops sales, and sales of services. Expenses may be separated into seed, fertilizer, other crop supplies, machinery hire, feed purchased, feeder livestock purchased, veterinary services, livestock supplies, fuel and oil, utilities, machinery repairs, insurance, rents, hired labor to name a few. Additional inventory details may include livestock and crops held for sale and feed, value of growing crops, farm supplies, and prepaid expenses.
Data deficiencies. Another difference between HQN’s financial statements and financial statements of actual firms is the quality of the data. HQN’s data are assumed to be accurate and consistent. Data supplied by actual firms is sometimes neither accurate nor consistent. Other data deficiencies of actual firms may include the following. 1) The data is rarely complete, especially for large complex firms with several activities. 2) Data from the firm’s activities may be reported by different persons using different metrics. 3) Some of the same data are provided from different sources and are not equal. 4) Personal data.
Exogenous and endogenous variables. There are two types of variables in CFS: exogenous versus endogenous. The value of exogenous variables are determined outside of the CFS . It can be observed and supplied by sources other than the firm. Endogenous variables are calculated using exogenous variables so that any change in exogenous variables produces changes in endogenous variables. For example, the cash flow variable is an exogenous variable because it can be observed and recorded. Other data, such as firm’s equity or additions to retained earnings are computed using exogenous and sometimes other endogenous variables. The problem occurs where the a value in the CFS can be observed and calculated. For example, end of period cash is calculated from beginning period cash plus change in cash position. But end of period cash may be observed by referring the firm’s checkbook. If the exogenous variable is accurate, then the observed and calculated numbers will be equal and consistent. But in some cases they are not equal and the firm will be required to take steps designed to reconcile the differences.
Consistency versus accuracy. Two words describe financial statements: “consistency” and “accuracy”. Consistency means that we compute values for variables in the CFS in the same way every time so that changes in primary data produce predictable changes in calculated data. Accuracy means that our measurement conforms to correct value of what is being measured. The financial statements are consistent if the following are true: “additions to retained earnings” reported in the accrued income statement reconciles retained earnings in the ending period balance sheets. The reconciling equation is: beginning retained earnings plus additions to retained earnings equals retained earnings in the ending period balance sheet. A second consistency requirement is that the change in cash position reported in the statement of cash flow reconciles cash balances in the ending period balance sheets. The reconciling equation is: beginning cash plus change in cash position equal ending cash. Finally, the third consistency condition is that the fundamental accounting identity is true; namely, that assets equal liabilities plus equity.
The financial statements may be consistent, but not all the data may be accurately recorded. On the other hand, if the financial statements are not consistent, we can be sure they are not accurate. We summarize our description of financial statements by declaring that consistency is a necessary condition for an accurate set of financial statements but consistency is not sufficient for an accurate set of financial statements.
Hard and soft data. Faced with the data challenges described above, financial managers are charged with the task of preparing the most accurate and consistent set of CFS possible. Guidelines for this task include the following. Determine which data is “soft” and which data is “hard.” Soft data is estimated or may lack a supporting data trail. Still, it represents the best guesstimates available. Hard data has a reference or an anchor. For example, the sale of a product is usually recorded although there may be some benefits or costs associated with the sale that are not recorded. Interest costs and taxes are recorded and can be considered hard data. Inventories are more difficult to determine if they are hard or soft because they change over a reporting cycle and their estimated value at the beginning and ending balance sheets may not be available. So, an important task of the financial manager is to assess the reliability of the different data.
Constructing Consistent Coordinated Financial Statements (CFS): A Case Study
We now construct a consistent set of financial statements for an actual firm using the data they supplied. In the process, we will experience some of the data deficiencies described earlier and the challenge of having our CFS be both accurate and consistent. We will call our case study firm, Friendly Fruit Farm (FFF) because producing and selling fruit is the firm’s main commercial activity.
To assure that our financial statements are consistent, we will use the template prepared for analyzing HQN. The categories in the HQN template are aggregated compared to actual firms. To fit the data supplied by FFF to the HQN template will require side-bar calculations that organize the data to correspond with the general categories described in Tables 4.1, 4.4, 4.5, and 4.6. The general rule for deciding when side-bar calculations are required is the following: if for any given entry of the HQN CFS there are two or more instances of that item supplied by FFF, a side bar calculation is required. Therefore, the number of side-bar calculations will depend on the firm being examined and the data which the firm supplies.
FFF balance sheets. FFF supplied the following balance sheet data.
Table 4.7. FFF supplied Ending Period Balance Sheets
12/31/17 12/31/18
Cash and checking balance (\$7,596) (\$24,333)
Prepaid expenses & supplies \$7,467 \$15,369
Growing crops \$0 \$0
Accounts receivable \$33,400 \$45,668
Hedging accounts \$0 \$0
Crops held for sale or feed \$178,098 \$204,530
Crops under government loan \$0 \$0
Market livestock held for sale \$7,933 \$6,500
Other current assets \$278 \$278
Total current farm assets \$219,581 \$248,011
Breeding livestock \$10,583 \$18,019
Machinery and equipment \$85,001 \$87,387
Titled vehicles \$2,889 \$2,667
Other intermediate asses \$9,689 \$8,893
Total intermediate farm assets \$108,162 \$116,966
Farm Land \$166,200 \$179,348
Buildings and improvements \$76,852 \$81,021
Other long-term assets \$6,229 \$6,229
Total long-term assets \$249,281 \$266,599
Total Farm Assets \$577,023 \$631,576
Accrued interest \$1,078 \$1,487
Accounts payable \$2,080 \$1,637
Current notes \$67,935 \$74,644
Government crop loans \$0 \$0
Principal due on term debt \$28,511 \$30,072
Total current farm liabilities \$99,604 \$107,840
Total intermediate farm liabilities \$43,793 \$31,782
Total long-term farm liabilities \$118,617 \$124,420
Total Farm Liabilities \$262,015 \$264,042
Having collected financial data for FFF’s balance sheets we proceed to organize it into categories described by the balance sheets prepared for HQN. The main reason for doing so is to insure consistency. The second reason for doing so is to organize it into categories amenable to ratio analysis important for financial analysis and management. The balance sheet categories used by HQN which we want to duplicate for FFF are described in Table 4.1 .
Cash and marketable securities. We begin by noting that ending period cash balances cannot be negative. Otherwise they are liabilities. But in the balance sheets provided by FFF, they report negative cash balances in both end of period balance sheets. We set them to zero and include them as liabilities included in accounts payable. Our first line in FFF’s ending period balance sheets is:
12/31/17 12/31/18
Cash and marketable securities \$0 \$0
Accounts receivable. FFF lists accounts receivables. They also lists prepaid expenses and hedging accounts that have properties similar to accounts receivable. All three measures represent short-term sacrifices by the firm for benefits they have not yet received. Usually, accounts receivables reflect firm sales for which it has not yet been compensated in cash. In the case of prepaid expenses, it represents payments for goods they have not yet received. In the case of a hedging account, they represent funds paid for options not yet exercised. Adding to accounts receivable, prepaid expenses and hedging funds produces a more inclusive measure of accounts receivable equal to:
12/31/17 12/31/18
Accounts receivable \$33,400 \$45,668
Prepaid expenses and supplies \$7,467 \$15,369
Hedging accounts \$0 \$0
Accounts receivable \$40,867 \$61,037
Inventories. FFF lists several inventories in its ending period balance sheets. We list and sum these below.
12/31/17 12/31/18
Growing crops \$0 \$0
Crops for sale or feed \$178,098 \$204,530
Crops under government loan \$0 \$0
Market livestock for sale \$7,933 \$6,500
Other current assets \$278 \$278
Inventories \$186,309 \$211,308
We now find the sum of FFF’s current assets by adding cash and marketable securities, accounts receivable, and inventories and report the results below.
12/31/17 12/31/18
Cash and marketable securities \$0 \$0
Total accounts receivable \$40,867 \$61,037
Total inventories \$186,298 \$211,308
Current assets \$227,165 \$272,345
We now find FFF’s depreciable long-term assets. Note that FFF listed intermediate and long-term assets. In the HQN template, we distinguish long-term as either depreciable or non-depreciable. We consider property, plant, and equipment as depreciable long-term assets and land and buildings as non-depreciable long-term assets. Note that in the FFF supplied balance sheets, they list non-farm assets, which we ignore since our analysis is focused on the farm firm. We now list FFF’s depreciable and non-depreciable long-term assets and find their sum.
12/31/17 12/31/18
Breeding livestock \$10,583 \$18,019
Machinery and equip. \$85,001 \$87,387
Titled vehicles \$2,889 \$2,667
Other intermediate assets \$9,689 \$8,893
Depreciable long-term assets \$108,162 \$116,966
Land \$166,200 \$179,348
Buildings and improvements \$76,852 \$81,021
Other long-term assets \$6,229 \$6,229
Non-depreciable long-term assets \$249,281 \$266,598
Total long-term assets \$357,443 \$383,564
We find FFF’s total assets as the sum of current and long-term assets and report the result below.
12/31/17 12/31/18
Total current assets \$227,165 \$272,345
Total long-term assets \$357,443 \$383,564
Total assets \$584,608 \$655,909
Notice that the total firm assets calculated above do not match the total firm assets calculated by FFF. This is because the negative cash balances have been shifted to the liabilities section of the balance sheet.
Next we prepare FFF’s liabilities data to match HQN’s reduced categories template. We begin by listing notes payable. We include in this category current notes payable and government loans.
12/31/17 12/31/18
Current notes \$67,935 \$74,644
Government crop loans \$0 \$0
Notes payable \$67,935 \$74,644
Next we include accrued interest and current portion of the long-term debt and current payments on loans in the category current portion of long-term debt.
12/31/17 12/31/18
Accrued interest \$1,078 \$1,487
Principal due on long-term debt \$28,511 \$30,072
Current portion of long-term debt \$29,589 \$31,559
Next we list FFF’s accounts payable including negative balances in cash reported in the asset portion of the balance sheet.
12/31/17 12/31/18
Accounts payable \$2,080 \$1,637
Negative cash balances \$7,596 \$24,333
Accounts payable \$9,676 \$25,970
Combining our current liabilities entries and summing we find the sum of FFF’s current liabilities:
12/31/17 12/31/18
Notes payable \$67,935 \$74,644
Current portion of LTD \$29,589 \$31,559
Accounts payable \$9,676 \$25,970
Accrued liabilities \$43,793 \$31,782
Total current liabilities \$150,993 \$163,955
Now we consider our long-term liabilities described as long-term debt. The first long-term liabilities is noncurrent long-term debt which is listed below.
12/31/17 12/31/18
Noncurrent long-term debt \$118,617 \$124,420
We add current liabilities to noncurrent long-term debt to find FFF’s total liabilities.
12/31/17 12/31/18
Current liabilities \$150,993 \$163,955
Noncurrent long-term debt \$118,617 \$124,420
Total Liabilities \$269,610 \$288,375
Finally, we compute FFF’s equity as the difference between its total assets and it total liabilities and find it equal to:
12/31/17 12/31/18
+ TOTAL ASSETS \$584,608 \$655,909
TOTAL LIABILITIES \$269,610 \$288,375
= EQUITY \$314,998 \$367,534
Table 4.8. FFF’s 2018 Ending Period Balance Sheets
12/31/17 12/31/18
Cash and marketable securities \$0 \$0
Accounts receivable \$40,867 \$61,037
Inventories \$186,298 \$211,308
Total current assets \$227,165 \$272,345
Depreciable long-term assets \$108,162 \$116,966
Non-depreciable long-term assets \$249,281 \$266,598
Total long-term assets \$357,443 \$383,564
TOTAL ASSETS \$584,608 \$655,909
Notes payable \$67,935 \$74,644
Current portion of LTD \$29,589 \$31,559
Accounts payable \$9,676 \$25,970
Accrued liabilities \$43,793 \$31,782
Total current liabilities \$150,993 \$163,955
Noncurrent long-term debt \$118,617 \$124,420
TOTAL LIABILITIES \$269,610 \$288,375
EQUITY \$314,998 \$367,534
TOTAL LIABILITIES AND EQUITY \$584,608 \$655,909
Populating FFF’s Cash Income Statements to Conform to HQN’s Income Templates
To enable FFF to populate its income statements, it supplied the following data.
+ Apples \$274,069
+ Cherries \$52,123
+ Peaches \$23,046
+ Grapes \$1,467
+ Pears \$638
+ Plums \$508
+ Raspberries \$2,580
+ Blueberries \$900
= Total cash fruit sales \$355,331
+ Asparagus \$7,872
+ Cordwood \$31
+ Pumpkins \$360
+ Rhubarb \$179
+ Squash \$246
+ Sweet corn \$1,666
+ Tomatoes \$429
+ Other crops \$7,560
= Total cash crops and vegetable sales \$18,343
Finally we sum the cash receipts categories:
+ Total cash fruit sales \$355,331
+ Total cash crops and vegetable sales \$18,343
+ Total cash receipts of finish beef calves \$1,898
+ Government payments \$5,376
+ Dividend and Insurance Payments \$1,651
+ Other farm income \$7,144
= Cash farm income \$389,743
+ Seed \$2,039
+ Fertilizer \$4,652
+ Chemicals \$55,640
+ Crop insurance \$4,523
+ Packaging and supplies \$7,266
+ Marketing \$137
+ Crop miscellaneous \$31,940
+ Feed \$128
+ Livestock supplies \$794
= Total Cash COGS \$107,119
+ Supplies \$638
+ Fuel \$13,458
+ Repairs \$19,882
+ Custom hire \$3,317
+ Hired labor \$99,671
+ Land rent \$29,777
+ Machinery lease \$2,827
+ Insurance \$8,593
+ Utilities \$7,177
+ Hauling \$86
+ Dues \$4,288
+ Miscellaneous \$7,092
= Total Cash OE \$196,806
FFF also reported that in 2018 it paid \$12,712 in interest charges, \$4,628 in taxes, and that the owners withdrew \$44,402. FFF also reported the purchase and sale of assets as \$57,048 and \$1,185 respectively. We assume that the sale of assets was at their book value.
We now populate FFF’s AIS, using cash receipts and expense data supplied by FFF and changes in FFF’s completed balance sheet entries.
Table 4.9. FFF’s 2018 Accrual Income Statement
(all numbers in \$000s)
+ Cash receipts \$389,743
+ Change in Accounts Receivable \$20,170
+ Change in Inventories \$25,010
+ Realized Capital Gains / Depreciation Recapture \$0
= Total Revenue \$434,923
+ Cash Cost of Goods Sold (COGS) \$107,119
+ Change in Accounts Payable \$16,294
+ Cash Overhead Expenses (OE) \$196,806
+ Change in Accrued Liabilities (\$12,011)
+ Depreciation \$47,059
= Total Expenses \$355,267
Earnings Before Interest and Taxes (EBIT) \$79,656
Interest \$12,712
Earnings Before Taxes (EBT) \$66,944
Taxes \$4,628
Net Income After Taxes (NIAT) \$62,316
Dividends and owner draws \$44,402
Additions To Retained Earnings \$17,914
Detailed explanations of the AIS entries follow.
• FFF reported total cash receipts equal to \$389,743.
• Change in accounts receivables was calculated by finding the difference between accounts receivable in FFF’s ending period balance sheets equal to (\$61,037 – \$40,867) = \$ 20,170.
• Change in inventory was calculated by finding the difference between inventories in FFF’s ending period balance sheets equal to (\$211,308 – \$186,298) = \$25,010.
• FFF reported Cash COGS equal to \$107,119.
• Change in Accounts Payable was calculated by finding the difference between accounts payable reported in FFF’s ending period balance sheets equal to \$25,970 – \$9,676 = \$16,294.
• FFF reported Cash OE equal \$196,806.
• Change in accrued liabilities was calculated by finding the difference between accrued liabilities in FFF’s ending period balance sheets equal to (\$31,782 – \$43,793) = (\$12,011).
• The next expense category required by FFF’s AIS is depreciation. The data for calculating the change in long-term assets was available in FFF’s balance sheets. FFF also reported its sale and purchases of long-term assets as \$57,048 and \$1,185 respectively. The formula for depreciation is:
• Purchases of depreciable LTAs – sales of depreciable LTAs (book value) – ∆ depreciable LTAs (book) = depreciation.
• Making the necessary substitutions, we find FFF’s 2018 depreciation:
• \$57,048 – \$1,185 – (\$116,966 – \$108,162) = \$47,059.
• Summing cash and noncash receipts we find total revenue.
• Summing cash and noncash expenses we find total expenses.
• Subtracting total expenses from total revenue, we find earnings before interest and taxes (EBIT) equal to \$79,656.
• FFF reported interest costs equal to \$12,712 which were subtracted from EBIT to obtain Earning Before Taxes (EBT) equal to \$66,944.
• FFF reported taxes equal to \$4,628 which were subtracted from EBT to obtain Net Income after paying interest and taxes (NIAT) of \$62,316.
• FFF reported paying dividends and owner withdrawals of \$44,402 which were subtracted from NIAT to find changes in retained earnings of \$17,914.
Cash income statement. Using the cash receipts and expense data supplied by FFF, we can easily find its cash income statement
Table 4.10. FFF’s 2018 Cash Income Statement
Cash receipts 389,743
+ Realized Capital Gains \$0
Cash COGS \$107,119
Cash overhead expenses \$196,806
Depreciation \$47,059
= Cash Earnings Before Interest and Taxes (CEBIT) \$38,759
Interest paid \$12,712
= Cash Earnings before Taxes (CEBT) \$26,047
Taxes paid \$4,628
= Cash Net Earnings After Taxes (CNIAT) \$21,419
Dividends and owner draws \$44,402
= Cash Additions to Retained Earnings (\$22,983)
Statement of Cash Flow. We now have all of the data required to find FFF’s statement of cash flow. We begin by finding FFF’s net cash flow from operations.
+ Cash receipts \$389,743
Cash COGS \$107,119
Cash OE \$196,806
Interest paid \$12,712
Taxes paid \$4,628
= Net Cash Flow from Operations: \$68,478
Net cash flow from investment activity is calculated from data used to find depreciation and equals
+ Sale of long-term assets \$1,185
Purchases of long-term assets \$57,048
= Net Cash Flow from Investments (\$55,863)
Net cash flow from financing activities reflects the difference between borrowing of long-term debt and notes payable and principal and interest payments on long-term debt and notes payable. Finally, dividends paid are subtracted and the difference between new equity contributed and purchased is computed.
Change in non-current LTD (borrowing less payments) \$5,803
+ Change in current portion of LTD \$1,970
+ Change in notes payable (borrowing less payments) \$6,709
Payment of dividends and owner withdrawal \$44,402
= Net Cash Flow from Financing (\$29,920)
Table 4.11. Statement of Cash Flow
+ Cash receipts \$389,743
Cash COGS \$107,119
Cash OE \$196,806
Interest paid \$12,712
Taxes paid \$4,628
= Net Cash Flow from Operations \$68,478
+ Realized capital gains + depreciation recapture \$0
Purchases of depreciable long-term assets \$57,048
+ Sales of depreciable long-term assets \$1,185
= Net Cash Flow from Investments (\$55,863)
+ Change in non-current long term debt \$5,803
+ Change in current portion long term debt \$1,970
+ Change in notes payable \$6,709
Dividends and owner’s draw \$44,402
= Net Cash Flow from Financing (\$29,920)
Change in cash position of the firm (\$17,305)
What to do? Consider the following example. You are visiting in a new town and are trying to find your way to an important site. Suppose that you stop a person you assume is familiar with the location and ask for directions which the person provides. You thank the person for directions and begin your journey to your destination. But just to make sure you are on the right path, you consult your map and find that the directions you just received are in conflict with your map. You are faced with a choice. Which set of directions do you choose? They both can’t be correct.
We face a similar problem when our completed financial statements aren’t consistent. Somewhere in our entries there is an error(s). Therefore to populate our template we have to decide what numbers to believe.
In our case the conflict arises when reported primary data and calculated data required to reconcile the various financial statements are inconsistent. The first requirement is to establish consistency beginning with the calculated entries. Consistency is a necessary condition for accuracy and makes it a logical place to begin. Then we determine if the primary data that conflicts with the calculated number is hard or soft. If it is reasonably hard data, and is higher that the calculated data we explore the data for under estimates of cash inflows and over estimates of cash outflows. We follow the reverse process if the primary data is less than the calculated data. If we can find soft data that can be changed to make the calculated data consistent with the primary data—we make the changes.
So what have we learned? We learned from the FFF example that actual firms have more complicated data sets that we illustrated using the HQN example. Yet, the variable categories we used when computing the HQN study apply generally even though some side-bar calculations may be required to reduce actual firm data to the variable categories used to describe HQN.
Summary and Conclusions
In this chapter we have learned how to construct CFS. Coordinated financial statements are tools that we will use in the next chapter to analyze the firm’s strengths and weaknesses. Constructing financial statements for actual firms with less than perfect and complete data is somewhat of an art.
Questions
1. Define the differences between consistent financial statements and accurate financial statements.
2. Discuss the statement: “consistent financial statements are necessary but not sufficient for accurate financial statements.”
3. What are some conditions required for financial statements to be consistent?
4. In a typical data set provided by a farm firm, what data is most reliable (hard) and which data is least likely to reliable (soft)?
5. Below is a completed 2018 checkbook and 2017 and 2018 ending period balance sheets for the “Grow Green” vegetable farm. Use the numbers in their checkbook and their two balance sheets to create a 2018 cash and AIS and statement of cash flow.
Grow Green 2018 Checkbook
Date Item Check amount Deposit amount Checkbook balance
12/31/17 Beginning cash balance \$930
Cash receipts \$40,940 \$41,870
Seed, feed, fertilizer \$20,000 \$21,870
Labor cost of producing products \$8,350 \$13,520
Insurance \$2,000 \$11,520
Utilities \$9,632 \$1,888
Purchase of LTAs \$100 \$1,788
Sale of LTAs (at book value) \$30 \$1,818
Interest paid \$504 \$1,314
Taxes paid \$71 \$1,243
Payment on current-term debt \$50 \$1,193
Long-term debt payments \$57 \$1,139
Payment on notes \$230 \$906
Owner draw \$390 \$516
12/31/18 Ending cash balance \$516
Grow Green Balance Sheet
12/31/17 12/31/18
Cash and Marketable Securities \$930.00 \$516.00
Accounts Receivable \$1,640.00 \$1,200.00
Inventory \$3,750.00 \$5,200.00
Total Current Assets \$6,320.00 \$6,916.00
Depreciable long-term assets \$2,990.00 \$2,800.00
Non-depreciable long-term assets \$690.00 \$600.00
Total Long-term Assets \$3,680.00 \$3,400.00
Total Assets \$10,000.00 \$10,316.00
Notes Payable \$1,500.00 \$1,270.00
Current Portion of LTD \$500.00 \$450.00
Accounts Payable \$3,000.00 \$4,000.00
Accrued Liabilities \$958.00 \$880.00
Total Current Liabilities \$5,958.00 \$6,600.00
Noncurrent Long-term Debt \$2,042.00 \$1,985.00
Total Liabilities \$8,000.00 \$8,585.00
Other Capital \$1,900.00 \$1,689.00
Retained Earnings \$100.00 \$42.00
Equity \$2,000.00 \$1,731.00
Total Liabilities and Equity \$10,000.00 \$10,316.00
1. Compare the differences and the advantages and disadvantages of cash and AIS.
2. In problem 5, you should have found ending cash to equal \$630 which is the same as the observed ending cash. Instead assume that the ending cash balance recorded in the balance sheets provided was equal to \$650. Describe the possible adjustments you might make to observed variables to make consistent observed ending cash and the calculated ending cash. Provide a revised set of CFS that are consistent with ending cash calculated and observed.
3. Most firm managers who are also the firm’s financial manager keep less than the complete data set required to construct a complete set of financial statements. And even the data they collect are not in the format we expect, requiring us to reformat the data we do have. With less than complete data sets, we are forced to do the best we can with what we have. What follows is a typical data set which ABM 435 teams have used in the past to construct a set of consistent and accurate set of financial statements. Using the data provided, construct a consistent and, to the extent possible, accurate set of financial statements.
Farm A 12/31/18
Acres owned 488
Acres rented 449
Machinery investment / crop acre @ cost \$95
Machinery investment / crop acre @ market \$520
Average price received
Corn \$6
Soybeans \$13
Wheat \$7
Hay \$97
Average yield
Corn \$175
Soys \$54
Wheat \$76
Gross Cash farm income including government payments & patronage dividends \$863,561
Cash Farm Expense including land rent but excluding interest \$637,231
Interest \$23,232
Other balance sheet related data include the following:
12/31/17 12/31/18
Cash and checking \$63,211 \$66,696
Crops and Feed \$470,632 \$430,532
Market livestock 46,696 \$55,463
Accounts receivable \$34,062 \$44,550
Prepaid expenses and supplies \$104558 \$101,381
Hedging activities \$1916 \$2374
Other current assets \$18,901 \$15,822
Other capital assets \$29,140 \$36,539
Breeding livestock \$29,140 \$40,053
Accounts payable \$26,149 \$29,789
Accrued interest \$7,222 \$7470
Current notes \$111,819 \$127,402
Government crop loans \$1,400 \$1,733
Loan principal due \$59,849 \$68,559
Intermediate liabilities \$130,409 \$124,872
Long-term liabilities \$344,658 \$347,834
Machinery and Equipment (book) \$132,656 \$179,366
Titled vehicles (book) \$3,096 \$3,563
Buildings/improvements (book) \$105,559 \$110,232
Land (book) \$508,571 \$574,410
Purchases of Breeding Livestock \$901
Sale of Breeding Livestock \$291
Purchases other capital assets \$11,924
Sale of other capital assets \$8,443
Land sales (50% of sale were realized cap. Gains \$21,970
Purchase of titled vehicles \$1,948
Sale of titled vehicles \$636
Investments in buildings/improvements \$21,970 | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/04%3A_Financial_Statements.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) calculate financial ratios using information included in a firm’s coordinated financial statements (CFS); and (2) answer the question: “what are the firm’s financial strengths and weaknesses?”
To achieve your learning goals, you should complete the following objectives:
• Learn how to interpret ratios.
• Learn how financial ratios allow us to compare the financial condition of different firms.
• Learn how to construct (S)olvency, (P)rofitability, (E) fficiency, (L)iquidity, and (L)everage ratios—what we refer to collectively as SPELL ratios.
• Learn how SPELL ratios help us describe the financial strengths and weaknesses of a firm.
• Learn how the times interest earned (TIE) ratio and the debt-to-service (DS) ratio can provide information about the firm’s solvency.
• Learn how the profit margin (m) ratio, the return on assets (ROA) ratio, and the return on equity (ROE) ratio can provide information about the firm’s profitability.
• Learn how to find the after-tax ROE where T is the average tax rate paid by the firm on its earnings before taxes (EBT).
• Learn how to relate ROE and ROA to each other.
• Learn how the inventory turnover (ITO) ratio, the inventory turnover time (ITOT) ratio, the asset turnover (ATO) ratio, the asset turnover time (ATOT) ratio, the receivable turnover (RTO) ratio, the receivable turnover time (RTOT) ratio, the payable turnover (PTO) ratio, and the payable turnover time (PTOT) ratio can provide important efficiency information about the firm.
• Learn how the current ratio (CT) and the quick ratio (QK) can provide information about the firm’s liquidity.
• Learn how leverage ratios including the debt-to-equity (DE) ratio and the equity multiplier (EM) ratio can be used to monitor and measure the firm’s risk.
• Understand how comparing the firm’s SPELL ratios to industry standard ratios can help answer the question: what are the financial strengths and weaknesses of the firm?
• Learn how to construct after-tax ROE and after-tax ROA measures.
• Learn how unpaid family labor affects ROE and ROA measures.
• Learn why the firm may consider profit and solvency ratios key to a firm’s survival and success.
• Learn how the DuPont ratio demonstrates the interdependencies of some SPELL ratios.
Introduction
Coordinated financial statement (CFS) variables. CFS contain exogenous and endogenous variables. Exogenous variables take on values that can be observed or are determined by activities occurring outside of the firm. Endogenous variables take on values determined by activities within the firm and the values of exogenous variables.
The variables included in CFS become more valuable, especially for analyzing the strengths and weaknesses of the firm, when formed into ratios. We could look at the variables included in the CFS and draw some conclusions about the firm’s strengths and weaknesses by comparing them with other firms, but our conclusions would be limited because no two firms are alike. Ratios, however, provide a means for comparing the performance of firms using a standardized measure which is easier to interpret.
A ratio consists of two numbers when one number is divided by the other. Suppose two numbers are represented by the variables X and Y and form a ratio (X/Y). The ratio tells us how many units of X exist for each unit of Y. This standardized number, the number of units of X that exists for each unit of Y , allows us to make comparisons between firms using similarly constructed ratios. One other way to interpret the ratio X/Y is to multiply the ratio by 100 converting the ratio to a percentage. In this case the ratio multiplied by 100 tells us what percentage of Y is X.
To illustrate the importance of ratios, consider the purchase of a breakfast cereal. Suppose you go to the grocery store to purchase your favorite breakfast cereal (Super Sweet Sugar Snacks). You find a 10-ounce box of Super Sweet Sugar Snacks that sells for $3.20 and a larger 15-ounce box of the same cereal that sells for$4.50. Which box of cereal is the best buy? The price of each box of cereal won’t tell you the answer because the more expensive box also contains more cereal. However, if we divide the price of each box by the amount of cereal in the box we can compare “apples to apples,” or in this example we can compare the price per ounce of cereal in each box. Finding the ratio of dollars to ounces in the box, we see that cereal in the small box costs $0.32 per ounce ($3.20/10 oz.) while cereal in the large box costs $0.30 per ounce ($4.50/15 oz.). The large box of cereal costs less for each ounce of cereal and is the better buy.
The cereal example illustrates an important fact: one ratio without another ratio to compare it with is not very helpful. Knowing the price of cereal per ounce of the small box makes the information about the price per ounce of cereal in the large box more meaningful. Similarly, having standardized industry ratios against which we can compare our ratios is important for a financial manager’s efforts to discover the firm’s strengths and weaknesses.
What have we learned? We learned that when answering the question: what are the firm’s financial strengths and weaknesses, it is important that we look at the firm from several different points of view represented by the SPELL ratios.
We discuss next the different views required to adequately describe the firm’s financial condition. Each of the different views are represented by a set of ratios.
Financial Ratios
Financial ratios constructed using coordinated financial statement variables can be grouped into five categories. The categories can be remembered using the acronym SPELL. The five categories of financial ratios include: (S)olvency ratios, (P)rofitability ratios, (E)fficiency ratios, (L)iquidity ratios, and (L)everage ratios. Ratios in each of these five categories provide a different view of the firm’s financial strengths and weaknesses.
Ratios and points in time measures. When constructing financial ratios using data from the CFS, the “point in time” or the “period of time” reflected by the ratio deserves careful attention. Numbers from balance sheets reflect the financial condition of the firm at a point in time. Numbers from income statements and statements of cash flow describe financial activity over a period of time. When forming a ratio using two numbers from the balance sheet, the numbers should reflect the same point in time.
Ratios of points and period of time measures. There are two approaches when forming a ratio with one number from the income statement or statement of cash flow describing activity over a period of time and another number from the balance sheet reflecting financial conditions at a point in time. One approach uses a number from the previous period’s end of period balance sheet that corresponds with the point in time in which activities reported in the income statement begin. The second approach uses the average of beginning and ending period balance sheet measures that span the period of time during which activities reported in the income statement occurred. Later we will discuss in more detail when each of the two methods is preferred.
Cash versus accrual ratios. We construct several ratios in this chapter that include an income or a COGS variable. The question is: should these be cash receipts and cash COGS or accrued income and accrued COGS? We use accrual variables that focus on when financial transactions occurred rather than when transactions were converted to cash.
Useful comparisons. The usefulness of ratios depends on having something useful to compare them to. Suppose we wish we compare ratios of different firms. Obviously, we would expect ratios constructed for different firms to have been calculated at comparable points and periods of time. We would also expect that firms being compared are of the same size and engaged in similar activities. Fortunately, we can often find such measures described as industry average ratios.
Sometimes the relevant comparison for the firm is with itself at different points in time. Having the same ratio over a number of time periods for the same firm allows the firm manager to identify trends. One question trend analysis may answer is: in what areas is the firm is improving (not improving) compared to past performances. Of course, trend analysis can be performed using absolute numbers as well as ratios.
What follows. In what follows, we will introduce several ratios from each of the five “SPELL” categories. Then we will discuss how each of them, alone and together with other SPELL ratios, can help answer the question: what are the firm’s financial strengths and weaknesses. Since data from HQN’s financial statements will be used to form the SPELL ratios, HQN’s balance sheets, AIS, and statement of cash flow for 2018 are repeated in Table 5.1.
So what have we learned? We learned that the ratio of variables X and Y (X / Y) tells us how many units of X are associated with each unit of Y. As a result we can compare the ratio X/Y in firms A and B because the two ratios provide the same information about the same variable in the two firms—the number of units of X that exist for each unit of Y.
Table 5.1. Coordinated financial statement for HiQuality Nursery (HQN) for the year 2018
Open HQN Coordinated Financial Statement in MS Excel
BALANCE SHEET ACCRUAL INCOME STATEMENT STATEMENT OF CASH FLOW
12/31/17
12/31/18
2018 2018
Cash and Marketable Securities
$930$600
+ Cash Receipts $38,990 + Cash Receipts$38,990
Accounts Receivable
$1,640$1,200
+ Δ Accounts Receivable ($440) Cash COGS$27,000
Inventory
$3,750$5,200
+ Δ Inventories $1450 Cash OE$11,078
Notes Receivable
$0$0
+ Realized Capital Gains / Depreciation Recapture $0 Interest paid$480
CURRENT ASSETS
$6,320$7,000
= Total Revenue $40,000 Taxes paid$68
Depreciable Long-term Assets
$2,990$2,710
+ Cash Cost of Goods Sold (COGS) $27,000 = Net Cash Flow from Operations$364
Non-depreciable Long-term Assets
$690$690
+ Δ Accounts Payable $1,000 + Realized capital gains + depreciation recapture$0
LONG-TERM ASSETS
$3,680$3,400
+ Cash Overhead Expenses (OE) $11,078 + Sales non-depreciable assets$0
TOTAL ASSETS
$10,000$10,400
+ Δ Accrued Liabilities ($78) Purchases of non-depreciable assets$0
Notes Payable
$1,500$1,270
+ Depreciation $350 + Sales of depreciable assets$30
Current Portion LTD
$500$450
= Total Expenses $39,350 Purchases of depreciable assets$100
Accounts Payable
$3,000$4,000
Earnings Before Interest and Taxes (EBIT) $650 = Net Cash Flow from Investments ($70)
Accrued Liabilities
$958$880
Interest $480 + Change in noncurrent LTD ($57)
CURRENT LIABILITIES
$5,958$6,600
Earnings Before Taxes (EBT) $170 + Change in current portion of LTD ($50)
NONCURRENT LONG-TERM DEBT
$2,042$1,985
Taxes $68 + Change in notes payable ($230)
TOTAL LIABILITIES
$8,000$8,585
Net Income After Taxes (NIAT) $102 Payment of dividends and owner’s draw$287
Contributed Capital
$1,900$1,900
Dividends and owner draws $287 = Net Cash Flow from Financing ($624)
Retained Earnings
$100 ($85)
Additions To Retained Earnings ($185) Change in cash position of the firm ($330)
TOTAL EQUITY
$2,000$1,815
TOTAL LIABILITIES AND EQUITY
$10,000$10,400
Solvency Ratios
Solvency ratios, sometimes called repayment capacity ratios, can be used to answer questions about the firm’s ability to meet its long-term debt obligations. Here we will examine two solvency ratios: (1) times interest earned (TIE) and (2) debt-to-service ratio (DS).
Times interest earned (TIE) ratio
The TIE ratio measures the firm’s solvency or repayment capacity. The TIE ratio combines two period of time measures obtained from the firm’s income statement and is defined as:
(5.1)
In the above formula, INT represents the firm’s interest obligations accrued during the period. EBIT measures the firm’s earnings during the period before paying interest and taxes. The TIE ratio answers the question: how many times can the firm pay its interest costs using the firm’s operating profits (for every dollar of interest costs how many dollars of EBIT exist? Generally, a healthy firm’s TIE ratio exceeds one (TIE > 1), otherwise the firm won’t be able to pay its interest costs using its current income. HQN’s TIE ratio for 2018 is:
(5.2)
HQN’s 2018 TIE ratio indicates for every dollar of interest the firm owes, it has $1.35 dollars of EBIT to make its interest payments. Debt-to-service (DS) ratio Like the TIE ratio, the DS ratio answers questions about the firm’s ability to pay its current long-term debt obligations. In contrast to the TIE ratio, DS ratio recognizes the need to pay the current portion of its long-term debt in addition to interest. Finally, the DS ratio (in contrast to the TIE ratio) adds depreciation to EBIT because depreciation is a non-cash expense. Subtracting depreciation from revenue to obtain EBIT understates the liquid funds available to the firm to pay its current long-term debt obligations. To illustrate the logic behind this formula, assume that cash receipts equals$100, depreciation equals $30, other expenses equal$10, and EBIT is equal to $60. But more than$60 is available to pay interest and principal because depreciation of $30 is a non cash expense. Thus we add depreciation to EBIT to improve our measure of income available for interest and debt repayment:$60 + $30 =$90, which is the numerator in the DS ratio equation.
This book recommends that the current portion of the long-term debt at the beginning of the current period be used to calculate the denominator in the firm’s DS ratio. After making these adjustments, we obtain the firm’s DS ratio equal to:
(5.3)
If the DS < 1, a firm will not be able to make principal and interest payments using EBIT plus depreciation. In this case, the firm will be required to obtain funding from other sources such as restructuring debt, selling assets, delaying investments in assets, and/or increasing EBIT to meet current debt and interest obligations. If the firm were unable to meet its interest and principal payment over the long term, the firm’s survival would be threatened.
We can solve for HQN’s 2018 DS ratio. According to HQN’s income statement EBIT was $650 and depreciation was$350. Interest paid equaled $480 and the current portion of the long-term debt listed on the firm’s 2017 end of period balance sheet was$500. Making the substitutions into Equation \ref{5.3} we find HQN’s DS ratio equal to:
(5.4)
According to HQN’s DS ratio, its EBIT plus depreciation are sufficient to meet 102 percent of its interest and current principal payments, a more accurate reflections of its solvency than its TIE ratio of 1.35.
Profitability Ratios
Profitability ratios measure the firm’s ability to generate profits from its assets or equity. The firm’s accrual income statement (AIS) provides three earnings or profit measures useful in finding rates of return: earnings before interest and taxes (EBIT), earnings before taxes (EBT), and net income after interest and taxes (NAIT).
We examine three profitability ratios: (1) profit margin (m), (2) return on assets (ROA), and (3) return on equity (ROE). In some cases, the profitability measures are reported on an after-tax basis requiring that we know the average tax rate for the firm which we calculate next.
Finding the average tax rate. In some cases, particularly with profitability measures, we need to know the average tax rate paid by the firm. We find the average tax rate by solving for T in the following formula that equates net income after taxes (NIAT) to EBT adjusted for the after-tax rate T:
(5.5)
And solving for T in Equation \ref{5.5}:
(5.6)
Solving T for HQN in 2018 using EBT and NIAT values from Table 5.1 we find:
(5.7)
Profit margin (m) ratio
The ratio m measures the proportion of each dollar of cash receipts that is retained as profit after interest is paid but before taxes are paid.
The ratio m, is defined as:
(5.8)
In 2018, HQN had a before-tax profit margin equal to:
(5.9)
In other words, for every $1 of revenue earned by the firm, HQN earned$0.00425 in before-tax profits. Meanwhile, the after-tax profit margin m is defined as:
(5.10)
In 2018, HQN had an after-tax profit margin equal to:
(5.11)
In other words, for every $1 of cash receipts, HQN earned$0.00255 in after-tax profits.
Return on assets (ROA) ratio
The ROA measures the amount of profits generated by each dollar of assets and is equal to:
(5.12)
HQN’s 2018 before-tax ROA using beginning period assets is equal to:
(5.13)
Interpreted, each dollar of HQN’s assets generates $.065 cents in before-tax profits. Return on equity (ROE) ratio The ROE ratio measures the amount of profit generated by each dollar of equity after interest payments to debt capital are subtracted but before taxes are paid. Profits after interest is subtracted equals EBT (earnings before taxes). The ROE ratio can be expressed as: (5.14) HQN’s 2018 before-tax ROE using beginning period equity is equal to: (5.15) After-tax return on equity, ROE(1 – T), can be expressed as EBT adjusted for taxes, or NIAT. Therefore, ROE(1 – T) can be expressed as NAIT divided by equity: (5.16) HQN’s 2018 after-tax ROE is equal to: (5.17) Interpreted, each dollar of equity generated about$0.085 in before-tax profits and $0.051 in after-tax profits during 2018. The relationship between ROE and ROA. Before leaving profitability ratios, there is one important question: which is greater for a given firm: ROE or ROA? To answer this question, we simply define (ROE) / (E) as equal to the return assets (ROA)(A) less the cost of debt (i)(D): (5.18) After substituting for A, (D + E) and collecting like terms and dividing by equity E, we obtain the result in Equation \ref{5.19}: (5.19) Equation (5.19) reveals ROE > ROA if ROA > i; ROE = ROA if ROA = i; and ROE < ROA if ROA < i. If ROE is not greater than ROA, then the firm is losing money on every dollar of debt. For HQN, ROE is 8.5% and greater than its ROA of 6.5%. Meanwhile HQN’s average interest rate on its debt (total interest costs divided by debt at the beginning of the period equal to i) during 2018 was equal to: (5.20) Efficiency Ratios Efficiency ratios compare outputs and inputs. Efficiency ratios of outputs divided by inputs describe how many units of output each unit of input has produced. More efficient ratios indicate a unit of input is producing greater units of outputs than smaller efficiency ratios. Consider two types of efficiency ratios: turnover (TO) ratios and turnover time (TOT) ratios. The turnover ratios measure output produced per unit of input during the accounting period, in our case 365 days. For example, suppose our TO ratio is 5. A TO ratio of 5 tells that during 365 days, every unit input produced 5 units of output. We may want to find the number of days required for a unit of input to produce a unit of output. We can answer the question by dividing 365 days by the number of turnovers that occurred during the year. This tells us the number of days required for a unit of input to produce a unit of output, what we call a turn over time, or TOT, ratio. Continuing with our example, if an input was turned into an output 5 times during the year, then dividing 365 days by 5 tells us that every turnover required (365 days)/5 = 73 days. We now consider four TO efficiency measures: (1) the inventory turnover (ITO) ratio, (2) the asset turnover (ATO) ratio, (3) the receivable turnover (RTO) ratio, and (4) the payable turnover (PTO) ratio. We also find for each TO ratio their corresponding TOT ratio. Inventory turnover (ITO) ratio The ITO ratio measures the output (total revenue) produced by the firm’s inputs (inventory). Total revenue is a period of time measure. Inventory is a point-in-time measure. We use the beginning of the period inventory measure because it reflects the inventory on hand when revenue generating activities began. ITO is defined below. (5.21) The 2018 ITO ratio for HQN is: (5.22) The ITO ratio indicates that for every$1 of inventory, the firm generates an estimated 10.67 dollars of revenue during the year. A small ITO ratio suggests that the firm is holding excess inventory levels given its level of total revenue. Likewise, a large ITO ratio may signal potential “stock outs” which could result in lost revenue if the firm is unable to meet the demand for its products and services.
We can find the number of days required to sell a unit of the firm’s beginning inventory, its inventory turnover time (ITOT) ratio, by dividing one year (365 days) by the firm’s ITO:
(5.23)
The ITOT ratio for HQN in 2018 is equal to:
(5.24)
In other words, a unit of inventory entering HQN’s inventory is sold in roughly 35 days.
Asset turnover (ATO) ratio
The ATO ratio measures the amount of total revenue (output) for every dollar’s worth of assets (inputs) during the year. The ATO ratio measures the firm’s efficiency in using its assets to generate revenue. Like the ITO ratio, the ATO ratio reflects the firm’s pricing strategy. Companies with low profit margins tend to have high ATO ratios. Companies with high profit margins tend to have low ATO ratios.
Let A represent the value of the firm’s assets. The ATO ratio is calculated by dividing the firm’s total revenue by its total assets:
(5.25)
Using beginning of the period assets, HQN’s 2018 ATO ratio is equal to:
(5.26)
We can find the firm’s asset turnover time (ATOT) ratio, the number of days required for a dollar of assets to generate a dollar of sales, by dividing 365 by the firm’s ATO ratio. Using the ATO previously calculated for HQN in 2018 we find:
(5.27)
In other words, a dollar of HQN’s assets generates a dollar of cash receipts in roughly 91 days.
Receivable turnover (RTO) ratio
The RTO ratio measures the firm’s efficiency in using its accounts receivables to generate cash receipts. The RTO ratio is calculated by dividing the firm’s total revenue by its accounts receivables. Using account receivables measured at the beginning of the year, the firm’s RTO ratio measures how many dollars of revenue are generated by one dollar of accounts receivables held at the beginning of the period. The RTO reflects the firm’s credit strategy. Companies with high RTO ratios (strict customer credit policies) tend to have lower levels of total revenue than those with low RTO ratios (easy credit policies). We express the RTO ratio as:
(5.28)
Using data from HQN for 2018, cash receipts from the income statement, and accounts receivables from the ending 2017 balance sheet, we find HQN’s RTO to equal:
(5.29)
In the case of HQN during 2018, every dollar of account receivables generated $24.39 in revenue or an output to input ratio of 24.39. We can estimate the firm’s receivable turnover time (RTOT) ratio or what is sometimes called the firm’s average collection period for accounts receivable ratio, the number of days required for a dollar of credit sales to be collected, by dividing 365 by the firm’s RTO ratio. (5.30) In the case of HQN during 2018, we find its RTOT ratio equal to: (5.31) Interpreted, it takes an average of nearly 15 days from the time of a credit sale until the payment is actually received. The RTOT ratio, like the RTO ratio, reflects the firm’s credit policy. If the RTOT is too low, the firm may have too tight of a credit policy and might be losing revenue as a result of not offering customers the opportunity to purchase on credit. On the other hand, remember that accounts receivable must be financed by either debt or equity funds. If the RTOT is too high, the firm is extending a lot of credit to other firms, and the financing cost may become excessive. Another concern is that the longer a firm extends credit, the greater is the risk that the firm’s accounts receivable will ever be repaid. In some cases, it is useful to construct a schedule that decomposes accounts receivable into the length of time each amount has been outstanding. For example, the schedule might break the accounts receivable into: 1) the amount that is less than 30 days outstanding, 2) the amount that is 30–60 days outstanding, and 3) the amount that is more than 60 days outstanding. This breakdown provides additional information on the risk of the firm’s accounts receivable and the likelihood of repayment. Payable turnover (PTO) ratio The PTO ratio measures the firm’s efficiency in using its accounts payable to acquire its accrued COGS. The PTO is calculated by dividing accrued COGS (equal to cash COGS plus change in account payable) by accounts payable measured at the beginning of the year. The firm’s PTO ratio measures how many dollars of accrued COGS are generated by one dollar of accounts payable held at the beginning of the period. The PTO reflects the firm’s credit strategy. Does it prefer equity or debt financing. Firms with low PTO ratios tend to favor the use of debt to finance the firm which tends to generate higher variability in its ROE. The PTO ratio is expressed as: (5.32) Using data from HQN for 2018, we find its PTO to equal: (5.33) In the case of HQN, every dollar of accounts payable produced 9.33 dollars in accrued COGS. We can estimate the firm’s payable turnover time (PTOT) ratio by dividing 365 days by the firm’s PTO ratio. The PTOT ratio measures the number of days before a firm repays its credit purchases. The PTOT formula, like the other average period ratios, is found by dividing 365 by the PTO ratio. The PTOT ratios can be expressed as: (5.34) HQN’s 2018 PTOT ratio is calculated as: (5.35) Interpreted, HQN’s PTOT ratio of nearly 39 days implies that it takes the firm an average of 39 days from the time a credit purchase is transacted until the firm actually pays for its purchase. The PTOT ratio, like the PTO ratio, reflects the firm’s credit policy. If the PTOT is too low, the firm may not be using its available credit efficiently and relying too heavily on equity financing. On the other hand, PTOT ratios that are too large may reflect a liquidity problem for the firm or poor management that depends too much on high cost short term credit. Note of caution. Economists and others frequently warn against confusing causation and correlation between variables. Descriptive data reflected in the ratios derived in this section on efficiency ratios do not generally reflect a causal relationships between variables nor should they be used to make predictions. For example, in the previous section, we are not suggesting that PTOT can be predicted by the PTO or vice versa. The only thing that can be inferred is that PTOT times PTO will always equal 365 days. Liquidity Ratios A firm’s liquidity is its ability to pay short-term obligations with its current assets. Also implied by liquidity is the firm’s ability to quickly convert assets into cash without a loss in their value which would be the case if the exchange of an asset for cash required a large discount. However, before we review important liquidity ratios, we review an important liquidity measure that is not a ratio: a firm’s net working capital. Net working capital (NWC). Even though NWC is not a ratio, it provides some useful liquidity information that should not be ignored. If NWC is positive, then CA which are expected to be converted to cash during the upcoming year will be sufficient to pay for CL, those liabilities expected to come due during the upcoming year. HQN’s net working capital, described in Table 5.2, is positive for years 2016, 2017, and 2018, suggesting the firm was capable of meeting its short-term debt obligations by using only the assets expected to be liquidated during the upcoming year. Table 5.2. Net Working Capital for HQN Year rrent CuAssets Current Liabilities = Net Working Capital 2016$5,910,000 $5,370,000 =$540,000
2017 $6,320,000$5,958,000 = $362,000 2018$7,000,000 $6,600,000 =$400,000
Another aspect of HQN’s NWC is its trend. Is NWC increasing or decreasing over time? We measure the trend in NWC by calculating the change in NWC between calendar years. HQN’s NWC decreased by $178,000 during 2017 ($362,000 – $540,000). It increased by$38,000 during 2018 ($400,000 –$362,000).
The decrease in NWC during 2017 and the slight increase in 2018 calls for an explanation. Was the drop in NWC justified? Did it represent a conscious liquidity decision by the firm? Was it due to external forces? It is the duty of financial managers to find answers to these questions.
Current (CT) ratio
Liquidity ratios measure a firm’s ability to meet its short-term or current financial obligations with short-term or current assets. The CT ratio is the most common liquidity measure. It combines two point-in-time measures from the balance sheet, current assets (CA), and current liabilities (CL). The point-in-time measures of the two numbers must be the same. We write the CT ratio as:
(5.36)
In principle we would like to see the CT ratio exceed one (CT > 1), because it suggests that for every dollar of CL there is more than one dollar of CA sufficient to cover the liquidation of CL if necessary. If the CT ratio is less than one (CT < 1), then liquidating current assets will not generate enough funds to pay for the firm’s maturing current liabilities obligations which may create a significant problem. If the firm’s current liabilities exceed its current assets, the firm may have to liquidate long-term assets to meet it current obligations. But liquidating long-term (usually illiquid) assets is often costly to do because they cannot be easily converted to cash and end up being sold for a price less than their value to the firm.
The current ratio is constructed from the firm’s balance sheet (see Table 5.1). The CT ratio for HQN at the beginning of 2018 (the end of 2017) was:
(5.37)
HQN’s beginning 2018 CT ratio value of 1.06, suggests that its current liquid resources were just sufficient to meet its current obligations.
As with all the ratios we will consider, there is generally no “correct” CT ratio value. Clearly a firm’s CT ratio can be too low, in which case the firm might have difficulty paying its maturing short-term liabilities. Nevertheless, a CT < 1 does not mean that a firm will not be able to meet its maturing obligations. The firm may have access to other resources that can be used to help meet maturing obligations, such as earnings from operations, long-term assets that could be liquidated, debt which could be restructured, and/or investments in depreciating assets which can be delayed.
On the other hand, a firm’s CT ratio can be too high. CA usually earn a low rate of return and holding large levels of current assets may not be profitable to the firm. It may be more efficient to convert some of the CA to long-term assets that generate larger expected returns. To illustrate, think of the extreme case of a firm that liquidates all of its long-term assets and holds them as cash. The firm might have a large CT ratio and be very liquid, but liquid assets are unlikely to generate a high rate of return or profits.
Quick (QK) ratio
The QK ratio is sometimes called the acid-test ratio. The QK ratio is very similar to the CT ratio, except that inventories (INV), another point-in-time measure obtained from the firm’s balance sheet, are subtracted from CA. The QK ratio is defined as:
(5.38)
In forming the QK ratio, inventories are subtracted because inventories are most often the least liquid of the current assets, and their liquidation value is often the most uncertain. Thus the QK ratio provides a more demanding liquidity measure than the firm’s CT ratio.
Using balance sheet data from Table 5.1, we find the beginning 2018 QK ratio for HQN equal to:
(5.39)
In other words, liquidating all current assets except inventory will generate enough cash to pay for only 43 percent of HQN’s current liabilities. Once again, there is no right or wrong QK ratio. This partly depends on the form of one’s inventories. Product inventories are liquid. Inventories of inputs are less liquid. Clearly, HQN’s liquidity is much lower if its inventory is not available to meet currently maturing obligations. Nevertheless, similar to the CT ratio, a QK ratio of less than one does not necessarily mean the firm will be unable to meet the maturing obligations.
Leverage Ratios
A lever is bar used for prying or dislodging something. We can move more weight with a lever than by applying force directly. The concept of leverage has application in finance. In finance, we define leverage ratios as those ratios used to describe how a company obtains debt and assets using its equity, as a lever. There are several different leverage ratios, but the main components of leverage ratios include debt, equity, and assets. A common expression that associates leverage with equity and debt is: How much debt can we raise (leverage) with our equity?
In general, higher leverage ratios imply greater amounts of debt financing relative to equity financing and greater levels of risk. Greater levels of firm risk also imply less ability to survive financial reversals. On the other hand, higher leverage is usually associated with higher expected returns. Here, we consider two key leverage ratios: (1) debt-to-equity ratio (DE) and (2) equity multiplier ratio (EM).
Debt-to-equity (DE) ratio
DE ratios are the most common leverage ratios used by financial managers. They combine two point-in-time measures from the same balance sheet. The DE ratio measures the extent to which the firm uses its equity as a lever to obtain loan funds. As the firm increases its DE ratio, it also increases its control over more assets.
The DE ratio is equal to the firm’s total debt (D) divided by its equity (E). If dollar returns on assets exceed the dollar costs of the firm’s liabilities, having higher DE ratios (greater leverage) increases profits for the firm. We write the firm’s DE ratio as:
(5.40)
In general, having a lower DE ratio is preferred by creditors, because more equity funds are available to meet the firm’s financial obligations. (Why?) HQN’s DE ratio at the beginning of 2018 was:
(5.41)
Interpreted, HQN’s DE ratio of 4 implies that each dollar of its equity has leveraged \$4.00 of debt. As with liquidity ratios, there is no magic value for DE ratios. If too much debt is used per dollar of equity, the risk of being unable to meet the fixed debt obligations can become excessive. On the other hand, if too little debt is used, the firm may sacrifice returns that can be realized through leverage.
Equity multiplier (EM) ratio
The EM ratio is equal to the firm’s total assets A divided by its equity E. The EM ratio tells us the number of assets leveraged by each dollar of equity. The EM ratio like the DE ratio combines two point-in-time measures from the balance sheet. The EM ratio is a financial leverage ratio that evaluates a company’s use of equity to gain control of assets.
The EM ratio is particularly useful when decomposing the rate of return on equity using the DuPont equation that we will discuss later in this chapter. The formula for EM can be written as:
(5.42)
HQN’s assets and equity are used to calculate its EM at the beginning of 2018, and can be expressed as:
(5.43)
Leverage ratios are often combined with income statement measures to reveal important information about the riskiness of the firm beyond those provided by leverage ratios. We need to include income and cash flow data to answer the question: what is the optimal leverage ratio? We considered these issues when we earlier examined repayment capacity ratios.
Other Sets of Financial Ratios
Other sets of financial ratios besides SPELL ratios have been proposed and used elsewhere. For example, one popular set of ratios is referred to as the Sweet 16 ratios. These are compared to the SPELL ratios in Table 5.3.
Table 5.3. Comparing Sweet 16 Ratios with SPELL ratios
SPELL Ratios Sweet 16 List Comments
(S)olvency Solvency Same ratios.
(P)rofitability Profitability Same ratios.
(E)fficiency Efficiency Same ratios.
(L)iquidity Liquidity Same ratios.
(L)everage Repayment Capacity Different interpretation. Equates repayment capacity with leverage.
The DuPont Equation
The DuPont equation equals ROE multiplied by two identities assets (A) over A and total revenue over total revenue.
(5.44)
The second half of Equation \ref{5.44}, after substituting and rearranging ratios, shows that ROE depends on the asset turnover ratio (ATO), sales margin (m) and the equity multiplier (EM) ratio:
(5.45)
The DuPont equation is important because it provides a detailed picture of the firm’s ability to generate profits efficiently from its equity across several of the SPELL ratios. The first ratio measures operating efficiency using the firm’s profit margin ratio m. The second ratio measures asset use efficiency using the firm’s asset turnover ratio ATO. And the third ratio measures financial leverage or risk using the firm’s equity multiplier ratio EM.
ROE depends on = Efficiency in generating profits from sales Efficiency in generating sales from assets Amount of assets leveraged by each dollar of equity
The DuPont is only one of a large number of DuPont-like equations. Multiplying by ROE assets/assets and one of the following: accounts receivables/accounts receivables, inventories/inventories, and accounts payables/accounts payables produces many versions of the DuPont equation. We list a few possibilities below:
(5.46)
The interdependencies described in the DuPont equation help us to perform strengths and weaknesses analysis. HQN’s DuPont equation for 2018 is found using previously calculated values for m, ATO, and EM:
(5.47)
Since our ROE calculation of 8.5% equals the DuPont calculation of ROE, we are confident that our calculations, which mix point and period of time measures, are consistently calculated and reflect the interdependencies of the system. Comparing the components of the DuPont equation with industry standards we find:
ROE depends on = m: lowest quartile of the industry ATO: highest quartile of the industry EM: significantly higher than the highest quartile of the industry
Based on the above analysis, the ROE is at or near the industry average despite a weak profit margin because its ATO and EM are both high. HQN is efficient in its generation of cash receipts from assets and it is also highly leveraged so that as long as its average cost of debt is less than its ROA, its ROE increases.
To explore the profit margin further, note that the low profit margin is determined by EBT that in turn depends on the level of cash receipts and the cost to generate that level of cash receipts. Our earlier analysis suggested that operating costs and interest costs were relatively high, and these may be having a major impact on the profit margin.
Looking at the ATO ratio, we see that fixed assets impact the ratio, and we were concerned that the firm may not be reinvesting enough in replacing assets. Failing to replace assets as they are used up would artificially inflate the ATO and the firm’s ROE. Also, the inventory levels may be too high. Lowering the inventory levels would increase the ATO and improve ROE. Finally, the high level of leverage helped ROE but is putting the firm in a risky position. The large withdrawal of equity in 2018 has further increased this risk.
Comparing Firm Financial Ratios with Industry Standards
Financial ratios calculated for an individual firm can be made more useful by having a set of standards against which they can be compared. One might think of the limited usefulness of one’s blood pressure readings without some reference level of what is considered a normal of healthy blood pressure. Consider how one can learn more about a firm by comparing it to similar firms in the industry or by comparing it to the distribution of ratios of similar firms.
Major sources of industry and comparative ratios include: Dun and Brad- street, a publication of Dun and Bradstreet, Inc.; Robert Morris Associates, an association of loan officers; financial and investor services such as the Standard and Poor’s survey; government agencies such as the Federal Trade Commission (FTC), Securities and Exchange Commission (SEC), and Department of Commerce; trade associations; business periodicals; corporate reports; and other miscellaneous sources such as books and accounting firms. Table 5.4 shows selected HQN’s ratios for 2018, as well as ratios for other firms in the industry. The industry ratios are broken into quartiles. For example, 1/4 of the firms in the industry have current ratios above 2.0.
Table 5.4. HQN ratios for 2018 & Industry Average Ratios in Quartiles
Open HQN Coordinated Financial Statement in MS Excel
Ratios HQN for 2018 Lower Quartile Median Upper Quartile
SOLVENCY RATIOS
TIE (times interest earned) 1.35 1.6 2.5 5.8
DS (debt-to-service) 1.02 0.9 1.4 3.3
PROFITABILITY RATIOS
m (margin) 0.43% 0.44% 1.03% 1.79%
ROA (return on assets) 6.50% 0.66% 3.30% 7.00%
ROE (return on equity) 8.50% 2.10% 10.70% 17.20%
EFFICIENCY RATIOS
ITO (inventory turnover) 10.67 4.8 7.7 14.9
ITOT (inventory turnover time) 34.21 76.04 47.40 24.50
ATO (asset turnover) 4 1.5 3.2 3.9
ATOT (asset turnover time) 91.25 243.33 111.06 93.59
RTO (receivables turnover) 24.40 15.21 11.41 8.90
RTOT (receivables turnover time) 14.96 24 32 41
PTO (payable turnover) 9.33 9.36 12.59 15.21
PTOT (payable turnover time) 39.12 39 29 24
LIQUIDITY RATIOS
CT (current) 1.06 0.9 1.3 2
QK (quick) 0.43 0.5 0.7 1.1
LEVERAGE RATIOS
DE (debt-to-equity) 4 2.8 1.9 0.9
EM (equity multiplier) 5 3.8 2.2 3.24
Using Financial Ratios to Determine the Firm’s Financial Strengths and Weaknesses
Comparing SPELL ratios with industry standards. In what follows we compare the ratios computed for HQN with the ratios calculated for similar firms. Comparing HQN’s SPELL ratios with industry standards is the essence of strengths and weaknesses analysis and answers the question: what is the financial condition of the firm?
In Table 5.4, the industry is described by the ratio for the firm, the median firm, and the average of firms in the upper and lower quartile of firms. Consider how comparing HQN to the other firms in its industry might allow us to reach some conclusions about HQN’s strengths and weaknesses and to determine its financial condition.
Solvency ratios. HQN’s solvency ratio compared to its industry indicates that it may have a difficult time paying its fixed debt obligations out of earnings. The TIE ratio in 2018 is 1.35 which is less than the industry’s lowest quartile. HQN’s DS ratio in 2018 is 0.94, which implies that only about 94 percent of the firm’s interest and principal can be paid out of current earnings which is only slightly higher than the industry’s lowest quartile. In effect, compared to industry standards, HQN’s significant weakness is its solvency. HQN will need to refinance, raise additional capital, or liquidate some assets in order to make the interest and principal payments and remain in business.
Profitability ratios. Compared to industry averages, HQN is profitable. Its ROE is reasonably close to the industry average and its ROA is close to the upper quartile industry average. Paradoxically, HQN’s m margin is close to the industry’s lowest quartile average.
Efficiency ratios. Compared to the industry averages, HQN is very efficient. Both HQN’s ITO and ATO ratios are near the top in its industry. Its ITO ratio in 2018 was 10.67, indicating that HQN has sold its inventory over 10 times during the year. This ITO ratio is above the median value for firms in this industry of 7.7, and strong. The ATO ratio has a 2018 value of 4.0, indicating the firm had sales of 4 times the value of its assets, compared to an industry median of 3.2 which is in the upper quartile of firms in its industry. The firm appears to be using assets efficiently which undoubtedly contributes to HNQ’s profitability even though its margin in low.
The RTOT ratio has a 2018 value of 14.96. This value is well below industry averages, and raises a question about the firm’s credit policies. The industry average RTOT was 32 and suggests that HQN might consider a more generous credit policy. On the other hand, HQN’s PTOT ratio is 39 and is in the lowest quartile for the industry. This suggests that HQN is depending on dealer supplied credit more than other firms in its industry because of its low solvency. Still, HQN’s strength may be its efficiency.
Liquidity ratios. The current ratio is 1.06, which suggests the firm is liquid, but barely. Its ratio is near the lower quartile of firms in the industry. The quick ratio is 0.43, suggesting the firm cannot meet its short-term obligations without relying on inventory. HQN’s quick ratio is in the lower quartile of firms in the industry, indicating that the firm is less liquid than most of its competitors and is an HQN weakness.
Leverage ratios. The leverage ratios indicate that the HQN’s use of debt is high. Comparison with industry ratios shows that HQN is highly leveraged relative to other firms in the industry. As long as ROA exceeds the average interest costs of debt, high leverage increases the firm’s profitability—but increases its risk associated with adverse earnings.
Limitations of Ratios
While ratio analysis can be a powerful and useful tool, it does suffer from a number of weaknesses. We discussed earlier how the use of different ac- counting practices for such items as depreciation can change a firm’s financial statements and, therefore, alter its financial ratios. Thus, it is important to be aware of and understand accounting practices over time and/or across firms.
Difficult problems arise when making comparisons across firms in an industry. The comparison must be made over the same time periods. In addition, firms within an “industry” often differ substantially in their structure and type of business, making industry comparisons less meaningful. Another difficulty is that a departure from the “norm” may not indicate a problem. As mentioned before, a firm might have apparent weaknesses in one area that are offset by strengths in other areas.
Furthermore, things like different production practices in a firm may require a different financial structure than other firms in the industry. Additionally, shooting for financial ratios that look like the industry average may not be very desirable. Would you want your business to be average?
Inflation can have a significant impact on a firm’s balance sheet and its corresponding financial ratios. As a results, it is important to keep in mind the difference between a capital item’s book value and it market value. Firms that keep a set of market value financial statements in addition to their book value financial statements should conduct financial analysis with both their book value and market value financial statements.
We should recognize that a single ratio does not provide adequate information to evaluate the strength or weakness of a firm. A weak ratio in one area might be offset by a strong ratio in another area. Likewise, a perfectly healthy firm, from a financial standpoint, may have some special characteristics which result in a ratio which would be out of line for other firms in the industry who do not have these characteristics.
Finally, it must be understood that financial analysis does not in itself provide a management decision. The analysis provides information which will be a valuable input into making management decisions, but there is no “cook book” formula into which you plug the financial analysis number and produce the correct management decisions.
Financial ratios can be an effective strengths and weaknesses analysis tool. Their principal use is to assess the firm’s ability to survive. To survive in the long term, the firm must be profitable and solvent. Profitability is defined as the difference between a firm’s revenues and its expenses. Solvency is the firm’s ability to meet its cash obligations when they become due. Solvency depends on the firm’s holdings of liquid assets—assets that can easily and with little expense be converted into cash in the current period.
If a firm is not both profitable and solvent, it cannot survive in the long term. In the short term, a firm can be solvent but not profitable. For a limited time, an unprofitable firm can convert assets to cash and remain solvent by borrowing, refinancing existing debt, selling inventory, liquidating capital assets, increasing accounts payable, or depleting its capital base. These acts may improve the firm’s solvency in the short run, but are likely to erode the firm’s future profitability.
In contrast, a firm may be profitable and not solvent, in which case it cannot survive even in the short term. Once a firm fails to meet its cash flow obligations, even if it is profitable, in most cases it loses control over its assets. Therefore, short-term survival may require some firms to sacrifice profitability for solvency. Thus, financial managers must monitor both the firm’s solvency and profitability. An appropriately constructed set of financial ratios will allow financial managers to monitor both the firm’s profitability and solvency.
Financial ratios may also provide information about the liquidity of the firm, which is related to the firm’s solvency because the firm’s liquidity position tells us something about the firm’s ability to meet unforeseen outcomes and survive. Also related to the firm’s solvency and liquidity is the probability of achieving different rates of return. Measures of the probability of alternative rates of return are sometimes examined under the general heading of risk, a subject we will return to later in this book (see Chapter 15).
Strengths and Weaknesses Summary
How do we summarize our strengths and weaknesses analysis? One way is to assign a grade to each of the SPELL categories ranging from 5 (superior) to 1 (on life support). Clearly, the grades assigned are somewhat subjective, but perhaps useful, in summarizing a great deal of financial information. Then what? Do we assign equal weight to each of the SPELL categories depending on their relative importance? The answer to this question depends on the vision, goals, and objectives of the firm manager. To complete this discussion of how to assign weights to the SPELL categories, we treat them equally important in this example—although a strong case exists for assigning a greater weight to profitability measures. In Table 5.5 we summarize our strengths and weaknesses ratings.
Table 5.5. Summary of HQN’s 2018 Financial Strengths & Weaknesses
SPELL Category weights Grades: 5 (very strong) to 1 (very weak)
Solvency .2 2.0
Profitability .2 3.0
Efficiency .2 4.0
Liquidity .2 3.0
Leverage .2 2.0
Weighted Summary 2.8
So what have we learned? We learned that a firm’s SPELL ratios can be compared to financial ratios of similar firms to determine the firm’s financial strengths and weaknesses. In the case of HQN, we assign to it a strengths and weaknesses score of 2.8 which is less than the median or average financial conditions of similar firms in its industry. Significant in arriving at an overall financial strengths and weaknesses score of 2.8 was HQN’s high leverage that places it in a risky position and its weak solvency condition.
Summary and Conclusions
When using financial ratios from one’s own firm and comparing them with industry standard ratios, it is often useful to take notes or summarize the major points as you work through the ratio analysis. In our analysis of HQN, the firm is highly leveraged and is in a risky position. We might ask why is the firm relying so heavily on debt and why is its equity being withdrawn at such a relatively high rate? The overhead expenses seem to be too high. Why? How can the situation be improved? Why are the firm’s assets being depleted? What is the cause of the increasingly high level of inventory being held?
After gathering information on these questions and others, the firm’s financial manager may produce a detailed strengths and weaknesses report. In the report, key financial management issues can be explored, and forecasts of future financial needs and situations can be made. Continued monitoring of the firm’s financial statements and ratios will allow the firm’s management to gain solid understanding of the relationship between the firm’s operations and its financial performance and to recommend changes when required.
So what have we learned? We learned that by using the information contained in its CFS, firms can construct financial ratios that provide five different views of the firm’s financial condition: its solvency, its profitability, its efficiency, its liquidity, and its leverage. A logical next step is to a assign a weight to each of the firm’s financial conditions reflected by its ratios after comparing them to industry standards. The overall weighted average reflects the firm’s financial strengths and weaknesses and answers the question: what is the financial condition of the firm.
Questions
When calculating 2018 ratios, please refer to Tables 4.1, 4.4A or 4.4B, and 4.6 in Chapter 4. When asked for industry standard comparisons, use industry measures provided in Table 5.4.
1. Explain why financial statement data is made more useful by forming SPELL ratios?
2. Describe the kinds of questions related to the firm’s financial strengths and weaknesses each of the SPELL ratios can help answer.
3. Calculate the 2018 SPELL ratios for Friendly Fruit Farm (FFF) described in Chapter 4.
4. Do FFF’s DS and TIE ratios, both solvency ratios, tell consistent stories? Defend your answer.
5. Explain why a firm might be reluctant to meet its short-term liquidity needs by liquidating long-term assets.
6. Describe the connections between the m ratio and FFF’s ROE.
7. What is the essential difference between ROA and ROE profit measures? What do they each measure?
8. What conditions guarantee that ROE > ROA or that ROA > ROE?
9. Explain the connections between efficiency and ROE or ROA measures.
10. Create an efficiency ratio for your class preparation efforts? (Hint: what are the inputs and what are the outputs?) What could you do to improve the efficiency of your class preparation efforts?
11. What might be implied by very high or very low ITO ratios?
12. Calculate ITO ratios using 2018 total revenue measures for FFF. Then compare your results with ITO ratios using accrued COGS. Explain the differences.
13. The optimum RTOT ratio seeks to balance the need to generate cash receipts by offering easy credit versus the need to meet liquidity need by limiting its accounts receivable. Looking at the financial statements for HQN, what is an ideal RTOT ratio (state a number)? Defend your ideal number RTOT number, and if it is different than HQN’s actual number, what actions could you take to align HQN’s actual RTOT to its ideal RTOT?
14. Explain why it is difficult to compare net working capital numbers between firms.
15. The DuPont equation allows us to decompose the ROE measure. Replace total revenue with COGS in Equation \ref{5.45} and recalculate the components of the revised DuPont equation. Interpret the results. Does the resulting equation still equal HQN’s ROE?
16. Calculate and compare FFF CT ratios at the end of years 2017 and 2018. What can you learn from the changes in FFF’s CT ratios? Compare FFF CT ratios with industry standards. What do you learn from the comparison?
17. Using FFF’s QK ratios at the end of years 2017 and 2018, what strengths and weaknesses score would you assign to its liquidity?
18. Suppose FFF’s long-term debt was 10% above the book value of their long-term assets and only 50% of the current value of their long-term assets. Calculate DE ratios using current and book values of their long-term assets. If FFF were applying for a loan, which DE ratios would they most likely present?
19. If ROA exceeds the average costs of the firm’s liabilities, having higher DE ratios (greater leverage) increases profits for the firm. Why might lenders want lower DE ratios while borrowers may want higher DE ratios?
20. Compare firms with low ITO ratios such as jewelry stores with firms with high ITO ratios like grocery stores or gas stations. How might their profit margin requirements for success differ? Explain.
21. Using FFF’s SPELL ratios and the industry standards used to evaluate HQN’s strengths and weaknesses, write a brief report of FFF’s financial strengths and weaknesses. Organize your report into the five SPELL categories: solvency, profitability, efficiency, liquidity, and leverage. Complete a table similar to Table 5.5 that was prepared for HQN. What is the summary measure of FFF’s financial strengths and weaknesses? | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/05%3A_Financial_Ratios.txt |
Learning Objectives
After completing this chapter, you should be able to (1) define a system; (2) recognize system properties included in coordinated financial statements (CFS); and (3) connect changes in exogenous variables determined outside the CFS system to changes in endogenous variables calculated inside the CFS system to answer”what if” and “how much” kinds of questions.
To achieve your learning goals, you should complete the following objectives:
• Learn what is a system
• Learn how CFS satisfy system requirements.
• Learn how individual financial statements included in the CFS are connected.
• Learn how subsystems can be created from a system.
• Learn how to answer the question: what if the value of an exogenous variable included in the CFS system changes, then how will the values of endogenous variables included in the CFS change?
• Learn how to answer the question: how much does the value of an exogenous variable included in the CFS system need to change for the value of a specified endogenous variable included in the CFS to equal a specified value?
• Learn how asking what if and how much questions about changes in exogenous variables allows firm managers to conduct opportunity and threat analysis.
• Learn how to create a subsystem of the CFS system that describes a firm’s rate of return on equity (ROE).
• Learn how to create a subsystem of the CFS system that describes a firm’s solvency.
• Learn how to compute common size balance sheets and accrual income statements (AIS) and describe the trade-off perspectives they provide.
Introduction
In what follows we define a system and distinguish between the different kinds of systems. Then we make the point that CFS are a system.
CFS are a system. Indeed we have already used the system properties of CFS to answer the question: “what is” the financial condition of the firm? We answered that question by constructing ratios that described the firm’s (S)olvency, (P)rofitability, (E)fficiency, (L)iquidity, and (L)everage (SPELL) ratios. However, the value of information gained from SPELL ratios has its limit. Answering “what is” kinds of questions is a static (timeless) analysis because its focus is on the current financial condition of the firm. We need addition information that is forward looking such as knowing how the financial condition of the firm may change in response to changes in the external environment of the firm. We may also want to know what kinds of changes are required in the firm’s external environment for specified changes to occur within the CFS system.
Because CFS is a system, we can use it as our primary strengths, weaknesses, opportunities, and threats analysis tool. We summarize several reasons why the system’s properties of CFS are important for financial managers conducting strengths, weaknesses, opportunities, and threats analysis:
• Because it allows us to answer the question: what is the financial condition of the firm reflected by its SPELL ratios. Answering the what is question is the primary means for conducting strengths and weakness analysis.
• Because the relationships between CFS variables and financial statements are consistent (they don’t change and cannot produce a contradiction), we can check the accuracy of our numbers by looking for extraordinary numbers in the statements. If we observe unrealistic results, they can only be attributed to the data’s inaccuracy.
• Because it allows us to ask what if questions by changing conditions in the external environment of the firm and noting changes in the financial condition of the firm. Answering what if questions is one of two primary means for conducting opportunities and threats analysis.
• Because it allows us to ask how much questions and determine how much of an external change is needed to change a particular variable inside the system. Answering how much questions is one of two primary means for conducting opportunities and threats analysis.
• Because it allows us to define subsystems to focus on parts of the system such as profitability and solvency that we want to emphasize.
Coordinated Financial Statements as a System
What is a system. A system is an interacting and interdependent group of items forming a unified whole and serving a common purpose (Wikipedia). Every system has boundaries that separate activities that occur within the system from those that occur outside of the system. Each element of the system contributes to a common purpose.
There are, of course, several kinds of systems. An abstract system uses variables to represent tangible or intangible things and may or may not have a real world counterpart. On the other hand, physical systems are generally concrete operational systems made up of people, materials, machines, energy, and other physical things. Physical systems are the actual systems that abstract systems may attempt to represent.
Finally, systems may be closed or open. Open systems allow for exogenous forces outside of the system to influence endogenous activities within the firm. Closed systems are immune to exogenous forces. Finally, systems may be stochastic such that endogenous outcomes within the system can only be described with probabilities. Meanwhile deterministic systems are connected endogenously and exogenously with certain (non probabilistic) relationships.
Coordinated financial statements are a system. The CFS are an abstract system whose variables and statements are described using mathematical equations and numbers. The CFS are designed to represent the financial condition of the firm at the beginning and ending of a period with balance sheets and financial activities between the beginning and ending balance sheets using an accrual income statement (AIS) an a statement of cash flow (SCF). The CFS are an open system. They allow for an external environment represented by exogenous variables to influence activities within the firm represented by endogenous variables. Finally, for our purposes, we assume that the relationships between financial statements and variable values included in the CFS system are deterministic.
To understand the CFS system, we must be able to distinguish between endogenous and exogenous variables. One easy way to distinguish between CFS’ endogenous and exogenous variables is to ask: was this variable calculated somewhere in the system? Or was this variable’s value determined outside of the system? If the variable was calculated within the system, it is an endogenous variables. If the variable was calculated outside of the system, it is an exogenous variable. A firm’s coordinated financial statements for a given time period includes its end-of-period balance sheets, an (accrual) income statement (AIS), and a statement of cash flow (SCF). The firm’s CFS constitute a system because their endogenous and exogenous variables are interdependent. The variables are connected with equations that describe how the endogenous variables are calculated and how the financial statements are connected.
To illustrate, cash balances in the previous period’s ending balance sheet is an exogenous variable. It’s value was determined by activities in previous time periods. In contrast, the current period’s ending period cash balances depend on cash balances at the end of the previous period and changes in cash position calculated in the SCF. Therefore the firm’s cash balance in the current period’s ending balance sheet is an endogenous variable.
Endogenous and exogenous variables create interdependencies between the financial statements in the CFS system. In general, financial activities described in the AIS and statement of cash flow link the beginning and ending balance sheets. To illustrate:
1) Change in cash position calculated in the statement of cash flow equals the difference in cash and marketable securities recorded in the beginning and ending period balance sheets.
2) Cash flow from changes in notes and long-term liabilities in the beginning and ending period balance sheets equal cash flow recorded in the financing section of the statement of cash flow.
3) Addition to retained earning calculated in the AIS equals the difference between the firm’s retained earnings recorded in the beginning and ending period balance sheets.
Over identified variables and systems. We discussed over identified variables in Chapter 4. We review and illustrate the concept again here. Suppose that we use the system properties of the CFS to find the ending period cash balances. Then suppose we observe that the ending cash balance calculated as an endogenous variable in our balance sheet is different than the ending cash balance in our check book.
The problem is that the ending cash balance value is over identified. It can be calculated as an endogenous variable within the financial system or observed externally as an exogenous variable. When the two values differ, we say the system is inaccurate because exogenously and endogenously variable values differ from one another and the financial manager must employ his/her best effort to find the error in the data. Resolving data errors revealed by over identified variables may be the most challenging task facing financial managers whose data is often incomplete and not always accurate. Sometimes the data errors revealed by over identified variables provides financial managers the opportunity to encourage the principals of the firm to reexamine their financial records and look for errors or missing data.
Prioritizing Opportunities and Threats Questions
Financial ratios. Chapter 5 described the financial system of the firm using SPELL ratios. Of course the ratios in each of the SPELL categories provide some information by themselves. Alone, they help us answer what is the financial condition of the firm and what are its strengths and weaknesses. However, ratios are more useful when their interdependence is recognized. In other words a change in the firm’s solvency is likely to change the firm’s liquidity. A change in the firm’s efficiency is likely to change the firm’s profitability. And the list of possible interdependencies continues. Since the variables in the financial system are interdependent, the ratios composed of system variables are also interdependent.
How do we proceed to examine the interdependencies of the firm? We limit and organize our examination of the financial interdependencies by focusing on the firm’s bottom line—its profitability ratios.
A firm can exist for many reasons. It may satisfy the firm owners’ desires to engage in a particular production activity. (For example, I just want to farm!) It may be organized to provide family members and others employment. It may exist to provide some public service. There are undoubtedly other reasons why firms exist. But, the firm financial manager is charged with only one mission—to ensure the firm’s survival and its profitability. This requires a proper balance at least between the firm’s return and its solvency.
In this view, solvency ratios described by the times interest earned (TIE) and debt-to-service (DSR) ratios and profitability ratios described by margin (m), return on equity (ROE), and return on asset (ROA) ratios are the most important of the SPELL ratios. However, efficiency, leverage, and liquidity ratios also matter to the firm because they influence its profitability measured by its ROE and ROA ratios and its solvency measured by its TIE and DSR ratios. One such formula that connects the firm’s profitability ratios and other considerations of the firm including leverage and efficiency is the DuPont equation introduced in Chapter 5.
System Metaphors
A metaphor compares two ideas or objects that are dissimilar to each other in some ways and similar to each other in other ways. We use three metaphors to describe how changes in an exogenous variable—a shock—change endogenous variables.
Balloons. One might compare the CFS to a balloon. If you squeeze one part of the balloon (an exogenous force), there will be an (endogenous) bulge somewhere else in the balloon. This action-reaction nature of a system (and balloons) leads to us examine shocks in pairs and answer the question: “what if” a change in an exogenous variable occurs, “then” what happens to the endogenous variables of the system?
Predicting the weather. Predicting the financial future of the firm has characteristics in common with predicting the weather. Meteorologists look at where the weather fronts have been, the direction they have been traveling, and then predict where they will likely be in the future. To hedge their bets, they often predict future weather patterns with probabilities. Predicting the future financial condition of the firm also looks at the condition of the firm now, how it has changed over time, and then predicts with probabilities where it will be in the future.
The detective. Trying to describe how changes in an exogenous variable will affect endogenous variables is like a detective trying to put all the clues together to solve a case that explains who committed the crime. The detective observes a crime—a condition different than what existed before the crime occurred. The financial manager observes changes in the firm’s endogenous variables and attempts to link them to changes in one of the exogenous variables.
What does this mean? Since the CFS constitute a system, we ask and answer questions related to changes in the values of exogenous variables and observe how these changes produce changes in the values of endogenous variables within the system. In addition, by creating balance sheet and CFS subsystems, we can examine trade-offs within the firm: if one variable value within the balance sheets or CFS increases, what other variable(s) is likely to decrease, reminiscent of squeezing one part of a balloon and observing a bulge in another part of the balloon. Or we may ask how much an exogenous variable must change to produce a desired change in an endogenous variable.
CFS systems are not unique because every financial system may define its endogenous and exogenous variables differently. As a result, each system may define its interdependencies differently, which in turn defines how consistency is achieved in the system. Nevertheless, a template that describes the system may be our best and only approach for answering system-wide what if and how much types of questions.
What If Analysis
At the beginning of this chapter, we emphasized how endogenous and exogenous variables created interdependence in the CFS system. Therefore, any change in an exogenous variable in one part of the CFS system will produce changes in endogenous variables in other parts of the system. Tracing the impact of a change in an exogenous variable on endogenous variables in the system is referred to here as what if analysis. The exogenous variable changed by the analyst is often referred to as a control variable—a special kind of exogenous variable.
What if analysis can be helpful in several ways. First, changes in exogenous variables outside of the firm’s control may be examined by following their consequences throughout the CFS system. This exercise helps the firm anticipate and plan for different outcomes. A second benefit that may be derived from what if analysis is that changes in exogenous variables may reflect the need for alternative financial strategies that can be evaluated before being adopted and those most beneficial to the firm can be adopted.
The first step in the what if analysis is to introduce the change in an exogenous or control variable. The second step is to recalculate the endogenous variables in the financial statements. The third step is to recalculate the SPELL ratios and compare them to the previous ratio values and to industry averages. And finally, the fourth step is to interpret the results which should include describing connections between changes in the firm’s SPELL ratios. Fortunately, steps one, two, and three can be automated using Excel spreadsheets.
To help analyze the changes in exogenous variables described in the scenarios below, we use an Excel integrated set of financial statements described in this chapter. The Excel spreadsheet describes HQN’s coordinated financial system and allows those interested in answering what if questions to substitute actual numbers and note the changes in absolute values in the financial statements and ratios.
To illustrate what if analysis, consider the following change in an exogenous variable. Suppose cash receipts for HQN were $39,990 instead of$38,990. The changes that result in HQN’s financial statements are highlighted in Table 6.1. As a result of an increase in cash receipts reported in the statement of cash flow (an exogenous variable), EBIT and EBT increased by $1,000. Taxes increased by 40% of the increased earning, from$58 to $468. NIAT increased by$600 of after-tax income to $702 as did retained earnings. Finally assets and equity and liabilities all increased by$600 of after-tax income.
Table 6.1. Coordinated Financial Statements for Hi-Quality Nursery Cash Receipts = $39,990 Open Table 6.1 in Microsoft Excel BALANCE SHEET ACCRUAL INCOME STATEMENT STATEMENT OF CASH FLOW DATE 12/31/2017 12/31/2018 DATE 2018 DATE 2018 Cash and Marketable Securities$930 $1,200 + Cash Receipts$39,990 + Cash Receipts $39,990 Accounts Receivable$1,640 $1,200 + Change in Accounts Receivable ($440) Cash Cost of Goods Sold $27,000 Inventory$3,750 $5,200 + Change in Inventories$1,450 Cash Overhead Expenses $11,078 Notes Receivable$0 $0 + Realized Cap. Gains/Depr. Recapture$0 Interest paid $480 Total Current Assets$6,320 $7,600 Total Revenue$41,000 Taxes $468 Depreciable Assets$2,990 $2,710 + Cash Cost of Goods Sold$27,000 Net Cash Flow from Operations $964 Non-depreciable Assets$690 $690 + Change in Accounts. Payable$1,000 + Realized Cap. Gains + Depr. Recapture $0 Total Long-Term Assets$3,680 $3,400 + Cash Overhead Expenses$11,078 + Sales Non-depreciable Assets $0 TOTAL ASSETS$10,000 $11,000 + Change in Accrued Liabilities ($78) Purchases Non-depreciable Assets
Notes Payable $1,500$1,270 + Depreciation $350 + Sale Depreciable Assets$30
Current Portion Long-Term Debt $500$450 Total Expenses $39,350 Purchases Depreciable Assets$100
Accounts Payable $3,000$4,000 Earnings Before Interest and Taxes (EBIT) $1,650 Net Cash Flow from Investment ($70)
Accrued Liabilities $958$880 Less Interest Costs $480 + Change in Non-Current Long Term Debt ($57)
Total Current Liabilities $5,958$6,600 Earnings Before Taxes (EBT) $1,170 + Change in Current Portion of Long Term Debt ($50)
Non-Current Long-Term Debt $2,042$1,985 Less Taxes $468 + Change in Notes Payable ($230)
TOTAL LIABILITIES $8,000$8,585 Net Income After Taxes (NIAT) $702 Less Dividends and Owner Draw$287
Contributed Capital $1,900$1,900 Less Dividends and Owner Draw $287 Net Cash Flow from Financing ($624)
Retained Earnings $100$515 Addition to Retained Earnings $415 CHANGE IN CASH POSITION$270
Total Equity $2,000$2,415
TOTAL LIABILITIES AND EQUITY $10,000$11,000
Table 6.2. HQN Ratio Analysis after a $1,000 increase in Cash Receipts Open Table 6.2 in Microsoft Excel Ratios Industry Average Activity Ratios HQN Base Increase CR by$1000
Solvency
TIE 2.50 3.44 1.35 3.44
DSR 1.40 2.04 1.02 2.04
Profitability
ROA 3.30% 16.50% 6.50% 16.50%
ROE 10.70% 58.50% 8.50% 58.50%
m margin 29.00% 2.85% 0.43% 2.85%
Efficiency
ITO 7.7 10.93 10.67 10.93
ITOT 47.4 33.38 34.22 33.38
ATO 3.2 4.10 4.00 4.10
ATOT 114.1 89.02 91.25 89.02
RTO 11.41 25.00 24.39 25.00
RTOT 32 14.60 14.97 14.60
PTO 12.59 9.33 9.33 9.33
PTOT 29 39.11 39.12 39.11
Liquidity
Current Ratio 1.30 1.06 1.06 1.06
Quick Ratio 0.70 0.43 0.43 .43
Leverage
Debt/Assets 0.91 0.80 0.80 .8
Debt/Equity 2.00 4.00 4.00 4.00
Asset/Equity 2.20 5.00 5.00 5.00
In Chapter 5, we focused on ratio analysis. As a result of changes from increased cash receipts, we ask: how many ratios calculated in the previous chapter change? In other words, compare the new and old ratios. The new ratios resulting from an increase in CR of $1,000 are reported in the activity column in Table 6.2. Compare these to the HQN base ratios. The TIE solvency ratio increased from 1.35 to 3.44. The ROA profitability ratio increased from 6.5% to 16.5%. The ITO efficiency ratio increased from 10.67 to 10.93. Liquidity and leverage ratios that depend on beginning balance sheet values remain unchanged. Based on the changes in SPELL ratios resulting from an increase of$1,000 in CR, life is good at HQN!
What If Analysis and Scenarios
In what follows, we describe several scenarios facing HQN that could be analyzed by changing exogenous variables and noting their effect on CFS endogenous variables. Obviously, each of the changes has the capacity to produce changes in HQN’s SPELL ratios. Following these consequences throughout the financial system, a what if analysis exercise, is really answering the question: what if something happens, then what?
What complicates our scenario analysis is that more than one exogenous variable change may be required to answer the what if question. Consider several scenarios that we describe next.
Scenario 1. The firm has not been replacing its long-term assets. As a result, its cost of goods sold has been increasing due to increased repairs and maintenance. What are the consequences of this scenario on the financial condition of the firm?
Scenario 2. A financial manager is risk-averse and decides to increase the firm’s current assets. What actions can the firm manager take to increase the firm’s level of current assets. What are the consequences of increasing the firm’s current assets relative to its fixed assets?
Scenario 3. Suppose the firm decides to increase the time it takes to repay its notes payable. What are the advantages/disadvantages of adopting such a strategy? What conditions facing the firm might prompt it to increase the time it takes to repay its notes payable? What ratios would you want to investigate to confirm your assumptions?
Scenario 4. To boost its cash receipts, the firm offers easy credit terms to its customers. What are the implications for the firm? How would you expect the firm’s credit policies to be reflected in the firm’s financial statements?
Scenario 5. Market conditions have reduced the demand for the firm’s products. As a result, cash receipts are falling. Unfortunately, most of the firm’s costs are fixed and don’t adjust to changing output levels. What changes would you expect to find in future financial statements of the firm?
Scenario 6. The firm’s owners face serious medical costs and must extract funds from the business. Describe the impact of these expenses on the firm’s financial statements.
Scenario 7. The firm makes a major investment in long-term assets to improve its efficiency. One impact of the change is to reduce its taxes because of the increased depreciation. Describe other consequences on the firm’s financial statements.
Scenario 8. Hard economic times have reduced the firm’s customers’ ability to pay for their purchases in the usual amount of time. Describe the consequences on the firm’s financial statements.
Scenario 9. Cash receipts have been inadequate for the firm to meet its notes payable and current long-term liabilities. As a result, it is forced to sell off some of its long-term assets at values less than reported on its balance sheet. What other strategies can the firm adopt to meet its solvency demands?
Scenario 10. Reduced cash receipts without changes in production levels have led to increased inventories. To meet its financial demands, the firm has restructured its debt, decreasing the current portion of the long-term debt. How will these changes be reflected in its financial statements?
Scenario 4 illustration. Consider performing what if analysis on scenario 4. The analysis requires that we assume specific numbers. In our illustration assume that CR increased by 5% from $38,990 to$40,940. Then, because production has increased, assume that cash COGS increase by 8% from $27,000 to$29,160. There may be other changes in exogenous variables, but these are sufficient to illustrate our scenario analysis. After making the changes, we resolve the CFS template and report the consequences in the activity column. In case we want to save our results for later analysis, we save them under scenario 4 column in Table 6.3 below.
Table 6.3. HQN’s SPELL Analysis for Scenario 4.
Open Table 6.3 in Microsoft Excel
Ratios Industry Average Activity Ratios HQN Base Scenario 4
Solvency
TIE 2.50 0.92 1.35 0.92
DSR 1.40 0.81 1.02 0.81
Profitability
ROA 3.30% 4.40% 6.50% 4.40%
ROE 10.70% -2.00% 8.50% -2.00%
m margin 29.00% -0.10% 0.43% -0.10%
Efficiency
ITO 7.7 11.19 10.67 11.19
ITOT 47.4 32.63 34.22 32.63
ATO 3.2 4.20 4.00 4.20
ATOT 114.1 87.01 91.25 87.01
RTO 11.41 25.58 24.39 25.58
RTOT 32 14.27 14.97 14.27
PTO 12.59 10.05 9.33 10.05
PTOT 29 36.31 39.12 36.31
Liquidity
Current Ratio 1.30 1.06 1.06 1.06
Quick Ratio 0.70 0.43 0.43 0.43
Leverage
Debt/Assets 0.91 0.80 0.80 0.80
Debt/Equity 2.00 4.00 4.00 4..00
Asset/Equity 2.20 5.00 5.00 5.00
While HQN successfully increased its CR, its ROA decreased from 6.5% to 5.6% and its ROE decreased from 8.5% to 3.98%. A homework exercise asks you to examine other consequences of increases in CR and COGS. However, one lesson learned from this scenario analysis is to be careful what you wish for—especially if your ultimate goal is to increase the profitability of your firm.
How Much Questions and Goal Seek
CFS system’s properties allow us to ask and answer important what if kinds of questions by changing an exogenous variable and observing its effect on the endogenous variables of the system. Goal Seek is an important Excel function that allows us to ask and answer how much kinds of questions. How much questions take the form: how much change is required in an exogenous variable x for variable y to reach a particular value, a goal, equal to a? To illustrate using HQN data, suppose we asked: how much must HQN’s CR increase for ROE to equal 9%?
Table 6.4. Coordinated Financial Statements for Hi-Quality Nursery
Open Table 6.4 in Microsoft Excel
BALANCE SHEET ACCRUAL INCOME STATEMENT STATEMENT OF CASH FLOW
DATE 12/31/2017 12/31/2018 DATE 2018 DATE 2018
Cash and Marketable Securities $930$606 + Cash Receipts $39,000 + Cash Receipts$39,000
Accounts Receivable $1,640$1,200 + Change in Accounts Receivable ($440) Cash Cost of Goods Sold$27,000
Inventory $3,750$5,200 + Change in Inventories $1,450 Cash Overhead Expenses$11,078
Notes Receivable $0$0 + Realized Cap. Gains/Depr. Recapture $0 Interest paid$480
Total Current Assets $6,320$7,006 Total Revenue $40,010 Taxes$72
Depreciable Assets $2,990$2,710 + Cash Cost of Goods Sold $27,000 Net Cash Flow from Operations$370
Non-depreciable Assets $690$690 + Change in Accounts. Payable $1,000 + Realized Cap. Gains + Depr. Recapture$0
Total Long-Term Assets $3,680$3,400 + Cash Overhead Expenses $11,078 + Sales Non-depreciable Assets$0
TOTAL ASSETS $10,000$10,406 + Change in Accrued Liabilities ($78) Purchases Non-depreciable Assets Notes Payable$1,500 $1,270 + Depreciation$350 + Sale Depreciable Assets $30 Current Portion Long-Term Debt$500 $450 Total Expenses$39,350 Purchases Depreciable Assets $100 Accounts Payable$3,000 $4,000 Earnings Before Interest and Taxes (EBIT)$660 Net Cash Flow from Investment ($70) Accrued Liabilities$958 $880 Less Interest Costs$480 + Change in Non-Current Long Term Debt ($57) Total Current Liabilities$5,958 $6,600 Earnings Before Taxes (EBT)$180 + Change in Current Portion of Long Term Debt ($50) Non-Current Long Term Debt$2,042 $1,985 Less Taxes$72 + Change in Notes Payable ($230) TOTAL LIABILITIES$8,000 $8,585 Net Income After Taxes (NIAT)$108 Less Dividends and Owner Draw $287 Contributed Capital$1,900 $1,900 Less Dividends and Owner Draw$287 Net Cash Flow from Financing ($624) Retained Earnings$100 ($79) Addition to Retained Earnings ($179) CHANGE IN CASH POSITION ($324) Total Equity$2,000 $1,821 TOTAL LIABILITIES AND EQUITY$10,000 $10,406 To answer this question on an Excel spreadsheet that describes HQN’s CFS, we press the [Data] tab and the [What If Analysis] button. Finally, we press “Goal Seek” in the drop down menu. Goal Seeks asks us to supply three pieces of information: the cell where the goal value is located, the numeric value for the variable identified in the goal cell, and the cell location of the variable we wish to change to achieve our goal. The number we wish to change must be an exogenous variable—not a calculated variable. We want to change the ROE located in cell H53 to a value of 9% by changing cash receipts of landscaping services located in cell D3 located on the exogenous variables page. We record this information in the Goal Seek menu below. Figure 6.1. Goal Seek Pop-up Menu Then we click [OK] and that find cash receipts from landscaping services must increase to$30,010 to earn an ROE of 9%. Furthermore, increasing cash receipts from landscaping services to $30,010 increases total cash receipts to$39,000. Changes in the endogenous variables included in system are described next in the activity column of the what if page.
Table 6.5. What If Analysis using SPELL Ratios.
Open Table 6.5 in Microsoft Excel
Ratios Industry Average Activity Ratios HQN Base Goal Seek
Solvency
TIE 2.50 1.38 1.35 1.38
DSR 1.40 1.03 1.02 1.03
Profitability
ROA 3.30% 6.60% 6.50% 6.60%
ROE 10.70% 9.00% 8.50% 9.00%
m margin 29.00% 0.45% 0.43% 0.45%
Efficiency
ITO 7.7 10.67 10.67 10.67
ITOT 47.4 34.21 34.22 34.21
ATO 3.2 4.00 4.00 4.00
ATOT 114.1 91.23 91.25 91.23
RTO 11.41 24.40 24.39 24.40
RTOT 32 14.96 14.97 14.96
PTO 12.59 9.33 9.33 9.33
PTOT 29 39.11 39.12 39.12
Liquidity
Current Ratio 1.30 1.06 1.06 1.06
Quick Ratio 0.70 0.43 0.43 0.43
Leverage
Debt/Assets 0.91 0.80 0.80 0.80
Debt/Equity 2.00 4.00 4.00 4..00
Asset/Equity 2.20 5.00 5.00 5.00
Note that increasing CR from landscaping services to $39,000 resulted in an increase of ROE to 9.00%. Of course, there were other consequences. ROA increased to 6.6%. The TIE solvency ratio increased slightly from 1.35 to 1.38. These and other changes we observe by comparing the activity and goal seek columns with the HQN base column. Creating Subsystems It is important to be able to answer what if and how much questions, especially about such important endogenous variables as ROE in a smaller system than the CFS. We create subsystems by redefining the boundaries between exogenous and endogenous variables in the system. To simplify the connections between exogenous and endogenous variables in systems, we define subsystems and ask what if and how much questions about the subsystems. We create a subsystem by redefining some endogenous variables in the system as exogenous variables. This permits us to examine the consequences of particular shocks on a reduced number of particularly interesting endogenous variables. We can construct a large number of subsystems. However, we focus on the two subsystems that matter most to the firm: those that describe the firm’s ROE and its solvency. To illustrate, suppose we wanted to build a subsystem around the firm’s ROE. Letting letters represent system endogenous variables, we might begin by assuming that the firm sells each item of what it produces at an exogenously determined price p, that its marginal cost is c, its fixed overhead expenses (OE) cost is b, and that its interest costs are iD where i is the average cost of its debt and D is the sum of the firm’s liabilities determined in the previous period. Finally, letting the number of physical units sold equal S, we define our ROE subsystem by assuming all other variables except ROE to be exogenous. We have now created an ROE simplified subsystem. We define Earning Before Taxes (EBT) in the subsystem as: (6.1) Now we can write the ROE subsystem as: (6.2) Having defined an ROE subsystem, we are prepared to ask what if questions such as: what would happen to the firm’s ROE if we could increase the ATO by increasing cash receipts? Since our subsystem has defined all of the interdependencies, we can find the answer to this what if question by observing the change in the firm’s ROE in response to changes in the system’s exogenous variables. We illustrate the approach using HQN’s data. Initially, HQN’s ROE equals: (6.3) Suppose the value of the exogenous variable cash receipts increased to$40,100? The results on the firm’s ROE can be found to equal:
(6.4)
Another subsystem might involve solvency and the TIE ratio. To analyze this subsystem, we begin with the simplified EBT subsystem defined earlier and remove interest costs to obtain earnings before interest and taxes (EBIT) equal to:
(6.5)
Next we write a DuPont type equation focused on TIE equal to:
(6.6)
where DE is the debt-equity leverage ratio. Having now defined a solvency subsystem reflected by the firm’s TIE ratio, we can ask the following what if question. What if the firm increased its debt D? Then, what would be the effect on the firm’s solvency? To answer this what if question, we substitute the simplified EBIT formula into Equation \ref{6.10} to obtain:
(6.7)
To illustrate, we substitute HQN’s data into Equation \ref{6.11} to find its initial TIE value. Making the substitution we find:
(6.8)
Now suppose we ask: what if the firm’s equity falls by $1,000? In response to this change in an exogenous variable, HQN’s TIE ratio would decline to: (6.9) And what if the firm’s interest rate increased by one percent to 7.0%? Then its TIE ratio becomes: (6.10) It is important to recognize that the answers to our what if questions answered in our subsystems are only approximations of what would happen if we considered the entire system. Nevertheless, the subsystem approach provides some useful intuitive explanations that may be disguised in a full system analysis. So what have we learned? We learned that open systems like CFS require endogenous variables whose values are determined with the system and exogenous variables who values are determined outside the system. However, systems and subsystems are arbitrary constructs, and we can create open subsystems including one that describes the firm’s ROE and TIE ratios by arbitrarily defining some exogenous variables. Common Size Balance Sheets and Common Size Income Statements When comparing financial statements across time and across firms, it is often useful to standardize the statements. The typical way this is done is by expressing all items in the balance sheet as a percentage of total assets and all items in the income statement as a percentage of total revenue. Common size balance sheets and common size income statements facilitate comparison across time and across firms because absolute size effects are eliminated by expressing numbers in the statements as percentages of the same whole. One of the significant advantages of common size balance sheets and common size income statements is that they allow all items in either the balance sheet or income statement to be compared to an industry standard. There is one other thing, however, that happens when we convert balance sheets and income statements to ratios reflecting a percentage of the whole: all the variables in the statements become interdependent—an increase in one variable requires decreases in other variables in the statements because their sum must equal 100%. Furthermore, this requirement that they sum to 100% creates a type of closed system in which all the entries except one sum to 100%. This enables us to do trade-off analysis. Consider what we can learn from common size balance sheet statements. Suppose that a firm’s cash position was$100,000 at the end of 2017 and $110,000 at the end of 2018. In addition, suppose the firm’s total assets were$2,000,000 at the end of 2017 and $3,000,000 at the end of 2018. The absolute value of the firm’s cash position increased by$10,000 over the year which might suggest the firm is now more liquid. However, the firm’s cash position must now support a larger amount of total assets. Looking at the cash position as a percentage of total assets, we find the firm’s cash position was 5% of total assets at the end of 2017, and only 3.67% at the end of 2018. Thus, the amount of cash available per dollar of assets held by the firm actually decreased during the year. Common size balance sheets for HQN are presented in Table 6.7.
Table 6.6. Common Size Balance Sheets for HQN
2016 2017 2018 Ind. Ave.
ASSETS
Cash and Marketable Securities 12.13% 9.30% 5.77% 6.3%
Accounts Receivable 15.77% 16.40% 11.54% 26.4%
Inventory 31.85% 37.50% 50.00% 25.6%
CURRENT ASSETS 59.76% 63.20% 67.31% 58.3%
Depreciable long-term assets 33.06% 29.90% 26.92% 35.7%
Non-depreciable long-term assets 7.18% 6.90% 5.77% 6.0%
LONG-TERM ASSETS 40.24% 36.80% 32.69% 41.7%
TOTAL ASSETS 100.00% 100.00% 100.00% 100.00%
LIABILITIES
Notes Payable 4.16% 15.00% 12.21% 13.9%
Current Portion LTD 7.085% 5.00% 4.33% 3.6%
Accounts Payable 24.27% 30.00% 38.46% 18.7%
Accrued Liabilities 8.80% 9.58% 8.46% 6.8%
CURRENT LIABILITIES 54.30% 59.58% 63.46% 43.0%
NON-CURRENT LONG-TERM DEBT 25.88% 20.42% 19.09% 13.4%
TOTAL LIABILITIES 80.18% 80.00% 82.55% 56.4%
Equity 19.82% 20.00% 17.45% 43.6%
TOTAL EQUITY 19.82% 20.00% 17.45% 43.6%
TOTAL DEBT AND EQUITY 100.00% 100.00% 100.00% 100.00%
Entries in HQN’s common size balance sheet can be examined by comparing them with other firms in the industry described in the last column of Table 6.7. HQN’s level of current assets is above the industry average and rising, primarily as a result of relatively high and increasing inventory levels. The accounts receivable levels are low in terms of the industry levels. Long-term asset levels are also low, relative to industry levels, and declining. Current liabilities are well above the average levels in the industry, and rising mostly as a result of increasingly high levels of accounts payable. Although falling, long-term debt is still above industry averages. Owner equity levels are well below the average firm in the industry.
Common size income statements. Entries in HQN’s common size income statement can be examined by comparing them with other firms in the industry described in the last column of Table 6.8. Consider what we might learn from HQN’s common size income statements. HQN’s cost of goods sold (COGS) as a percentage of cash receipts in 2018 was close to the industry average. However, its overhead expenses (OE) were much higher than the industry average in both 2017 and 2018. As a result, its EBIT as a percent of cash receipts was much lower than the industry average. Furthermore, its interest costs as a percentage of cash receipts were almost double the industry average. HQN’s high OE and high interest costs relative to the industry were somewhat mitigated by HQN’s lower than industry standards depreciation and taxes. Still, HQN’s net income after taxes (NIAT) as a percentage of cash receipts in 2018 is low compared to the industry average: 0.25% for HQN versus 2.28% for the industry.
“What if” questions and the common size financial statements. Common size balance financial statements are derived from the CFS. As a result they respond to changes in endogenous and exogenous variables that make up the common size financial statements. Furthermore, we can ask what if and how much kinds of questions of the CFS and observe their changes in the common size financial statements.
For example, suppose that HQN’s cash receipts increased from $38,000 in 2017 to$40,000 in 2018. Meanwhile, suppose its COGS increased from $25,600 to$28,000. We may want to know if COGS increased in proportion to its increased cash receipts. From the common size income statement we see that as a proportion of its cash receipts, COGS increased from 67.37% in 2017 to 70% in 2018, suggesting that its COGS increased at a rate greater than its cash receipts—a result that should concern the financial manager.
Table 6.7. Accrued Common Size Income Statements for HQN
2017 2018 Ind. Ave.
Total Revenue 100.00% 100.00% 100.00%
Cost of Goods Sold (COGS) 67.37% 70.00% 71.40%
Overhead Expenses 29.82% 27.50% 22.50%
Depreciation 1.24% 0.88% 1.75%
EARNING BEFORE INTEREST AND TAXES (EBIT) 1.58% 1.62% 4.35%
Interest 1.22% 1.20% 0.55%
EARNINGS BEFORE TAXES (EBT) 0.36% 0.42% 3.80%
Taxes 0.17% 0.17% 1.52%
NET INCOME AFTER TAXES (NIAT) 0.19% 0.25% 2.28%
Common Size Statements and Trade-offs
That entries in common size statements sum to 100% means that we cannot increase one variable in the statements without decreasing another variable in the statement. Therefore, any change in an exogenous variable that affects the proportion of that variable in the common size statement will have some offsetting impact on at least one other variable in the system. We may refer to these cause-and-effect changes in exogenous variables as trade-offs. There are various ways we can describe these trade-offs.
The Squeeze versus the Bulge. One way to examine trade-offs is to assume the financial system has some characteristics similar to a balloon. If a squeeze happens somewhere on the balloon, a corresponding bulge will occur somewhere else—because balloons require equal pressure on its surface. This balloon-like characteristic is evident in common size financial statements.
For example, suppose the firm wishes to increase its liquidity and so increases the percentage of its assets held as accounts receivable. However, if the percent of assets must add to 100%, increasing the percentage of short-term assets will require that the percentage of long-term assets decrease—and profitability and perhaps efficiency suffers.
CFS and trade-offs. Trade-offs are obvious within common size statements. They exist within the CFS system but may be less obvious. Some usual trade-offs are summarized in the table the follows. Consider the left-hand column as the “squeeze” and the right-hand column is a possible “bulge.” However, the “squeeze” and “bulge” comparisons described below are only qualitative possibilities. To find out the quantitative connections, we must look at the firm’s ratios and common size statements. Still, the principle is important: when analyzing the firm by examining a particular ratio, look for its companion ratio.
Table 6.8. The Squeeze vs. The Bulge
The Squeeze The Bulge
leverage ratio (D/E): High rate of return on equity (ROE): High
cash receipts/inventory ratio (ITO): High cash receipts/accounts receivable (RTO): Low
cash receipts/inventory ratio (ITO): Low profit margin (m): Low
current assets/current liabilities ratio (CR): High rate of return on equity (ROE): Low
cash receipts/assets ratio (ATO): High operating and repair: High
COGS/notes payable (PTO): High interest costs: High
Companion ratios. We apply the principle of looking for interesting things in pairs to HQN. Is anything else unusual about HQN? Yes! Look at its inventories in the common size balance sheet: 50% of its assets in 2018 versus an industry average of 25.6%. We have found a squeeze. The bulge? Look at accounts receivable: 11.54% versus an industry standard of 26.4%. Does this suggest that the firm has adopted a stringent credit policy that has discouraged customers? Perhaps. It’s an area the firm should likely explore. If HQN’s stringent credit policy were indeed affecting cash receipts, then its inventory turnover ratio (ITO) would be affected, but this ratio isn’t too far out of the ordinary: 10.67% versus the industry median of 7.7%. However, the upper quartile for the industry is 14.9%, suggesting a large variability for the industry. So, the firm’s credit policy is not off the hook yet.
Anything else unusual about HQN? Well, yes. Its debt to equity ratio is 4.0 in 2018 versus the industry average of 1.9. Unfortunately for HQN, a high leverage ratio hasn’t increased profits or rates of return as much as might be expected because of its low efficiency and possibly an ineffective cash receipts strategy. Continuing, if HQN has unusually high levels of debt relative to its equity, we should expect its interest payments to be above the industry average. They are 1.2% of cash receipts in 2018 versus an industry average of .55%. Already we are alarmed; high leverage is usually accompanied by high risk. One reason that high leverage implies high risk is that the firm’s equity relative to its liability is small, and not able to handle and survive a market reversal. Is HQN’s equity low relative to the industry? Very much so: 17.45% in 2018 versus the industry average of 43.6%.
Trend Analysis
Using historical data, we attempt to look ahead to financial conditions likely to be experienced in the future. Consider the common size balance sheets reported earlier in Table 6.7. The first step is to look for any significant changes or trends in the asset or liability accounts. Current assets have increased over the three year period mostly due to a significant increase in inventory levels. Cash levels declined during the three years for the same reason—current assets being tied up in inventory. Long-term assets have fallen primarily as a result of declining values of the firm’s property, plant, and equipment. The worrisome result of this trend is that it may project increased maintenance costs associated with aging machinery.
On the debt side of the balance sheet, current liabilities have increased during the three year period mostly as a result of increases in accounts payable. Long-term debt has declined, and owner equity has remained relatively constant. The question associated with this trend is, can increasing dependence on notes payable be sustained? Are there less expensive sources of financing available?
Examining HQN’s common size income statement, reported in Table 6.8, we see that both EBIT and NIAT increased in 2018 as a percentage of cash receipts. Comparing HQN’s income statement with other firms in the industry, we note that HQN’s EBIT and NIAT were low compared to industry averages, primarily as a result of relatively high overhead expenses and interest expenses. High OE, COGS, and interest costs have reduced HQN’s taxes.
The statement of cash flow in Table 6.9 confirms that cash levels in the firm have been declining. However, cash flow from operations was positive in both 2017 and 2018. The firm had positive income and additional cash flow was generated by depreciation expense and increases in current liabilities. A large cash inflow was also received in 2017 as a result of a decrease in accounts receivable. One salient point is that the firm sacrificed significant amounts of cash in 2017 and 2018 to increase inventory levels.
Table 6.9. HQN’s Coordinated Financial Statements for Year 2018 after a cash receipts change in an exogenous variable
BALANCE SHEET ACCRUAL INCOME STATEMENT STATEMENT OF CASH FLOW
DATE 12/31/2017 12/31/2018 DATE 2018 DATE 2018
ASSETS + Cash Receipts $39,990 + Cash Receipts$39,990
Cash and Marketable Securities $930$1,600 + Change in Accounts Receivable ($440) Cash Cost of Goods Sold$27,000
Accounts Receivable $1,640$1,200 + Change in Inventories $1,450 Cash Overhead Expenses$11,078
Inventory $3,750$5,200 + Realized Cap. Gains/Depr. Recapture $0 Interest paid$480
Current Assets $6,320$7,000 Total Revenue $41,000 Taxes$68
Property, Plant, and Equipment $2,990$2,800 + Cash Cost of Goods Sold $27,000 Net Cash Flow from Operations$1,364
Other Assets $690$600 + Change in Accounts. Payable $1,000 + Realized Cap. Gains + Depr. Recapture$0
Long-Term Assets $3,680$3,400 + Cash Overhead Expenses $11,078 + Sales Non-depreciable Assets$0
TOTAL ASSETS $10,000$11,400 + Change in Accrued Liabilities ($78) Purchases Non-depreciable Assets LIABILITIES + Depreciation$350 + Sale Depreciable Assets $30 Notes Payable$1,500 $1,270 Total Expenses$39,350 Purchases Depreciable Assets $100 Current Portion Long-Term Debt$500 $450 Earnings Before Interest and Taxes (EBIT)$1,650 Net Cash Flow from Investment ($70) Accounts Payable$3,000 $4,000 Less Interest Costs$480 + Change in Non-Current Long Term Debt ($57) Accrued Liabilities$958 $880 Earnings Before Taxes (EBT)$1,170 + Change in Current Portion of Long Term Debt ($50) Total Current Liabilities$5,958 $6,600 Less Taxes$68 + Change in Notes Payable ($230) Non-Current Long Term Debt$2,042 $1,985 Net Income After Taxes (NIAT)$1,102 Less Dividends and Owner Draw $287 Contributed Capital$1,900 $1,900 Less Dividends and Owner Draw$287 Net Cash Flow from Financing ($624) Retained Earnings$100 $915 Addition to Retained Earnings$815 CHANGE IN CASH POSITION $670 Total Equity$2,000 $2,815 TOTAL LIABILITIES AND EQUITY$10,000 $11,400 Cash was used each year to increase investments in long-term assets. However, the amount of assets used each year was significantly greater than the amount reinvested in long-term assets. For example, in 2018 the firm used up$350 in assets (the amount of depreciation expense) and only had a net investment of $70,000, a depletion of$280,000 in the firm’s assets.
Cash was also used each year in the firm’s financing activities. The firm made a large payment of long-term debt in 2017. Then in 2018, a large equity withdrawal was made. Both of the payments were larger than the cash flow produced out of the firm’s operations.
Common Size Statements and Pro Forma Financial Statements
Consider how financial managers can use financial ratios to forecast the financial condition of the firm by asking what if questions whose answers produce pro forma balance sheet and income statements. Financial forecasting is a method used by firms to help plan for future financial needs. However, using pro forma income statements and pro forma balance sheets both require that each one is defined as a subsystem.
Pro forma income statements and balance sheets are forecasts of what these statements will look like in the future and provide essential planning information. There are several ways to construct pro forma statements. The usual technique is to select a key variable and predict its future value. Then assume constant SPELL ratios which include the key variable and solve for other values using other ratios. We demonstrate this approach in what follows.
Assume that HQN wants to achieve a projected level of cash receipts. Also assume that SPELL ratios will remain constant even in the face of projected total revenue increases. Specifically, assume that next year’s projected total revenue for HQN will equal $42,000, an increase of 5%. What does this imply for HQN’s level of inventory? From HQN’s financial ratios, we see that the inventory turnover ratio was 10.67%. Assuming that this year’s ratios will hold next year, we can use the projected level of cash receipts to forecast the pro forma levels of inventories (INV). The first step in these types of problems is to write out the definition of each ratio and their assumed values: (6.11) From the inventory turnover (ITO) equation we find: (6.12) Next we use the projected cash receipts level of$42,000 and divide by ITO to find projected HQN’s inventory in 2019:
(6.13) | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/06%3A_System_Analysis.txt |
Learning Objectives
At the end of this chapter, you should be able to: (1) properly construct a present value (PV) model; (2) understand the need for homogeneous measures when building PV models; and (3) describe PV model dimensions that require homogeneous measures.
To achieve your learning goals, you should complete the following objectives:
• Define PV models and describe their uses.
• Learn how to compare challenging and defending investments.
• Learn how to convert a challenging investment’s future earnings and costs to their value in the present.
• Learn how to represent the cost of sacrificing a defending investment by using its internal rate of return (IRR).
• Learn about PV model dimensions that require homogeneous measures to accurately and to consistently compare investments.
Introduction
Firm managers either continue their commitment to an existing investment called a defender or disinvest in the defender and commit to a new investment called a challenger. The financial manager’s assignment is to analyze and to rank defenders and challengers. What adds complexity to the ranking process is that defenders and challengers are sometimes measured in different units. These differences in measures between challenging and defending investments may result in unstable and inconsistent rankings when more than one ranking method is used. This chapter intends to describe present value (PV) models that consistently and accurately rank defending and challenging investments using homogeneous (same) measures.
What is a Present Value (PV) Model?
A PV model is a mathematical expression that represents the value of future cash flow in present dollars. The present value of future cash flow earned by a challenging investment exchanged at the discount rate equal to the defender’s IRR is called net present value (NPV). The NPV of the future cash flow of an investment discounted by its own IRR is zero.
To rank uniquely a defending and challenging investment requires that we reduce their current and future earning to a single number in the same period. To make this point, that ranking investments uniquely requires a one-dimensional measure, assume that we determine the winner and loser of a sporting event by several different measures. For example, suppose that the winner of the Super Bowl football game depended on the following measures: points earned, yards gained, yards earned on the ground divided by the yards earned passing, yards penalized, injuries sustained, and the number of persons viewing the contest. Most football sports fans would agree that the success measures just described matter—but we will never determine who wins and who loses with such multidimensional measures unless in some rare event one team dominated in all dimensions. So, we must decide which measure matters most and in the case of football—the measure that matters most is points earned.
To avoid the indecisiveness of a multi-dimension metric when ranking investments, we convert future cash flow to the present creating a one-dimensional number that allows us to rank investments uniquely.
The Need for Homogeneous Measures
The idea that future cash flow can be valued by its worth in the present period may be one of the most important and pervasive concepts in financial management. It is the basis for ranking physical investments and for valuing bonds, stocks, insurance, pension funds, housing, land, cars—and almost anything that has more than one period of economic life generating cash flow.
We might have hoped that converting investments’ future cash flow to their value in the present would produce one agreed on method for valuing investments. It has not—because PV models have several dimensions and PV models have only resolved differences in measurement for one dimension—time. Other dimensions such as investment size, term, loan terms, taxes, measures of return, liquidity, and risk also require that we measure them using the same—homogeneous—measures before we can rank investments consistently and accurately.
To make the point that a lack of homogeneous measures may create ranking conflicts, compare ranking investments to a horse race. We organize horse races so that other factors besides the horses’ speed do not influence the horse race outcome. For example, we expect that only horses enter the race. We require that the horses all begin the race at the same time and place. We expect that all horses will run the same distance—that implies that not only has the starting point been determined but the finish line as well. Finally, we expect that everyone agree that the criterion for ranking horses is the time interval between when each horse starts and finishes the race.
Ranking investments is, of course, not a horse race. Yet, the process of ranking investments according to their earnings and horses according to their speed have many elements in common. First, we assume that we are comparing investments of the same size (only horses run the race). We also assume that we are comparing investments over the same time-period, term, (the length of the race is the same for all horses). Finally, we assume that the criterion used to rank investments (present value) would provide the same rankings for each investment just as the time required to run the race would be used to rank the speed of the horses.
In the remainder of this chapter and in the following chapters, we focus on several PV model dimensions that must be measured the same, homogeneously, so that our investment rankings will be consistent and accurate.
Homogeneous Time Measures
The first and most important homogeneous measure requires that investment cash flow from defenders and challengers be measured in present dollars. Creating homogeneous time measures by discounting future cash to flow to their value in the present is in essence what PV models achieve. They convert future cash flow to equivalent values in the present. But how do we find the present value of future cash flow? The key is to recognize that prices, including the price of future dollars valued in the present, are ratios. Ratios tell us the per unit value of what is in the denominator. For the ratio A/B, the ratio tells us the number of units of A for one unit of B.
To illustrate, consider the price of a tank of gas. To calculate the price per gallon of gasoline, we divide the money paid for a tank of gas (A) by the gallons of gas purchased (B). The ratio tell us the per unit price of a gallon of gasoline. If the ratio (money paid)/(gallons of gas purchased) were ($20) / (10 gallons) =$2.00, we would say that the price of a one gallon of gasoline is $2.00. Exchanging future dollars for a present dollar. Now consider a special kind of ratio that describes the rate at which we exchange present dollars (A) and future dollars (B) between time-periods. We exchange present and future dollars every time we lend or borrow money, make or liquidate an investment, or invest in or withdraw money from a retirement account. To illustrate, suppose I borrow (lend) present dollars V0 (A) now and in one year from now, I repay (receive) future dollars R1 (B) where the subscript indicates the end of the time-period in which the cash flow occurs. The result of the division (A/B) is equal to (1 + r) where r is expressed as a decimal because the dollar units in the ratio cancel. Thus, the ratio of A/B or future dollars to present dollar is equals to 1 plus r percent: $\frac{R_{1}}{V_{0}}=(1+r)\label{7.1}$ Using our convention for describing ratios, we would describe Equation \ref{7.1} as follows: (1 + r) future dollars can be exchanged for one present dollar or that a present dollar is compounded to its future value at the rate of r percent. To illustrate, suppose V0 equals$100 and R1 equals $110. In this example the ratio of future to present dollars is:$110/$100 = 110%, and we could say that one present dollar can be exchanged for$1.10 future dollars. Sometimes we simply say that one dollar in the present can be compounded to 1.10 future dollars.
Were we to describe the ratio of future dollars for present dollars, we would say $1.00 future dollar can be exchange for 1/(1 + r) present dollars. $\label{7.2} \frac{V_{0}}{R_{1}}=\frac{1}{(1+r)}$ To illustrate, suppose V0 equals$100 and R1 equals $110. In this example the ratio of present to future dollars is$100/$110 =$0.91 and we could say that one future dollar can be exchanged for $0.91 present dollars. Sometimes we say that one dollar in the future can be discounted to 0.91 present dollars. At this point, it may be useful to explain the use of the variable r. It appears frequently in PV models that involve comparing money across time. In its most general use, it is a percent or a rate. It could be the market rate of interest. It could be the rate of interest earned on one’s assets or equity. Or it could be the rate charged on loans, of which there are several. We will try to make it clear which rate r refers to and in some cases add a superscript to r to clarify. For example, the market rate of interest is defined as rm. If we want to refer to r in a particular period, we would subscript it with the appropriate time-period. The rate r in the tth period could be written as rt. Exchanging present dollars for a future dollar over more than one period. If we know the exchange rate between present and future dollars, then it is a small step to convert present dollars to their equivalent in the future or to convert future dollars to their equivalent in the present. We simply multiply by the appropriate ratio. To convert present dollars to their future value we multiply by (1 + r). $\label{7.3} V_{0}(1+r)=R_{1}$ To convert future dollars to their value in the present we multiply by 1/(1 + r). $\label{7.4} V_{0}=\frac{R_{1}}{(1+r)}$ This last ratio, the present value of future cash flow, is of particular interest. We find this ratio to be of special interest because, as was mentioned earlier, we live and make decisions in the present. Thus, converting future cash flows to their equivalent present value makes it possible to evaluate capital budgets with future consequences in terms of present dollars. To summarize, using numbers from our previous example where r = 10% or .1, the future value of$100 is $100(1.1) =$110. The present value of $110 future dollars is$110[1/1.1)] = $100. Completing the gasoline purchase analogy, if the price of gasoline were$2 per gallon, we might ask how much will 10 gallons of gasoline cost? Ten gallons times $2 is equal to$20. Or we might ask how many gallons of gasoline can I purchase for $20? Twenty dollars divided by$2 is equal to 10 gallons.
To illustrate the importance of calculating the present value of future cash flow, suppose that a “down-on-her-luck friend” approaches you. She explains that her wealthy aunt has promised her $100 in one year, but she needs the money now. She asks you what you would offer in present dollars in return for her future$100 dollars. You quickly calculate (assuming an exchange rate of 110%), and report that the present value of $100 future dollars (received in one period from now) is$90.91. Or, we might say that the discounted present value of $100 future dollars is$90.91.
Just as we found the present value of one period in future dollars, we can also find the present value of future cash flows received in two or more periods in the future. Returning to our earlier example, suppose this same down-on-her-luck friend offers you R1 dollars in one period and R2 dollars two periods in the future and asks how many present dollars would you offer for the exchange if the exchange rate is 1 + r.
We can find the present value of R2 in two steps. First, convert R2 to its equivalent value in period-one dollars by using the ratio [R2/(1 + r)]. The important point is that the exchange rate is assumed to be (1 + r) between any two periods, including between periods one and two. Next, discount period one dollars to their equivalent in the present:
$V_{0}=\frac{\left[R_{1}+\frac{R_{2}}{(1+r)}\right]}{(1+r)}=\frac{R_{1}}{(1+r)}+\frac{R_{2}}{(1+r)^{2}} \label{7.5}$
We would follow a similar procedure to find the present value of dollars received in three periods from the present. Suppose you were offered $100 for the next three periods. What is the present value of these future cash flows if the exchange rate were 110 percent between any two periods? The answer is: $V_{0}=\frac{\ 100}{1.1}+\frac{\ 100}{1.1^{2}}+\frac{\ 100}{1.1^{3}}=\ 90.91+\ 82.64+\ 75.13=\ 248.68 \label{7.6}$ In the remainder of this book, models which evaluate financial strategies by converting future cash flows to their equivalent in the present are referred to as PV models. So what have we learned? We learned that we can find the value of future dollars in the present by discounting them using one plus the appropriate discount rate r. Furthermore, we can find the value of present dollars in the future by compounding then using one plus the appropriate discount rate r. All this assumes, of course, that the exchange rate of dollars between time periods is a constant r. Homoegenous Measures and Cash Flow The second homogeneous measure required when building a PV model is to represent economic activities of the firm by their cash flow. In our horse race analogy, the cash flow principle is equivalent to letting only horses run the race. Some activities of the firm we characterize as noncash flow such as appreciation (depreciation) of assets, increases in inventories of unsold goods, and increases in accounts receivable and payable. But these events are not included in PV models because they do not produce cash flow. One justification for the cash flow principle is that, at some point, we expect all economic activities to generate cash flow. At some point, we expect inventories to be liquidated and generate cash. At some point, we expect accounts receivable and accounts payable to be settled for cash. At some point we expect long-term assets that have appreciated (depreciated) to be sold and the difference between their acquisition and sale price to capture the noncash flow of depreciation (appreciation). Thus, in effect, we do count all economic activities of the firm by recognizing only cash flow; however, we count them only when they create cash flow. Defenders and Challengers and Homogeneous Measures The defender’s opportunity cost. An opportunity cost is a benefit, profit, or value of something that must be given up to acquire or achieve something else. A PV model compares the returns from a defender that must be sacrificed to acquire the challenger with the returns from the challenger. Both the opportunity costs of the defender and the returns from the challenger must be measured in homogeneous units. To represent what we sacrifice by liquidating the defender to purchase the challenger, we find the defender’s internal rate of return (IRR) r that equates the defender’s discounted future earnings to its liquidated value in the present. We represent this trade-off in Equation \ref{7.7}. In this equation, Rtt = 1, …, n are the defender’s cash flow in period t if it were not liquidated. The variable Sn is the defender’s liquidation value assuming it would be held for n periods. And, V0 is the present value of the defender’s future cash flow and liquidation value exchanged for present dollars at rate r: $V_{0}=\frac{R_{1}}{(1+r)}+\frac{R_{2}}{(1+r)^{2}}+\dots+\frac{R_{n}}{(1+r)^{n}}+\frac{S_{n}}{(1+r)^{n}} \label{7.7}$ The discount rate r is the opportunity cost of the sacrificing the defender to acquire the challenger measures as a percent. Another way to describe the defender’s opportunity cost is to describe it as the exchange rate between the defender’s present and future dollars. Prices are not opportunity costs. The price of a good is the amount of money, or money equivalent, paid to obtain it. The amount of money or money equivalent paid to obtain the good represents the direct cost of what is given up to obtain something desired or to avoid something disliked. However, there may be other costs to acquire a good—or to avoid a bad—besides the price paid. For example, one might consider the cost of attending a movie to be the price of the ticket. However, transportation costs to and from the theater could add to the actual value of what must be exchanged to attend the movie. And there may be other costs of attending the movie such as lost earnings as a result of missing work. Suppose the movie was playing at the same time that the moviegoer ate his or her prepaid dinner meal. Now the cost of the movie includes not only the price of the ticket plus transportation costs and lost wages but also the value of the skipped meal. The cost of the ticket, transportation costs, lost wages, and the skipped meal together represent the opportunity cost of attending the movie, which is different from the price of the movie ticket. So what have we learned about opportunity costs? If we consider only the prices paid for goods and services as costs, we may underestimate true costs, the opportunity costs. When we consider attending a movie, making an investment, or taking out a loan, we should be careful to measure the opportunity costs of these investments. These opportunity costs will be expressed as the rate at which we exchange present dollars for future dollars. Opportunity costs and perfect capital markets. The capital (or financial) market is where people trade today’s present dollars for future dollars and vice versa. In a perfect capital market, dollars trade between adjacent time-periods at the (same) market rate of interest rm. For a perfect capital market to exist, the following conditions are required: no barriers to entry; no participant can influence the price; transactions are costless to complete; relevant information about the market is widely and freely available; products and services are homogeneous; no distorting taxes exist; and investment possibilities are continuously divisible. Finally, the firm’s opportunity cost of capital is the same regardless of the size or purpose of the amount being borrowed or lent. Though markets for some financial investments are considered highly efficient, they are not perfect. Rates of return on savings rarely equal the rate paid to borrow funds. Moreover, rates of return on investments typically depend on the size and economic lifetime of the investments. Hence, in the real world, investors face imperfect capital markets. We allow for imperfections in capital markets in our PV models by allowing the rate of return on an investment being considered for adoption, a challenger, to differ from the rate of return on an investment that must be sacrificed to adopt the challenger, a defender Defenders may include investments that must be liquidated, investments that must be foregone, or credit reserves (unused borrowing capacity) that must be exchanged for debt funds. Thus, an interest rate on a loan equals the opportunity cost of capital on a defender only if the credit reserve used up has no value. In imperfect markets, the opportunity cost of the defender and the market rates of interest on loans are rarely equal. Since PV models focus on retaining the defender or acquiring the challenger, deciding between them requires that they be measured in the same homogeneous measures. Indeed, as we will show in later chapters, one reason why PV models may rank challengers and defenders inconsistently is because they fail to measure them in homogeneous measures. This point is so important that we will discuss it in more detail in later chapters. The focus on homogeneous measures leads us to consider other principles that will guide us when constructing PV models. Homogeneous Rates of Return Measures Another homogeneous measure is the rate of return measures used in PV models. The homogeneity of returns measure requires that if the return to the challenger is measured as a return to equity invested, then the discount rate that measures the defender’s opportunity cost must also measure the defender’s return on equity invested. If the return to the challenger is measured as a return on the investment, then the discount rate that measures the defender’s opportunity cost must also measure the defender’s return on the investment. The return on the investment (ROI) corresponds to the return on assets (ROA) when describing a firm. To avoid confusion we will describe the rate of return on equity in the investment or in the firm as ROE. And we will describe the return to the firm’s assets or investment as ROA. So how do we build PV models that homogeneously measure returns on assets, ROAs, and returns on equity, ROEs? We begin by finding ROAs. When finding the ROA for the defender, we ignore cash flow that includes borrowing or lending activities. The advantage of this approach is that it measures the rate of return on assets independent of the returns from the loan used to finance the investment. We write the defender’s cash flow and its corresponding IRR that measures ROA as: $V_{0}=\frac{\left(R_{1}+S_{1}\right)}{(1+R O A)} \label{7.8}$ Where V0 is the initial investment, R1 is net cash flow earned in the first period, and S1 is the liquidation value of the investment after one period. Then we write the ROA as: $\label{7.9} R O A=\frac{R_{1}+\left(S_{1}-V_{0}\right)}{V_{0}}$ Interpreted, Equation \ref{7.9} equates ROA to cash returns R1 plus the cash value of capital appreciation (depreciation) equal to the difference between the liquidation value and the beginning value of the asset all divided by the beginning value of the asset. It measures the rate of returns on all of the firm’s assets including returns generated by human capital, manufactured capital, social capital, natural capital, and financial capital. Why would we want to exclude earnings from debt capital while including earnings from other forms of capital? To do so would overstate or understate the earnings generated by the other forms of capital. This is the argument for accounting for cash flow associated with debt capital, an approach consistent with the calculation of the return on equity. To measure the rate of return on the firm’s equity, we pay the cost of debt used to finance the firm’s assets—netting out the contributions of debt capital. We calculate the firm’s rate of return on its equity (ROE). To include cash flow associated with debt capital, assume that an asset is acquired using debt D0 plus equity E0 whose sum is equal to V0. At the beginning of the project, the firm supplies equity capital to purchase the investment creating a negative cash flow of E0 dollars in the beginning period. Then it receives D0 from the lender and pays D0 to the seller to complete the purchase of the investment. The receiving and paying debt capital D0 at the beginning of the period cancel out making net cash flow from debt capital at the beginning of the investment zero. At the end of the period, the investment repays debt capital D0 plus interest iD0 to the lender. Thus at the end of the period, cash flows of D cancel each other out. Thus, we can express these cash flow as: $\label{7.10} E_{0}=\frac{R_{1}-i D+S_{1}-D_{0}}{(1+R O E)}$ And we can write the ROE as follows: $\label{7.11} R O E=\frac{R_{1}-i D+S_{1}-D_{0}-E_{0}}{E_{0}}$ We are interested in the relationship between ROA and ROE. To determine that relationship, we first solve for R1 in Equation \ref{7.9} and find that it equals: $R_{1}=(R O A) V_{0}-\left(S_{1}-V_{0}\right) \label{7.12}$ Then we make the substitution for R1 in Equation \ref{7.11} and obtain the result: $\label{7.13} R O E=\frac{(R O A-i) D_{0}}{E_{0}}+R O A$ What Equation \ref{7.13} reveals is that ROE > ROA as long as the firm earns a positive return on its debt capital (ROA > i) confirming an earlier result. The cash flow principle requires that careful distinction be made between a cash transaction and a noncash transaction. Sometimes the distinction is not always clear. For example, an asset’s book value depreciation does not itself generate a cash flow. Depreciation expenses of an investment do, however, generate a tax shield that creates a cash flow in the form of reduced tax payment. Thus, we include the cash flow associated with tax savings resulting from depreciation of an asset but not the depreciation. Increased inventories of unsold goods do not create a cash flow. However, when the inventory is liquidated at the end of the period, it is converted to cash and enters in the present value calculations. Total Costs and Returns Measures All cash costs and cash returns associated with an investment should be included when determining an investment’s present value. Consider how the total costs and returns principle is applied in several practical situations. Whenever low-interest loans or preferential tax treatments are tied to the ownership of a durable, these concessions will influence the present value of the investment. To ignore these benefits (costs) would lead to an under or over evaluation of the worth of the investment. Sometimes an investment such as land has more than one source of returns. Mineral deposits, potential recreational use, and urbanization pressures may create expected returns over and above those associated with agricultural use. Pollution standards may impose costs in addition to those normally experienced. All these expected cash costs and returns that influence the value of the durable should be included in the PV model. Other Homogeneous Measures We require that cash flow associated with both the challenger and defender be measured in homogeneous units. Therefore, we have discussed the requirement that their returns both be measured in the present time period and that only cash flow be included when measuring economic activities of the defender and challenger. There are at least four other homogeneous measure requirement that are so important that we devote a chapter to each one. • Homogeneous size measures (Chapter 9) require that initial and periodic investment sizes for challengers and defenders must be equal. • Homogeneous term measures (Chapter 10) require that the defenders and challengers experience economic activity over equal terms. • Homogeneous tax-rate measures (Chapter 11) require that we account for differences in effective tax rates for defenders and challengers that depend on cash flow patterns and capital gains (loses). • Homogeneous profit measures (Chapter 12) require that we calculate rates of return in PV models and AIS following the same (homogeneous) methods. • Homogeneous investment measures (Chapter 13) recognize that PV models may be constructed for an incremental or a stand-alone investment, and homogeneity of investment types requires that both the defender and challenger are either incremental or stand-alone investments. • Homogeneous liquidity measures (Chapter 14) recognize that firms and investments can be differentiated by their liquidity and requires that the defender and challengers are measured using consistent liquidity measures. • Homogeneous risk measures (Chapter 15) recognize that risk tolerance is different for individuals. Therefore, to measure risk in homogeneous units, we must account for influence of risk attitudes of certainty equivalent representations of risky investments. So what have we learned? To compare the value of a potentially new investment, a challenging investment, with an investment to be sacrificed, a defending investment, we need to apply homogeneous measures to both. At least seven cash flow units associated with challengers and defenders must be homogeneous (the same) in order to construct consistent PV models: (1) initial and periodic investment sizes; (2) investment terms; (3) effective tax rates; (4) rates of return; (5) investment types; (6) liquidity; and (7) risk. If the cash flow for a prospective challenger is measured in after-tax nominal values with no risk over n years with an initial investment of V0 dollars, then the defender whose ROA or ROE is used as the discount rate when calculating the challenger’s net present value (NPV) should be measured in similar units—in after-tax nominal values with no risk over n years with an initial investment of V0 dollars. Summary and Conclusions The discount rate in a PV model represents the rate of return earned by a defender. It is the rate of return sacrificed by disinvesting in the defender to acquire the challenger. The defender’s rate of return measures either its ROA or ROE. Choosing the appropriate discount rate for PV models describing a challenger is perhaps the most difficult task of investment analysis. The choice essentially involves the identification of challengers and opportunity costs associated with defenders. The relevant costs in economic models have always been opportunity costs. These costs reflect what is given up when an alternative is chosen. This chapter has examined how the calculation of opportunity costs is influenced by time. This chapter also discussed homogeneous measures that should direct the construction of PV models. They should measure cash flow in the present. We should count only cash flow when finding present values for challengers and defenders. And we should measure the defender’s opportunity cost of capital and the challenger’s cash flow as either ROA or ROE. We will devote entire chapters on special homogeneous measures such as homogeneous sizes, homogeneous terms, homogeneous tax rates, homogeneous investment types, homogeneous rates of return, homogeneous liquidity measures, and homogeneous risk measures. Our goal is that by using homogeneous measures to construct PV models we can obtain consistent, stable, and accurate investment ranking. Knowing that one’s investment rankings are stable, accurate, and consistent is essential for the success of a financial manager whose goal is to maximize the present value of the firm’s investments. Questions 1. Underlying present value (PV) analysis is the fundamental concept that a dollar today is not valued the same as a dollar received in the future. List several reasons that might explain why a dollar today may not be valued the same as a dollar in the future. 2. The idea that the value of a good today is not the same as the value of the good in the future is a universal concept. Suppose you were offered a 2018 Ford F-150 pickup truck for delivery today or the same truck in exactly the same condition delivered in 2023. What would you offer for the truck today versus what you would offer for the identical truck delivered in 2023? If the prices you would offer are different, please explain why? 3. Building on the concept of present and future dollars, suppose that you invest$100 today. Then assume that one year later your investment returns $110 in cash. 1. What is the present value of the future earnings? 2. What is the future value of$100?
3. What is the ratio that converts dollars received one period in the future to their present value?
4. What is the ratio that converts present dollars to their value one period in the future?
5. Interpret the ratios: $100/$110 and $110/$100 in terms of the problem described above. How would you use the two ratios? (Hint: what ratio would convert a present dollar to a future dollar and what ratio would convert a future dollar to its worth in the present?)
4. Suppose you are considering a ten-day spring break vacation. Transportation, lodging, and meals will cost about $2,300. Explain the difference between the cost of$2,300 and your opportunity cost of the vacation?
5. Suppose that you invest $100 today. Then assume that one year later your investment returns$110 in cash. Assume that your opportunity cost of capital is 12%.
1. What is the present value of the future earnings?
2. What is the future value of $100? 3. What is the ratio that converts dollars received one period in the future to their present value? 4. What is the ratio that converts present dollars to their value one period in the future? 5. Compare the ratios:$100/$110 and$110/$100 in terms of the problem described in problem 3 and the ratios 1/1.12 and 1.12/1 described in this problem. What is the main difference between the problems and what difference does it make? 6. In a PV model, two investments are being compared, a defender and a challenger. Briefly distinguish between a defending and a challenging investment. Suppose you are considering replacing an aging orchard with new trees. What would be the challenging investment and what would be the defending investment? What consideration would you include when comparing a challenger and a defender? What are the possible decisions you might take in this investment problem? 7. In practice, financial managers face more complicated investment problems than deciding between a single defender and a single challenger. Describe how you might solve an investment problem with more than one challenger? One challenger but more than one defender? When choosing between multiple defenders, what would be the appropriate criterion for the preferred defender? How would you analyze a problem consisting of multiple challengers and defenders? What principle from micro economic theory might guide you in preparing your answer? 8. A financial manager believes that a defending investment can earn$500 for the next six years. He also believe that his defending investment can be sold today for $2,500. What is the opportunity cost of sacrificing the defender to invest in a challenger. In other words find the IRR of the defending investment. 9. Reconsider the defender in question 8 and suppose that the defending investment is financed by a$2,000 that does not require principle payment—only interest payments at the rate of 4% per year. Now find the rate of return on equity invested in the defender. Compare your results with those obtained in question 8 and explain the differences if they exist. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/07%3A_Homogeneous_Measures.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) identify the different kinds of present value (PV) models; (2) understand the types of questions different PV models can answer; and (3) construct PV models that represent defending and challenging investments.
To achieve your learning goals, you should complete the following objectives:
• Learn about the different kinds of PV models.
• Learn about the unique questions each kind of PV model can answer.
• Learn how to construct the following PV models:
• net present value (NPV),
• internal rate of return (IRR),
• maximum (minimum) bid (sell),
• annuity equivalent (AE),
• break-even,
• optimal life, and
• payback.
• Learn how to represent the opportunity cost of the defender using its return on equity (ROE) or its return on assets (ROA).
Introduction
Picture yourself traveling across the country driving a luxury car or a tractor. Alternatively, picture yourself pulling a plow with a luxury car or a tractor. While both a luxury car and a tractor can provide transportation and pulling services, they are not equally suited for the two assignments.
One word economists use to describe activities a firm can perform but with unequal efficiency is comparative advantage. Luxury cars are perfectly suited for traveling across country but not for pulling a plow. A tractor is well designed for pulling a plow but not for long-distance travel.
Similarly, there are several different kinds of PV models, but they are designed for answering different kinds of questions. Each model has a comparative advantage for answering a particular kind of question. In what follows we examine some of the most important PV models and the questions they can be used to answer.
Net Present Value Models
In a static (timeless) model, profits describe the difference between costs and returns. In a PV model, an equivalent concept is called the Net Present Value (NPV). The NPV measures the difference in present dollars between cash outflows and cash inflows. NPV models reveal whether the present benefits of an investment outweigh its present costs. The important difference between NPV models and profit calculations is that profits may include non-cash returns and expenses such as increases in inventory and depreciation. The numbers that enter PV models besides the discount rate and the exponents on the discount rate of dollar are cash flow measures where the liquidation value of the investment at the end of its economic life is treated as though it were converted to cash.
Suppose an investment in a challenger requires an outflow of V0 dollars and generates a positive cash flow of R1 dollars one period later plus the investment’s liquidation value S1. For now, assume that the discount rate, or the rate of exchange between present and future dollars for the defender, is r percent, and represents the opportunity cost of sacrificing the defender to invest in the challenger. To determine if the benefits of this investment outweigh the costs, we find the NPV defined as:
$\label{8.1} N P V=-V_{0}+\frac{R_{1}+S_{1}}{(1+r)}$
Suppose a challenging investment costs $100 and returns R1 =$100 and S1 = $20 in period one while the defending investment could earn r equal to 10%. Then the NPV of this investment would be: $N P V=-100+\frac{\ 100+\ 20}{1.1}=\ 9.09 \label{8.2}$ For this investment, NPV is positive, and the present value of cash benefits outweighs the present value of cash costs. Another way to describe this result is that the challenger earned a higher rate of return than the defender. How much more? The exchange rate for the challenger is ($100 + $20)/$100 = 1.20 compared to $110/$100 = 1.10 for the defender.
But what does it mean to say that the challenger earned a higher rate of return than the defender? An investment is a commitment you make to a project. If the project pays you more than the rate of return on the defender, then the investment’s NPV is positive. In our example the project pays at the rate of 20%. In NPV models, think of the discount rate as the rate earned by the defending investment. And if NPV is positive, the challenger will earn a rate of return higher than could be earned by continuing to invest in the defender.
Of course, investments can be much more complicated than described above. For example, an investment may generate (positive and negative) cash flows for n periods (R1, R2, ⋯, Rn) rather than just one period. Furthermore, most capital assets generate a positive or negative liquidation value (Sn) at the end of its economic life which should be accounted for explicitly.
Using subscripts to indicate the time periods in which the cash flows occur, we write a more complete NPV model as:
$N P V=-V_{0}+\frac{R_{1}}{(1+r)}+\frac{R_{2}}{(1+r)^{2}}++\frac{R_{n}}{(1+r)^{n}}+\frac{S_{n}}{(1+r)^{n}} \label{8.3}$
Internal Rate of Return (IRR) Models
Assume that the cash flow represented in Equation \ref{8.3} are largely determined by the market or from other sources of information and are known. But where do we find r, the opportunity cost of capital, the rate of return earned on the defender? The answer is that we set the NPV of the cash flow that describes the defender equal to zero and solve for the discount rate which we then refer to as the defender’s internal rate of return or its IRR. In such a model, the IRR will be equal to the defender’s ROE or its ROA depending on the focus of the PV model. To make clear the distinction between cash flows associated with the challenging and defending investments we adopt the following notation: we superscript cash flow for the challenger with the lowercase letter “c” and cash flow for the defender with the lowercase letter “d”.
$N P V^{d}=-V_{0}^{d}+\frac{R_{1}^{d}+S_{1}^{d}}{(1+r)} \label{8.4}$
Now set NPVd equal to zero. Such a PV model in which NPV is set equal to zero is called an Internal Rate of Return (IRR) model, and r is the rate at which dollars are exchanged between time periods for the defender. Because NPV is zero in this model, r is exactly the rate of return earned on the defending investment, the rate at which future dollars earned on the investment are exchanged for present dollars. Finally, the internal rate of return earned on the defender is what is sacrificed to invest in the challenger, and equals the opportunity cost in the NPV model. (The calculation of the defender’s IRR in multi-period models can be much more complex.) To illustrate, we solve for the rate of return earned on the defender or the IRR in the previous model. The IRR equals:
$r=\frac{R_{1}^{d}}{V_{0}^{d}}-1 \label{8.5}$
Next substitute the defender’s IRR into the NPV model of the challenger:
$N P V^{c}=-V_{0}^{c}+\frac{R_{1}^{c}+S_{1}^{c}}{(1+r)} \label{8.6}$
If the NPV of the challenger is positive, the challenger is preferred to the defender. Why? Because exchanging future dollars for present dollars at the same rate of exchange as the defender leaves the investor with a positive net present value.
Maximum Bid (Minimum Sell) Models
Different kinds of investment questions created the need for different kinds of PV models. The maximum bid and minimum sell models assume r is known and NPV is zero. The models then solve for the purchase price of an investment in a maximum bid price model, or the sale price in a minimum sell price model. In a maximum bid model, the sale price that equates NPV to zero indicates how much the buyer can bid for the investment and still earn the IRR rate r on the defender. Or, from the seller’s perspective, the minimum sell price is the lowest price a seller can accept in exchange for the cash flow stream generated by the investment and still earn the IRR rate r earned on the defender.
To illustrate, begin by assuming that r, the IRR of the defender, is known as well as the cash flow that can be earned by the challenger. Now evaluate the challenger by setting NPV equal to zero and finding the maximum bid (minimum sell) price :
$N P V^{c}=-V_{0}^{c}+\frac{R_{1}^{c}+S_{1}^{c}}{(1+r)}=0 \label{8.7}$
The maximum bid (minimum sell) price is:
$V_{0}^{c}=\frac{R_{1}^{c}+S_{1}^{c}}{(1+r)} \label{8.8}$
The Break-even Model
Assume that the investor knows the investment cost , its liquidation value , and the IRR of the defender r but doesn’t know the amount of returns on the challenger that would be required if the investment were to earn a rate of return equal to that available on the defender. The firm can find the amount required to return break-even earnings by setting the NPV model to zero and solving for R1 as follows:
$\label{8.9} N P V^{c}=-V_{0}^{c}+\frac{R_{1}^{c}+S_{1}^{c}}{(1+r)}=0$
and the break-even earnings amount is:
$R_{1}^{c}=(1+r) V_{0}^{c}-S_{1}^{c} \label{8.10}$
If r were 10%, the liquidation value were zero, and the initial investment of were $100, then the break-even return would be$100(1.1) = $110, the amount the investment would be required to earn in order to break-even. Break-even here has a specific meaning which is to earn the defender’s IRR. The Annuity Equivalent (AE) Model An annuity is a financial product sold by financial institutions. The essence of an annuity is that an individual pays into a fund that is invested and grows until some point in time when the investment is paid back to the investor as a constant stream of payments for a specified period of time. In this book we define a related concept, an annuity equivalent. An annuity equivalent is a constant stream of payments whose present value is equivalent to some other stream of payments that may not be constant. The annuity equivalent model finds an annuity associated with an investment. An annuity is like a time adjusted average. Suppose we wished to find the annuity equivalent associated with the generalized NPV model below: (8.11) Now consider an alternative model in which the NPVA is equal to the NPVA in Equation \ref{8.11}: (8.12) The value for R in Equation \ref{8.12} is the annuity equivalent cash flow that yields NPVA in Equation \ref{8.11}. Because annuity equivalents appear in so many contexts, including constant payment loans, retirement benefit payouts, and others, we adopt a notation to describe them. Factoring R in Equation \ref{8.12} we write: (8.13) The notation equals the bracketed expression in Equation \ref{8.13} and stands for the sum of a uniform series of$1 payments discounted by a rate of r for n periods. Obviously, there is a direct correlation between NPVs and annuity equivalents, and both are used to rank investments.
To illustrate, suppose that NPV were $10,000, monthly installments were for 5 years, and the discount rate were 3 percent. The AE for this investment is equal to$179.69 and
Optimal Life Models
Optimal life models ask what is the optimal life of this investment? The optimal life model can be written as:
(8.14)
or in continuous time as:
(8.15)
The optimal solution has a specific meaning in the context of the optimal life model. It is that value of n that maximizes the NPV. Formally, the solution employs calculus to optimize the NPV. In the discrete models which are most often employed in practice, the optimal value is found through trial and error or through repeated calculations of alternative values for n.
A related optimal life model asks: what is the optimal value of n that maximizes NPV if there are replacements for the investment? In this case, NPVS is the sum of NPVs from individual investments. Such a replacement model is described below:
(8.16)
The Payback Model
While PV models are generally carefully deduced and the data required to solve them is explicit, sometimes decision makers just want a “ball park” estimate of the desirability of a financial strategy. In such cases, decision makers are willing to sacrifice rigor and precision for approximations. When this is the case, the payback model is often employed. To obtain an approximation, it assumes the discount rate in PV models is zero. In other words, the payback model assumes that present and future dollars are valued the same—a very unrealistic assumption. Then the payback model calculates the number of periods required to earn the investment’s present value. The number of periods required to earn the investment’s value is the payback period, the criterion used to rank investments. All cash flow after the payback period is assumed to have no influence on the criterion. To illustrate, n is the payback period in the payback model that follows.
(8.17)
And if periodic cash flows are constant we can express the payback period as:
To illustrate, consider an initial outflow of $5,000 with$1,000 cash inflows per month. In this case, the payback period would be 5 months. If the cash inflows were paid annually, then the result would be 5 years. More generally, cash flows will not be equal to one another. If $10,000 is the initial outflow investment, and the cash inflows are$1,000 at year one, $6,000 at year two,$3,000 at year three, and $5,000 at year four, then the payback period would be three years, as the first three years are equal to the initial outflow. Despite its popularity, the payback model is not recommended for several reasons. Mainly, ignoring the time value of money basically treats an inter temporal investment as though it were a static profit problem. Furthermore, it treats cash flows earned after the payback period as though they were of no worth. In sum, in many respects it inadequately accounts for important elements of the investment problem. Ranking Investments Questions PV models answer. It may be helpful to categorize PV models into similar types by recognizing the questions they can answer. The first type answers the question: what is the break-even price such that NPV is zero. Included in this category are maximum bid (minimum sell) models, break-even models, and annuity-equivalent models. A second type of model answers the question: what is they optimal life of the investment. These models find the time period that maximizes NPV. The third type of PV model—and the most popular—are PV models that rank investments. They answer the question: which investment is preferred? The two most popular ranking PV models are the NPV and IRR models. In one survey, about 75% of chief financial officers of large corporations used IRR and NPV models nearly equally (Graham and Harvey, 2001). About 50% used payback models. The advantage of the NPV model is that we can experiment with several different IRRs to find out how sensitive the NPV of the challenger is to alternative discount rates or IRRs. As we will discover in later chapters, consistency between NPV and IRR rankings exists only under homogeneous measures of size, term, taxes, and other measures. There are alternative, easier ways of ranking investments such as the payback model. They are not recommended here because they fail to recognize a fundamental property of PV models: dollars in different time periods are valued differently and ignore cash flows after the payback period. More complicated investment ranking problems. When we described the NPV model, the discount rate was equal to the defender’s IRR. When the firm is considering the adoption of two mutually exclusive investments, then which investment is the defender and which is the challenger is an arbitrary decision. If the capital budgeting decision is to replace an existing investment with one of two mutually exclusive investments, then typically the defender is the investment in place. Then, the investment problem becomes calculating the NPV of the two challenging investments and selecting the one with the greater NPV. More complicated ranking problems involve replacing a defender with a newer version of the same investment. Such an investment might be when to replace a cohort of growing chickens or other livestock grown for slaughter with a new cohort. In this case, there are multiple defenders equal to the same investment at several different ages. This class of NPV models and their corresponding criterion is referred to as replacement models and is the focus of Chapter 10. Consider the investment problem involving the least cost source of financing. We have decided on an investment, but we have alternative ways to fund the investment and we want to find the least cost source of funding. In this problem, we designate one of the funding sources as the challenger and the other as the defender. We then compare the IRRs of the two funding sources. In this case, the funding source with the smallest IRR is preferred and used as the discount rate in finding the NPV of the potential new investment. One can easily imagine more complicated investment problems where the designation of the defender is not always clear. In these circumstances, we ask the question do the rankings depend on which investment is selected as the defender? The answer depends on whether or not the investments being ranked are compared using homogeneous units. If the investments are adjusted to make the units consistent, then ranking them by their NPVs will result in the same rankings, regardless of which investment is chosen as the defender. IRR, ROA, and ROE So far, the opportunity cost of capital has been introduced without specifying whose capital is being invested. Is it equity capital, debt capital, or a combination of debt and equity capital? Or does it matter? The short answer is that it does matter as we will demonstrate in Chapter 12. If the focus is on the return on equity, then the discount rate represents the return on equity (ROE). In this model, interest costs on debt are subtracted from the cash flow included in the model. If the focus is on the return on assets (ROA), then the cost of the investment is subtracted at the beginning of the model and returns reflect a return to the assets and interest costs are irrelevant since the asset is treated as though it were purchased at the beginning of the investment. The two approaches, ROE versus ROA, represent two schools of thought in investment analysis. The ROA approach focuses on the returns generated by the firm’s assets. The ROE approach focuses on the returns generated by the firm’s equity invested net of any interest payments on debt. The difference between the two approaches matter because most firms rely on a combination of debt and equity to fund assets. Reduced to its essence, the issue is whether the opportunity cost of capital reflects the rate of return on the firm’s assets or equity. We now describe the two approaches in more detail. Return on Assets (ROA) In the ROA approach, the cost of the investment is subtracted in the present period and net cash flow representing return to assets do not subtract debt or principal payments because the investment is paid for “up-front” or at the beginning of the investment. The advantage of this approach is that the analysis considers the rate of return on the entire investment made at the beginning of the period. The NPV for the ROA approach for the single period can be expressed as: (8.18) Note that in Equation \ref{8.18}, if NPV = 0 as it would in an IRR model, then (1 + ROA)V0 is equal to R1 + S1. If we replace V0 with E0 + D, we can write R1 + S1 = (1 + ROA)(E0 + D). This fact will be helpful as we connect ROA and ROE measures. Return on Equity (ROE) In the ROE approach, the analysis depends on how the asset is financed. In this approach, the cost of interest and debt payments is subtracted explicitly, and the initial investment is equal to the amount of equity invested, since the debt is paid directly to whoever supplies the investment. However, the debt D plus average interest costs charged at interest rate i (iD) are subtracted at the end of the period. The NPV for the ROE model is expressed as: (8.19) The fundamental rates of return identity. One of the issues to consider when comparing the ROE versus the ROA approach is that in equations (8.18) and (8.19), E0 and V0 are not equal because part of the acquisition of the investment is supported by debt, V0 = D0 + E0. The main point here is that the two approaches are not equivalent. We made this point when we derived Equation \ref{7.13} which is repeated here as Equation \ref{8.20}. (8.20) Notice that in Equation \ref{8.20}, if the cost of debt i is equal to the return on assets ROA, then ROA and ROE will be equal. But if i is less than the return on assets, then ROE > ROA. A homework problem at the end of this chapter asks you to explain this result. Equation (8.20) is so important in financial analysis that we give it a special name: the fundamental rates of return identity. IRRs, ROAs, and ROEs We earlier defined IRRs as the discount rate that corresponds to NPVs of zero. Now we illustrate how to find IRRs on assets and equity. The fundamental rates of return identity alerts us to the fact that IRRs calculated on equity invested in the project and assets invested in the project will not usually be equal. To find the IRRs on assets invested in the project, we charge the entire investment at the beginning of the period and include its liquidation value as a return at the end of the period. This approach ignores the fact that investments may be financed and paid for over the life of the investment and charging for the investment at the beginning of the project doesn’t accurately reflect its cash flow. This is the ROA approach. In this case, the ROA approach, we ignore financing because our interest is in the productive capacity of the long-term asset, independent of the terms under which it can be financed. We illustrate how to find IRRs for assets (IRRA) in a simple example. Suppose the firm’s defender is a$1,000, non-depreciable investment that will earn $100 for one period and then will be liquidated at its acquisition price. We find the IRRA associated with$1,000 of assets invested in the defender by setting its NPV equal to zero in Equation \ref{8.18} and solving for ROA.
(8.21)
We find that the IRRA of the defender is equal to 10%.
Now reconsider the same example, except that the $500, or half of the defender, is financed at 9%. The other half of the investment,$500, is financed by the firm’s equity. We continue to assume that, after one period, the investment is liquidated for its acquisition value, the loan of $500 is repaid, and the firm recovers its investment of$500. The firm also earns in one period, $100, the same as before. But now it has to pay a rental fee for the use of the loan’s funds of 9% times$500, or $45. By setting the NPV model of the defender in Equation \ref{8.19} equal to zero, we can find its IRR associated with the firm’s equity (IRRE) in the project equal to. (8.22) Now the defender’s IRR on its equity is 11%. In this case, the firm gained access to the use of an asset because of financing. The gains from a lender providing the firm access to$500 of debt capital to acquire a $1000 investment using only$500 of its own money increased its earnings on its equity from 10% to 11%. Meanwhile the investment earned only 10%. The value of the financing increased the rate of return on equity by 1%.
ROE or ROA?
For a variety of reasons, financial managers may prefer to represent the defender’s IRR as the defender’s ROA or the defender’s ROE. However, this same manager must be careful to make sure that the cash flows associated with the challengers are consistent with the method used to find the IRR of the defender. If the IRR of the defender represents the defender’s ROE, then debt and interest costs should be accounted for explicitly. If the ROA of the defender is preferred, the cash flows associated with the challenger and the defender do not separate debt and interest costs from the calculations.
In practice, PV models appear to prefer the ROA approach, even though both approaches are valid and provide unique information. Nevertheless, the dominance of the ROA approach has resulted in the identification of ROAs as simply the IRR of the investment, a practice we will also adopt in the remainder of this book.
Summary and Conclusions
This chapter reviewed several different kinds of PV models. They differ because they are designed to answer different kinds of questions. Some PV models, NPV and IRR, help us rank alternative investments. Others like AE models can be used to find the optimal time for replacing an investment—or what our periodic loan payments will be. And still other PV models like the maximum bid (minimum sell) models help us know the maximum (minimum) we can offer to purchase (sell) an investment and still earn our defender’s IRR. Finally, still other PV models such as capitalization formulas and payback models offer at most a crude rule of thumb for evaluating and making investment decisions.
Regardless of the PV model type, they all have one measure in common: it is the opportunity cost of a defending investment represented by the discount rate. The discount rate is the ROA or the ROE of the defender that must be sacrificed to acquire the new or challenging investment. This construction of PV models emphasizes the important role of opportunity costs in the construction of PV models and reminds us that we focus on opportunity rather than direct costs when making applied economic decision.
Questions
1. Explain the connection between investment questions and corresponding PV models.
2. Suppose you found the maximum bid price for a purchase you are considering. What would you conclude from your calculations?
3. Suppose that you found that an investment’s AE reached its maximum at year 10 while its NPV reached its maximum at 15 years. How would you interpret your results?
4. When finding the ROE measure in Equation \ref{8.22}, we explicitly accounted for the debt used to finance the investment. However, when finding the ROA measure in Equation \ref{8.21}, we did not account for the debt used to finance the investment. Explain the difference between the two approaches.
5. When comparing the ROAs and ROEs, we concluded that the ROE > ROA as long as the ROA was greater than the average interest rate on the debt used to finance an investment. Please explain these finding and provide an example on these results. Refer to the fundamental rates of return identity when formulating your answer.
6. Provide numerical PV models in which you find an investment’s IRR and NPVs using ROA-IRR and ROE-IRR, AE, maximum bid price, and the investment’s payback period. Defend your choice of a discount rate.
7. Explain how the “life of the investment” principle guarantees that all economic activity associated with an investment will be captured by its cash flow.
8. Most of the time, we don’t identify discount rates in PV models as being either a ROE or a ROA. Instead we seem to prefer to identify the defender’s ROA with the letter “r”. Why do we tend to prefer ROA to ROE measures? Can you describe a case when it would be important to evaluate the projects using the defender’s ROE instead of its ROA?
9. Assume you were considering one investment that could be financed from two different financial institutions. Thus the only difference between the projects were their cash flow associated with their use of debt capital. How would you proceed to rank the two investments?
10. In a previous chapter, we calculated the rates of return on equity and rates of return on assets for HQN for the year 2018 for the entire firm. But this calculation was for only one year and included non-cash items in the calculation. What is different between IRRs calculated as ROA or ROE for the entire firm versus IRRs calculated as ROA or ROE in a PV model?
11. Suppose you ranked two challengers using their IRRs and by finding their NPVs using the IRR of the defender. What would you conclude if the IRR and NPV ranking provided conflicting ranking? | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/08%3A_Present_Value_Models.txt |
Learning Objectives
At the end of this chapter, you should be able to: (1) understand how internal rate of return (IRR) and net present value (NPV) models can produce inconsistent rankings; (2) produce consistent IRR and NPV rankings by adjusting for investment size differences and by adopting common reinvestment rate assumptions; (3) understand why some NPV and IRR rankings are unstable; (4) recognize how different initial size adjustment methods (addition, scaling, or some combination) produce consistent but sometimes different investment rankings; and (5) recognize how investment type differences can be used to identify the proper size adjustment method.
To achieve your learning goals, you should complete the following objectives:
• Recognize that IRR and NPV rankings may be inconsistent and that NPV rankings may be unstable.
• Understand the difference between periodic investment sizes and initial investment sizes.
• Describe how different reinvestment rate assumptions can produce inconsistent IRR and NPV rankings.
• Show how resolving periodic and initial size differences and a common reinvestment rate produce consistent challenging investment rankings.
• Illustrate the different methods available for resolving periodic size investment differences.
• Demonstrate how scaling and addition can be used to resolve initial size differences in investments.
• Demonstrate that while different methods for resolving periodic and initial size differences can each produce consistent rankings, the consistent rankings may not be the same.
• Understand the conditions under which IRR and NPV provide the same rankings as the size adjusted IRR and NPV models.
• Recognize the four basic investment models
• Recommend the appropriate investment model based on challenger characteristics.
Introduction[1]
In the single equation NPV model, we assumed that cash flow was exchanged between time periods at the defender’s IRR. In the single equation IRR model, we assumed that cash flow was exchanged between time periods at the challenger’s IRR. In the NPV model, the challenger (defender) was preferred to the defender (challenger) if the NPV were positive (negative). Furthermore, the NPV ranking of the defender and challenger was the same ranking obtained by comparing their respective IRRs. As a result, both IRR and NPV criteria produce the same ranking.
This chapter recognizes that when we rank multiple challengers funded by one defender, their IRR and NPV rankings may be different. Furthermore, we observe that changes in the defender’s IRR may produce unstable NPV rankings. We demonstrate these results in Table 9.1 that ranks three challengers.
Table 9.1. Inconsistent IRR and NPV rankings and unstable NPV rankings among three mutually exclusive investments of different initial and periodic cash flows.
initial investments where i = 1,2,3 period one cash flows where t = 1 generated by initial investments where i = 1,2,3 period two cash flows where t = 2 generated by initial investments where i = 1,2,3 NPVi earned by initial investments where i = 1,2,3 assuming r = 5%
(ranking)
NPVi earned by initial investments where i = 1,2,3 assuming r = 10%
(ranking)
IRRi earned by initial investments where i = 1,2,3 (ranking)
$1,000$800 $400$124.72
(3)
$57.85 (2) 14.8% (1)$2,000 $1,560$800 $211.34 (2)$79.34
(1)
13.3%
(2)
$3,000$2,250 $1,200$231.29
(1)
$37.10 (3) 11.0% (3) We describe the challenging investments’ NPV rankings in columns 4 and 5 for investments of$1,000, $2,000, and$3,000. The investments’ IRR rankings appear in column 6. We indicate investment rankings by parenthesized numbers in columns 4, 5, and 6.
If the defender’s IRR is 5% for challenging investments 1, 2, and 3, their NPV rankings are 3, 2, and 1 respectively. If the defender’s IRR is 10% for challenging investments 1, 2, and 3, their NPV rankings are 2, 1, and 3 respectively. Meanwhile, for challenging investments 1, 2, and 3 their IRR rankings are different still: 1, 2, and 3 respectively. These results demonstrate that IRR and NPV rankings may provide inconsistent rankings and NPV rankings may vary with the defender’s IRR.
The inconsistent IRR and NPV rankings require decision makers to choose between conflicting recommendations. They must decide: which ranking method should they believe. Among practitioners, the NPV approach is considered more reliable for wealth maximization. However, the ease in which decision makers can interpret IRRs has made it the more popular of the two ranking methods. Both ranking methods, however, have their drawbacks. Investments may have multiple IRRs and NPV rankings may be unstable—varying with changes in the defender’s IRR what is often referred to as the discount rate.
The problem produced by inconsistent IRR and NPV rankings is obvious—it leaves decision makers without a clear recommendation. On the other hand, NPV rankings that vary with the discount rate (see columns four and five) can be just as problematic. The reason is that if we are not sure of the discount rate, then we cannot be sure of the NPV rankings either.
The purpose of this chapter is to demonstrate that by resolving periodic and initial investment size differences between challenging investments and by adopting a common reinvestment rate, we can guarantee consistent IRR and NPV rankings. We will also explain why some NPV rankings vary with changes in the defender’s IRR. Finally, we show that depending on how we adjust for size differences and the reinvestment rate we adopt, we an produce four different present value (PV) models. We also discuss the conditions under which each investment model is appropriate for ranking challenging investments—rankings that will be consistent but possibly different across models.
Periodic and Initial Investment Sizes
Sometimes when IRR and NPV methods produce inconsistent rankings, it is because the challenging investments being ranked lack investment size homogeneity. Challenging investments may lack investment size homogeneity in two ways. First, their initial investment sizes may be different. In Table 9.1 note that challenging investments 1, 2, and 3 invested initial amounts of $1,000,$2,000, and $3,000 respectively. The second way challenging investment sizes may differ is their periodic cash flows. These differences change periodic investment amounts between challenging investments. Notice that in Table 9.1 cash flows in period one are different:$800, $1,560, and$2,250 for investments 1, 2, and 3 respectively. Differences in initial and periodic investment sizes contribute directly to inconsistent and unstable rankings.
Notation. This chapter employs more than the usual amount of mathematical notation. It is required to tell the story about consistent and stable IRR and NPV rankings. The good news is that there are no complicated mathematical operations besides adding, subtracting, canceling like terms, and factoring. The notation that will be used throughout this chapter includes variables with subscripts and superscripts. The superscript on a variable associates it with an investment, i = 1, 2, …, m. The subscript on a variable associates it with a time period t = 1, …, n. If a superscripted variable is raised to a power, the variable is placed in parentheses and the power to which the variable is raised is placed outside of the parentheses. To illustrate, the variable describes the value for the variable R associated with investment i = 2 in the t = 5 time period raised to the third power. Finally, when we write an expression like we are saying that function S depends on values assumed by variables r and without specifying the exact nature of the function or the values of the variables represented by r and . When we want to represent a vector of values for investment i we bold R and write .
How differences in periodic cash flow can create periodic investment size differences. Applying the notation described earlier, we now demonstrate how differences in cash flow create differences in investments sizes over time. Assume that initial investments of for investments i = 1 and i = 2 equal V0. Also assume that cash flows in period one earned by investments one and two are equal to and respectively. These positive (negative) cash flows represent investments (disinvestments) in the underlying investment. If the initial investments earned a rate of return equal to the defender’s IRR equal to r, then beginning in period two, investment one equals and investment two equals which are not equal if . As a result, unequal periodic cash flows create unequal periodic investments, even if their initial investments are equal, a cause of inconsistent rankings.
To illustrate numerically, suppose that V0 = $100 and and . If r is 10% then after one period the amount invested in investment one is$100(1.1) – $15 =$95 and the amount invested after one period in investment two is $100(1.1) –$20 = 90. After one period the investment amounts are unequal and violate the homogeneity of measures requirement. The implication of these results is that even though two investments begin with equal initial investments, IRR and NPV rankings may still be inconsistent and unstable if periodic cash flows are unequal. So what have we learned? We’ve learned that the two homogeneous investments size conditions required for consistent NPV and IRR rankings are 1) equal initial challenging investments sizes, and 2) equal periodic cash flows except in the last period. We require equal periodic cash flows except in the last period to ensure that the challenging investments will satisfy equal periodic investment sizes. Besides these two size conditions, one of two reinvestment rate assumptions must be adopted for both NPV and IRR rankings. These two reinvestment rate assumption are that cash flow are either reinvested at the defender’s IRR or at the challengers’ respective IRRs. Consistent IRR and NPV Rankings When the Reinvestment Rate is the Defender’s IRR To be clear, reinvestment rates indicate where periodic cash flows will be reinvested. If the reinvestment rate is the defender’s IRR, then we assume that earnings from the challenging investments will be reinvested in the defender. If the reinvestment rates are the challenging investments’ respective IRRs, then we assume that earnings from the investments will be reinvested in the challenging investments. If there is some other reinvestment rate, it must correspond to a separate investment and be evaluated as another challenger. Hence, the only reinvestment rates we consider are the defender’s IRR and the challenging investments’ IRRs. NPV models implicitly assume that the reinvestment rate is the defender’s IRR and earnings from the investment will be reinvested in the defender. IRR models assume that the reinvestment rate is the investment’s own IRR and that the funds will be reinvested in itself. However, to remove ranking inconsistencies, we impose the same reinvestment rate across IRR and NPV models and produce what others have referred to as modified IRR (MIRR) and modified NPV (MNPV) models. Next we demonstrate that if the two sufficient size conditions are satisfied and challenger earnings are reinvested in the defender, we are guaranteed consistent NPV and IRR rankings. NPV rankings will be consistent and under some conditions stable. NPV rankings. Consider ranking two mutually exclusive n period investments in a similar risk class by their respective NPVs. The NPV model for investment one is described as: $\label{9.1a} N P V^{1}=-V_{0}^{1}+\frac{R_{1}^{1}}{(1+r)}+\cdots+\frac{R_{n}^{1}}{(1+r)^{n}}$ The NPV model for investment two is described as: $\label{9.1b} N P V^{2}=-V_{0}^{2}+\frac{R_{1}^{2}}{(1+r)}+\cdots+\frac{R_{n}^{2}}{(1+r)^{n}}$ In the equations above, r is the defender’s IRR, and are initial investments one and two respectively, and Rt1 and Rt2 are periodic cash flows in periods t = 1, ⋯, n generated by mutually exclusive investments one and two. We assume that the terms of the two investments are equal. To resolve size differences caused by differences in periodic cash flows, we set them equal to zero in every period except the last one by reinvesting them at rate r until the last period. Generally, the discount rate and the reinvestment rate in NPV models are equal. To distinguish the original NPV model with the NPV model with funds reinvested until the last period, many finance scholars refer to the later model as the modified NPV model or the MNPV model. We write the MNPV model as: (9.2a) where Similarly the MNPV model for investment two can be rewritten as: (9.2b) where Finally, we impose the additional condition that 0" title="Rendered by QuickLaTeX.com" height="20" width="169" style="vertical-align: -4px;">, otherwise the investment decision is no longer interesting. The difference between MNPV1 and MNPV2 which ranks the two investments can be expressed as: (9.3) If the initial investment sizes are the same as required by the homogeneity of measures principle, then the difference in the first bracketed expression in Equation \ref{9.3} is zero and the rankings will depend only on the difference between the sums of reinvested cash flows: (9.4) Equation (9.4) provides an interesting result. We obtained these results by reinvesting and discounting cash flow at the same rate so NPVs of the two investments are unaffected allowing us to write: (9.5) We now illustrate the results of Equation \ref{9.5}. Let the initial investment equal100 and cash flows in periods one and two equal $50 and$70 respectively. Finally let the discount rate and the implied reinvestment rate equal 10%. Then we write:
(9.6a)
Then we write the equivalent MNPV model as:
(9.6b)
The results illustrate NPV and MNPV models are equal and provide the same rankings when the reinvestment rate is the same as the discount rate.
Finally, it should be noted that the difference between the NPVs in Equation \ref{9.5} may be unstable and change as the defender’s IRR changes as we demonstrated in Table 9.1.
IRR rankings. Consider ranking two mutually exclusive n period investments in a similar risk class by their respective IRRs. If the IRR rankings are to be consistent with the NPV rankings, they must satisfy the sufficient conditions described earlier, including assuming the same reinvestment rate r. The IRR model for investment one is described as:
(9.7a)
The IRR model for investment two is described as:
(9.7b)
In the equations above, V01 and V02 are initial investments one and two respectively, and and are periodic cash flows in periods t = 1, ⋯, n generated by mutually exclusive investments one and two.
To resolve differences in periodic cash flows, we set them equal to zero in every period except the last period by reinvesting them at rate r until the last period. Generally, the discount rate and the reinvestment rate in IRR models are equal. Here, the reinvestment rate is r rather than their respective IRRs. To distinguish the original IRR model from the IRR model with funds reinvested until the last period, many finance scholars refer to the later model as the modified IRR model, the MIRR model. We write the MIRR model as:
$\label{9.8} V_{0}^{1}=\frac{S\left(r, \mathbf{R}^{1}\right)}{\left(1+M I R R^{1}\right)^{n}}$
Solving for MIRR1 in Equation \ref{9.8} we obtain:
(9.9)
which has one positive root.
Investment two is described as:
(9.10)
Solving for MIRR2 in Equation \ref{9.9} we obtain:
(9.11)
which has one positive root.
Finally, we write the difference between MIRR1 and MIRR2 assuming initial investments and are equal to V0 as:
(9.12)
If the initial sizes and terms of investments one and two are equal, then their MIRR ranking will depend on the same criterion that ranked the investments’ MNPVs—the difference in the sum of their reinvested cash flows and and the MIRR rankings and MNPV rankings will be consistent. However, we cannot be certain that the MIRR rankings will equal the IRR rankings because we changed the reinvestment rate assumption in the IRR models.
Consistent IRR and NPV Rankings Assuming Reinvestment Rates are the Challenging Investments’ IRRs
In this section, we demonstrate that we can also guarantee consistent NPV and IRR rankings by imposing the second reinvestment rate assumption—that periodic cash flows are reinvested in the challenging investments’ IRRs.
Suppose the reinvestment rates were the IRRs of the challengers being evaluated. This reinvestment rate is appropriate under the condition that the cash flows are reinvested in the challengers as opposed to being reinvested in the defending investment. To demonstrate the consequences of assuming that the reinvestment rates equal the challengers’ IRRs, consider the following.
Assume that the initial sizes of the challenging investments are equal and that their cash flows are reinvested in themselves earning their respective IRRs and the discount rate applied to the NPVs is the defender’s IRR. Then we could write the difference between MNPVs as:
(9.13a)
Meanwhile, we can write the difference between MIRRs as:
(9.13b)
Notice that the MNPV and MIRR rankings depend on the same sums making their rankings consistent. However, in contrast to the NPV model, the MNPV rankings are stable and likely different that the original NPV rankings. But there is one thing more. Look at the original IRR equations. They are equivalent to the MIRR equations. Reinvesting and discounting by the challengers’ IRRs are offsetting operations and don’t change the original IRRs. Therefore, if the initial sizes are equal, and the assumption is that cash flows are reinvested in the challenging investments, then IRR and MIRR rankings are equivalent! This is such an important point, we illustrate it with an example.
Assume net cash flows of $50 and$70 in periods one and two respectively, an initial investment of $100, and a reinvestment rate of the investment’s IRR or MIRR. Then we can write the IRR as: (9.14a) Now we can write the MIRR model as: (9.14b) Because the IRR and MIRR values are the same, they will return identical rankings. To emphasize the main point, if the periodic cash flows are reinvested in the challengers, then ranking investments using the investments’ IRR is the same as ranking them with their MIRRs. So what have we learned? We learned that when we satisfy the two sufficient size conditions required for consistent rankings, equal initial and period investment sizes (except in the last period), and satisfy the second reinvestment rate assumption that we reinvest in the challenging investments—then MNPV and MIRR rankings of the challengers will be consistent. And there is one thing more, the MIRR rankings will be the same as the original IRR rankings. We have also learned that inconsistent challenging investments IRR and NPV rankings are often the results of the two ranking methods adopting different reinvestment rate assumptions. NPV models assume the reinvestment rate is the defender’s IRR. IRR models assume the reinvestment rate is the challenger’s IRR for the same investment. Consistency requires that the reinvestment rate for each investment be the same regardless of whether the ranking tool is IRR or NPV. Once we have satisfied initial and periodic investment size differences and adopted a consistent reinvestment rate assumption, investments can be ranked consistently using IRR or NPV methods. Reinvestment rates and inconsistent rankings. To make clear that consistent IRR and NPV rankings require that the same reinvestment rate for each investment regardless of the ranking methods, IRR or NPV, we describe three investments with the same initial sizes and assume the defender’s IRR is 5%. We allow NPV models to reinvest at the defender’s IRR rate of 5%. We allow the challenger’s cash flow to be reinvested at their respective IRRs. The inconsistent rankings produced by allowing investments’ reinvestment rate to be different when using IRRs versus NPVs, we describe in Table 9.2. The results demonstrate that even if we adjust for initial and periodic size differences but fail to require consistent reinvestment rates, IRR and NPV rankings could still be inconsistent. Table 9.2. Rankings Allowing NPV models (IRR models) to reinvest periodic cash flows at the defender’s IRR (challengers’ IRRs). Investment rankings indicated in parentheses below NPVs and IRRs values. Period Variables Challenger 1 cash flow Challenger 2 cash flow Challenger 3 cash flow 0 V0 –$3,000 – $3,000 –$3,000
1 R1 – $100$2,010 $2,250 2 R2$3,800 $1,560$1,200
NPVs assuming r=5%
$351.47 (1)$329.25
(2)
$231.29 (3) IRRs 10.89% (3) 13.01% (1) 11.03% (2) Now assume that investment three was the defender and we used its IRR equal to 11.03% to reinvest period one cash flow to period two. Then because we employed the same reinvestment rate for each model regardless of whether we used IRR or NPV ranking models, consistency is restored. We describe these results in Table 9.3. Table 9.3. Allowing NPV and IRR models to reinvest periodic cash flows at same reinvestment rate equal to challenger 3’s IRR. Investment rankings indicated in parentheses below NPVs and IRRs values. Period Variables Challenger 1 cash flow Challenger 2 cash flow Challenger 3 cash flow 0 V0 –$3,000 – $3,000 –$3,000
1 R1 $0$0 $2,250 2 R2$3,800 – $100 x 1.1103 =$3688.97 $1,560 +$2010 x 1.1103 = $3791.70$1,200
NPVs assuming r=11.03%
– $7.57 (3)$83.82
(1)
$0 (2) IRRs assuming r=11.03% 10.89% (3) 12.57% (1) 11.03% (2) So what have we learned? We learned that when we rank challengers using their NPVs and IRRs even when we adjust for initial and periodic size differences—we can produce conflicting rankings because IRR and NPV models assume different reinvestment rates. For IRRs and NPVs to produce consistent rankings, each investment must assume the same reinvestment rates. Different investments may assume different reinvestment rates; however, if IRR and NPV ranking are to be consistent, they must be the same reinvestment rate for the same investment regardless of whether the ranking models are IRRs or NPVs. Resolving Initial Size Differences by Scaling Scaling and a reinvestment rate equal to the defender’s IRR Consider the possibility of eliminating initial investment size differences between mutually exclusive investments by scaling the challengers to a common initial size. To scale challengers requires that they are available in continuous sizes. To scale an investment requires that it leaves the relative size of the investment and its cash flows constant over the continuous sizes. For example, scaling an investment by two assumes that there exists an investment twice the size that produces twice the cash flow of the original investment in each period. To illustrate, assume net cash flows of$50 and $70 in periods one and two respectively, an initial investment of$100, and assume the reinvestment rate equals the defender’s IRR of r = 10%. Then we can write the MIRR model as:
(9.15a)
Suppose now that we scale the MIRR model by 2. Then we can rewrite the model as:
(9.15b)
Notice that the scaling factor “2” cancels so we are left with the original MIRR equation in (9.15a). And even if the reinvestment rate is the IRR, the scaling factor still cancels. Thus, the MIRR and the scaled MIRR are equal. (Can you demonstrate that the scaling factor cancels regardless of the reinvestment rate?)
Scaling and a reinvestment rate equal to the challengers’ IRR
What if the reinvestment rate is the challenger’s own IRRs, which assumes that the funds are reinvested in the challengers, then MIRRs, scaled MIRRs and the IRR equations are the same.
To make the point absolutely clear, that scaling will not change MIRRs or IRRs when the reinvestment rate is the investment’s IRR, we illustrate these results by comparing the original IRR calculations from Table 9.1 with MIRRs, and scaled MIRRs calculated in Table 9.4.
Table 9.4. Consistent MIRR, scaled MIRR, and IRR rankings obtained by scaling initial investment sizes and periodic cash flows assuming the reinvestment rates are equal to the investments’ IRRi where i = 1,2,3.
initial investment and scaling factor where i = 1,2,3 period one cash flows where t = 1 period two cash flows where i = 1,2,3 period two cash flows where i = 1,2,3 MIRRi where i = 1,2,3 assuming r = IRRi (ranking) Scaled MIRRi where i = 1,2,3 assuming r = IRRi (ranking) IRRi where i = 1,2,3 assuming r = IRRi (ranking)
0 $400 + (1.148)$800 = $1,318.40 (3)$400 +
(3)(1.148)$800 =$3,955.20
14.8%
(1)
14.8%
(1)
14.8%
(1)
0 $800 + (1.133)$1,560 = $2,567.48 (3/2)$800 +
(3/2)(1.133)$1,560 =$3,851.22
13.3%
(2)
13.3%
(2)
13.3%
(2)
0 $1,200 + (1.110)$2,250 = $3,652.50$1,200 +
(1.110)$2,250 =$3,652.50
11.0%
(3)
11.0%
(3)
11.0%
(3)
We next demonstrate how scaling achieves ranking consistency between MNPVs and MIRRs and scaled MNPVs when the reinvestment rate is the defender’s IRR. The MIRR, scaled MIRR and MNPV rankings in Table 9.5 are consistent because the MNPV rankings have been scaled to conform to the MIRR, and scaled MIRR.
Table 9.5. Consistent size adjusted MIRR and MNPV rankings obtained by scaling initial investment sizes and periodic cash flows assuming the reinvestment rate equal to the defender’s IRR of r = 5%.
initial investment and scaling factor where i = 1,2,3 period one cash flows where t = 1 period two cash flows where i = 1,2,3 Scaled MNPVi where i = 1,2,3 assuming r = 5% (ranking) MIRRs and Scaled MIRRi where i = 1,2,3 assuming r = 5% (ranking)
0 (3)$400 + (3)(1.05)$800
= $3,720$374.15
(1)
11.4%
(1)
0 (3/2)$800 + (3/2)(1.05)$1,560
= $3,657$317.01
(2)
10.4%
(2)
0 $1,200 + (1.05)$2,250
= $3,562.50$231.29
(3)
9.0%
(3)
While MIRRs are not affected by scaling, even when the reinvestment rate is the defender’s IRR, scaling does have an effect on MNPVs. We observe the effect of scaling on MNPVs by rewriting Equation \ref{9.4} as:
(9.16)
Note that the scaling factor does not cancel out in Equation \ref{9.19} and may affect the values and rankings of scaled and unscaled MNPVs. To summarize, scaled and unscaled MIRRs are equal in rank and amount. However, scaled and unscaled MNPVs are not necessarily equal in rank or amount.
(3)
7.2%
(3)
0 $800 +$1,000(1.05)2 + $1,560(1.05) =$3,540.50 $211.34 (2) 8.6% (2) 0$1,200 + $2,250(1.05) =$3,562.50 231.29 (1) 9.0% (1) Four Consistent Investment Ranking Models We have demonstrated that differences in initial and periodic sizes can cause inconsistent ranking. We resolved differences in periodic sizes by reinvesting cash flow until the last period. However, we noted that the reinvestment rate for each investment could be the challenger’s IRR or the defender’s IRR. Then we noted that consistency requires that their initial sizes are equal as well as their periodic sizes. Several methods can be employed to resolve initial size differences. We emphasized two: scaling and addition. Each of these methods will generate consistent initial size adjusted MIRR and MNPV rankings as long as cash flows are reinvested until the last period. The methods employed to adjust for periodic and initial size differences produce four distinct ranking models that depend on which size adjustment method and reinvestment rate we adopt. We describe the four investment ranking models in Table 9.7 below. Table: 9.7. Alternative methods for adjusting challenging investments to resolve periodic and initial size differences assuming equal term and risk. Assume the reinvestment rate is the defender’s IRR equal to r Assume the reinvestment rate is the challengers’ IRR Resolve initial size differences by scaling the smaller challenger with a factor equal to 1" title="Rendered by QuickLaTeX.com" height="16" width="42" style="vertical-align: -4px;"> model 1 model 2 Resolve initial size differences by adding amount to the smaller challenger model 3 model 4 We now list below the PV models consistent with models 1 through 4. We first write the unadjusted IRR and NPV models as: (9.20) and (9.21) Model 1. We write the adjusted IRR* and NPV* model 1 as: (adjusted IRR model 1) (IRR 1) (adjusted NPV model 1) (NPV 1) Model 2. We write the adjusted IRR and NPV as: (adjusted IRR model 2) (IRR 2) (adjusted NPV model 2) (NPV 2) Model 3. We write the adjusted IRR* and NPV* model 3 as: (adjusted IRR model 3) (IRR 3) (adjusted NPV model 3) (NPV 3) Model 4. We write the adjusted IRR* and NPV* model 4 as: (adjusted IRR model 4) (IRR 4) (adjusted NPV model 4) (NPV 4) Comments on the Four Investment Models and Ranking Consistency A comment about ranking consistency. Before commenting on models 1 through 4, we note the following. In some cases periodic and initial size-adjusted IRRs and NPVs produce the same rankings as the original IRRs and NPVs. In these cases, it simplifies our efforts to be able to use the original NPV or IRR rankings knowing they will provide the consistent rankings produced by the size adjusted IRR and NPV models. Comments on model 1. Notice that we can factor out the scaling factor in NPV model 1 producing the original NPV multiplied by the scaling factor—NPV. Moreover, ranking investments by NPV provides the same ranking as size adjusted IRRs and NPVs. So, if ranking needs to occur under conditions consistent with model 1, our recommendation is to rank challengers using NPV. Comments on model 2. Notice that the scaling factor in IRR model 1 cancels so that we are left with our original IRR model except that periodic cash flow are reinvested until the last period. But, compounding and discounting by the same term are offsetting actions. As a result, the IRR rankings provides the same ranking as the adjusted IRR model. So, if ranking needs to occur under conditions consistent with model 2, our recommendation is rank challengers using their original IRRs. Comments on model 3. Notice that compounding and discounting by the factor (1 + r) in model 3 are offsetting actions so that the adjustment produces the original NPV model except for the added factor that is added at the beginning and subtracted at the end of the period—eliminating it’s influence in the model. As a result, the original IRR rankings are the same as the size adjusted IRR and NPV models. So, if ranking needs to occur under conditions consistent with model three, our recommendation is rank challengers using their original IRRs. Comments on model 4. Notice that compounding and discounting using the challenger’s IRR are offsetting actions so that the adjustment produces the original IRR model except for the added factor . However, is added at the beginning and subtracted at the end of the period eliminating it from the model. As a result, the IRR rankings are the same rankings provided by the size adjusted IRR and NPV models. So, if ranking needs to occur under conditions consistent with model four, our recommendation is rank challengers using their original IRRs. Other size adjustment models. For completeness, it is important to note that there are a number of other size adjustment methods we could employ. For example, we could combine challengers 1 and 2 in Table 9.1 to achieve initial size consistency with challenger 3. Or we could use some combination of scaling and addition to adjust for initial size differences. And the alternative reinvestment rates we could employ to resolve periodic size differences is large indeed. The only consideration when employing these nonstandard size adjustments is that the recommendations included in comments for models one through four no longer apply, requiring decision makers to find size adjusted NPVs or IRRs. When to Rank Challengers Using Four Models Adjusting initial investment sizes: scaling versus addition. The appropriate initial size adjustment method depends on the characteristics of the challengers in which investments are made. To compare challengers of different initial sizes, scaling to achieve initial size differences is appropriate when the challengers are available in continuous sizes or approximately so. We describe such investments as producing constant returns to scale. For constant returns to scale, the relationship between the investment and the cash flow it produces is constant. To illustrate, hours of services may often be purchased in divisible units, each unit producing the same output as earlier ones. In sum, models 1 and 2 apply when the investments are models available in continuous sizes. On the other hand, some investments are available only in a few sizes. Machinery is available in a limited number of sizes. Sometimes, land may be purchased in fixed quantities depending on physical configurations. The same is true for buildings. So how do we compare investments available in a few sizes? Suppose we are comparing two investments of different sizes. Assume we find the difference in their initial cost and ask: if the smaller challenger is adopted, where is the difference in their initial cost employed and what does it earn? The answer is it remains invested in the defender and these must be included with the earnings of the smaller challenger. In this way we achieve initial size consistency while allowing the underlying investments to be different in their initial sizes. Adjusting periodic size differences: reinvestment rate assumptions. We resolved periodic size differences by setting cash flow in all of the periods to zero except cash flow in the last period. We set all of the cash flow in all but the last period equal to zero by reinvesting them. The implicit reinvestment rate for NPV and IRR models is the defender’s or the challengers’ IRRs. Ranking Investments when the Challengers are not Mutually Exclusive So far we have treated our challengers as mutually exclusive investments—only one can be chosen. For firms with a fixed investment budget, treating investments as mutually exclusive may be justified. Suppose that we face a set of challenging investments that are not mutually exclusive and their adoption depends on their passing some IRR hurdle. How should the investment problem be analyzed? In other words, suppose that we have a portfolio of different investment challengers and of different sizes. How big or how many challengers should be adopted ? Economic theory can help us answer this question. Usually we array our challengers according to their IRRs and invest in the most profitable ones first. Of course, the size of the defender must match the size of the challenger, but the criterion for arranging defenders to match the size of our challenger is somewhat different. We give up, sacrifice, the defender with the smallest IRR first. To assume that defenders are infinitely scalable is to believe that the firm is in a perfect market, an assumption we earlier rejected. Of course, investments may not come in infinitely small amounts; one large investment may be more profitable than a small investment because it is larger. If challengers come in lumpy amounts, that is the size of the challenger we investigate. So, we are back to the place we started. Begin with the highest rate of return challenger, and sacrifice the lowest rate of return defender. Then analyze the next highest rate of return challenger and sacrifice the next lowest rate of return defender, all the time maintaining size equality. Keep analyzing challengers and defenders sequentially, maintaining size homogeneity, until you fail to adopt the next highest rate of return challenger compared to the next lowest rate of return defender. This rule is comparable to the marginal cost equals marginal return rule employed in comparative economic static analysis. The logic behind this arrangement is that we begin by considering the most favorable challenger, and compare it with the least favorable defender. Then we continue to the next most favorable challenger and second least favorable defender. Once we have found a challenger unable to earn a higher IRR than the IRR of the defender being sacrificed, we end our investment analysis. Common Practice, Common Problems, and Reinvestment Rates Common practice is to rank challengers using IRR or NPV methods. We have emphasized that this common practice can frequently produce a common problem of inconsistent rankings. Then we made the point that when challengers were adjusted for initial and periodic size differences and employed a common reinvestment rate—either the defender or the challengers’ IRRs—then the ranking were consistent. The question is, can consistent IRR and NPV rankings be achieved under fewer restrictions? For example, could we relax the common reinvestment rate assumption and still find consistent rankings—all the time? The answer is no! Since we require only one counter-example to disprove the general claim, we provided one in Table 9.2. Consider three challengers of equal initial size and different periodic cash flow. Since reinvesting the cash flow to achieve periodic size equality at the defender’s IRR doesn’t change NPV rankings and reinvesting at the challenger’s IRR doesn’t change IRR rankings, we can rank the three challengers using NPV and IRR under initial and periodic size equality. We reported the results of such a comparison earlier in Table 9.2. Note the conflicting NPV and IRR rankings. NPV ranks the three challengers 1, 2, and 3. IRR ranks the three challengers 3, 1, and 2. These results provide the one counter example needed to disprove the claim that different reinvestment rates are not required for consistent rankings. Furthermore, since we are describing the reinvestment rate for the same investment and are only changing the ranking method, consistency would require the same reinvestment rate assumption regardless of the ranking method employed. Summary and Conclusions This chapter has demonstrated that equal initial investments and periodic cash flows reinvested until the last period plus a common reinvestment rate across IRR and NPV models are sufficient conditions for consistent MIRR and MNPV investment rankings. We can make unequal initial investments equal by scaling or adding investments to the small challengers—and by some other methods, if required. Whether or not initial size differences are resolved by scaling or by addition depends on whether the challenger is available in continuous sizes in which case scaling is appropriate. Otherwise, if it is unique and cannot be scaled, size differences are resolved by additions. All other methods for resolving initial size differences ultimately create additional challengers. Resolving periodic size differences required that we reinvest cash flow until the final period. We considered the defender’s IRR and the challengers’ IRRs as possible reinvestment rates. Of course, there are a number of other possible reinvestment rate choices. The important point is that if the discount rate and the reinvestment rate are different, then the NPV rankings will be stable and will not vary with the discount rate. So what have we learned? As long as the homogeneity of size principle is observed, whatever common reinvestment rate is assumed or whatever initial size adjustment method is employed will generate consistent rankings. These possibilities we described as four basic models. In addition, while all size adjusted PV models will produce consistent rankings, the ranking may vary with the methods adopted. The main implication of these results is to shift the debate from which ranking method to use, IRR versus NPV, to what is the appropriate size adjustment model to adopt? Questions 1. Discuss why some investment analysts prefer NPV methods to rank investments while others prefer IRR methods. Which do you prefer? Defend your answer. 2. Provide three reasons why NPV and IRR rankings may be inconsistent. 3. Refer to the investment problems described in Table Q9.1 below. Notice that initial investment sizes are unequal as are the periodic cash flows in period one which produce the inconsistent NPV and IRR ranking reported in the last two columns and rows of Table Q9.1. We will refer to the results in Table Q9.1 in several questions that follow. Table Q9.1. NPVs and IRRs for two mutually exclusive investments assuming a discount rate equal to the defender’s IRR of r = 5%. initial investments where i = 1,2 period one cash flows where t = 1 generated by initial investments where i = 1,2 period two cash flows where t = 2 generated by initial investments where i = 1,2 NPVi earned by initial investments where i = 1,2 assuming r = 5% (ranking) IRRi earned by initial investments where i = 1,2 (ranking)2,000 $1,500$265.31
(1)
11.51%
(2)
$800$400 $124.72 (2) 14.83% (1) 1. Complete Table Q9.2 by finding MNPVs and MIRRs for the two investments assuming a discount rate and reinvestment rate equal to the defender’s IRR, of r=5%. Include the investment rankings in the parentheses. Table Q9.2. MNPVs and MIRRs for two mutually exclusive investments assuming a discount and reinvestment rate of r = 5%. initial investments where i = 1,2 period one cash flows where t = 1 generated by initial investments where i = 1,2 period two cash flows where t = 2 generated by initial investments where i = 1,2 MNPVi earned by initial investments where i = 1,2 assuming r = 5% (ranking) MIRRi earned by initial investments where i = 1,2 assuming r = 5% (ranking)$1,500 + $2,000(1.05) =$3,600 $( ) % ( )$400 + $800(1.05) =$1,240 $( ) % ( ) 1. Complete Table Q9.3 by finding MNPVs and MIRRs for the two investments assuming a discount rate and reinvestment rate equal to the defender’s IRR, of r = 5% and a reinvestment rates equal to the investments’ IRRs. Include the investment rankings in the parentheses. Table Q9.3. MNPVs and MIRRs for two mutually exclusive investments assuming a discount and reinvestment rate of r = 5%. and reinvestment rates equal to the investments’ IRRs initial investments where i = 1,2 period one cash flows where t = 1 generated by initial investments where i = 1,2 period two cash flows where t = 2 generated by initial investments where i = 1,2 MNPVi earned by initial investments where i = 1,2 assuming the discount and reinvestment rate equal r = 5% (ranking) MIRRi earned by initial investments where i = 1,2 assuming the reinvestment rate equals r = 5% (ranking)$1,500 + $2,000(1.1151) =$3,730.20 $( ) % ( )$400 + $800(1.1483) =$1,318.64 $( ) % ( ) 1. Complete Table Q9.4 by finding scaled MNPVs and scaled MIRRs for the two investments assuming a discount rate and reinvestment rate equal to the defender’s IRR, of r=5%. What is the scaling factor you are using? Include the investment rankings in the parentheses. Table Q9.4. Scaled MNPVs and MIRRs for two mutually exclusive investments assuming a discount and reinvestment rate of r = 5%. initial investment where i = 1,2 period one cash flows where t = 1 generated by initial investments where i = 1,2 period two cash flows where t = 2 generated by initial investments where i = 1,2 Scaled MNPVi earned by scaled initial investments where i = 1,2 assuming the discount and reinvestment rate equal r = 5% (ranking) Scaled MIRRs earned by scaled initial investments where i = 1,2 assuming the discount and reinvestment rate equal r = 5% (ranking)$1,500 + [$2,000(1.05)] =$3,600 $( ) % ( ) [(3)$400] + [(3)$800(1.05)] =$3,720 $( ) % ( ) 1. Complete Table Q9.5 by finding scaled MNPVs and scaled MIRRs for the two investments assuming a discount rate equal to the defender’s IRR, of r = 5% and reinvestment rates equal to the investments’ IRRs. Include the investment rankings in the parentheses. Table Q9.5. Scaled MNPVs and MIRRs for two mutually exclusive investments assuming a discount rate of r = 5% and reinvestment rates equal to the investments’ IRRs initial investment where i = 1,2 period one cash flows where t = 1 generated by initial investments where i = 1,2 period two cash flows where t = 2 generated by initial investments where i = 1,2 Scaled MNPVi earned by scaled initial investments where i = 1,2 assuming the discount rate r = 5% and reinvestment rates equal to the investments’ IRRs (rankings) Scaled MIRRs earned by scaled initial investments where i = 1,2 assuming the reinvestment rate equals r = 5% (ranking)$1,500 + [$2,000(1.1151)] =$3,730.20 $( ) % ( ) [(3)$400] + [(3)$800(1.1483)] =$3,955.92 $( ) % ( ) 1. Complete Table Q9.6 by finding added MNPVs and MIRRs for the two investments assuming a discount and reinvestment rate equal to the defender’s IRR, of r = 5%. What is the additional investment amount added to the smaller investment? Include the investment rankings in the parentheses. Table Q9.6. Added MNPVs and MIRRs for two mutually exclusive investments assuming a discount rate of r = 5% and reinvestment rates equal to the defender’s IRR of r = 5%. Initial plus added investments where i = 1,2 period one cash flows where t = 1 generated by initial plus added investments where i=1,2 period two cash flows where t=2 generated by initial plus added investment where i = 1,2 Added MNPVi earned by initial plus added investments where i = 1,2 assuming the discount rate and reinvestment rate r = 5% (rankings) Added MIRRi where i = 1,2 earned by initial plus added investments where i = 1,2 assuming the reinvestment rate r = 5% (rankings)$1,500 + $2,000(1.05) =$3,600 $( ) % ( ) where$400 + $800(1.05) +$2,000(1.05)2 = $3,445$
( )
%
( )
1. Complete Table Q9.7 by finding added MNPVs and MIRRs for the two investments assuming a discount rate equal to the defender’s IRR, of r = 5% and reinvestment rates equal to the investments’ IRRs. Include the investment rankings in the parentheses.
Table Q9.7. Added MNPVs and MIRRs for two mutually exclusive investments assuming a discount rate of r = 5% and reinvestment rates equal to the investments’ IRRs
Initial plus added investments where i = 1,2 period one cash flows where t = 1 generated by initial plus added investments where i=1,2 period two cash flows where t=2 generated by initial plus added investment where i = 1,2 Added MNPVi earned by initial plus added investments where i = 1,2 assuming the discount rate r = 5% and reinvestment rates equal to the investments’ IRRs (rankings) Added MIRRi earned by initial plus added investments where i = 1,2 assuming the reinvestment rate r = 5% (rankings)
$1,500 + [$2,000(1.1151)] = $3,730.20$
( )
%
( )
where $400 + [$800(1.1483)] + $2,000(1.1483)2 =$3,955.83 \$
( )
%
( )
1. To answer the questions that follow, first complete Table Q9.8 using data from the completed Tables in question 3. Cells indicated with an “n.a.” do not require an answer.
Table Q9.8. Summary of rankings described in Tables Q9.1 through Q9.7
Table provide the data Type of ranking Assuming reinvestment rate is defender’s IRR Assuming reinvestment rate is investments IRR
Investment 1 Investment 2 Investment 1 Investment 2
Q9.1 NPV n.a. n.a.
IRR n.a. n.a.
Q9.2 MNPV n.a. n.a.
MIRR n.a. n.a.
Q9.3 MNPV n.a. n.a.
MIRR n.a. n.a.
Q9.4 Scaled MNPV n.a. n.a.
Scaled MIRR n.a. n.a.
Q9.5 Scaled MNPV n.a. n.a.
Scaled MIRR n.a. n.a.
Q9.6 Added MNPV n.a. n.a.
Added MIRR n.a. n.a.
Q9.7 Added MNPV n.a. n.a.
Added MIRR n.a. n.a.
1. Referring to your completed Table Q9.8, which ranking methods produce consistent results? Please explain your answer.
2. Referring to your completed Table Q9.8, which consistent ranking method(s) are consistent with NPV rankings? Please explain your answer.
3. Referring to your completed Table Q9.8, which consistent ranking method(s) are consistent with scaled NPVs? Please explain your answers.
4. Referring to your completed Table Q9.8, which consistent ranking method(s) are consistent with IRRs? Please explain your answers.
1. Explain why investments of unequal term can be examined using the ranking methods described in this chapter.
1. Much of the material in this chapter was published in Robison, Myers, and Barry (2015). | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/09%3A_Homogeneous_Sizes.txt |
Learning Objectives
Assuming reinvestment rate is investments IRR After completing this chapter, you should be able to: (1) consistently rank one-time investments using internal rate of return (IRR) or net present value (NPV) methods; (2) find time adjusted cash flow averages called annuity equivalents (AE); (3) use AE to find the optimal life of a repeatable investment; and (4) use capitalization rates to find the present value of long-lived investments and repeatable investments.
To achieve your learning goals, you should complete the following objectives:
• Learn appropriate methods for ranking one-time investments with unequal terms using IRR or NPV ranking criteria.
• Learn how to represent the time adjusted average of an investment’s cash flow using AE.
• Learn how IRR and NPV methods may provide conflicting optimal replacement ages for repeatable investments.
• Learn how to use an investment’s cash flow patterns and its AE to determine the optimal life of a repeatable investment.
• Learn how to find the present value of future earnings from repeatable investments using the capitalization formula.
Introduction
One-time investments. In the previous chapter, we developed methods for ranking one-time mutually exclusive investments with unequal initial and periodic sizes. In that effort, we employed a simplifying assumption: that the terms of the competing challengers and the defender were equal. This assumption is frequently violated. Not all challengers and defenders have equal terms or economic lives. Therefore, we develop methods for ranking one-time mutually exclusive challengers of unequal terms which is the first goal of this chapter. An important characteristic of one-time investments is that owning a one-time investment does not require replacement in order to invest in a similar investment.
Repeatable investments. Some investments provide essential services. As a result, when they wear out, they need to be replaced (think of a light bulb). What replaces the existing investment may be an identical, improved, or remodeled version of the original investment. We call these investments that require replacement, repeatable investments because they are owned in sequence rather than simultaneously. Examples of repeatable investments include orchards, breeding livestock, roofs on houses, and equipment. Since repeatable investments are owned in sequence, we must determine what is the optimal time to replace a repeatable investment.
AE and cash flow patterns. Finding the optimal life of a repeatable investment requires that we review the concept of a time-adjusted average cash flow, an AE. AE, of course, change as new periods of cash flow are included in its calculation. Using AE for different time periods and patterns of cash flow, we can determine the optimal life of the investment.
Capitalization rates. To rank repeatable investments, we must value the present value of the original investment and their future replacement’s cash flow. We accomplish this task by using capitalization rates, a common tool used by appraisers to value long-term investments.
Present Values and Capitalization Rates
The economic life and term of an investment. The term of an investment is the number of periods the financial manager expects to manage an investment. The economic life of an investment is the number of periods the investment is expected to generate cash flow. The PV of an investment for an individual depends on its cash flow during the term of the investment plus its liquidation value. The liquidation value of the investment depends on its economic life. Therefore, to estimate the present value for an investment, we must find the discounted present value of all future cash flows. In practice, we often estimate the present value of an investment using the capitalization formula.
The capitalization formula and capitalization rate. Consider a challenging investment that earns R constant cash flow dollars for n period and is liquidated at the end of the nth period for Vn. We assume that the defender funding the investment has an IRR of r. We write the maximum bid (minimum sell) price PV model that equates V0 to its discounted future earnings over a term of n periods discounted by its defender’s IRR as:
(10.1)
Now assume that the second owner of the investment has the same earnings expectations as the first owner of the durable so that we can write:
(10.2)
Finally, substituting for Vn in Equation \ref{10.1} the right hand side of Equation \ref{10.2} we obtain:
(10.3)
And if the investment’s salvage value were continually exchanged with its expected cash flows we could write:
(10.4)
Clearly, the farther away from the present is the constant cash flow R, the less it contributes to the present value of the investment. To demonstrate the diminishing contributions of future cash flow, note how the value of discount rate that multiplies R decreases with n. To illustrate we let r = 10%, R=100, and alternative values of n.
And
So what is the sum of an infinite stream of constant payments R discounted by r percent? To find that sum, multiply both sides of Equation \ref{10.1} by (1 + r) and subtract from the result the original equation:
(10.5)
After subtracting and simplifying and letting m get very large, we find the sum of the infinite series to equal:
(10.6)
The far right-hand side of Equation \ref{10.6} we refer to as the capitalization formula where the investment’s AE is equal to R divided by the defender’s IRR equal to r, the capitalization rate. The capitalization formula allows us to relate the present value of all future cash flow to the value of the investment.
(10.7)
To illustrate the capitalization formula, suppose that you purchase an annuity for $100 that pays you and your heirs$5 a year forever. The capitalization formula for this investment is equal to:
(10.8)
If we knew the investment’s initial value and its infinite stream of AEs, we could always estimate the capitalization rate equal to:
(10.9)
Comments about the capitalization formula and capitalization rate. In textbooks and references to the capitalization rate, it is often expressed as:
(10.10)
Then when practitioners implement the capitalization formula, Equation \ref{10.9}, they estimate R as the first period’s net cash flow and an industry capitalization rate for r. For example, if the industry standard were 5%, we would write the capitalization formula that estimates the maximum bid price for the investment as:
(10.11)
PV models and capitalization formulas. The capitalization formula is a PV model. The unknown variable in the capitalization formula identifies the kind of PV model represented. If the unknown variable is the discount rate or the capitalization rate r, the capitalization formula is an IRR model. Most often, capitalization formulas solve for V0 making them maximum bid (minimum sell) type models.
So what have we learned? We learned that we can best understand the capitalization formula and the capitalization rate in the context of a PV model. Despite its various descriptions in applied publications, the capitalization formula is the AE of the investment over its economic life divided by defender’s IRR.
More Complicated Capitalization Formulas
In the discussion to this point, we implemented the capitalization formula by assuming that the future cash flow were constants, AEs. This of course, is rarely the case. We now ask: how can we find the capitalization formula if future cash flow are expected to increase (decrease) at g% over time as you might expect on rental property? To answer this question we return to our PV model.
Suppose that we wanted to find the capitalization formula for an investment whose cash flow are expected to increase (decrease) at an average rate of g percent (g < 0 percent). Then the capitalization formula that accounts for R is increasing (decreasing) at rate g (g < 0) as:
(10.12)
Now the capitalization rate, the defender’s IRR is equal to: (rg)/(1 + g). We write the capitalization rates depending on alternative values of g and r = 10 in Table 10.1
Table 10.1a. Alternative percentage capitalization rates (rg)/(1 + g) depending on alternative values of g > 0 and r
g = 0% g = 1% g = 2% g = 3% g = 4% g = 5%
r = 10% 0.1 0.089 0.078 0.068 .058 0.048
r = 9% 0.09 0.079 0.069 0.058 0.048 0.038
r = 8% 0.08 0.069 0.059 0.049 0.038 0.029
r = 7% 0.07 0.059 0.049 0.039 0.029 0.019
r = 6% 0.06 0.050 0.039 0.029 0.019 0.01
Table 10.1b. Alternative percentage capitalization rates (rg)/(1 + g) depending on alternative values of g < 0 and r
g = 0% g = –1% g = –2% g = –3% g = –4% g = –5%
r = 10% 0.10 0.111 0.122 0.134 0.146 0.158
r = 9% 0.09 0.101 0.112 0.124 0.135 0.147
r = 8% 0.08 0.091 0.102 0.113 0.125 0.137
r = 7% 0.07 0.081 0.092 0.103 0.115 0.126
r = 6% 0.06 0.071 0.082 0.093 0.104 0.116
So what have we learned? We have learned that expected increases in cash flow decrease capitalization rates and increase the value of capitalized income. For example if R = $100, r = 10% and g = 0% so that the capitalization rate is 10%, then V0 =$1000. If R = $100, r = 10%, and g = 5% then the capitalization rate is 4.8%, and V0 =$2,083.33. We have also learned that expected decreases in cash flow increase capitalization rates and decrease the value of capitalized income. For example, if R = $100, r = 10%, and g = –5% then capitalization rate is 15.8%, then V0 =$632.91.
Ranking One-time Investments with Unequal Terms using NPV Models
Notation. Before proceeding to the first focus of this chapter, we confirm the notation used earlier and which will be used again in this chapter. The mathematical notation will describe two challenging investments and a defender. We assume that the initial investment sizes are equal to V0. The defender’s IRR for the two investments is r. The term of investments one and two are n1 and n2 respectively. Periodic cash flows for investments i = 1, 2 in period t = 1, …, ni can be expressed as . And the vector of cash flows is represented as: for i = 1, 2.
Finally, we define the sum S of compounded periodic cash flows at rate r as: . We also define the sum of periodic cash flows compounded at the investment’s IRR as: . Note that the value of the function S depends on three variables defined in the equation: the reinvestment rate r or IRRi, the vector of periodic cash flows , and the term of the investment ni.
Sufficient conditions for consistently ranking mutually exclusive one-time investments using IRRs and NPVs. We discovered in Chapter 9 that there are two sufficient conditions for consistently ranking investments using NPVs and IRRs—assuming their terms were equal. These two sufficient conditions are equal initial investment sizes and equal periodic cash flows except in their common last period.
In this chapter we will assume that initial sizes of investments are equal. However, we will allow for differences in periodic cash flows because investment terms differ. As a result, we can no longer be sure that the NPVs and IRRs rank investments the same. To solve the problem of unequal periodic cash flows, we need to rationalize investment term differences. Our focus in the first part of this chapter is on how to create equal terms and periodic cash flows except for the last period for mutually exclusive challengers.
Compounding and discounting by the same rate are offsetting operations. Essential to rationalizing term differences is the obvious fact that NPVs for investment one and two compounded and discounted at rate r have the same value as their original NPV function. We demonstrate this point using the following equations. For investment one, the result is:
(10.13a)
Similarly, for investment two:
(10.13b)
What equations 10.13a and 10.13b illustrate is the obvious: multiplying by one, the compound rate divided by the identical discount rate, cannot change the value of what is being multiplied.
In Chapter 9, we created equal periodic cash flows by reinvesting the periodic cash flows until the last period, creating MNPV and MIRR models. Then we learned that if the reinvestment rate was equal to the discount rate that NPV and MNPV and IRR and MIRR models produced identical results because reinvesting and discounting by the same rate are offsetting operations. What we learn in this chapter confirms this principle, that reinvesting and discounting by the same rate are offsetting operations. Furthermore, this principle can be used to resolve differences in investment terms.
Resolving term differences. We can convert challengers to the same term by reinvesting and discounting their cash flow to a common term. The compound factor that converts the periodic cash flows and the discount rate from period n2 to n1 is . This is applied to the extreme right-hand side of equation (10.13b) resulting in the expression:
(10.14)
Equation (10.14) confirms once again that compounding and discounting by the same rate are offsetting operations even when used to extend the term of investments. Nevertheless, by compounding and discounting by the same rate (multiplying by one), we convert the term of investment two to the term of investment one without changing the value of the function. It is still equal to the original NPV equation.
The rankings of investments one and two—assuming their reinvestment rates and discount rate are the defender’s IRR, r—can be expressed as:
(10.15)
Clearly, the only difference between the two NPVs are their vector of cash flow since they have equal initial investments, discount (reinvestment) rates, and terms.
So what have we learned? We learned that it is okay to compute and rank mutually exclusive investments using their original NPV equations even though their terms are not the same as long as the reinvestment rate is the defender’s IRR. In other words, the compounding and discounting are offsetting operations so that NPV models that convert future streams of cash flow to the present are unaffected.
Ranking One-time Investments with Unequal Terms using IRR Models.
Now suppose that we replace the reinvestment rate r in equations 10.13a with the IRR of challenger one equal to IRR1. Also assume that we replace the reinvestment rate r in 10.13b with the IRRs of challenger two, IRR2. We continue to assume that the discount rate for both investments is the defender’s IRR. The revised MIRR ranking equation can be expressed as:
(10.16)
So what have we learned about MIRRs and IRRs? Equation (10.16) reveals an interesting result: the MIRRs are equal to the IRRs because compounding and discounting IRR have offsetting effects. Therefore, Equation \ref{10.16} provides no new information beyond what we already had discovered when we found the investments’ IRR.
IRR and NPV Models for Analyzing Repeatable Investments
The two preceding sections resolve term differences by assuming the reinvestment rates were either the defender’s or the challengers’ IRRs. The problem is that we can no longer be certain that the NPV and IRR methods rank the challengers consistently since we violated the common reinvestment rate assumption—the reinvestment rates were the challengers’ own IRRs. If we allow each investment to reinvest in itself, we lose our consistency guarantee.
Another problem using IRR methods besides losing consistency with NPV rankings is that methods for finding the optimal term involve finding the term with the greatest IRR instead of finding the term with the largest AE. This complicates an already complicated subject.
For these and several other reasons, in the remainder of this chapter we will analyze repeatable investments using NPV model assumptions, the most notable of which is that the reinvestment rate is the defender’s IRR common to both challengers. To be clear, we could assume a common defender’s IRR or each challenger’s IRR but having more than one challengers’ IRR may produce inconsistent rankings and asymmetry in exchanges. Were we to assume a still different reinvestment rate besides these, the defender’s or the challengers’ IRR would imply there exists another challenger besides those being considered and, if so, should be considered as a separate challenger.
So in what follows, we assume that earnings from the challengers are reinvested in the defender and asymmetry between exchanges of dollars between time periods. In the next section we begin building the AE tool using NPV assumptions required to analyze repeatable investments.
Present Value (PV) Models and Averages
Ranking investments using their annuity equivalents (AE). Referring to our previous analogy, trying to rank two investments of different terms would be like trying to rank horses in a race in which they each ran different distances. If we did indeed wish to compare two horses that ran different distances, at least we could compare their average speed—their average speed per mile. Then, even though the comparison might not be perfect, at least the comparisons would be compatible.
This is the essence of ranking investments by their time adjusted averages, referred to earlier as their annuity equivalents (AE). Ranking investments using the AE will be essential when we find the optimal age of repeatable investments.
Arithmetic means, expected values, geometric means and AE. There are several measures of central tendency in a numeric series that include arithmetic means, expected values, and geometric means. An example of an arithmetic mean or average follows. Consider three numbers 3, 5, and 7. The average of these numbers can be calculated by dividing their sum by 3 since there are three numbers: (3 + 5 + 7) / 3 = 5. This is the average of this series. Now suppose we wanted to find the mean of the three numbers weighted by their probability of occurring. If the probability of 3 occurring were 25%, if the probability of 5 occurring were 25%, and the probability of 7 occurring were 50%, then the expected value of the series would be: [(.25)3] + [(.25)5] + [(.5)7] = 5.50. This is the weighted average or expected value of the series.
Next consider an example of a geometric mean. Consider three rates of return: 105%, 110% and 115%. The geometric mean is that number which, when multiplied together three times, equals the product of 105%, 110%, and 115%: [(1.05)(1.10)(1.15)] = (1.0991)3. Alternatively, the geometric mean is where n = 3 because there are three numbers in the series. Note that the geometric mean is not equal to the arithmetic mean: [(1.10 + 1.11 + 1.12)] / 3 = 1.11. It is also not necessarily equal to the expected value.
To illustrate AE, the constant R in Equation \ref{10.9} is an AE whose present value sum equals the present value of the sum of discounted cash flow .
(10.17)
For example, consider the AE in the following problem:
(10.18)
On the left hand side of Equation \ref{10.17} is a stream of unequal periodic cash flow. On the right hand side of Equation \ref{10.17} is a stream of equal periodic cash flow each of which is an AE. The important fact, however, is that the discounted AE on the right-hand side of Equation \ref{10.17} equals the discounted periodic cash flow on the left-hand side of Equation \ref{10.17}. The AE for the series on the right-hand side of Equation \ref{10.17} is 16.85. We demonstrate how to find an AE using Excel as follows.
Table 10.2a. How to find an AE for an irregular stream of cash flow
Open Table 10.2a. in Microsoft Excel
B6 Function: =NPV(B2,B3:B4)
A B C
1 How to find an AE for an irregular stream of cash flow
2 rate 0.1
3 R1 15
4 R2 20
5 nper 2
6 NPV $30.17 NPV(rate, R1:R2) Calculating AE from an irregular stream of cash flow is a two-step procedure. The first step is to find the net present value (NPV) of the irregular cash flow stream. We illustrate this step using Excel’s NPV function. In our example, the NPV of$15 received at the end of period one and $20 received at the end of period two is$30.17.
The next step is to find the AE, a constant payment, for the NPV equal to $30.17. Using Excel’s PMT function we find the AE for an NPV of$30.17 equal to $17.38. We display the Excel solution below. Table 10.2b. How to find an AE for an irregular stream of cash flow Open Table 10.2b. in Microsoft Excel B7 Function: =PMT(B2,B5,B6,,0) A B C 1 How to find an AE for an irregular stream of cash flow 2 rate .1 3 R1 15 4 R2 20 5 nper 2 6 NPV$30.17 NPV(rate,R1:R2)
7 AE ($17.38) PMT(rate,nper,NPV,,0) So what have we learned about AE? An AE is a constant cash flow stream whose discounted value is to equal the present value of another stream of unequal cash flow. Each value in the stream of equal cash flow is an AE. If one calculated the arithmetic mean of the AE in the steam of cash flow, the arithmetic average would also equal the value of any other AE in the series. If the discount rate were an interest rate and V0 were an amount borrowed, then AE would be the constant loan payment whose present value would equal the original loan amount. Some observations on NPV and AE rankings. Consider an NPV model and its value expressed as the present value of a series of AE in Equation \ref{10.19}. Since the present value of the AE is equal to the NPV of the investment, then the two sums must provide equal NPV rank. Important to note, however, is that it is the present value of the series of AE payments that is equal to the NPV, while a number of unequal payments could equal the same NPV. Therefore, there is a direct relationship (i.e. they both go up or down together) between NPVs and AEs. Furthermore, (10.19) any change in NPV must be matched by a corresponding change in the AE and in the same direction. For any two investments of equal size and term, and where investment one has a larger NPV than investment two, then investment two must increase its AE in order for it to equal the higher NPV amount. We illustrate this point in more detail. Consider again the expression: (10.20) Then, suppose the term of the model in Equation \ref{10.20} is increased by one period. Then the equality in Equation \ref{10.20} no longer holds: (10.21) To preserve the equality in Equation \ref{10.20}, the AE equal to R must be decreased by some amount to reestablish the equality allowing us to rewrite the earlier equality: (10.22) So what have we learned? We learned that NPVs and the present value of their AE provide equal rankings. Furthermore, any sum or vector of cash flow can be converted to its present value equivalent annuity. To maintain the equality between a present value and a stream of annuities requires the following. If the present value sum is increased, then either the term or the amount of the annuity must increase. Numerical Demonstrations Term difference and inconsistent rankings. Consider Table 10.3. Note that the two challengers are not periodic size consistent because they withdraw funds at different rates. Challenger one withdraws all of its earnings after one period. Meanwhile, challenger two withdraws some of its earnings in period one and the remainder in period two. As a result, the two investments have unequal terms. In Table 10.3 panel a, we rank the two challengers using their NPV, IRR, and AE assuming that the discount rate and the reinvestment rate is 10%. In Table 10.3 panel b, we make the two challengers periodic size-consistent by reinvesting period one earnings for one period at the defender’s IRR. This operation also resolves term differences between the two investments. Table 10.3. The Influence of periodic Size and Term Differences Created by Differential Withdrawals. Panel a. NPV, IRR and AE rankings assuming different periodic cash flows and terms for challengers one and two and a discount rate equal to the defender’s IRR of 10%. Challengers Initial Outlay Cash Flows in period one Cash Flows in period two NPV (rankings) IRR (rankings) AE (rankings) C1$1,000 $1,180$0
$72.73 (2) 18% (1)$72.73
(1)
C2 $1,000$160 $1,160$104.13
(1)
16%
(2)
$60.00 (2) Panel b. NPV, IRR, and AE rankings assuming equal periodic cash flows and terms for challengers one and two where equal periodic cash flows and terms are achieved by reinvesting period one cash flows at the defender’s IRR rate of 10% to a common ending period. NPV and IRR rankings after adjusting for term differences assuming a reinvestment rate of r. Challengers Initial Outlay Cash Flows in Period one Cash Flows in Period two NPVs and MNPVs (rankings) IRR (rankings) AE (rankings) C1$1,000 $0$1,180 (1.10) = $1,298$72.73
(2)
6.7%
(2)
$49.91 (2) C2$1,000 $0$160 (1.10) + $1,160 =$1,336
$104.13 (1) 15.6% (1)$60.00
(1)
Panel c. NPV, IRR, and AE rankings assuming equal periodic cash flows and terms for challengers one and two where equal periodic cash flows and terms are achieved by reinvesting cash flows at the investments’ IRRs. The discount rate is assumed to equal the defender’s IRR of 10%
Challengers Initial Outlay Cash Flows in Period one Cash flows in Period two
NPV (MNPV)
(rankings)
IRR
(rankings)
AE
(rankings)
C1 $1,000$0 $1,180 (1.18) =$1,392.40
$150.74 (1) 18% (1)$86.66
(1)
C2 $1,000$0 $160 (1.16) +$1,160 = $1,345.60$112.07
(2)
16%
(2)
$64.57 (2) Term and periodic cash flow differences in Table 10.3 panel a produced inconsistent rankings using NPV versus IRR and AE methods. However, in Table 10.3 panel b, when term and periodic cash flow differences were eliminated except for the common last period through reinvesting at the defender’s IRR of 10%, NPV, IRR, and AE rankings were consistent. In Table 10.3 panel c, when term and periodic cash flow differences were eliminated through reinvesting at the challengers’ respective IRRs of 18% and 16%, NPV, IRR, and AE rankings were again consistent but changed from the rankings produced when the reinvestment rate was the defender’s IRR. There are two things to be emphasized about Table 10.3. First, NPVs in panel a and panel b are the same even after adjusting for differences in periodic cash flows and terms. This is because the reinvestment rate was the defender’s IRR, and reinvesting and discounting cash flows are offsetting operations. Second, when we adjusted for periodic size inconsistencies using the investments’ IRRs as the reinvestment rate, NPVs changed but the investments’ IRRs were equal to their MIRRs in panels a and c. This is again the result of reinvesting and discounting by the same rate—the investments’ IRRs. So what have we learned? We learned that if investments have term differences and the reinvestment rate is the defender’s IRR then NPV rankings are appropriate. If investments have term differences and the reinvestment rates are the investments’ IRRs then IRR rankings are appropriate. Alternative reinvestment rate assumptions. In Table 10.3, we made the first challenger into a two-period model by reinvesting its earnings at the defender’s IRR. Suppose the one-period challenger was available for investment in each period. In other words, suppose that challenger one could be repeated. Since challenger one is an investment of size$1,000, then only $1,000 of period one earnings could be reinvested in the one-period challenger. The difference between the challenger’s first-period earnings and$1,000 we assume will be invested at the defender’s IRR. The new investment problem is summarized in Table 10.4.
Table 10.4. Resolving Term Differences Between Two Challengers by Reinvesting $1,000 of Period One Earnings at its One-period IRR of 18% and Reinvesting other Funds at the Defender’s IRR of 10%. Challengers Initial Outlay Cash Flow in period one Cash Flow in period two NPV assuming defender’s IRR is 10% (rankings) IRR (rankings) AE (rankings) C1$1,000 $0$1,000 (1.18) + $180 (1.1) =$1,378
$138.84 (1) 17.4% (1)$80.00
(1)
C2 $1,000$0 $1,160 +$160 (1.1) = $1,336$104.13
(2)
15.6%
(2)
$60.00 (2) The interesting result of Table 10.4 provides an example of a blended reinvestment rate not equal to either the defenders IRR of 10% or the investment’s own IRR but a weighted average of them both equal to 17.4% for investment one and 15.6% for investment two. However, viewing investment opportunities as combinations of investments in the defender and the challenger must be considered to be a new challenger with a unique reinvestment rate. Using Annuity Equivalents (AE) to Rank Repeatable Investments The difficulty of finding finite number of replacements to resolve term differences. In our previous example, we resolved term differences between a one-period investment and a two-period investment by repeating the first investment. Now suppose we have a more complicated term inconsistency problem. For example, assume challenger one’s term is 7 periods while challenger two’s term is 8 periods. Now repeating an investment one or several times won’t resolve term differences. Indeed, to resolve term differences in this problem would require that challenger one be repeated 8 times and challenger two be repeated 7 times. Now we have a 58-period model—which requires a lot of work. Using Annuity Equivalents (AE) to rank repeatable investments. We can resolve term differences by calculating and comparing the AE of the investments, even though they have different terms. The reason we can use the AE to rank investments of different terms is because the annuity equivalent doesn’t change when you increase the term by repeating investments. Thus, the AE from one investment repeated 2, 3, 4, 7, 8, m, or an infinite number of times is the same. This is an important fact because the AE calculated over the lives of multiple (infinite) replacements can be compared to the AE of another repeatable investment and the two investments can be ranked by their difference. We now support the claim that we can rank repeatable investments by their AE. We write the one-period model as: (10.23a) We write the NPV model with one replacement as: (10.23b) And we could write the NPV model with enough replacements to equalize their term as: (10.23c) Next, factoring, we obtain: (10.23d) Then, canceling the two bracketed terms at the end of each equation, we regain our original one-investment problem: (10.23e) A numerical example that the AE for a single investment is equal to the AE calculated over two investments. Note that the same AE that solved the one-investment problem solves the multiple-replacement problem. We demonstrate this result in Table 10.5 which calculates AE for one investment and then recalculates the AE for an investment and one replacement. Table 10.5. Resolving Term Inconsistencies by Calculating AE for an Investment and the Investment and a Replacement Assuming Defender’s IRR is 10% Challenger V0 R1 R2 R3 R4 NPV (rankings) IRR (rankings) AE (rankings) C1$2,000 $1,200$1,200
$82.64 (2) 13.1% (1)$47.65
(1)
C1 plus replacement $2,000$1,200 $1,200 –$2,000 = –$800$1,200 $1,200$150.95
(1)
13.1%
(1)
$47.65 (1) Table 10.5 illustrates the importance of AE rankings to resolve term (and size) inconsistencies for repeatable investments. Note first that term inconsistencies produce different NPVs. The NPVs are positive because the challenger earns a higher rate of return than the defender. Furthermore, collecting these returns for two challengers, the challenger and its replacement, earns more than just one investment. Hence, the NPV for the challenger and its replacement is greater than the NPV for just one challenger. On the other hand, both the IRR and the AE rank the investments the same, because their calculations are adjusted for the term of the investment. These results are also helpful because they confirm that the IRR of a single defender can be used to discount the challenger and still maintain consistency. So what is our best advice? Resolve term inconsistencies for repeatable investments by calculating AE. So what have we learned about ranking repeatable investments? When asked to rank two challengers that are repeatable but have unequal term and their reinvestment rate is the defender’s IRR, rank them by their respective first investment’s AE. Finding AE that account for technologically improved replacements. Suppose that one of the challengers will be replaced by a technologically improved replacement that perhaps costs more, but also produces higher returns. For γ > 1 the investment problem takes the following form: (10.24) Including enough replacement to equalize terms, we find the sum of the discounted NPVs. Call this sum S which is equal to: (10.25) The details of the derivation are not included here, but require nothing more that the summation of geometric series. The interpretation of Equation \ref{10.25} is that technological improvements result in NPV increases in the first replacement by percent. The second replacement’s NPV increase by —over the first one. Thus, the NPVs increased from NPV to etc. We demonstrate the effect of technologically improved replacement on the ranking of investments in Table 10.5. To simplify our calculations, we assume that we have already found the NPV of the two challengers equal to$100 for the first investment and $150 for the second investment. The term differences of the two investments are n1 = 10 for the first investment and n2 = 20 for the second investment. The rate of technological improvements are 5% for investment one and 3% for investment two. To demonstrate the importance of accounting for technological improvements, we find the AE unadjusted for technological improvement and the AE accounting for technological improvement. Table 10.6. Ranking Adjusted for Term Differences and Technologically Improved Replacements. Rankings Assuming Defender’s IRR is 10% Challenger NPV (rankings) Terms Technological change coefficient Adjustment coefficient AE not adjusted for technological change (rankings) NPVs adjusted for technological change (rankings) C1 NPV1 =$100
(2)
n1 = 10 = 5% 1.68
$16.27 (2)$100(1.68) = $168 (1) C2 NPV2 =$150
(2)
n2 = 20 = 3% 1.18
$17.62 (1)$150(1.18) = $177.12 (2) It is useful to note in Table 10.6 that NPV and AE unadjusted for technological change are consistent as our theory implies. However, once we account for technological change, the investment rankings based on the investments AE are reversed. Investment one is preferred even though its NPV is less than that of challenger’s two NPV. Inconsistent rankings were not caused by failing to adjust for differences in size and terms. As we have already demonstrated, these can be rationalized using AE. What produced the inconsistencies was comparing the rankings without technologically improved replacements (unadjusted AE) versus including the assumption of technologically improved replacements (adjusted for technology rankings). Capitalizing AE to find the present value of a stream of repeatable investments. If we are comparing repeatable investments with different terms, then the comparisons are not between individual investments but with the present value sum of all the investments in each cash flow stream. In this regard we could compare the AE since the AE ordering of investment is the same as the NPV orderings. Or, we could capitalize the AE to find the present value sum of all of the investments. To understand how to capitalize the AE, that is, to find its value over an infinite number of repeatable investments, we write Equation \ref{10.26}: (10.26) To get some idea of how fast convergent to the capitalization formula R/r occurs in Equation \ref{10.26}, if n = 10 and r = 10%, then for m = 2, then [1 – 1/(1 + r)mn] = .85; for m = 3, then [1 – 1/(1 + r)mn] = .94, and for m = 4, then [1 – 1/(1 + r)mn] = .98. Finally, for m = 5, then [1 – 1/(1 + r)mn] = .991. Finding the Optimal Replacement Age for Different Repeatable Investments The condition that identifies the optimal replacement age for a repeatable investment. The optimal age for each repeatable investment in a stream of repeatable investments is that age that maximizes the NPV for the entire stream of repeatable investments. Finding the optimal age of a repeatable investment is a ranking problem. Only in this case, each challenger is defined by its replacement age, and each age-differentiated investment is considered to be a different challenger. Our goal is to find optimal replacement age. The key to understanding when to replace repeatable investments (without employing a lot of calculus) is to think about averages—or in our case, AE. We want to maximize the present value sum of NPVs for the entire stream of repeatable investments—not just the NPV for an individual investment. If the investments in a series of repeatable investments have identical cash flow patterns, then the rule for maximizing the NPV of the present value sum for all repeatable investment is to find the term that maximizes the AE for a single investment. Thus, for a repeatable investment, if holding the investment for an additional period increases the AE for the challenger, then the investment should be held for at least another period—until holding the investment another period decreases the AE. Of course, the periodic cash flows could still be positive and NPV increasing even though AE are decreasing. Thus holding the investment for the term that maximizes its NPV is definitely not the same rule as holding the investment for the term that maximizes its AE. The pattern of cash flows is the ultimate determinant of an investment’s optimal life. Since the calculus requires a smooth inverted cup-like shape for maximization, we typically assume investment cash flows have corresponding patterns. However, the pattern for an investment’s periodic cash flows are not the same as the pattern of AE for an investment at different ages. Consider some different kinds of investments and cash flow patterns and their corresponding optimal lives. Finding the optimal replacement age for a growth and decay type investment. The growth and decay type of investment, after the initial investment, is identified by increasing periodic cash flows followed by decreasing periodic cash flows. Specifically, suppose that we have a repeatable investment with cash flows reported for 6 periods. Assuming the reinvestment rate and the discount rate are 10%, we find the NPV for each investment assuming it has an economic life of one period, two periods, three periods, and up to six periods. Then we find the AE for the investments at their alternative economic lives. Finally, we capitalized the AE by 10% (divide the AE by .1) to find the lifetime present value of the multiple investments at their alternative ages. The results are reported in Table 10.7. Table 10.7. An Example of a Growth and Decay Type Investment. Time period Cash flow per period NPV per investment for alternative investment lives discounted at 10% AE per investment for alternative investment lives discounted at 10% Present value sum of an infinite number of repeatable investments 0 ($300.00) ($300.00) 1$150.00 ($163.64) ($180.00) ($18,000.00) 2$275.00 $63.64$36.67 $3,667.00 3$130.00 $161.31$64.87 $6,487.00 4$70.00 $209.12$65.97 $6,597.00 5$30.00 $227.75$60.08 $6,008.00 6 ($10.00) $222.10$51.00 $5,100.00 If our goal were to maximize the NPV for one of the repeatable investments, we would hold the investment until it no longer produced positive cash flows—in our example until period 5 with a cash flow of$30 and lifetime present earnings of $6,008.00. But if our goal is to optimize our lifetime earnings from a large number of repeatable investments, then we would hold each investment until they reach age 4 with a cash flow of$70 and lifetime earnings of $6,597.00. Another way to report the results of Table 10.6 is to note that as long as the periodic cash flow exceeds the AE in a period, adding that period to the life of the investment will increase the AE and the lifetime earnings of the repeatable investments. Finding the optimal replacement age for a light bulb type investment. Recall that the “light bulb” type of investment describes a category of investments which, after the initial investment, produce a nearly constant level of services that are virtually undiminished over its economic life. Then, at some point, the investment stops providing services and the investment dies a sudden death. An example cash flow pattern for this investment assumes that the investment dies in period 5. The investment is described in Table 10.8. Table 10.8. An Example of a Light Bulb Type Investment. Time period Cash flow per period NPV per investment for alternative investment lives discounted at 10% AE per investment for alternative investment lives discounted at 10% Present value sum of an infinite number of repeatable investments 0 ($300.00) ($300.00) 1$100.00 ($209.09) ($230.00) ($23,000.00) 2$100.00 ($126.45) ($72.86) ($7,286.00) 3$100.00 ($51.31) ($20.63) ($2,063.00) 4$100.00 $16.99$5.36 $536.00 5$0 $16.99$4.48 $448.00 6$0 $16.99$3.90 $390.00 The light bulb type investment has an important pattern that is easily recognized. It is that as long as its constant cash flows are positive, it’s NPV and AE are increasing. However, once the investment dies and its positive cash flows end, its NPV is constant but its AE is continually decreasing. Thus, the optimal life of a light bulb is to keep it until it dies. Of course, this recommendation could be modified if there were serious costs associated with an interruption of services and that the exact period in which the investment died was not known with certainty. Finding the optimal replacement age for a continuous decay type investment. The continuous decay type investment is one in which the investment performs best when new and then, with use and time, its service capacity decreases and its maintenance requirements increase so that its periodic cash flows exhibit a continuous decay. An example of such a periodic cash flow pattern is described in Table 10.9. Table 10.9. An Example of the Continual Decay Type Investment. Time period Cash flow per period NPV per investment for alternative investment lives discounted at 10% AE per investment for alternative investment lives discounted at 10% Present value sum of an infinite number of repeatable investments 0 ($4300.00) ($300.00) 1$190.00 ($127.27) ($139.96) ($13,996.00) 2$152.00 ($1.65) ($.95) ($95.00) 3$129.00 $95.27$38.31 $3,831.00 4$85.00 $153.32$48.37 $4,837.00 5$38.00 $175.92$46.41 $4,641.00 6$8.00 $181.43$41.66 $4,166.00 In the continual decay model, after the cost of the initial investment is paid, the periodic cash flows of the investment continually decrease. Still they increase the NPV of the investment as long as they are positive. At some point, the value of earning high returns during the early life of the investment swamps the cost of acquiring a new investment and the AE decrease indicating the optimal age of the investment. In this example, the optimal life of the investment is 4 periods with a corresponding present value sum of earnings over an infinite number of repeatable investments equal to$4,837.00.
Finding the optimal replacement age for an investment with irregular periodic cash flows. The last category of investments considered are those whose cash flow patterns are unique. That is, the cash flow pattern for an investment owned one year is different than the same investment owned two years, three years, and so on. To illustrate this type of investment, consider a machinery owner who custom hires using his machine to perform services for customers. The cash flow pattern for the machine begins with a capital purchase followed by three years of nearly constant cash flows which then decrease by 25% per year—mostly because of repairs but also because the demand for custom hires using older machines decreases. In the year the machine is replaced, the old machine earns a liquidation value that depends on the age of the machine. In this problem, the machine at each age is considered a unique challenger even though it is the same machine differentiated by age. A description of the cash flows for this problem follows.
Table 10.10 Investments With Irregular Cash Flow Characterized by Constant and then Declining Cash Flow with an Income Spike in the last Period of the Investment’s Economic Life. The Discount and Reinvestment Rates are Assumed to Equal 10%.
Period 3 year old challenger 4 year old challenger 5 year old challenger 6 year old challenger 7 year old challenger 8 year old challenger
0 ($100) ($100) ($100) ($100) ($100) ($100)
1 $40$40 $40$40 $40$40
2 $40$40 $40$40 $40$40
3 liquidation = $64$32 $32$32 $32$32
4 0 liquidation = $51.20$25.60 $25.60$25.60 $25.60 5 0 0 liquidation =$40.96 $20.48$20.48 $20.48 6 0 0 0 liquidation =$32.77 16.38 $16.38 7 0 0 0 0 liquidation =$26.21 $13.11 8 0 0 0 0 0 liquidation =$20.97
Summary Measures
NPVs $17.51$28.43 $36.38$42.16 $46.36$49.42
AE $7.04$8.97 $9.60$9.68 $9.52$9.26
Capitalized AE $70.40$89.70 $96.00$96.80 $95.20$92.60
Note that NPVs are increasing with the age of the challengers. The maximum AE is earned in the sixth period and declines for each of the older challengers. Thus the optimal age for the challengers is age 6.
Summary and Conclusions
In Chapter 9, we found two sufficient conditions for consistently ranking mutually exclusive investments. The two conditions are that initial investment sizes and periodic cash flows are equal except for their last common period. In this chapter we extended the results of Chapter 9 by developing methods to rank investments of unequal terms. Ranking unequal term investments are problematic because unequal terms create unequal periodic cash flows, violating the second of two sufficient conditions for consistently ranking investments using IRRs and NPVs.
In our efforts to find methods for ranking investments of unequal terms, we found that MNPV and MIRR models would rank investments equally. But we also found that under some conditions, IRR and NPV models could produce equal rankings. In this chapter, we emphasized that adjusting for term differences by reinvesting and discounting by the defender’s IRR that NPV and MNPV and MIRR models would produce consistent rankings. These results would not hold when some other reinvestment rate applies. These findings led to some important practical results: when the reinvestment rate and the discount rate are the same, rank investments using NPVs. When the reinvestment rates are the investments’ IRRs, rank using investments’ IRRs.
In the second part of this chapter, we considered repeatable investments. If by repeating investments for a required number of times the investments had a common ending date, then individual investment term differences could be ignored. In effect, the entire stream of repeatable investments could be considered to be a single investment. Of course, if the number of repeatable investments was considered to be infinite then the term problem is resolved.
Assuming equal initial investment sizes, we found that the repeatable investment’s optimal age was the age that maximized AE for a single investment. Thus, we can find the optimal replacement age for repeatable investments in a stream of replacements by finding the age that maximizes AE for any one investment. Capitalizing the AE provides us with an estimate of the present value of the earnings from the stream of repeatable investments.
Questions
1. Describe the three sufficient conditions required for consistent IRR and NPV rankings for one-time investments? Explain how investment term differences violate one of the two sufficient conditions.
2. Some investments are one-time investments. Others are repeatable. Describe what conditions produce one-time investments. Then describe what conditions produce repeatable investments. Give examples of one-time and repeatable investments.
3. One way to resolve term differences is to reinvest the periodic cash flows of both investments to a common ending period. Explain the implications of assuming that the reinvestment rates are the defender’s IRR, the investments’ IRR, or some other rate.
4. Explain the effects on an investment’s NPV if term differences are resolved by reinvesting its periodic cash flows to some common period using the defender’s IRR, while discounting the reinvested funds over the changed terms by the same rate, the defender’s IRR.
5. Explain the difference, if any, between an investment’s IRR and its MIRR if the reinvestment rate is the investment’s IRR. Depending on your answer, what practical recommendation would you offer to financial managers wanting to rank investments whose earnings would be reinvested in themselves?
6. In the table below, term differences are resolved by reinvesting periodic cash flows to the common ending period assuming the reinvestment rate and the discount rate is the defender’s IRR of 10%. Produce a similar table assuming the same initial investment sizes and cash flows, only assume the defender’s IRR is 5% not 10%. Then associate your results with the ranking possibilities described in Table 10.1 by declaring which of the four models correspond to your table.
Table Q10.1. The influence of periodic size and term differences created by differential withdrawals assuming a reinvestment rate equal to the defender’s IRR of 10%. The discount rate for the NPV and MNPV models equal the defender’s IRR. The discount rate for the IRR and MIRR models are the IRRs and MIRRs
Challengers Initial Outlay Cash Flow in period one Cash Flow in period two
NPV
(rankings)
IRR
(rankings)
MNPV
(rankings)
MIRR
(rankings)
C1 $900$1090 0 $90.91 (2)$21.11%
(1)
$90.91 (2) 15.42% (2) C2$900 $160$1050 $113.22 (1) 17.27% (2)$113.22
(1)
16.71%
(1)
1. In the table below, term differences are resolved by reinvesting periodic cash flows to the common ending period assuming the reinvestment rates are the investments’ IRRs and the discount rate is 10%. Produce a similar table assuming the same initial investment sizes and cash flows, only assume the defender’s IRR is 5% not 10%. Then associate your results with the ranking possibilities described in Table 10.1 by declaring which of the four models correspond to your table.
Table Q10.2.The influence of periodic size and term differences created by differential withdrawals assuming a reinvestment rate equal to the challenger’s IRRs. The discount rate for the NPV and MNPV models equal the defender’s IRR. The discount rate for the IRR and MIRR models are the IRRs and MIRRs.
Challengers Initial Outlay Cash Flow in period one Cash Flow in period two
NPV
(rankings)
IRR
(rankings)
MNPV
(rankings)
MIRR
(rankings)
C1 $900$1090 $0$90.91
(2)
$21.11% (1)$190.91
(1)
21.11%
(1)
C2 $900$160 $1050$113.22
(1)
17.27%
(2)
$122.83 (2) 17.27% (2) 1. Referring to the completed tables in Questions 6 and 7, please answer the following. Why are NPV and MNPV ranking consistent and equal in amounts in the Question 6 table but inconsistent and different in amounts in the Question 7 table? And why are IRR and MIRR rankings inconsistent and unequal in the Question 6 table but consistent and equal in amount in the Question 7 table? What are the practical implications of these results? 2. Annuity equivalents are elements in a stream of constant periodic cash flows whose present value equals the present value of some fixed amount or the present value of a non-constant cash flow stream. What is the arithmetic mean of a series of AE? If the discount rate is 8% and the term is 10 periods, find the AE for the periodic cash flows 21, 34, 5, and 13. Then find the AE for a fixed present value amount of$199 assuming the same discount rate and term. Finally, recalculate the AE if the term is decreased from 10 periods to 5 periods.
3. A potential Uber driver can purchase a new car for $18,000. Then the car is expected to earn constant periodic cash flows for the next three years of$6,000. After that, mostly because of decreased demand for rides in older cars and higher repair costs, periodic cash flows decrease by 25% per year. The liquidation value of the new car after three years is \$9,000 and then declines each year thereafter by 25%. Find the optimal age at which the Uber driver should replace cars. Then find the capitalized value of an investment in one car assuming each car is owned until its optimal age. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/10%3A_Homogeneous_Terms.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) construct effective tax rates on defending and challenging investments; (2) describe how effective tax rates depend on investment types; and (3) find effective tax rates on defending and challenging investments by calculating tax adjust coefficients.
To achieve your learning goals, you should complete the following objectives:
• Learn how to compute a defender’s after-tax IRR by finding its tax adjustment coefficient.
• Learn how capital gains alter a defending investment’s tax adjustment coefficient.
• Learn how to compute the tax adjustment coefficient for a single period.
• Learn how to compare the average effective tax rate for an investment.
• Learn how to find the tax adjustment coefficient for loans and investments with increasing (decreasing) cash flow.
• Learn how taxes and tax adjustment coefficients influence investment rankings.
Introduction
According to Benjamin Franklin, taxes are one of the two constants in life (the other one is death). Taxes need to be included in present value (PV) models because only what the firm earns and keeps after paying taxes really matters. Therefore, proper construction of PV models requires that taxes be consistently applied to defending and challenging investments.
A single-equation PV model compares two investments: a challenger, described by time-dated cash flow, and a defender, usually described by its internal rate of return (IRR) of its time-dated cash flow. Homogeneous tax rates require that the same units are used when describing the cash flow of the challenger as the cash flow used when finding the IRR of the defender. And in particular, homogeneous tax rates require that when the cash flow of the challenger are adjusted for taxes, the IRR of the defender must also be adjusted for taxes. This chapter shows how to find homogeneous tax rates in PV models.
It is popular to adjust a defender’s before-tax IRR to an after-tax IRR by multiplying it by (1 – T), where T is the average tax rate applied to the investment. This chapter points out that this method for adjusting the defender’s IRR for taxes is only appropriate in a few special cases. Finally, this chapter shows how to find appropriate tax rates for adjusting the defender’s IRR for taxes in a variety of tax environments.
After-tax PV Models for Defenders and Challengers
The goal is to find a defender’s after-tax IRR. The first step is to find the defender’s before-tax IRR. Recall that the defender’s before-tax IRR is that rate of return such that the NPV of the defender’s before-tax net cash flow is zero. The defender’s after-tax IRR discounts the defender’s after-tax cash flow so that its NPV remains equal to zero.
There is an easy test to determine if taxes have been properly introduced into a PV model. First consider the defender’s cash flow stream and its IRR. Then introduce taxes into the defender’s cash flow stream and its IRR. If taxes have been properly introduced, then the NPV of the defender’s after-tax cash flow stream discounted by its after-tax IRR is still zero.
To illustrate, consider a defending investment that earns constant net cash flow of R dollars per period in perpetuity. The maximum bid (minimum sell) price V0 for this defending investment whose before-tax IRR is r. We describe this investment in Equation \ref{11.1}.
(11.1)
where r = R/V0 is the before-tax IRR. Now suppose that we describe the defender’s cash flow and the IRR for this same investment on an after-tax basis. We do so by introducing the constant marginal income tax rate T into the model:
(11.2)
Income R and the before-tax IRR of the defender are both adjusted for taxes by multiplying by (1 – T). We can be sure that r(1 – T) is the after-tax IRR, since V0 is the same in the before and after-tax models. However, we need to be aware that only in the special case of constant infinite income can we multiply r by (1 – T) to obtain the after-tax IRR.
A General Approach for Finding the Defender’s After-tax IRR
A general approach for finding the defender’s after-tax IRR follows. Consider a defender that has a market-determined value of V0 and earns a before-tax cash flow stream of R1, R2, …, and whose defender’s before-tax IRR is r. A before-tax PV model for this defender can be written as:
(11.3)
Now we express the PV model for the defender one period later as:
(11.4)
Note that the bracketed expression in Equation \ref{11.3} equals the right-hand side of Equation \ref{11.4}. This equality allows us to substitute V1 for the bracketed expression in Equation \ref{11.3}. After making the substitution in Equation \ref{11.3} we solve for capital gains equal to:
(11.5)
Using the expression in Equation \ref{11.5} we can solve for the defender’s before-tax IRR equal to:
(11.6)
We now want to find the after-tax IRR for the defender described in Equation \ref{11.6}. To do so, the IRR and the cash flow for the defender must be adjusted for taxes in such a way that V0 in Equation \ref{11.3} is not changed (and the defender’s NPV is still zero). The defender’s cash flow is adjusted for taxes by multiplying them by (1 – T). The defender’s before-tax IRR is adjusted for taxes by multiplying it by where , a tax adjustment coefficient, adjusts r to its after-tax equivalent such that V0 is the same whether calculated on a before-tax or after-tax basis. Besides these tax adjustments, let Tj equal other taxes applied to the defender’s cash flow that may include property taxes in the case of land, depreciation tax credits in the case of depreciable investments, and capital gains taxes when appropriate for assets earning capital gains. What all these taxes have in common is their functional dependence on the previous period’s asset value.
The after-tax PV model corresponding to Equation \ref{11.3} that leaves V0 unchanged can be written as:
(11.7)
Similarly, V1 can be expressed as:
(11.8)
Replacing the bracketed expression in Equation \ref{11.7} with V1, we find the after-tax IRR for the defender as:
(11.9)
Finally, substituting for r in Equation \ref{11.9} from the right-hand side of Equation \ref{11.6} and solving for , we obtain:
(11.10)
The value for in Equation \ref{11.10} adjusts the defender’s before-tax IRR to obtain homogeneity of measures between the defender’s after-tax IRR and the defender’s after-tax cash flow in Equation \ref{11.7}. When homogeneity of measures is maintained, the defender’s NPV is still zero whether calculated on a before-tax or after-tax basis. We now find some specific after-tax IRRs for various types of defenders.
Case 11.1. and . In this case, the defender earns neither capital gains nor suffers capital losses, in which case Tj = 0 . This case is illustrated by an infinite constant cash flow series, described in equations 11.1 and 11.2. Because the cash flow is constant, capital gains are zero. Furthermore, the defender’s return in each period is equal to its cash receipts, which is fully taxed at income tax rate T. Therefore, the entire before-tax rate of return must be adjusted by (1 – T). In Equation \ref{11.10}, substituting zero for capital gains and depreciation or capital gains tax results in:
(11.11)
Case 11.2. 0" title="Rendered by QuickLaTeX.com" height="18" width="103" style="vertical-align: -4px;"> and . In this case the investment earns capital gains that are not taxed, which lowers the defender’s effective tax rate. Thus, and . The greater the capital gains, the lower the effective tax rate in period t. We illustrate this type of model next.
Consider a defending investment whose before-tax cash flow grows geometrically at rate g. Then before-tax cash flow in period t, Rt, equals: R0 (1 + g)t, and we write the investment’s IRR model as:
(11.12)
One period later, we can write:
(11.13)
and capital gains equal:
(11.14)
Then, substituting the right-hand side of Equation \ref{11.12} for V0 in Equation \ref{11.14}, we obtain:
(11.15)
Now we are ready to find the tax-adjustment coefficient in this model. Substituting into Equation \ref{11.10} for capital gains and first period cash flow, we obtain:
(11.16)
Suppose that we naively introduced taxes into the growth model described in Equation \ref{11.12} and obtained:
(11.17)
In this case, an increase in T increases V0:
(11.18) 0. \end{equation*} " title="Rendered by QuickLaTeX.com">
Since increasing T increases V0, we know that r(1 – T) cannot equal the after-tax IRR for the defending investment.
So what have we learned? We learned how to interpret in the geometric growth model. Earlier we demonstrated that in the geometric growth model, capital gains are earned at rate g. But in this model, capital gains are not converted to cash, and so they are not taxed. Therefore, not all earnings on the investment are taxed, only the portion earned as cash. As a result, the effective tax rate is not T but , where is the percentage of returns earned as cash.
If, for example, r = 8%, g = 3%, then
(11.19)
Furthermore, for an investor in the 35% tax bracket whose cash flow is increasing at 3%, the effective tax rate would be .
Case 11.3. and . In this case the investment suffers capital losses for which no tax savings are allowed, which increases the defender’s effective tax rate. Thus, 1" title="Rendered by QuickLaTeX.com" height="13" width="40" style="vertical-align: -1px;"> and (1 - T)" title="Rendered by QuickLaTeX.com" height="18" width="145" style="vertical-align: -4px;">. The greater the capital losses, the higher is the effective tax rate in period t. We illustrate this type of model next.
Consider a defending investment whose before-tax cash flow declines geometrically at rate d > 0. Then before-tax cash flow in period t, Rt, equals: , and we write the investment’s maximum bid price as:
(11.20)
One period later, we can write:
(11.21)
and capital losses equal:
(11.22)
Then, substituting the right-hand side of Equation \ref{11.20} for V0 in Equation \ref{11.22} we obtain:
(11.23)
Now we are ready to find the tax-adjustment coefficient in this model. Substituting into Equation \ref{11.10} for capital losses and first period cash flow, we obtain:
(11.24)
So what have we learned? We learned that in the geometric decay model, capital losses are suffered at rate d. But since capital losses are not converted to cash, they do not create a tax shield. As a result, the effective tax rate is not T but , where is (r + d)/r which is greater than one and depends on the decay rate d. It should be obvious that the two previous cases are equivalent since d could be replaced by g < 0. On the other hand, it may be helpful later on to distinguish between growth in cash receipts g% and book value depreciation d%.
If for example, r = 8%, d = 3%, then,
(11.25)
Furthermore, for an investor in the 35% tax bracket, the effective tax rate on cash flow described by a geometric growth pattern would be The conclusion of Case 11.3 is that suffering losses on investments which are not used to shield income from taxes increases the investor’s effective tax rate.
Case 11.4. 0 " title="Rendered by QuickLaTeX.com" height="18" width="103" style="vertical-align: -4px;"> and In this model, the defending investment earns capital gains but pays property tax on its previous period’s value times the property tax rate Tp. However, property taxes are tax deductible, so we can write the after-tax IRR model for the defending land investment as:
(11.26)
We can sum the IRR model above by recognizing that it consists of two geometric sums. However, after summing, V0 appears on both sides of the equation. Therefore, we solve for V0 using Equation \ref{11.26} and obtain:
(11.27)
Capital gains and V0 in this model are the same as in Case 11.2, which allows us to write:
(11.28)
Consider the effect of property taxes compared to the geometric model without property taxes. In Case 11.2, we assumed that r = 8% and g = 3%, so that . We continue with the assumption that the decision maker is in the 35% tax bracket and add the assumption that the property tax rate is 2%. We now substitute into Equation \ref{11.28} and find:
(11.29)
So what have we learned? We learned that property taxes increase the effective tax rate. To illustrate, for an investor in the 35% tax bracket, the effective tax rate on cash flow described by a geometric growth pattern with property taxes would be . Obviously, property taxes increase an investor’s effective tax rate.
Case 11.5. 0" title="Rendered by QuickLaTeX.com" height="18" width="103" style="vertical-align: -4px;"> and A most fortuitous tax environment is an investment that appreciates but is considered to depreciate at rate d for tax purposes. In this case the investor is not required to pay taxes on the capital gains and is allowed a tax credit for depreciation that occurs only on the books. An example of such a model is the following:
(11.30)
Because the before-tax model is the geometric growth model, we can write:
(11.31)
So what have we learned? We learned that the effective tax rate for depreciable assets whose value is actually increasing while the investor is able to claim a tax deduction for book value depreciation results in a significant reduction in the investor’s effective tax rate.
To illustrate, suppose that d = 5%. Then, using numbers from our previous example, we substitute into Equation \ref{11.31} and find:
(11.32)
In other words, the tax rate for the investment is effectively zero.
Tax Adjustment Coefficients in Finite Models
So far we have obtained tax adjustment coefficient models for infinite time examples. As a result, the tax adjustment coefficients have been the same for each period. This approach has been convenient for exposition purposes. However, this result is not generally applicable. In practice, the tax adjustment coefficients vary by time period. We demonstrate using a finite time horizon model, a loan model in which the interest paid is tax deductible.
In many applications, the defender is a loan. When a loan is the defender, we immediately want to know if the interest paid is tax deductible. To keep our analysis simple, assume a constant-payment loan made for n periods at an interest rate of i percent. In which case, loan amount L0 at interest rate i with annuity payments A can be written as:
(11.33)
And the firm’s before-tax IRR is i. The loan balance after one period can be written as:
(11.34)
Furthermore, capital loss for loans can be expressed as:
(11.35)
The after-tax IRR model can be expressed as:
(11.36)
With Equation \ref{11.36} in a familiar form, we can write as:
(11.37)
In words, the effective after-tax IRR for a loan whose interest is tax-deductible is (1 – T).
Ranking Investments and Taxes
In this section, we acknowledge that the effective tax rates vary by the different types of investments being considered. Furthermore, if the effective tax rate for defenders and challengers differ, then before and after-tax investment rankings may be changed. To make this point, consider the following example. Assume the defender’s before-tax IRR is 8%, the income tax rate is 35%, the rate of growth in net cash flow is 3%, and the last year’s before-tax net cash flow was $100. The maximum bid price for this investment with geometric growing income is: (11.38) If the minimum sell price is$3,000, then the NPV for the investment is a negative \$940 and the challenger is rejected.
Now suppose we introduce taxes into the model and recalculate the investment’s NPV. To simplify we assume an infinite life for the investment and assume for the defender and find:
(11.39)
Now the challenger’s NPV is positive. Introducing taxes into the NPV model has reversed the ranking: the challenger is now preferred to the defender. These results should alert financial managers to the importance of after-tax rankings.
Summary and Conclusions
Taxes are important when valuing and ranking investments because what really matters is the amount of your earnings you get to keep after paying taxes. It’s not the before-tax IRR that matters but the after-tax IRR that counts because that’s the rate you really earned on your defending investment.
In this chapter, we have introduced a method for finding a defender’s after-tax IRR. The method required that when a defender’s cash flow adjusted for taxes and was discounted by its after-tax IRR its change in NPV was zero. Then we used the equality to find the after-tax discount rate IRR. The implied tax rate in the after-tax IRR was compared to the firm’s average marginal income tax-rate.
While the usual practice is to multiply the defender’s before-tax IRR by (1 – T) to obtain the defender’s after-tax IRR, this chapter demonstrated that this cannot be generally relied on to obtain the defender’s properly adjusted after-tax IRR. Indeed, we demonstrated that capital gains that are not taxed can lower the effective tax rate. Capital losses that do not create tax shields can increase the effective tax rate. Property tax paid on land and other real property increases the effective tax rate paid. Allowing investors to write off an investment’s depreciation lowers the effective tax rate.
So what have we learned? We learned that when comparing defenders and challengers, it is important to find the correct after-tax IRR of the defender to discount the challenger’s after-tax cash flow. Other things being equal, we prefer challengers whose effective tax rate is less than the effective tax rate of the defender.
Finally, this chapter has employed simplifying assumptions, such as large values for n and average depreciation and growth rates, to find effective after-tax discount rates that have nice, closed-form solutions. Usually, this is not the case. It is often more difficult to find effective after-tax discount rates, and often these are not closed-form solutions.
Questions
1. Describe the appropriate test for determining whether or not taxes have been properly introduced into the defender’s IRR.
2. When finding after-tax IRRs for defenders, we solve for and claim that is the defender’s effective tax rate. Interpret the meaning of .
3. Under what condition is the defender’s effective tax rate equal to its income tax rate T or that ?
4. Assume that a defending investment’s price is V0, that d is the defender’s book value depreciation rate, that R is the constant stream of income earned by the defender, that T is the income tax rate, and that r is the defender’s before-tax IRR. Also assume that the defender is allowed to write off book value depreciation even though its income stream is constant. We write such a model as:
(Q11.1)
In this model, the depreciation is constant for 100/d periods beyond which the discounted cash flow is small enough to be ignored. The before-tax IRR model can be written as:
(Q11.2)
Solve for in the after-tax IRR model by substituting for V0 the right hand side of the second model R/r. Next, solve for a numerical value for assuming that d = 3% and r = 8%.
1. Suppose that you have found the NPV for a challenger. What impact will an increase in the defender’s effective tax rate have on the challenger’s IRR? Please explain your answers.
2. Calculate the effective tax rate for a depreciating challenger where d is the depreciation rate, T is the income tax rate, r is the defender’s before-tax IRR, and V0 is the price of defender. The IRR model is written below. (Hint: find by setting the right hand side of the equation below to the equivalent model without taxes (T = 0) and solve for .
(Q11.3)
1. Discuss the following. Suppose that cash flow was constant (Rt = R0), yet tax laws allowed the owner of the durable to claim depreciation at rate d. Without solving for , can you deduce whether it would be equal to, less than, or greater than one? Defend your answer.
2. Assume you are investing in land and that you borrow money to finance its purchase. Also assume that you pay property taxes on the land. In other words, land is the challenger and the loan is the defender. Which investment has the higher effective tax rate under three scenarios: g = 0, g > 0, and g < 0? What do you need to know about the property tax rate Tp to answer this question?
3. In this chapter, five different investment tax scenarios were described. Please provide an example of each type of investment and how the tax scenario might change its rankings compared to before-tax rankings. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/11%3A_Homogeneous_Tax_Rates.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) construct present value (PV) models using multi-period equivalents of an accrual income statement (AIS); (2) find multi-period before and after-tax rates of return by solving internal rate of return (IRR) models; and (3) solve practical investment problems using present value model templates that are consistent with generalized AIS construction principles.
To achieve your learning goals, you should complete the following objectives:
• Describe the similarities and differences between an AIS and IRR PV models.
• Construct multi-period IRR models by generalizing AIS earning measures.
• Demonstrate that before and after-tax return on assets (ROA) and return on equity (ROE) measures derived from an AIS are equivalent (equal) to rate of return measures derived from multi-period (one-period) IRR models.
• Learn how to divide the PV model construction process into three phases: the acquisition phase, the operating phase, and the liquidation phase.
• Construct net present value (NPV) models by discounting a challenger’s cash flow using a defender’s IRR.
• Show how NPV models that discount a challenger’s cash flow and changes in operating and capital accounts with a defender’s IRR can be used to rank defenders and challengers.
• Develop PV construction skills by using Excel templates.
Introduction
In this chapter, we find before and after-tax one-period rates of return on assets and equity by calculating cash flow and changes in operating and capital accounts. Operating accounts include accounts receivable (AR), inventories (Inv), accounts payable (AP), and accrued liabilities (AL). Depreciation (Dep) plus changes in realized capital gains measure changes in the firm’s capital account.
Next, we point out the similarities and differences between AIS and IRR PV models. Then using HQN data introduced in Chapter 4, we derive ROA and ROE measures in an AIS and a one-period IRR model demonstrating that the two models produce equal results. Next, we show how AIS construction principles guide the construction of multi-period IRR PV models.
We acknowledge that AIS and IRR models are descriptive tools. They describe the rate of return on assets or equity of the firm (industry or sector) or investment. Prescriptive PV models that produce investment recommendations require that we combine before and after-tax ROA and ROE measures for a defending investment, the investment owned by the firm, and cash flow and changes in operating and capital accounts for a challenging investment, a potential replacement for the defending investment. Continuing, we divide the IRR and NPV PV model construction into three stages: the acquisition phase, the operating phase, and the liquidation phase. Finally, we operationalize the construction of PV models by introducing a generalized PV model.
Accrual Income Statement (AIS) versus Internal Rate of Return (IRR) Present Value Models
Consider the similarities and differences between an AIS and IRR models.
Descriptive versus prescriptive focus. An AIS generates one-period before and after-tax ROA and ROE. IRR models generate one or multi-period before and after-tax IRRA and IRRE that estimate average rate of return measures on assets and equity respectively. One-period IRRA and IRRE are equal to ROA and ROE AIS measures respectively. However, using multi-period IRR models we can find IRRA and IRRE that estimate average before and after-tax rates of return over several periods for which there are no AIS equivalent measures. However, one-period AIS construction processes can guide the construction of multi-period IRR models.
IRR models like AIS are descriptive in nature—they do not enable us to rank firms or investments unless we compare them to other firms or investments’ rates of return. In contrast, NPV PV models can rank investments because they contain information about two investments, a defending and a challenging investment. A defending investment is one in use. A challenging investment is a potential replacement for a defending investment. NPV models represent a defending investment by its IRR. NPV models represent a challenging investment by its cash flow and changes in its operating and capital accounts over one or more periods. Maximum bid (minimum sell) PV models are variations of NPV models that find break-even investment prices that make the firm indifferent between a defender and a challenger. A positive (negative) NPV infers that the challenger earns a higher (lower) rate of return than does the defender that it replaces.
Past versus future time focus. Most of the time, an AIS measure cash flow and changes in operating and capital accounts resulting from financial and production activities already completed or in the process of being completed. Of course, it is possible to forecast future coordinated financial statements (CFS) by predicting future values of exogenous variables or by changing control variables in the CFS. Multi-period IRR models, on the other hand, are forward looking, attempting to measure anticipated cash flow and changes in operating and capital accounts resulting from projected future financial and production activities.
The firm versus an investment. An AIS focuses on finding returns on the firm’s assets and equity. Meanwhile, IRR models focus on finding the rate of return on an investment. We may say that the focus of an AIS is the firm while the focus of PV models is an investment.
Measuring returns to assets and equity. We can divide returns to assets and equity into three categories:
• cash flow during the period(s) of analysis,
• changes in the firm’s noncash operating accounts; and
• changes in the firm’s capital accounts.
Liquidation of noncash operating and capital accounts. Both AIS and IRR models include the liquidated value of noncash operating and capital accounts. An AIS includes the liquidated value of accounts at the end of one-period. IRR models include the liquidated value of operating and capital accounts at the end of the analysis that may be one or several periods. Liquidated values depend on what the next owners of the operating and capital accounts are willing to pay to acquire them.
So what have we learned? We learned that before and after-tax ROE and ROA derived from AIS and one-period IRR models are equal. In addition, we learned that AIS construction principles can guide the construction of multi-period IRR models. Finally, we learned that rate of return measures derived from AIS and IRR models are descriptive and that we can build prescriptive PV models by combining IRR measures from a defending investment and cash flow and changes in operating and capital accounts for a challenging investment.
Finding Changes in Assets and Equity
We now describe how to find cash flow and changes in operating and capital accounts using AIS and IRR models. Consider the AIS for HQN in Table 4.6 in Chapter 4 and repeated here as Table 12.1. Notice that we organize AIS into total revenue and total expenses. Then, after adjusting for interest, taxes, and dividend/owner draw, we find Addition to Retained Earnings.
Table 12.1. 2018 Accrual Income Statement for HQN.
Open HQN Coordinated Financial Statement in MS Excel
ACCRUAL INCOME STATEMENT
DATE 2018
+ Cash Receipts $38,990 + Change in Accounts Receivable ($400)
+ Change in Inventories $1,450 + Realized Cap. Gains/Depr. Recapture$0
Total Revenue $40,000 + Cash Cost of Goods Sold$27,000
+ Change in Accounts. Payable $1,000 + Cash Overhead Expenses$11,078
+ Change in Accrued Liabilities ($78) + Depreciation$350
Total Expenses $39,350 Earnings Before Interest and Taxes (EBIT)$650
Less Interests Costs $480 Earnings Before Taxes (EBT)$170
Less Taxes $68 Net Income After Taxes (NIAT)$102
Less Dividends and Owner Draw $287 Addition to Retained Earnings ($185)
Equation (12.1) summarizes the AIS statement in Table 12.1. It equates total revenue to cash receipts (CR) plus changes in accounts receivable (∆AR) plus change in inventory (∆Inv) plus realized capital gains/depreciation recapture (RCG). It equates total expenses to cash cost of goods sold (COGS) plus changes in accounts payable (∆AP) plus cash overhead expenses (OE) plus changes in accrued liabilities (∆AL) plus the change in the book value of capital assets or depreciation (Dep).
The difference between total revenue and total expenses equals HQN’s asset earnings. We refer to a firm’s asset earnings as earnings before interest and taxes (EBIT).
(12.1)
We find HQN’s rate of return on its assets, ROA, by dividing its EBIT by its beginning assets (A0) of $10,000 reported in Table 4.1 and repeated here in Table 12.2. Table 12.2. Year End Balance Sheets for HQN (all numbers in 000s) Open HQN Coordinated Financial Statement in MS Excel BALANCE SHEET DATE 12/31/2017 12/31/2018 Cash and Marketable Securities$930 $600 Accounts Receivable$1,640 $1,200 Inventory$3,750 $5,200 Notes Receivable$0 $0 Total Current Assets$6,320 $7,000 Depreciable Assets$2,990 $2,710 Non-depreciable Assets$690 $690 Total Long-Term Assets$3,680 $2,400 TOTAL ASSETS$10,000 $10,400 Notes Payable$1,500 $1,270 Current Portion Long-Term Debt$500 $450 Accounts Payable$3,000 $4,000 Accrued Liabilities$958 $880 Total current Liabilities$5,958 $6,600 Non-Current Long Term Debt$2,042 $1,985 TOTAL LIABILITIES$8,000 $8,585 Contributed Capital$1,900 $1,900 Retained Earnings$100 ($85) Total Equity$2,000 $1,815 TOTAL LIABILITIES AND EQUITY$10,000 $10,400 (12.2) We find HQN’s ROE the rate of return on its equity by subtracting from EBIT interest costs that represent return on debt. We refer to the result as earnings before taxes (EBT). Dividing EBT by the firm’s beginning equity E0 reported in Table 12.2 as$2,000 we find:
(12.3)
AIS estimates of EBIT and EBT represent changes in the firm’s assets and equity. However, these changes in assets and equity may not be reflected by the difference between assets and equity in the beginning and ending balance sheets unless we make some adjustments. In Table 12.2, the change in equity equals $1815 –$2,000 = ($185) compared to an EBT of$170 estimated from its AIS. If we subtract from EBT taxes of $68 and owner draw of$287 we find the same difference:
(12.4)
Table 12.2 reports a change in HQN’s assets of $400 ($10,400 minus $10,000). Meanwhile HQN’s AIS reports a change in HQN’s assets, EBIT, of$650. Again part of this difference can be explained by owner draw of $287 that when added to$400 equals $687 still leaving a discrepancy of$37. In this case, the discrepancy occurs because reducing cash balances to retire some liabilities also reduces assets but not equity.
Reorganizing AIS data entries. We can reorganize AIS data into cash flow and changes in operating and capital accounts to build an IRR model that is more appropriate for analyzing multi-period investment problems. This reorganization is required because cash flow and changes in operating and capital account liquidations in IRR models may occur in several different periods while in an AIS they occur in the same period. Separating AIS entries into cash flow and changes in operating and capital accounts produces Tables 12.3 and 12.4:
Table 12.3. HQN 2018 Cash Receipts minus Cash Expenses
Cash Receipts (CR)
+ Cash receipts from operations $38,990 + Realized capital gains$0
= Cash Receipts (CR) $38,990 Cash Expenses (CE) + Cash COGS$27,000
+ Cash OE $11,078 = Cash Expenses (CE)$38,078
Cash Receipts – Cash Expenses = CR – CE $912 Table 12.3 divides cash flow into cash receipts (CR) and cash expenses (CE). The sources of cash receipts include cash sales from operations, realized capital gains, reductions in accounts receivable (∆AR < 0), and reductions in inventories held for sale (∆Inv < 0). The sources of cash expenses include cash payments for costs of goods sold (COGS) and cash overhead expenses (OE), reductions in accounts payable (∆AP < 0), and reductions in accrued liabilities (∆AL < 0). We measure reductions in the book value of capital assets in the tth period as depreciation (Dept). We record changes in operating and capital accounts in Table 12.4. Asset account changes include ∆AR and ∆Inv. Changes in liability accounts include ∆AP and ∆OE Table 12.4. HQN 2018 Changes in operating accounts and depreciation + Change in accounts receivable (∆AR) ($440)
+ Change in inventories (∆Inv) $1450 Change in accounts payable (∆AP)$1,000
Change in accrued liabilities (∆AL) ($78) = Changes in operating accounts$88
Depreciation (Dep) $350 = Changes in capital accounts$350
= Changes in operating and capital accounts ($262) To summarize the calculations included in Tables 12.3 and 12.4 we express EBIT as: (12.5) Notice that the sum of cash flow recorded in Table 12.3 of$912 plus changes in operating accounts (∆AR + ∆INV – ∆AP – ∆AL – Dep) recorded in Table 12.4 of ($262) equal EBIT of$650, an amount equal to the difference in total revenue and total expenses recorded in Equation \ref{12.1}. Of course, the IRR model estimates of ROA and ROE must equal the AIS estimates of ROA and ROE since the changes in assets and equity are the same—merely rearranged entries in the two estimation methods.
Accrual Income Statements (AIS) and Internal Rate of Return (IRR) Models
EBIT and ROA
We previously calculated ROA as EBIT divided by beginning assets A0. Multiplying ROA by A0 we equate asset earnings to EBIT:
(12.6)
Now suppose that we add A0 to both sides of Equation \ref{12.6} and factor A0 on the left hand side of the equation to obtain (1 + ROA)A0. Finally, assume that we divide both sides of Equation \ref{12.5} by (1 + ROA) to obtain an IRR PV model:
(12.7)
Generally, a PV model is one that converts future values of changes in assets and equity to their present value equivalent. Consistent with that PV model definition, IRR is a PV model that discounts future assets earnings to an amount equal to its beginning assets. To avoid double counting returns and expenses in PV models, we only account for changes in operating and capital account when we convert them into cash.
To write the multi-period equivalent of Equation \ref{12.7}, we first subscript our variables for time t. To convert cash flow and liquidated values of noncash operating and capital accounts to their present value we discount them at the discount rate (1 + ROA). However, the discount rate in the multi-period equation is not the ROA derived from the one-period AIS but a multi-period average internal rate of return on assets (IRRA)that we substitute for ROA. We summarize our results in Equation \ref{12.8}:
(12.8)
We simplify Equation \ref{12.8} by substituting ∆Accountst for ∆ARt + ∆Invt – ∆APt – ∆ALt and by recognizing the equality between beginning and ending account balances and the sum of periodic changes in accounts:
(12.9)
Finally, since Accounts0 and V0 equal acquisition investment cash flow and Accountsn and Vn equal liquidation investment cash flow, we enter them in the period in which they occur and rewrite Equation \ref{12.8} as Equation \ref{12.10}:
(12.10)
EBT and ROE
The difference between ROA and ROE is that ROA computes earnings generated by all of the firm’s assets. ROE computes only earnings produced by the firm’s equity by subtracting from total asset earnings interest earned by the firm’s liabilities. To find the multi-period IRR for equity, IRRE, we subtract in each period t interest cost iDt–1 where Dt–1 equals the firm’s debt at the end of the previous period and i equals the average cost of debt. Cash flow changes in debt are ignored since they do not represent earnings from equity. To find the amount of equity invested, we subtract from initial assets initial debt D0. Outstanding debt during the period of analysis collects interest. No changes in debt occur in the last period and debt at the end of the period n–1, Dn–1, is retired in the last period. Revising Equation \ref{12.10} to account for interest costs and debt—and replacing IRRA with the multi-period equivalent of ROE, IRRE, we can write:
(12.11)
After-tax ROA and ROE Measures
PV models mostly use after-tax cash flow (ATCF). They focus on ATCF because it represents what the firm/investors keep after paying all their expenses including taxes. In what follows we present tax obligations in a simplified form to illustrate their impact on after tax rate of return measures.
Let the average tax rate applied to equity earnings be T. Let the average tax rate applied to asset earnings be T* that depends on T. Our goal is to find the average tax rate T that adjusts ROE to ROE(1–T) and T* that adjusts ROA to ROA(1–T*). We do not try to duplicate the complicated processes followed by taxing authorities to find T and T*.
AIS report taxes paid by the firm and subtracts them from EBT to obtain net income after taxes (NIAT). We assume interest costs found by multiplying the average interest rate i times beginning period debt Dt–1 (iDt-1), have already been subtracted from earnings and used to reduce tax obligations. As a result, NIAT represents changes in equity after both interest and taxes have been paid. In 2018, HQN paid 68 in taxes. To find the average tax rate HQN paid on its changes in equity we set taxes equal to the average tax rate T times EBT: (12.12) Solving for the average tax rate T HQN paid on its earnings we find: (12.13) Finally, we adjust ROE for taxes and find HQN’s after-tax rate of return to be: (12.14) AIS Statements and After-tax ROA. AIS compute taxes paid by the firm on its returns to equity but not on its returns to assets. AIS record only one value for taxes paid and these estimates account for interest payment tax savings. As a result, the average tax rate T calculated for taxes on equity cannot be used to adjust ROA for taxes. To find the average tax rate T* that adjusts ROA to ROA(1–T*), we calculate taxes “as if” there were no interest costs to reduce the average tax rate T*. We find ROA(1–T*) in Equation \ref{12.15} as: (12.15) Solving for T* we find: (12.16) Equation (12.16) emphasizes an important point, that adjusting ROE and ROA for taxes nearly always requires different average tax rates. The only time that T = T* is when interest costs are zero. In that particular case, we can easily demonstrate that T* = T since EBIT = EBT: (12.17) A note on discount rates and the weighted cost of capital (WCC). It is common in many finance texts to assume that the discount rate is an exogenous variable observed in the financial markets. In small firms, the focus of this book, the discount rate depends on the rate of return earned by the defender and sacrificed to acquire the challenging investment. The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to finance its assets. The WACC is commonly referred to as the firm’s cost of capital. Importantly, it is dictated by the external market and not by management. For small firms, we find a concept similar to the WCC that depends on the IRR of the defender and its average cost of debt. We can derive such a measure by solving for ROA in Equation \ref{8.20} that is repeated below: (12.18) from which we find that ROA is an equivalent measure to the WCC: (12.19) After-tax Multi-period IRR Models After-tax Multi-period IRRE Model Having found the after-tax discount rates ROE(1 – T) we are prepared to introduce taxes into multi-period IRRE PV model described in Equation \ref{12.11}. We begin by replacing IRRE with IRRE(1 – T). Then we adjust cash flow and changes in operating and capital accounts for taxes. Consider additional changes required in our IRRE PV model described in Equation \ref{12.11} to account for taxes. Interest costs. Interest costs are returns paid for the use of borrowed money, similar to rent. Therefore, interest costs represent an expense to the firm or investment and should reduce taxable income. Depreciation. Depreciation is a noncash event and by itself does not create a cash flow. However, it has cash flow consequences because it provides a tax shield for some income because it can be treated as an expense that reduces taxable income. Therefore ATCF must account for tax savings from depreciation equal to the average tax rate T times depreciation for the period: (T)(Dep). Capital gains (losses) and taxes. At the end of the analysis, PV models liquidate capital accounts for an amount equal to . For tax purposes, capital assets are valued at their depreciated book value of . If the difference between the liquidation and book value of capital assets is positive, 0," title="Rendered by QuickLaTeX.com" height="22" width="195" style="vertical-align: -4px;"> the firm or the investment has earned capital gains or depreciation recapture whose after-tax value is 0." title="Rendered by QuickLaTeX.com" height="22" width="252" style="vertical-align: -4px;"> On the other hand, if the difference is negative then the firm has suffered a capital loss and earned tax credits. In the case of capital losses, the difference that represents a loss in value to the firm is reduced to Finally, to adjust capital accounts for taxes, we add the original book value . We summarize these results below: (12.20) We make similar adjustments to the firm’s operating account balances. We adjust changes in account balances for tax consequences. Letting the liquidation value of accounts equal Accountsn and the acquisition value of accounts equal to Accounts0, we write the after-tax liquidation value of accounts as: (12.21) Now we can write the after-tax IRRE model for changes in equity consistent with principles followed when we constructed one-period AIS as: (12.22) After-tax Multi-period IRRA Model There is a paradox in applied PV models. The paradox is that there is no explicit measure for T* that can be used to find ROA(1 – T*). This peculiar result occurs because taxes must account for interest costs that are not considered in EBIT measures. Yet, most applied IRR models solve for after-tax return on assets that should be guided by ROA(1 – T*) calculations. To properly account for taxes when finding in an IRRA model we should apply the tax rate T* to earnings on assets. Adjusting (12.20) by eliminating interest costs while allowing them to influence taxes paid and replacing IRRE with IRRA, we can express the after-tax multi-period IRRA model as: (12.23) Consistency and IRRA(1 – T*) and IRRE(1 – T) PV model rankings We can construct PV models that find either before or after-tax returns on equity or assets and use them to rank investments. Furthermore, the IRRA(1 – T*) and IRRE(1 – T) rankings need not be consistent with IRRA and IRRE rankings. One reason they need not be consistent is that their initial and periodic sizes are different (see Chapter 9). Furthermore, interest costs included in the IRRE model and not in the IRRA model allow for ranking variations So, how do we decide on our ranking criterion? Do we focus on equity or asset earnings? Equity or asset earnings before or after-taxes are paid? Although there may not be any one satisfactory answer to this question, it surely must depend on, among other things, on what questions the financial manager wants to answer. Net Present Value Models The homogeneous measures principle requires that cash flow and changes in accounts for defenders and challengers be measured in consistent units. Both must be measured in either before or after-taxes. Both must be measured in return to assets or equity. Both must be measured in real or current dollars. Both must be similar in investment sizes. Both must reflect similar terms. And both should be adjusted to similar risk classes. The homogeneous measure requirements guarantee that if two investments are compared using their IRRs or NPVs—they will be ranked the same. Furthermore, satisfying homogeneity requirements also guarantee the usual number system properties apply. In particular, if investment A is preferred to B and B is preferred to C, then A is preferred to C. While any particular NPV model that satisfies homogeneity requirements will rank investments A and B consistently, it is not true that NPV and IRR models will produce the same rankings when homogeneity conditions change. Earlier we showed that rankings depended on which size adjustment method we adopted for rationalizing investment size differences. Now we show that rankings depend not only on what size adjustment method we adopt but also by what homogeneity conditions we adopted. For example, we can easily demonstrate that equity derived IRRs and NPVs may produce different rankings than asset derived IRRs and NPVs. To make clear that equity versus asset derived IRR and NPV measures may produce different rankings, consider HQN’s one-period IRRA of 6.5% (650/$10,000) and its one-period IRRE of 8.5% ($170/$2,000) respectively. Let the original HQN asset and earning measures describe investment A. Now without changing beginning assets or equity, suppose a different investment B incurred no interest costs. Then investment B’s ROA would be unchanged ($650/$10,000); however, its ROE would increase to 32.5% ($650/$2,000). Meanwhile the investor would continue to be indifferent between investments A and B based on their IRRAs (and NPVs) since both equal 6.5%. However, clearly investment B is preferred to A based on their IRREs (and NPVs). So what have we learned? By changing the homogeneity of measures requirement from measuring returns on assets to returns on equity, we showed that we can change investment rankings. Other changes in homogeneity conditions can produce similar conflicts. So what does it all mean? It means that decision makers must decide which homogeneity measures are most relevant because their investment rankings may depend on their choice. PV Model Templates PV models answer practical questions about investments whose costs and benefits extend over time. They can be descriptive such as IRR models that provide information about an investment’s rate of return. Or, they can be prescriptive such as NPV models that compare defender’s rate of return with a challenger’s cash flow. To facilitate the calculation of IRRs and NPVs and to emphasize the decision maker’s important role in providing accurate and consistent data, we provide two PV model templates that correspond to equations (12.22) for equity and (12.23) for assets. In each template we calculate before and after-tax NPVs, their respective IRRs, and annuity equivalents (AE). Finally, we note that we can use the PV templates to solve one-period problems producing results equivalent to those produced by AIS. More typically, we can use them to solve multi-period problems. Finally, while we can use PV models to describe and rank the firm’s financial performance, it is more common to use PV models to describe and rank investments. We illustrate the two templates by using HQN 2018 data. In effect, we calculate one-period NPV, AE, and IRR estimates that correspond to AIS estimates. In Chapter 13 we apply the model to describe multi-period investments. Before-tax PV Asset Models and EBIT We now introduce a template for assets described in Table 12.5 using HQN data for 2018 described in Tables 12.1 and 12.2. By setting T* equal to zero, the template corresponds to EBIT calculations in Table 12.1. We describe the template in Table 12.5 that follows. Table 12.5. PV Template for Rolling NPVs, AEs, and IRRs Earned by Assets Before Taxes are Paid. Open Table 12.5 in Microsoft Excel A B C D E F G H I J K L M N O P 3 Yr Capital accounts values Capital accounts liquidation value Capital accounts book value Operating accounts values (AR- INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OEs) The savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating Capital and operating accounts ATCF from operations and liquidations Rolling NPVs Rolling AEs Rolling IRRS 4 0$8,558 $8,558$1,442
5 1 $0$8,218 $8,208$1,520 $350$38,990 $27,000$11,078 $0$912.00 $9,738.00$10,650 $0.00$0.00 6.50%
The column headings in Table 12.5 describe exogenous and endogenous variables used to find rolling (every year) NPV, AE, and IRR estimates.
• Column A lists the periods at the end of which financial activity occurs.
• Column B lists capital investment amounts.
• Column C lists the liquidation value of capital investments.
• Column D lists the book value of capital investments.
• Column E lists the value of operating accounts at the end of each period (AR + Inv – AP – AL).
• Column F calculates depreciation equal to the change in the investment’s book value determined by tax regulations.
• Column G reports CR equal to the sum of cash sales plus negative changes in AR and Inv.
• Column H reports cash COGS equal to cash operating expenses plus reductions in AP.
• Column I reports cash OE equal to cash overhead expenses plus reductions in AL.
• Column J calculates tax saving created by depreciation, relevant only in after-tax models.
• Column K calculates cash flow from operations equal to CR less cash COGS and cash OE.
• Column L calculates cash flow from liquidation of capital assets and operating accounts.
• Column M sums cash flow from operations and liquidations.
• Column N calculates rolling NPVs as though the investment ended in each year.
• Column O calculates rolling AEs associated with the NPV for each year.
• Finally, column P finds rolling IRRs for each investment life.
Note that operating cash flow equal to $912 (Column K) correspond to the sum of operating cash flow in Table 12.3 and is found by adding cash receipts (Column G) less cash COGS (Column H) and cash OE (Column I). We report the total liquidation value in column L as an amount equal to the investment’s liquidation value reported in column C plus the change in the sum of accounts in successive years reported in Column E. The sum of operating cash flow reported in column K plus the liquidation value of operating and capital accounts reported in Column L equals the value of the firm reported in Column M. Finally, the change in assets equals the value reported in Column M less the beginning value of assets reported in cell B4 equals$650 corresponding the HQN’s EBIT value reported in Table 12.1. It follows that EBIT divided by assets of $10,000 is the one-period ROA calculated from the AIS and the one-period IRRA calculated in the PV template reported in Table 12.5, both equal to 6.5%. Furthermore, if we discount the ending value of the firm by its IRR, its NPV is zero as is its AE since the discount rate used in cell N4 is the IRR. Change in operating accounts. Table 12.5 is intended to model Equation \ref{12.21}. And for the most part, the similarities are transparent. The initial investment that includes operating accounts and capital assets equals total assets of$10,000. The change in the capital accounts equals depreciation of $350. Cash flow during the period is cash receipts less cash expenses equal to$912 is easy to associate with Equation \ref{12.21}. However, the change in operating accounts need some explanation.
Beginning (ending) operating accounts are calculated from HQN’s beginning (ending) balance sheet. Beginning assets less beginning operating account balances equal beginning capital account value. Beginning capital account balances less depreciation equals ending book value for capital account balances.
Before-tax PV Equity Models and EBT
We now introduce a PV template for equity described in Table 12.6 that corresponds to equation 12.20. We populate the template using HQN data for 2018 described in Tables 12.1 and 12.2. By setting the tax rate T equal to zero, the results corresponds to EBT calculations in Table 12.1.
Table 12.6. PV Template for Rolling Estimates of NPVs, AEs, and IRRs for Equity Earnings Before Taxes
Open Table 12.6 in Microsoft Excel
A B C D E F G H I J K L M N O P Q R
3 Yr Capital accounts values Debt Capital Capital accounts liquidation value Capital accounts book value Operating accounts values (AR- INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OEs) Interests Costs The savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating Capital and operating accounts ATCF from operations and liquidations Rolling NPVs Rolling AEs Rolling IRRS
4 0 $8,558$8,000 $8,558$1,442
5 1 $0$8,080 $8,208$8,208 $1,530$350 $38,990$27,000 $11,078$480 $0$432.00 $1,738$2,170 $0.00$0.00 8.50%
6 2 $0$8,000 $20,000$20,000 $1,200 -$6,792 $29,800$13,500 $11,189$485 $0$4,626.42 $13,120$17,746 $15,472.9$7,336.47 0.00%
The column headings in Table 12.6 are only slightly modified from those reported in Table 12.5.
• Column A lists the periods at the end of which financial activity occurs.
• Column B lists investment (equity) amounts for which NPVs, AEs, and IRRs are calculated.
• Column C lists the debt and other liabilities supporting the investment.
• Column D lists the liquidation value of the investment (equity).
• Column E lists the book value of investments.
• Column F lists the net value of operating accounts at the end of each period (AR + Inv – AP – AL).
• Column G calculates depreciation equal to the change in the investment’s book value determined by tax regulations.
• Column H reports cash receipts equal to the sum of cash sales plus negative changes in AR and Inv.
• Column I reports cash COGS equal to cash operating expenses plus reductions in AL.
• Column J reports cash OE equal to cash overhead expenses plus reductions in the AL account.
• Column K reports interest paid on debt and other liabilities.
• Column L calculates the tax saving created by depreciation, relevant only in after-tax models.
• Column M calculates cash flow from operations.
• Column N calculates cash flow from liquidation.
• Column O sums cash flow from operations and liquidation.
• Column P calculates NPV as though the investment ended in each year.
• Column Q calculates the AE associated with the NPV for each year.
• Finally, column R finds the IRR for each investment life.
Summary and Conclusions
We now make explicit the main point of this chapter. PV models are multi-period expressions of information found in single-period AIS. IRRA and IRRE derived in IRR models correspond to ROA and ROE measures derived from single-period AIS. Furthermore, EBIT measures calculated in AIS models correspond to earnings from assets in PV models. EBT corresponds to earnings from equity in PV models, and NIAT corresponds to after-tax earnings from equity in PV models. While there is no explicit AIS measure of after-tax earnings from assets, it can be implied and easily measured.
Rates of return measures derived in AIS and IRR models are descriptive in nature—they describe a single investment. However, we can use also use them prescriptively by comparing them with IRRs of other firms and investments. However, we can construct a prescriptive PV model, an NPV model, by discounting cash flow from a challenging investment using the IRR of a defending investment. (The challenging investment is one considered for a replacing to a defending investment already in use by the firm.). If the NPV is positive (negative), we recommend replacing (leaving in place) the defending investment.
There are other PV models besides IRR and NPV models. We described these in Chapter 8. Most other PV models are variants of the NPV or IRR model. Maximum bid (minimum sell) models find the maximum bid (minimum sell) that can be paid (received) for a challenger and still earn the IRR of the defender. Loan formulae are special PV models that describe the amount that must be paid to receive a challenging loan while the defending loan earns its interest rate. AE simply find a multi-period time adjusted average of a challenger’s cash flow. Replacement flows are special NPV models that find the optimal life of a repeatable investment that maximizes its NPV and the NPV of future replacements.
The next step in our study of PV models is to generalize them to multi-periods and use them to solve practical investment problems. Both of these tasks, we undertake in chapter, Chapter 13.
Questions
1. List similarities and differences between an AIS statement and a PV model.
2. Both AIS and PV models find rates of return on assets and equity using cash flow and changes in operating and capital asset accounts. However, they organize them differently. Explain how AIS and PV models organize cash flow and changes in operating and capital asset accounts differently.
3. We can describe ROA and ROE as measures of changes in assets and equity respectively divided by original asset and equity values. Please explain.
4. EBIT measures the change in the value of the firm’s assets before adjusting for taxes during a single period. Do you agree or disagree? Defend your answer.
5. EBT measures the change in the value of the firm’s equity before adjust for taxes during a single period. Do you agree or disagree? Defend your answer.
6. Measures the change in the value of the firm’s equity after adjusting for taxes during a single period. Do you agree or disagree? Defend your answer.
7. There is no measure in an AIS statement that finds the change in assets after adjusting for taxes. Can you explain why?
8. Use the template reported in Table 12.5 to find the change in assets after adjust for taxes. To find the after-tax change in assets, use an average tax rate of T*=10.46% and a discount rate of ROA(1 – T*) = (6.5%)(1 – 10.46%) = 5.8%.
9. Describe the conditions under which NPV or IRR asset and equity models would rank challenging and defending investment consistently.
10. Give an example in which NPV or IRR asset and equity models rank challenging and defending investments inconsistently.
11. As a financial manager tasked with ranking a defending and a challenging investment, which ranking criteria would you employ: NPV earned by equity or NPV earned by assets? Defend your answer. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/12%3A_Homogeneous_Rates_of_Return.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) distinguish between incremental and stand-alone investments; (2) understand how time and use costs determine the optimal service extraction rate from investments; (3) distinguish between net present values (NPV), annuity equivalent (AE), and internal rates of return (IRR) used to measure earnings by an investment or by equity committed to funding an investment; and (4) use Excel spreadsheets to find NPV, AE, and IRR for investments and equity funds committed to some practical multi-period investments.
To achieve your learning goals, you should complete the following objectives:
• Learn how to distinguish between incremental and stand-alone investments.
• Learn how an investment’s time and use costs determine its optimal service extraction rates.
• Learn how an investment’s liquidation and acquisition values determine its fixity.
• Learn how to find contributions from incremental investments by finding changes in the firm’s cash receipts (CR), cash cost of goods sold (COGS), cash overhead expenses (OE), and change in operating and capital asset accounts.
• Learn how the order of changes influences the returns on incremental investments.
• Learn how to project cash flow and changes in operating and capital accounts.
• Learn how to use Excel templates to find NPV, AE, and IRR measures earned by investments or by equity committed to some practical multi-period investments.
Introduction
The nature of investments. An investment is a commitment of resources for one or more periods. We invest instead of consume because we expect future investment earnings will more than compensate for the present investment sacrifice. If the commitment is to a firm, we talk about return on the firm’s assets (ROA). If the commitment is to an investment, we talk about the returns on an investment (ROI). However, since it is more common to use PV models to examine returns on an investment rather than a firm, rather than differentiate between commitments to a firm or an investment, we will refer to both as investment analysis. To make things a little more confusing, rather than introduce a new acronym, ROI, that would undoubted annoy the amazing editor of this book, we will refer to both returns on an investment and returns on the assets of a firm as ROA measures.
Returns on an investment versus returns on equity invested in an investment. We are interested in the rate of return on funds committed to an investment. We are also interested in the rate of return on equity committed to an investment. The main distinction between measures that reflect earnings on an investments and equity funds committed to an investment is the following. Returns on equity subtract from total returns interest costs earned by debt capital. Returns earned by the investment do not subtract interest costs earned by debt capital.
Return measures. In previous chapters and especially in the previous chapter we described several measures designed to measure the returns earned by an investment versus returns earned by equity committed to an investment. These measures include NPV that find the present value of profit earned by the investment or equity committed to the investment over its economic life. AE derived from NPV convert the present value of earnings to their equivalent annuity—the constant amount that could be paid each period over the economic life of the investment. Finally, IRR measure the average rate of return earned by the investment or by equity committed to the investment earned over its economic life.
Two kinds of investments. There are two kinds of investments: stand-alone and incremental. Stand-alone investments are independent of other investments. They are self-contained. Furthermore, we do not expect that increases or decreased in stand-alone investments will influence the returns or affect investment decisions of other investments. Stand-alone investment may include more than one capital investment but when they do—they are interdependent so that one investment cannot be studied independent of the other investments.
Incremental investments add to, replace, or modify existing investments. Therefore, when considering the PV of incremental investments, we must account for the contributions of other inputs and services from other investments. In most studies, we ignore the problem of incremental investments by assuming that we can measure their contributions independent of the contributions of other investments and nondurable inputs—treating them as stand-alone investments. The reality is quite different. Most of our investments are incremental ones and measuring their unique contributions is difficult because when we add an investment to another investment(s), the use of other investments and nondurable inputs often change as well—making it difficult to identify what part of the change in the investment’s returns and expenses we can attribute to the new investment.
Investment identities. Capital investments have a distinct property. They can supply services for more than one period without losing their identity and without exhausting their service potential. Think of a battery as an example. It can provide services for more than one period without losing its identity. Another property of capital investments is that their service extraction most often requires services from other durables and nondurable inputs–whose service capacity and identity change with a single use.
Fixed investments. A fixed investment is one already owned by the firm and unlikely to be removed from service. Glenn Johnson describe the conditions required for an investment to be fixed; namely, that the investment’s acquisition value (V0) and liquidation value (V0liquidation) bound its value in use (V0use). In other words an investment is fixed or unlikely to be removed from service if: V0liquidation < V0use < V0. Because the investment’s value in use is less than what it would cost to acquire another one and because its liquidation value is less than what it is earning—the firm has no incentive to invest or disinvest in them. An investment with a zero or negative liquidation value is one likely fixed as long as it contributes something positive to the firm.
Accrual income statements (AIS) and investment analysis. An AIS makes no effort to find the contributions of a single or subset of a firm’s investments. However, isolating earnings from a single or subset of the firm’s investments is exactly what we do when constructing PV models for incremental capital investments—we attempt to isolate returns from capital investments that add to, replace, or alter capital investments used by the firm. Otherwise, we have no basis for incremental investment decisions.
ROA, ROE, and IRR. AIS summarize the collective contributions of a firm’s assets and equity during a single period by accounting for cash flow and changes in operating and capital accounts. Furthermore, we can calculate AIS earning measures as a percentage of the firm’s beginning assets and equity and report them as one period ROA and ROE respectively. Incremental investment analysis finds IRR for investments and equity committed to investments for one or several periods and report the results as the internal rate of return earned by an investment (IRRA) and internal rate or return earned by equity committed to the investment (IRRE). To find IRRA and IRRE for incremental investments require that we find the incremental investment’s unique contributions over their economic life. As a result, we cannot use the firm’s AIS to evaluate an incremental investment, although we organize our analysis around changes in operating cash flow and changes in operating and capital accounts—just the same as we did when analyzing a firm or stand-alone investment.
What follows. To find NPV, AE, IRR that reflect investment earnings and equity committed to stand-alone and incremental investments, we organize the remainder of this chapter as follows. First, we describe the connection between incremental and stand-alone investments. Second, we describe how to project cash flow and changes in operating and capital account used to describe stand-alone and incremental investments. We are careful when calculating NPV, AE, and IRR to indicate returns on stand-alone versus incremental investments whether they measure returns on the investment or returns from equity committed to the investment. Finally, we demonstrate how to find NPV, AE, and IRR for several practical multi-period stand-alone and incremental investments problems using Excel spreadsheets.
Incremental Investments
Incremental investment analysis intends to separate the contributions of an incremental investment from those of existing investments and other nondurable inputs and services. To be clear, incremental investment analysis does not hold all other inputs constant when considering its contributions because doing so would underestimate its contributions and lead to less than optimal investment choices.
The contributions of a stand-alone versus an incremental investment. To emphasize the connection between a stand-alone and an incremental investment, consider investing in scissor-type investments whose blades we purchase separately. With only one blade, the scissors’ output is small—equivalent to a knife. When we purchase a second blade, the scissor output increases toward normal. However, the increase in the scissors’ production when we added the second blade changed because we changed the use of both blades. If we analyzed the contribution of the second blade keeping the first blade idle, output would have remained low. Is it fair to attribute to the second blade the contributions of the first blade? Yes, and that is the approach we follow in incremental investment analysis because we want to know how adding the second blade changes the productivity of the scissors. Since the firm already owns the first blade, the investment decision focus is on the second blade, not the first one.
Optimal Service Extraction Rates
We want to determine the rate of return on multi-period capital investments. In this analysis, we assume that our investment provides services at its optimal rate. Finding the optimal service extraction rate for capital investments is complicated and we often employ complex computer programs to find these optimal rates. To do so, we must determine the optimal rate at which to extract services from our capital investments. At our level of investment analysis, we assume that optimal service extraction rates have already been determined. Yet it is important to understand what determines optimal service extraction rates even though the focus of our analysis is on the investment’s rate of return.
To be clear, when we discuss the cost of extracting services from our capital investment, we include its change in salvage value, the cost of using other nondurable inputs, and the change in the value of other capital investments whose services support our investment. As it turns out, the costs of using a capital investment within a period conform to the categories already identified in our PV templates. The cost of using nondurable inputs are measures as cash costs of goods sold (COGS). The cost of extracting capital investment services that depend mostly on the passage of time, we measure as cash overhead expenses (OE). The cost equal to the change in the liquidation value of the capital investment we measure as depreciation (Dep) and most of the time we assume that this rate of depreciation is determined by the passage of time.
Service extraction rates when the cost of using the investment depends mostly on the passage of time. Consider, for example, an investment whose use cost depends mostly on the passage of time such as a storage facility. The roof, for example, has a finite time during which it can provide services. It simply wears out over time. Much the same is true for other parts of the building including its painted surfaces, floors, and other building features. While there may be some important costs associated with heating, ventilation, and air conditioning services, these costs depend mostly on the passage of time and weather conditions than on the amount of items stored or the activity that occurs in the building. Finally, investments in buildings are usually fixed because their liquidation value is often low. To use a building requires that the new owner relocate to the building site. Thus, location fixity reduces the liquidity of the investment and contributes to its fixity in the firm’s investment portfolio.
So what is the optimal use of an investment whose costs depend mostly on the passage of time and whose low salvage value contributes to its fixity within the firm? Since its marginal use cost is usually low, their optimal use is their maximum capacity as long as the investment is making some positive contributions to the firm. For investments whose use costs depend mostly on the passage of time, we are not likely to change their use when adding an incremental investment to the firm unless we operate them at less than full capacity before the incremental investment.
Service extraction rates when the cost of using an investment depends mostly on its use. Consider another kind of investment whose use costs depends mostly on services provided by other capital investments, including maintenance costs, and nondurable inputs. Electric motors or gasoline powered equipment have their cost of service extraction dependent mostly on the cost of using nondurable inputs and services from other durables.
So what determines the optimal service extraction rates from investments whose cost depends mostly on use and other inputs? The optimal service extraction rate depends mostly on the marginal use costs. Furthermore, we expect that service extraction rates change when incremental investments are added to the firm that alter these marginal use costs. In sum, investments whose costs depends mostly on their use will find that their optimal use is not fixed nor at their maximum capacity.
Opportunity costs. All investments that provide services for one period or more incur opportunity costs equal to the defender’s IRR times the value of the investment at the beginning of the period. We incur the cost when we sacrifice a defending investment to employ a challenging one. We account for these costs when discounting future costs and returns to their present value.
Therefore, when we analyze incremental investments that provide services for more than one period, we must account for their opportunity cost and treat them as a mostly time related cost and unlikely to influence optimal service extraction rates within the period.
Least cost expansion paths. We have described how the optimal service extraction rates for stand-alone and incremental investments depend on whether the cost of extracting services depend mostly on their use or the passage of time. If the cost of extracting services depends mostly on the passage of time, their use will not likely change even with the addition of an incremental investment.
On the other hand, if the cost of extracting services from an investment depends mostly on its use, then their optimal service extraction rates will depend on the variable cost of using other inputs and the marginal use cost of extracting services from other investments.
To find the optimal service extraction rate, we employ a tool from economic analysis we refer to as the least-cost expansion path that we describe in Figure 13.1.
Figure 13.1. A least cost expansion path that employ other inputs (OI) and capital investment services (CS) to produce outputs Q1 and Q2 using various combinations of OI and CS.
Assume that a firm produces output using a combination of capital services and other inputs. We graph the combinations of capital services and other inputs that produce the same output and call the result an isoquant (i.e. same quantity). In Figure 13.1 we represent two levels of output by isoquants Q1, and Q2 drawn convex to the origin to reflect diminishing marginal productivity—a subject covered in microeconomics.
Now suppose that the firm considers a capital investment that will allow the firm to increase its use of capital services from CS1 to CS3 and increase output from Q1 to Q2. If the cost of using other inputs depend mostly on the passage of time, we hold their contributions fixed at OI1. On the other hand, if the cost of using other inputs is variable, then economic production theory teaches that increasing production from Q1 to Q2 holding other inputs constant would be inefficient. Instead, the theory teaches that the firm should increase capital services and other inputs along some least cost line OC determined by the relative costs of increasing both the capital services from the new investment and from the other inputs.
Increasing production along the least cost line OC, the firm would increase capital service from CS1 to CS2 an amount less that was required to reach Q2 when we held other inputs constant. In other words, increasing the use of other inputs allowed the firm to use less capital services from the new investment compared to the capital services required if other inputs were held constant (CS2 – CS1) < (CS3 – CS1) while still producing the same level of output. Furthermore, expanding other inputs and services from the new durable along the least cost expansion path assures us that the cost of increasing other inputs from OI1 to OI2 is more than offset by reducing the cost of capital services from (CS3 – CS1) to (CS2 – CS1).
Which expansion path? We have demonstrated that whether to measure the cost of increasing production along the least cost line OC or the expansion path OF that holds other inputs constant at OI1 depends on the nature of the costs of increasing the use of other inputs depends mostly on the passage of time or use. If increases in other inputs makes the investment more productive, this productivity increase is credited to the investment. Finally, if we measure changes along the least cost path, we must recognize that we are answering a different kind of question than “what are the unique returns to a challenging investment?” When performing PV analysis on a stand-alone investment, we ask: does the investment earn a positive net present value (NPV)—greater than the PV sacrificed by liquidating the defender. In contrast, the incremental investment analysis asks: is this change in the capital structure of the firm and use of other inputs more efficient and profitable than before the change?
Incremental investments and comparing two challengers. Incremental investment analysis is a legitimate approach for attempting to isolate the change in a firm’s revenue and cost in response to an incremental capital investment and changes in the use of other inputs. We justify the incremental approach because we are adding an incremental investment that may change the optimal use of other nondurable inputs and use of existing durables.
But what about a firm choosing between two or more challenging investments? In this case, three scenarios are being considered: the defending firm with its existing capital structure and the firm with incremental investments one and two. In some instances, the analysis finds the present value difference between the two incremental investment’s cash flow discounted by the defender’s IRR. Although this approach is convenient, it not generally an acceptable approach.
The problem of discounting the cash flow difference between two possible incremental investments is that we design NPV models to rank only two investments, not three. We illustrate the problem of ranking two challengers using their differences and the defender’s IRR as the discount rate. In our example, we assume the defender’s IRR is 12% and incremental challenging investments C1 and C2 have similar two-period terms with the following cash flow:
Table 13.1. Ranking investments C1, C2,
and the difference (C1–C2) with rankings in parentheses
Period Cash flow for C1 Cash flow for C2 Cash flow for (C1–C2)
0 –$10$15 –$25 1$1 1 0
2 $15 -$10 $25 NPV at 12%$2.85
(2)
$7.92 (1) –$5.07
C2 is preferred to C1
IRR
27.58%
(1)
–21.62%
(2)
0%
Indifferent between C1 and C2
The first thing to note about the example is that NPV(C1) minus NPV(C2) equals NPV(C1–C2) Therefore, individual NPV rankings in this example are consistent with NPV difference rankings as long as their cash flows are independent. However, IRR and NPV rankings for C1 and C2 are inconsistent because they violate size homogeneity conditions. Furthermore, IRR rankings depend on multiplicative operations. As a result, IRR rankings for C1 versus C2 are inconsistent with the IRR of C1 versus C2 based on the IRR of the difference in cash flows (C1–C2).
So what have we learned? We have learned that investments may be of two kinds: stand-alone and incremental. Regardless of the type of investment being analyzed, the optimal rate of service extraction will depend on whether changes in the liquidation of the investment depends mostly on the passage of time or on the level of the investment’s use. Because we can likely never separate the productive contributions of the new versus the existing investments, we simply acknowledge that the best we can do is to measure the changes in cash flow and operating and capital asset accounts and that the order of incremental investments will matter.
Forecasting Future Values for PV Templates
Future values for PV template variables. Chapter 12 introduced two PV templates, one for assets and one for equity. We illustrated the templates in Tables 12.5 through 12.7 using period one data reported in the coordinated financial statements (CFS) for HQN. The two templates apply regardless of whether we are analyzing the PV of incremental or stand-alone investments. We now ask, where can we find future values for template variables that will permit us to solve multi-period PV incremental or stand-alone problems? The answer is that we estimate (guess) their values!
Excel PV templates often create a tab for each exogenous variable as well as a tab for discount rate and tax rate assumptions. These tabs feed exogenous variable values to the PV templates that calculate NPV, AE, and IRR. The columns/tabs may include:
• Investment. Typically, there will be several investment components for a project aggregated to a single value for the PV tab. In addition, some investments may take place over the course of the project. For example, for long-term projects, earnings may be reinvestment in shorter-lived investments. In the case of dairy expansions populated with purchased cows, there will be an initial investment followed by reinvestments of cows until the herd can generate its replacements.
• Annual investment market liquidation values.
• Annual investment accounting book value. This tab must also include depreciation schedules.
• Annual account balances.
• Annual CR that may reflect a wide range of patterns over the investment’s economic life including no change, constant rate of change, lower receipts in start-up years, growth to a plateau followed by a decline, and several years with no receipts followed by growth to a plateau followed by a decline (e.g., orchards).
• Annual cash COGS.
• Annual cash OE.
Our confidence in the estimates of future values for exogenous variables decreases as the distance in time of the projection from the present increases—simply because we know more about the present than the future. Still, our estimates of near present exogenous variable values are often seriously wrong. For example, present investment amount is usually a well-documented number. Nevertheless, we frequently hear reports of investment expenditure overruns. Yet current and recent past data may still represent our best starting point for projecting future exogenous variable values.
We often project future values as stable trends. However, the future is hardly ever so predictable. Consider, for example, nominal corn prices in the mid-1960s. Corn rice fell by two and one-half times in the 1970s, leading to a fall in related prices and the financial crisis of the 1980s. Land values fell as much as 50 percent. Later, in the 2006–2013 period corn prices nearly doubled over the previous twenty-year period only to fall again in 2013 with input prices substantially higher than in the previous period. In real terms, current profitability is lower than in was in the post 1980’s period.
Historically, it has taken grain and oilseed markets six to twelve years to find their “new normal” following large, sustained shocks. History again provides a guide to the future, but the internal confidence around these future projections should be wide.
There are research groups such as the Food and Agricultural Policy Research Institute (FAPRI) at the University of Missouri (fapri.missouri.edu/publication/2019-u-s-baseline-outlook/ FAPRI) who annually make 10-year baseline projections for grain, oilseed, livestock markets, and a variety of other indicators. Even here, it is important to moderate forecasts using microeconomic principles and experience in making projections including a range of scenarios. Understanding intermediate and longer-term industry supply curves including regional and international dimensions is very important for most projects.
Figure 13.2. Past, Current, and Forecasted values for Corn Prices in the U.S. from 1965 to 2020 (National Agricultural Statistics Service).
Testing for robustness. That we populate our PV templates with estimates suggests that our templates will not be completely accurate. They will be consistent because the templates relate variables to each other consistently, but they are not likely to be completely accurate. We simply are not likely to estimate all of the future values of our variables correctly. As a result, we should calculate NPV, AE, and IRR under a variety of assumptions about future values so that we have some impression about the robustness of our estimates.
Exogenous and Endogenous variables in the PV templates. Similar to CFS, we populate PV templates with exogenous and endogenous variables. The distinction we made between exogenous and endogenous variables when constructing CFS is modified only slightly when constructing PV templates. The distinction is required because CFS modeled financial activity for one period. PV templates can model financial activity for several periods, requiring that we project variable values for future periods.
We define exogenous variables in PV templates as those whose values are determined outside of the template. We define endogenous variables in PV templates as those whose values are determine by current and previous values of template variables.
We can identify exogenous variables within the template because their cell values do not reference variable values in other cells. We can identify endogenous variables within the template because they include a formula signaled by an “=” sign that references other cells.
We must project all variables values in a PV template except some of those described at the beginning and end of period one. What distinguishes between projected values is whether we project their values using current and previous periods or whether they are projected outside of the PV template. Projections made using current or previous period template values are endogenous. Projections made outside of the PV template are exogenous.
Expert opinion and forecasts. Often, we rely on experts to project revenue related variables such as yields, prices, sales, and margins between revenue and cost. For example, services such as the Food and Agricultural Policy Research Institute (FAPRI) at the University of Missouri (fapri.missouri.edu/publication/2019-u-s-baseline-outlook/ FAPRI) presents a summary of 10-year baseline projections for U.S. agricultural markets, farm program spending, farm income and a variety of other indicators. Extension specialists, such as Dr. Jim Hilker, who have distinguished themselves with accurate forecasts can also be an invaluable resource.
Populating the PV Templates
We now describe in more detail the variables and data needed to populate our PV templates that enable us to find rolling NPV, AE, and IRR estimates for investments and invested equity. We begin with the only information we know for sure, future dates: 2019, 2020, 2021, etc. Therefore, we begin populating our PV models templates with the one thing we know about the future: future dates recorded in column 1.
The investment acquisition amount. In both the investment and equity PV templates, we record the investment acquisition amount in cell B4. Its value is determined outside of the template making it an exogenous variable. We treat the investment’s acquisition value as though it were a cash expenditure unless funded by debt, an amount recorded in cell C4. When we employ debt to acquire the investment, the focus is on the equity invested—equal to the investment amount less the debt used to acquire the investment. The investment amount may be the most accurate data in our template because investments occur mostly in the present and we know much more about “now” than “later”.
The investment amount is usually a well-documented number. Durable sellers post their offer prices. Markets establish and record durable exchange prices. References for used farm equipment similar to Kelly’s Blue Book for cars are generally available.
Complicating our investment data are projects that incur investments costs over several time-periods. Indeed, one might consider repair and maintenance expenditures designed to improve the life and durable performance to represent additional investments. In other cases, the investment includes several durable that we replace at different intervals. For example, feeder calf operations routinely replaces one cohort of calves with another but the feeding equipment and physical facilities we replace less often than the feed calves.
Liquidation values. To find rolling NPV, AE, and IRR estimates, we require not only an investment acquisition amount, but investment liquidation and market values over time. An investment’s acquisition value, V0, is the amount of money exchanged to acquire the investment. An investment’s book value, Vbook, equals it acquisition value minus its accumulated depreciation. An investment’s liquidation value, Vliquidation, is the amount of money a buyer is willing to exchange for the investment when it the investment is sold. If an investment’s liquidation value is greater than its acquisition value, we refer to the difference as capital gains. If an investment’s liquidation value is less that its acquisition value but greater than its book value, we refer to the difference as depreciation recovery. Finally, if the liquidation value is less than its book value, we refer to the difference as capital losses. We describe capital gains, depreciation recovery, and capital losses in the following equations:
for
(13.1) V_0 > V^{book}, \,capital\, gains\, = V^{liquidation} - V^{book} > 0, \end{equation*} " title="Rendered by QuickLaTeX.com">
for
(13.2) V^{liquidation} > V^{book}, \,depreciation\, recapture\, \ & = V^{liquidation}- V^{book} > 0, \end {split} \end{equation*} " title="Rendered by QuickLaTeX.com">
and for
(13.3) V^{book}> V^{liquidation}, \,capital\, losses\, = V^{book}- V^{liquidation} > 0. \end{equation*} " title="Rendered by QuickLaTeX.com">
We determine accounting book values by applying tax regulations that specify depreciation amounts depending on the type and age of the investment. Since depreciation forecasts depend on the age and amount of the investment, we generally consider them endogenous variables. Furthermore, we recognize that liquidation values of investments are also generally determined by projecting market values and cost data and may be endogenously or exogenously variables. When we do not expect to liquidate the investments, but want to estimate their NPV, AE and IRR, we may equate market liquidation value with book values.
Endogenous variables in PV templates. When projecting COGS data we generally assume they are related to CR projections. COGS are likely to depend on CR because they mostly vary with production levels making them endogenous variables. However, COGS may also vary with time as relative supplies of inputs and inflation add a trend line to our COGS estimates. We might express this relationship between future value of COGS, an endogenous projection, and their connection to CR and time t as:
(13.4)
where and are estimated in such a way to reduce the average error in period t, εt, involved in the estimation of COGS while treating time t and CR as exogenous variables. When we have past values of the variables in Equation \ref{13.4} we can use statistical techniques such as linear regression analysis to find the coefficients.
Similarly, we can treat future OE as endogenous and estimate then from values of other variables. However, OE in contrast to COGS we expect to be more related to time and their previous values than CR values. This connection between OE, time and their previous values we can express as:
(13.5)
where are estimated in such a way to reduce the average error in period t, εt.
Endogenous variable projections. We often begin building a PV template data set by observing previous values of exogenous and endogenous variable reported in the current and past CFS. For example, suppose that we observe that prices and yields in the past have predictable trends and changes. We might use these observations of past template variable values to project their future value. To illustrate, suppose that over the past 10 years, corn yields g1, g2, ⋯, g10 have increased by 13%. Then letting [/latex]\bar{g}_y[/latex] equal the average percentage increase in corn yields we find its value in the equation equal to:
(13.6)
And solving for the annual average increase in yield we find:
(13.7)
Assuming the past trends in yield continue and if the yield last year were 140 bushels per acre, in 5 years we would expect yields to have increased to:
(13.8)
Finally, assume we employ the professional forecasting services to find future values corn prices which when multiplied by our projected yields produces an estimate of CR.
Projecting margins. One of the main ways we can improve our variable value forecasts is to observe their values and relationships to one another in the past—and the more observations, usually the better. One observation that is important using past data is the margin between revenue and costs. We can be confident that this difference is bounded, otherwise, competitors would flock to join our industry and begin replicating our operations. If the difference is negative for a significant period of time, we will become insolvent and leave the industry.
Past margin observations may guide our projection in the future. Taxes will be some function of the difference between revenue and sales. Changes in comparatives advantages and preferences may also be included in the description of how the variables are related. Future preferences will influence demand for what we produce. Changes in comparative advantage—who can produce least expensively and where—will also influence revenue and expenses. Favorable increases in comparative advantage will reduce our costs and put us in a position to expand our operation. And as we increase in sophistication, we might worry about local, national, and international politics that may influence tariffs and the challenges of competing in a global economy.
Other forecasts. Sometimes, failing to find forecasts of direct interest to the calculation of our investment’s NPV, AE, and IRR—we can often times find forecasts highly correlated with our forecasts of interest. For example, suppose we are interested in the price of hard red winter wheat but can only observe past prices of corn and soybeans. Using linear regression, a statistical technique that allows us to relate an endogenous variable to one or more exogenous variable—we can use the future estimates of corn and soybean prices to predict hard red winter prices.
Real versus nominal data values. In our PV templates, we project CR, cash COGS and cash OE. We can employ several assumptions about future cash flow associated with these values. The first one is that there is no change from data entered in year one. This assumption is consistent with capitalization formula that assume zero change in future cash flow. It may also be relevant if the model assumes that data are in real numbers so that numbers do not change with inflation. Furthermore, we may assume that the future is represented by the present and these relationships between variables in the present should be preserved.
Solving Practical Investment Problems: Green and Clean Services
Lon is considering investing in a lawn care and snow removal business that will require that he purchase lawnmowers, snow blowers, and other equipment. Lon intends to name his business Green and Clean Services (GCS). Assume that Lon has hired you to advise him on whether or not he should invest in the business. To solve Lon’s investment problem you intend to solve Equation \ref{13.6} (see Equation \ref{12.21} in Chapter 12).
(13.9)
To complete the PV template corresponding to Equation \ref{13.9} and described in Table 12.5, he provides the information that follows.
Acquisition cash flow. Lon estimates the initial investment will cost $40,000. The equipment falls into the MACRS 3-year depreciation class (25%, 37.5%, 25%, and 12.50%) and in four years Lon estimates he can sell his equipment for$10,000. With this information, Lon completes the acquisition stage of his investment analysis.
Operating cash flow. Lon intends to charge $40 per service for both lawn care and snow removal services. He estimates that his expenses (labor, fuel, maintenance) will average$18 per service. Lon projects the number of services for the next four years to be 500 in year one, 750 in year two, 900 in year three, and 1,000 in year four. Lon recognizes that not all his customers will pay for his services when he provides them. He expects his accounts receivable (AR) to equal $1,000 at the end of his first year of operation, to grow to$1200 at the end of year two, to decline to $800 at the end of year three, and to decline to$400 at the end of year four. The outstanding $400 balance at the end of year four, he expects to liquidate when he sells his business. To simplify, we assume that Lon’s marginal tax rate and capital gains tax rate both equal 20%. Lon also assumes that the before-tax IRR of the defending investment equals 10% and that the after-tax IRR of the defending investment is 8%. To determine Lon’s operating ATCF, we need to find CR, cash COGS, and cash OE. We begin with CR. CR equals sales less increases (plus decreases) in AR. Increases in AR represent sales for which Lon did not receive payment. Decreases in AR represent previous sales paid for in the current period in cash. We could also adjust CR for increases (decreases) in inventories. But in this example, GCS has no inventories. To find sales we multiply the number of services per year by the price paid per service. We find that cash sales equal$40 x 500 = $20,000 in year one;$40 x 750 = $30,000 in year two;$40 x 900 = $36,000 in year three; and$40 x 1000 = $40,000 in year four. In year one AR increased by$1,000. As a result, CR equal sales of $20,000 less$1,000 increase in AR or $19,000. In year two AR increased by$200 so that CR equal sales of $30,000 less$200 increase in AR or $29,800. In year three, AR declined by$400 so the CR was greater than sales of $36,000 by$400: $36,000 +$400 equals $36,400. Finally, at the end of year four, the last year Lon intends to operate GCS, AR declines to$400 increasing CR by $400 to$4,400. Finally, the remaining $400 balance of CR Lon liquidates when he sells the business. Similarly, we find COGS by multiplying the number of services provided times the cost to deliver a service unit. We find they equal$18 x 500 = $9,000 in year one;$18 x 750 = $13,500 in year two;$18 x 900 = $16,200 in year three, and$40 x 1000 = $18,000 in year four. We calculate depreciation by multiplying MACR 3-year class rates (25%, 37.5%, 25% and 12.5%) times the value of the capital accounts equal to$40,000. Depreciation is ($40,000 x 25%) =$10,000 in year one; $40,000 x 37.5% =$15,000 in year two, $40,000 x 25% =$10,000 in year three, and $40,000 x 12.5% =$5,000 in year four. Finally, we summarize our data and estimations in columns A through M in Table 13.2 below.
Table 13.2. PV Template for Rolling Estimates of NPV, AE, and IRR for Green and Clean Services (GCS)
Open Table 13.2 in Microsoft Excel
A B C D E F G H I J K L M N O P
3 Yr Capital accounts values Capital accounts liquidation value Capital accounts book value Operating accounts values (AR- INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OE) Tax savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating Capital and operating accounts ATCF from operations and liquidations Rolling NPV Rolling AE Rolling IRR
4 0 $40,000$40,000 $0$40,000 $40,000 5 1$0 $30,000$30,000 $1,000$10,000 $19,000$9,000 $0$2,000 $10,000$30,800 $40,800 ($2,222.22) ($2,222.22) 0.00% 6 2$0 $20,000$15,000 $1,200$15,000 $29,800$13,500 $0$3,000 $16,040$19,960 $36,000$123.46 $61.73 0.00% 7 3$0 $15,000$5,000 $800$10,000 $36,400$16,200 $0$2,000 $18,160$13,640 $31,800$8,254.84 $2,751.61 0.00% 8 4$0 $10,000$0 $400$5,000 $40,400$18,000 $0$1,000 $18,920$8,320 $27,240$17,449.18 $4,362.30 0.00% To find after-tax cash flow (ATCF) from operations during each year, we subtract from CR in column G, cash COGS in column H and cash OE in column I and multiply the result by (1 – T*) where T* equals the average tax rate paid on investment earnings that we set equal to 20%. Finally, we add tax savings from depreciation T*Dep reported in column J. These operations on exogenous variables estimate ATCF from operations reported in column K. Liquidation. At the end of four years of operating GCS, Lon’s equipment has a salvage value of$10,000 and an accounting book value of $0. Therefore, the after-tax liquidated equipment salvage value equals V4 (1 – T*) =$10,00(1 – .2) = $8,000. (See equation 13.6). The AR account has a value of$400 and when liquidated is treated as after-tax cash income of AR4(1 – T*) = $400(1 – .2) =$320. The sum of ATCF from liquidation is equal to $8000 +$320 plus and T*Accounts0 = $0 (see equation 13.6) or an after-tax liquidation value at the end of year four equal to$8,320.
Rolling NPV, AE, and IRR calculations. Lon assumes he will operate GCS for four years. He might have asked: what is the optimal life of GCS? To answer the optimal life question, we need to find annual or rolling NPV, AE, and IRR values. In this case, Lon is correct, four years is preferred to one, two, or three years of operation. Rolling NPV reported in column N increased from a negative NPV of ($2,222.22) if he operated the business for one year to an NPV of$17,449.18 if he operated his business for four years as planned. That the optimal life of operation is confirmed by increasing AE from a negative ($2,222.22) to a positive$4,362.30 in year 4. Meanwhile, IRR increases from 2.00% to 23.46% in year four.
To find rolling NPV, AE, and IRR estimates we divide the numbers in Table 13.2 into acquisition, operating, and liquidation cash flow. We record the acquisition value in all for years in cell L4. We record the ATCF from operations in column K and the ATCF from liquidation in column L. The sum of ATCF from operations and liquidations for the last year of operations we record in column M. We record the ATCF for each year of possible economic life in the IRR tab. In our case the ATCF for years 1,2,3, and 4 are recorded in columns B, C, D, and E in the Excel spreadsheet corresponding to the IRR tab.
Table 13.3. ATCF, NPV, AE, and IRR for GCS for economic lives of 1, 2, 3, and 4 years for an investment of $40,000. Open Table 13.3 in Microsoft Excel A B C D E 1 Economic Life 1 year 2 years 3 years 4 years 2 ATFC year 0 (investment) -$40,000.00 -$40,000.00 -$40,000.00 -$40,000 3 ATFC year 1$40,800.00 $10,000.00$10,000.00 $10,000 4 ATFC year 2$36,000.00 $16,040.00$16,040
5 ATFC year 3 $31,800.00$18,160
6 ATFC year 4 $27,240 7 8 NPVs -$2,222.22 $123.46$8,254.84 $17,449.18 9 AEs -$2,222.22 $61.73$2,751.61 $4,362.30 10 IRRs 2.00% 8.19% 17.15% 23.46% Equity invested in Green and Clean Services. Lon is not only interested in knowing his earnings from the GCS investment, he is also interested in knowing his earnings from his equity invested in GCS. To that end, he accounts for the investment less the debt supporting his investment in Table 13.3. Lon intends to borrow$10,000 and pay interest costs at a rate of 6% on principal that he intends to reduce each year by $1,000. As a result, at the end of the first year Lon expects his outstanding loan balance will equal$9,000, $8,000 at the end of year two,$7,000 at the end of year three, and $6,000 at the end of year four. Lon plans to liquidate his loan balance of$6,000 when he sells his business at the end of four years of operations.
To find his equity earnings, we solve Equation \ref{13.7} (see equation 12.20 in Chapter 12). The template corresponding to Equation \ref{13.7} and is only slightly changed from the template described in Table 13.2. We describe it next in Table 13.4. It records outstanding debt in column C, interest payments that reduce operating income and taxes, we record in column K.
(13.10)
To find rolling NPV, AE, and IRR estimates we divide the numbers in Table 13.4 into acquisition, operating, and liquidation cash flow. We record the acquisition value in all for years in cell N4. We record the ATCF from operations in column M and the ATCF from liquidation in column N. The sum of ATCF from operations and liquidations for the last year of operations is recorded in column O.
Table 13.4. PV Template for Rolling Estimates of NPV, AE, and IRR for Equity Invested in Green and Clean Services (GCS)
Open Table 13.4 in Microsoft Excel
A B C D E F G H I J K L M N O P Q R
3 Yr Capital accounts values Debt Capital Capital accounts liquidation value Capital accounts book value Operating accounts values (AR- INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OE) Interest Costs Tax savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating Capital and operating accounts ATCF from operations and liquidations Rolling NPV Rolling AE Rolling IRR
4 0 $40,000$10,000 $40,000$0 $30,000$30,000
5 1 $0$9,000 $30,000$30,000 $1,000$10,000 $19,000$9,000 $0$600 $4,000$9,640 $20,600$30,240 ($1,471.70) ($1,471.70) 0.80%
6 2 $0$8,000 $20,000$15,000 $1,200$15,000 $29,800$13,500 $0$540 $6,000$15,456 $9,720$25,176 $1,500.89$750.44 9.07%
7 3 $0$7,000 $15,000$5,000 $800$10,000 $36,400$16,200 $0$480 $4,000$15,832 $3,480$19,312 $9,064.85$3,021.62 19.89%
8 4 $0$6,000 $10,000$0 $400$5,000 $40,400$18,000 $0$420 $2,000$15,188 -$760$14,428 $17,571.30$4,392.83 27.80%
In the IRR tab we record the ATCF for each year of possible economic life. In our case the ATCF for years 1,2,3, and 4 are recorded in columns B, C, D, and E. In the IRR tab in rows 8, 9, and 10 we report NPV, AE, and IRR for each year and repeat them for convenience in columns P, Q, and R in Table 13.5.
Table 13.5. ATCF, NPV, AE, and IRR for GCS for economic lives of 1, 2, 3, and 4 years for equity of $30,000 invested in GCS. Open Table 13.5 in Microsoft Excel A B C D E 1 Economic Life 1 year 2 years 3 years 4 years 2 ATFC year 0 (investment) -$30,000 -$30,000 -$30,000 -$30,000 3 ATFC year 1$30,240 $9,640$9,640 $9,640 4 ATFC year 2$25,176 $15,456$15,456
5 ATFC year 3 $19,312$15,832
6 ATFC year 4 $14,428 7 8 NPVs -$1,471.70 $1,500.89$9,064.85 $17,571.30 9 AEs -$1,471.70 $750.44$3,021.62 $4,392.83 10 IRRs 0.80% 9.07% 19.89% 27.80% Excel Spreadsheets for Describing Exogenous Variable Forecasts As we increase the sophistication of our forecasts, we recognize the need to use additional Excel spreadsheets identified by tabs. These describe the procedures we followed to estimate the future values of exogenous variables and the values of exogenous variables we estimated. The tabs appear at the bottom of Tables 13.2 that we describe next. Similar tabs describe the exogenous variable projection procedures and values for Table 13.4. Constants tab After the template tab that contains Table 13.2 and Table 13.4 is the “constants” tab that contains key assumptions employed in the calculation of the Tables 13.2 and 13.4. Although they vary with projection method, they may include such constants as the average federal, state, and local tax rates paid on earnings from the investment or equity earnings, the defenders IRR, growth rate assumptions for debt, liquidation values, CR, COGS, OE and other variables. We represent arbitrary constant value assumption below that would be input to the PV template Table 13.6a. Excel Template Constants Worksheet Tab Open Template in Microsoft Excel A B 1 IRRs, tax rates, and growth rates 2 defender’s IRR 10.00% 3 average tax rate 20.00% 4 After-tax rate 8.00% 5 average interest rate 6.00% 6 debt growth rate 1.00% 7 liquid. growth rate -2.00% 8 Book value growth rate -2.00% 9 acct.bal.growth rate 1.00% 10 CR growth rate 1.00% 11 COGS growth rate 1.00% 12 OEs growth rate 1.00% IRR tab To calculate IRR required that we assemble ATCF for each PV model with a different term. These along with NPV, AE, and IRR computations we report in the IRR tab. Data for the IRR tab for GCS were reported in Tables 13.3 and 13.5. Table 13.6b. Excel Template IRRs Worksheet Tab Open Template in Microsoft Excel A B C D E 1 Economic Life 1 year 2 years 3 years 4 years 2 ATFC year 0 (investment) -$40,000 -$40,000 -$40,000 -$40,000 3 ATFC year 1$40,800 $10,000$10,000 $10,000 4 ATFC year 2$36,000 $16,040$16,040
5 ATFC year 3 $31,800$18,160
3 $0 4 40 Liquidation Value of Capital Investments tab To calculate rolling NPV, AE, and IRR estimates, we must estimate the liquidation value for capital investments. Generally, we treat capital account liquidation values as exogenous. We represent arbitrary projected capital account liquidation values below that would be input to the PV template. Table 13.6d. Excel Template Liquidation Value Worksheet Tab Open Template in Microsoft Excel 3 Yr Capital accounts values Capital accounts liquidation value 4 0$40,000
5 1 $0$30,000
6 2 $0$20,000
7 3 $0$15,000
8 4 $0$10,000
9 5 $0$10,000
10 6 $0 11 7$0
Book Value of Capital Assets tab
The purchase price of capital assets established a book or accounting value of capital assets. In the CFS, we record the book value of capital assets in firm’s balance sheets. The book value of the firm’s capital assets are adjusted by depreciation rates determined by taxing authorities. There are more than one methods for determining depreciation allowing capital investment owners some flexibility in establishing depreciation amounts. Generally, the time value of money encourages investment owners to depreciate their investments as rapidly as possible. In this tab, we generally describe the depreciation method that is used to establish the capital investments’ book values. We represent arbitrary projected book values of capital accounts below that would be input to the PV template.
Table 13.6e. Excel Template Book Value Worksheet Tab
Open Template in Microsoft Excel
A
1 Capital Accounts Book Value
2 $40,000 3$30,000
4 $15,500 5$5,000
6 $0 7$0
Depreciation Rate tab
The Excel spreadsheet that corresponds to the depreciation rate tab (Dep) describes the depreciation method applied to the capital investments to determine their book value. This tab most often includes the depreciation base for capital investments so that multiplying the depreciation rates times the base calculates the depreciation amount in each year. We represent arbitrary projected depreciation values below that would be input to the PV template
Table 13.6f. Excel Template Depreciation Worksheet Tab
Open Template in Microsoft Excel
A B C D
1 Year Depr. Base Depr. Rate Depr. Amount
2 0 $40,000 3 1 25%$10,000
4 2 37.50% $15,000 5 3 25%$10,000
6 4 12.50% $5,000 7 5 0% 0 Sum of Operating Accounts tab Increases in the sum of operating accounts (AR+Inv) represent income not received as cash. Decreases in the sum of operating accounts (AR+Inv) represent income earned previously received as cash in the current period. Increases in the sum of operating accounts (AP+AL) represent expenses not paid for in cash. Decreases in the sum of operating accounts (AP+AL) represent expenses incurred previously paid in the current period. The sum of operating accounts are reported in this tab. We represent arbitrary projected sums of operating accounts below that would be input to the PV template. Table 13.6g. Excel Template Operating Accounts Worksheet Tab Open Template in Microsoft Excel B C D E F 1 AR INV AP AL Op. Acc. Sum 2 1640 3750 3000 958 1432 3 1200 5200 4000 880 1520 4 1550 5 1580 6 1610 7 1500 Cash Receipts tab Cash receipts are the oxygen of the firm and investment. We might say that cash receipts are the sine qua non tab because without it nothing else exists for long. In addition, we might also claim that it is the leading exogenous variable because other cash flow variables such as COGS and OE are related to it. Finally, it is the variable most often the focus on professional forecasts or at least the focus of variables highly correlated with CR such as prices. We will have more to say about the Excel sheet that correspond to the CR tab later on. We represent arbitrary projected cash CR estimates below that would be input to the PV template. Table 13.6h. Excel Template Cash Receipts Worksheet Tab Open Template in Microsoft Excel A B 1 Cash Receipts 2 Year 3 0$19000.00
4 1 $19190.00 5 2$19381.90
6 3 $19575.72 7 4$19771.48
8 5 $19969.19 Cash COGS tab Cash COGS follow closely CR values since by definition they are the costs that vary with production. Therefore, most forecasts of Cash COGS use CR as a variable in the COGS forecast. COGS forecasts may also benefit from projections of input prices. We represent arbitrary projected cash COGS estimates below that would be input to the PV template. Table 13.6i. Excel Template COGS Worksheet Tab Open Template in Microsoft Excel A B 1 Cost of Goods Sold 2 Year 3 0 4 1$9,000.00
5 2 $9,090.00 6 3$9,180.90
7 4 $9,272.709 8 5$9,365.436
Cash OE tab
Cash OE may be related to CR but less so than cash COGS. The initial value for OE may be determined by the size of the business and production activity but in later periods overhead expenses may be less tied to production that input prices that vary over time. Therefore, we sometimes estimate cash OE based on their previous period’s value plus some function of time designed to capture changes in utility, labor, and general maintenance costs. We represent arbitrary projected OE estimates below that would be input to the PV template.
Table 13.6j. Excel Template Cash OE Worksheet Tab
Open Template in Microsoft Excel
A B
1 Cash Overhead Expenses
2 Year
3 0
4 1 $300.00 5 2$305.00
6 3 $310.00 7 4$315.00
8 5 $320.00 More Sophisticated Forecasts for GCS Multi-period PV models depend on forecasts of future values of exogenous variables. Our forecasts of exogenous variables differ in their sophistication and resources committed to their estimation. Obviously, we can never validate our forecasts until the time of the forecast has passed, leading us to infrequently report the accuracy of our predictions—which are usually “wide of the mark”. So as the quip goes, if you cannot guess correctly, guess often! That strategy is exactly what we recommend here: make frequent forecast updates as new information becomes available. We begin with a base forecast, the one we expect most likely to occur. In our case, we reported the base forecasts for GCS in Tables 13.2 and 13.4. Then we make additional forecasts employing a variety of methods and resources. Status quo We begin with the least sophisticated forecast—that the future will be the same as the present. The rational for this approach is that our best forecast is likely the closest to the present. In our case, we assume future CR and COGS in period one continue for the next four years and that AR remain at$1,000. We continue with our other assumptions and resolve the PV template for investments. We describe the results in Table 13.7.
Table 13.7. PV Template for Rolling Estimates of NPV, AE, and IRR for Green and Clean Services (GCS) Assuming Constant CR and COGS
Open Template in Microsoft Excel
A B C D E F G H I J K L M N O P
3 Yr Capital accounts values Capital accounts liquidation value Capital accounts book value Operating accounts values (AR + INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OE) Tax savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating capital and operating accounts ATCF from operations and liquidations Rolling NPV Rolling AE Rolling IRR
4 0 $40,000$40,000 $0$40,000 $40,000 5 1$0 $30,000$30,000 $1,000$10,000 $19,000$9,000 $0$2,000 $10,000$30,800 $40,800 ($2,222.22) ($2,222.22) 2.00% 6 2$0 $20,000$15,000 $1,000$15,000 $19,000$9,000 $0$3,000 $11,000$19,800 $30,800 ($4,334.71) ($2,167.35) 1.14% 7 3$0 $15,000$5,000 $1,000$10,000 $19,000$9,000 $0$2,000 $10,000$13,800 $23,800 ($2,416.81) ($805.60) 5.07% 8 4$0 $10,000$0 $1,000$5,000 $19,000$9,000 $0$1,000 $9,000$8,800 $17,800 ($288.16) ($72.04) 7.70% 9 5$0 $10,000$0 $1,000$0 $19,000$9,000 $0$0 $8,000$8,800 $16,800$4,677.38 $935.48 12.06% We can observe these consequences of our more conservative growth assumptions. NPV and AE remain negative throughout the four years. Only in the fifth year does the IRR exceed the after-tax discount rate of 8% turning NPV and AE positive. The IRR for GCS is increasing and we expect that by year five will exceed the after-tax IRR of the defender. Contributing to the positive NPV in period five is the liquidation of the capital accounts that Lon assumes will be the same value as in year four. Constant percentage change assumptions Next in forecast sophistication, we assume a constant growth (decay) rate assumption about CR and COGS. In this forecast we project and similarly we project COGS as: .Our assumptions for gCR and gCOGS we describe in the Excel sheet accessed through the constant tab—each assumed to equal 1%. We project the future values for CR and COGS and report them in the Excel sheets reference by the CR and COGS tabs. Then we copy them into the GCS investment template and report the results in Table 13.8. Table 13.8. PV Template for Rolling Estimates of NPV, AE, and IRR for Green and Clean Services (GCS) Assuming Constant % Δ in CR and COGS Open Table 13.8 in Microsoft Excel A B C D E F G H I J K L M N O P 3 Yr Capital accounts values Capital accounts liquidation value Capital accounts book value Operating accounts values (AR + INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OE) Tax savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating capital and operating accounts ATCF from operations and liquidations Rolling NPV Rolling AE Rolling IRR 4 0$40,000 $40,000$0 $40,000$40,000
5 1 $0$30,000 $30,000$1,000 $10,000$19,000 $9,000$0 $2,000$10,000.00 $30,800$40,800 ($2,222.22) ($2,222.22) 2.00%
6 2 $0$20,000 $15,000$1,000 $15,000$19,190 $9,090$0 $3,000$11,080.00 $19,800$30,880 ($4,266.12) ($2,133.06) 1.25%
7 3 $0$15,000 $5,000$1,000 $10,000$19,382 $9,181$0 $2,000$10,160.80 $13,800$23,961 ($2,220.57) ($740.19) 5.31%
8 4 $0$10,000 $0$1,000 $5,000$19,576 $9,273$0 $1,000$9,242.41 $8,800$18,042 $86.25$21.56 8.09%
9 5 $0$10,000 $0$1,000 $0$19,771 $9,365$0 $0$8,324.83 $8,800$17,125 $5,272.86$1,054.57 12.55%
Note that increasing CR and COGS by the same percent each period increased the margin between them over time. To illustrate, in year one, (CR – COGS) = ($19,000 –$9,000) = $10,000. In year five, we found the margin to be (CR – COGS) = ($19,771 – $9,365) =$10,406. Because of compounding CR and COGS, NPV turned positive in year four (one year earlier than under the constant value assumption) and the IRR in the constant percentage change model exceeded the IRR in the constant model in each year after the first one.
Linear growth rate assumption
To project linear grow rates is generally a most conservative assumption that projecting constant percentage growth rates—other things being equal. There are several different linear assumptions we can adopt. For example, we might assume that and where t = 1, 2, 3, 4, 5 and constants and . We project the future values for CR and COGS using our estimating and report them in the Excel sheets reference by the CR and COGS tabs. Then we copy them into the GCS investment template and report the results in Table 13.9.
Table 13.9. PV Template for Rolling Estimates of NPV, AE, and IRR for Green and Clean Services (GCS) Assuming Linear Δ in CR and COGS
Open Table 13.9 in Microsoft Excel
A B C D E F G H I J K L M N O P
3 Yr Capital accounts values Capital accounts liquidation value Capital accounts book value Operating accounts values (AR + INV – AP – AL) Capital Accounts Depr. Cash Receipts (CR) Cash Cost of Goods Sold (COGS) Cash Overhead Expenses (OE) Tax savings from depr. (TxDepr) After-tax cash flow (ATCF) from operations ATCF from liquidating capital and operating accounts ATCF from operations and liquidations Rolling NPV Rolling AE Rolling IRR
4 0 $40,000$40,000 $0$40,000 $40,000 5 1$0 $30,000$30,000 $1,000$10,000 $19,000$9,000 $0$2,000 $10,000$30,800 $40,800 ($2,222.22) ($2,222.22) 2.00% 6 2$0 $20,000$15,000 $1,000$15,000 $19,100$9,110 $0$3,000 $10,992$19,800 $30,792 ($4,341.56) ($2,170.78) 1.12% 7 3$0 $15,000$5,000 $1,000$10,000 $19,200$9,330 $0$2,000 $9,896$13,800 $23,696 ($2,506.22) ($835.41) 4.96% 8 4$0 $10,000$0 $1,000$5,000 $19,300$9,660 $0$1,000 $8,712$8,800 $17,512 ($589.27) ($147.32) 7.39% 9 5$0 $10,000$0 $1,000$0 $19,400$10,100 $0$0 $7,440$8,800 $16,240$3,995.14 $799.03 11.51% Projections based on related forecasts To this point, we have projected CR and COGS based on their past values and time. Most sophisticated projections take advantage of expert predictions based on observed value of related variables in the past. Suppose that for the last seven years, prices of lawn care and snow removal services were$13, $12,$13.5, $15,$16, $18,$17.5, and $17.9 for t = 0, 1, 2, 3, 4, 5, 6, 7. We project future prices p for t = 8, 9, 10, 11, 12, 13 for lawn care and snow removal services using Excel’s forecast option. Table 13.10. Excel Forecast Estimate Open Template in Microsoft Excel A B C D E 1 time observed Forecast(observed) Lower Confidence Bound(observed) Upper Confidence Bound(observed) 2 0 13 3 1 12 4 2 13.5 5 3 15 6 4 16 7 5 18 8 6 17.5 9 7 17.9 17.90 17.90 17.90 10 8 19.73214458 17.99 21.47 11 9 21.59962998 19.81 23.39 12 10 21.62645857 19.78 23.47 13 11 22.85993116 20.96 24.76 14 12 24.72741656 22.78 26.68 15 13 24.75424515 22.75 26.75 Figure 13.3. Graph of Projection Estimates Open Template in Microsoft Excel Having obtained price forecasts, our next step would be to re-estimate CR for GCS based on the forecasted prices. In addition, we may use the confidence interval forecasts to find a most optimistic forecast using the upper confidence interval forecasts and a pessimistic forecast using the lower bound forecasts. The forecasts above have been presented as coming from a “black box”. The black box, in this case contains well-known statistical methods that can easily be learned but beyond an already over ambitious collection of topics covered in this book. So what have we learned? We learned that PV models analysis requires projections of future values for exogenous variables. Furthermore, we learned that there is no way to validate our future estimates except by comparing them to their past values. Finally, project future values of exogenous variables from the past values is an art and unlikely to be accurate. Therefore, our approach should be to estimate several alternative forecasts to determine the robustness of our results under a variety of assumptions. Still, we recommend that when any new information that might affect our forecast becomes available, we should incorporate it into our models. Another approach to forecasting and making investment decisions based on our forecasts is to require a “cushion”. In other words, to commit to an investment if it not only earn the defender’s IRR—but that it earns much more—a cushion—so that if our forecasts are wrong, too optimistic, we are still likely to earn a positive NPV. Incremental Investments Incremental investments may replace, modify, or expand an existing investment. Regardless, the incremental investment analysis approach is the same: it compares the defending investment with changes that result from an incremental investment. What is common to incremental investments is that something of the original investment remains. In what follows, we illustrate an incremental investment with a bakery considering replacing its doughnut-making machine. Other investments supporting the doughnut making machine are assumed to be unaffected by the incremental investment. Brown and Round Doughnuts We next consider two alternative machines for making doughnuts. One machine is the one already in operation. In this case the challengers are an older version of the original machine and a new machine. Should you continue with the used machine, buy a new machine, or get out of the doughnut business? Continuing to make doughnuts with the old machine. In this example the challenger is an older version of the original investment. To be specific, suppose you bought a doughnut machine 3 years ago for$90,000. You are depreciating the machine over 5 years using the MACRS method, and the expected market value 5 years from today is $10,000. The machine generates$30,000 in cash revenues and produces $15,000 in cash expenses each year. If you sold the machine today, you could get$30,000 from a local competitor.
Your after-tax ROA-IRR, r(1 – T), is 10%, your marginal tax rate is 40%, and the capital gains tax is 20%. Assume book value depreciation can be used to offset ordinary income.
Let’s begin with the old machine. Keeping the old machine is equivalent to reinvesting its $30,000 current value (V0) in the business and forfeiting the tax refund from capital losses. To determine the tax refund forfeited, recall that the used machine was purchased 3 years earlier for$90,000, and has been depreciated using 5-year MACR, so the machine’s book value is $90,000(100% – 15% – 25.5% –17.85%) =$37,485.
Since book value exceeds liquidation value, a tax credit is owed to the seller equal to Now we can write the acquisition ATCF as = – $30,000 –$2,994 = –$32,994. Finally, 5 year MACR depreciation rates on the old machine equal: 16.66%, 16.66%, and 8.33%. We write the ATCF for the tth period as: (13.11) However, because ATCF per period differs, we describe it using Table 13.11. below. Table 13.11. Finding ATCF for Continuing to Operate with the Old Doughnut Machine Old Doughnut Machine Operating ATCF Year CRt CEt Dept (MACR) (CRt – CEt)(1– T) + T Dept ATCF1 1 30,000 15,000 14,994 (16.66%) (15,000 x .6) + (14,994 x .4) = 14,998 0$14,998
2 30,000 15,000
14,994
(16.66%)
(15,000 x .6) + (14,994 x .4) = 14,998 0 $14,998 3 30,000 15,000 7,470 (8.33%) (15,000 x .6) + (7470 x .4) = 11,988 0$11,988
4 30,000 15,000 0 (15,000 x .6) = 9,000 0 $9,000 5 30,000 15,000 0 (15,000 x .6) = 9,000 0$9,000
Finally, we write the salvage value for the old machine. Recalling that the salvage value of the old machine, V5, is $10,000, that the old machine is completely depreciated, and the capital gains tax rate Tg is 0.2, we can write the salvage value as: (13.12) Finally, we are prepared to combine the ATCF from the acquisition, operation, and liquidation of the old doughnut machine. We express these in Table 13.12. Table 13.12. Old Doughnut Machine Operating ATCF Year CRt CEt Dept (MACR) (CRt – CEt)(1– T) + T Dept ATCF1 0 V0T(V0 – V0book) = –$30,000 – (.4)($30,000 –$37,485) = – $30,000 –$2,994 = –$32,994 –$32,994
(Acquisition)
1 30,000 15,000
14,994
(16.66%)
(15,000 x .6) + (14,994 x .4) = 14,998 0 $14,998 2 30,000 15,000 14,994 (16.66%) (15,000 x .6) + (14,994 x .4) = 14,998 0$14,998
3 30,000 15,000
7,470
(8.33%)
(15,000 x .6) + (7470 x .4) = 11,988 0 $11,988 4 30,000 15,000 0 (15,000 x .6) = 9,000 0$9,000
5 30,000 15,000 0 (15,000 x .6) = 9,000 0 $9,000 5 V5T(V5V5book) =$10,000 – (.2)($10,000 – 0) =$10,000 – $2,000 =$8,000 $8,000 (Liquidation) The only other calculation left is to compute the NPV of the old doughnut machine which we complete using our Excel spreadsheet. Table 13.13. Old Doughnut Machine Open Table 13.13 in Microsoft Excel A B C 1 Old Doughnut Machine 2 variables data formulas 3 rate 0.1 4 Acquisition Cost ($32,994)
5 ATCF1 $14,998 6 ATCF2$14,998
7 ATCF3 $11,998 8 ATCF4$9,000
9 ATCF5 $9,000 10 Salvage Value$8,000
11 NPV $18,745 “= -V0 + NPV(rate, ATCF1:ATCF5) + Vn / (1 + rate)^5 12 IRR 30% “=IRR(Acquisition Cost, ATCF1:ATCF5, Salvage Value) 13 AE ($4,944.92) “=PMT(rate, nper, NPV)
14 nper 5
Purchasing a new doughnut machine.
Assume that, after completing the PV analysis of the old doughnut machine, a salesman for a “new and improved” doughnut machine stops by and wants to sell you a new machine. The new machine will increase your revenues to $45,000 each year, and decrease your expenses to only$10,000 each year. The new machine costs $90,000 and will require$10,000 for delivery and installation costs. Thus, the acquisition ATCF0 = $100,000. The machine will fall into the MACRS five-year depreciation class (15%, 25.5%, 17.85%, 16.66%, 16.66%, and 8.33%). The machine is expected to have a$40,000 salvage value after 5 years.
Next, we need to determine the operating ATCF for the new machine. Tax rates, the defender’s after-tax IRR, and MACR depreciation rates are the same as before—equal to those used to evaluate the continued use of the old doughnut machine. Because of the level of sales, accounts receivable and accounts payable increase by $5,000 and$2,000 in the first year respectively. They are reduced by the same amount in the fifth year. The formula for operating ATCF is the same as before except that sales and expenses are no longer just cash items and must be adjusted by the term ∆Vn = ∆CA – ∆CL = $5,000 –$2,000 = $3,000 (13.13) The new machine will be depreciated using the 5-year MACRS method. The depreciation for each machine, and the change in depreciation each year for the next 5 years is: Table 13.14a. New Doughnut Machine Depreciation Year$100,000 x MACR rate = Depreciation
1 $100,000 x 15% =$15,000
2 $100,000 x 25.5% =$25,500
3 $100,000 x 17.85% =$17,850
4 $100,000 x 16.66% =$16,660
5 $100,000 x 16.66% =$16,660
Remember that depreciation expense is a noncash expense, which by itself doesn’t generate a cash flow. However, you can use the depreciation expense to reduce taxable income. As a result, the firm realizes an additional tax savings from depreciation. The amount of the tax savings are described below.
Table 13.14b. New Doughnut Machine Tax Savings
Year Tax Savings = (Depreciation)(T = .4)
1 $15,000 x (.4) =$6,000
2 $25,500 x (.4) =$10,200
3 $17,850 x (.4) =$7,140
4 $16,660 x (.4) =$6,664
5 $16,660 x (.4) =$6,664
Finally, we find the salvage value as follows. We first recognize that the sale of the doughnut machine in 5 years will increase cash flow by $40,000. Next, we find the asset’s book value in year five as the difference between its acquisition value less its accumulated depreciation:$100,000 – ($15,000 +$25,500 + $17,850 +$16,600 + $16,660) =$8,330. Since the asset’s book value is less than its salvage value, there are capital gains taxes to be paid. Therefore, the salvage value ATCF can be written as the salvage value less the capital gains tax:
(13.14)
Finally, we combine acquisition, operation, and liquidation ATCF associated with the new doughnut machine in Table 13.15.
Table 13.15. New Doughnut Machine Operating ATCF
Year Sales Expense Dep.
(MACR %)
(Sales – Expenses) x (1 – T) + T Dep. ATCF
0 ATCF0(Acquisition) = –V0 = –$100,000 1 ATCF1 45,000 10,000 15,000 (15%) (35,000 x .6) + (15,000 x .4) = 27,000 3,000$24,000
2 ATCF2 45,000 10,000 25,500
(25.5%)
(35,000 x .6) + (25,500 x .4) = 31,200 0 $31,200 3 ATCF3 45,000 10,000 17,850 (17.85%) (35,000 x .6) + (17,850 x .4) = 28,140 0$28,140
4 ATCF4 45,000 10,000 16,660
(16.66%)
(35,000 x .6) + (16,660 x .4) = 27,664 0 $27,664 5 ATCF5 45,000 10,000 16,660 (16.66%) (35,000 x .6) + (16,660 x .4) = 27,664 -3,000$30,664
5 ATCF5 (Liquidation) = V5T[V5V5(book)] = $40,000 – .2($40,000 – $8,330) =$33,666
We find the NPV for the new doughnut machine in Table 13.16:
Table 13.16. New Doughnut Machine NPV
Year ATCF
0 1 –$100,000 –$100,000
1 .91 $24,000$21,840
2 .83 $31,200$25,896
3 .75 $28,140$21,105
4 .68 $27,664$18,812
5 .62 $30,664 +$33,666 = $64,330$39,885
(27,584 using CF worksheet)
Finally, we find the NPV for the new doughnut machine using our Excel Spreadsheet.
Table 13.17. New Doughnuts Machine
Open Table 13.13 in Microsoft Excel
A B C
1 New Doughnut Machine
2 variables data formulas
3 rate 0.1
4 Acquisition Cost ($100,000) 5 ATCF1$24,000
6 ATCF2 $31,200 7 ATCF3$28,140
8 ATCF4 $27,664 9 ATCF5$30,664
10 Salvage Value $33,666 11 NPV$27,584 “= -V0 + NPV(rate, ATCF1:ATCF5) + Vn / (1 + rate)^5
12 IRR 18% “=IRR(Acquisition Cost, ATCF1:ATCF5, Salvage Value)
13 AE ($7,276.60) “=PMT(rate, nper, NPV) 14 nper 5 The result of the analysis is that NPV will be positive for both options by continuing to use the old machine or by investing in the new one. However, the firm’s NPV will increase the most if it adopts the new machine—an increase of$8,839 ($27,584 –$18,745) over continuing to use the old machine. However, the IRR of the old machine is greater, and we have a conflict between IRR and NPV rankings. The ranking is resolved by deciding on the reinvestment rate for the differences in funding required by the two investments. If the difference in funding levels is invested at the discount rate, the NPV rankings are appropriate. If the investments can be scaled, then the IRR rankings are appropriate. It is assumed here that the reinvestment rate is the after-tax IRR of the defender, 10%, so that any differences in size would not change their respective NPVs, and NPV rankings are appropriate.
Summary and Conclusions
This chapter operationalized PV analysis by introducing two PV multi-period templates, one for analysis of investments and the second one for analysis of equity committed to investments. In this effort we adjusted the average tax rate to correspond to the average tax rate paid on investments versus the average tax rate paid on equity committed to investments.
We reached an important conclusion when we analyzed returns on investments (assets) and equity. They need not rank investments and equity committed to investment consistently. These results add you our earlier finding that NPV and IRR models need not rank investments consistently homogeneous size and term conditions are satisfied.
That returns on investments and equity committed to investments may produce inconsistent ranking leads to an important question: when should we rank investment using returns on investments (assets) versus returns on equity committed to investments? The general answer is: it depends on who is asking. An individual investor whose financial conditions including loan amounts and costs are likely to be most interested in knowing returns to his/her specific conditions. Those more interested in the general condition of an industry or class of investments will more likely be most interested in returns on the investment or class of firms.
Not only have we focused on analyzing firms and investments versus returns on equity invested in firm’s and investments, we have also focused on the analysis of stand-alone versus incremental investments. In Chapter 12 we used accrual income statement (AIS) to find rates on return on assets and equity for a firm. The analysis was for a single period and focused primarily on describing the condition of the firm. In contrast, this chapter has focused on investments that add to, alter, or replace firm investments. We referred to investments that add to, replace, or change the firm’s capital structure as incremental investments. Sometimes the language used to describe incremental investments is confusing and describes them as partial budgeting analysis. We may use partial budgets to describe an incremental investment—but should not be confused with the actual PV analysis of incremental investments.
An irony is that most often practical applications of PV analysis are focused on stand-alone investments while most practical investments are incremental ones. Included in this irony is that tax rates most often refer to equity commitments rather than investment commitments.
To illustrate PV analysis, we focused on two practical investments. One a stand-alone investment we referred to as Green and Clean Services (GCS) and the second, an incremental investment we referred to as Round and Brown Doughnuts. In the first case we focused on how to distinguish between investment versus equity committed to investment analysis. The important point is this example was how the financial terms of the loan can change the attractiveness of the investment and, of course, change the rankings between investments.
When conducting PV analysis and making prescriptive statements based on the analysis, we have to estimate the future. Of course, some may argue that this involves sophisticated guessing—or estimating as some would refer to the efforts. Estimates of the future range in their sophistication—but they have one thing is common, they are never completely accurate. To remedy this problem, we recommend analyzing one’s investment and equity committed to the investment using several different forecasts as illustrated in this chapter and only adopting an investment is the returns are sufficiently positive that we can still be too optimistic in our forecasts and yet earn a comfortable rate of return.
PV analysis and forecasting the future is an important and unavoidable task. Hopefully, the tools described in this chapter will aid in that effort.
Questions
1. Please describe the difference in investment focus between an AIS and a PV model?
2. What is the main difference between a stand-alone versus an incremental investment? Explain why some sources describe incremental investment analysis as partial budgeting analysis.
3. This chapter presented two main PV model templates. One focused on analyzing investments. The second one focused on analyzing equity committed to the investment. Describe the differences between the two templates. Then explain how these differences permit us to calculate returns associated with investments versus returns on equity committed to investments.
4. Describe the nature of a fixed investment.
5. A capital investment provides services over several periods. A nondurable provides services once. Explain how this difference in capital goods and nondurable inputs are recognized in PV models.
6. A capital investment provides services for more than one period without losing its identity. The cost of providing these services is the change in the liquidation of the capital asset and the use of nondurable goods. The change in the liquidation value of a capital asset may mostly depend on the passage of time and the intensity of its use. Please explain how these two costs that result from the passage of time an use influence the optimal service extraction rate from the capital asset.
7. Operating accounts include AR, INV, AP, and AL. Describe how decreases (increases) in capital accounts influence operating and liquidation ATCF.
8. What is the difference between exogenous and endogenous variables used to solve for NPV, AE, and IRR in PV models?
9. Solving PV models requires that we forecast the values of exogenous and endogenous variables for the economic life of the investment. Describe how these forecasts might vary in their sophistication.
10. Assume you are attending school, working part time, and need transportation. To satisfy your transportation needs, you consider three options: You could continue driving your old clunker. You could buy a new car. Alternatively, you could buy a newer used car.
Your parents, who will need to loan you the money if you buy a new or newer used car, prefer that you continue to drive your clunker. You have done your homework to determine which of the three transportation options is the least cost one—although there may be other considerations. The financial data for the three investments follows.
Continue driving the clunker. You list the following financial details associated with continuing to drive the clunker. The clunker’s current market value is V = $3,000 which is the amount that you would sacrifice if you keep the clunker. As a result, you consider it to be your acquisition price. You estimate that you will travel 1,000 miles per month for 24 months in the clunker. In addition you estimate repair costs will equal 14 cents per mile, maintenance costs will equal 2.5 cents per mile, fuel costs/mile ($3.00/gallon divided by 17 miles/gallon) will equal 17.6 cents per mile, insurance costs will equal 10 cents per mile, and the clunker’s salvage value in 2 years (24 months) you estimate will equal V24 = $375. The total operating cost per mile for the clunker you estimate to equal 44.1 cents per mile and monthly operating cost you estimate will equal$441.
A new car. It would take a lot of coaxing for your parents to loan you enough money to buy a new car, but you would prefer this option. You can imagine how impressive you would be offering rides to your friends in your new car. You found one that you think would work. The financial characteristics of the new car include an acquisition price of V0 = $24,000, and you estimate that you will travel 1,000 miles per month for 10 years or 120 months in the new car. In addition, you estimate repair costs will equal 3.5 cents per mile, maintenance costs will equal 2.5 cents per mile, fuel costs ($3.00/ gallon divided by 27 miles/gallon) will equal 11.1 cents per mile, insurance costs will equal 12 cents per mile, and the salvage value in 10 years (120 months) you estimate will equal V120 = $8,000 The total operating cost per mile for the new car you estimated will equal 29.1 cents per mile and monthly operating costs you estimate will equal$291.
A used car. In case you cannot get the loan to buy a new car, you consider a newer used car to be an acceptable alternative to continuing to drive your clunker. You found one that you think would work. The financial characteristics include an acquisition price of V0 = $19,800, and you estimate that you will travel 1,000 miles per month for 8 years or 96 months in the newer used car. You estimate repair costs will equal 5 cents per mile, maintenance costs will equal 2.5 cents per mil, fuel costs ($3.00/gallon divided by 21.4 miles/gallon) will equal 14 cents per mile, insurance costs will equal 11 cents per mile, and the salvage value in 8 years (96 months) you estimate will equal V96 = $7,000 The total operating cost per mile for the used car you estimate will equal 32.5 cents per mile and you estimate monthly operating costs will equal$325.
Summary of data. We summarize the financial characteristics of the three car options in the Table Q13.1 below. Included in the table are the three phases of the investment: the acquisition costs, the operating costs per month, and the salvage values. Note that the operating costs are lowest for the new car. The acquisition cost is lowest for the clunker. Not included in the Table Q13.1 data summary is the average value of the investment lost per year—the average depreciation cost. We find the average depreciation cost by subtracting from the acquisition value the liquidation value and this difference we divide by the number of service months. This cost is ($3,000 –$ 375) / 24 = $109.38 for the clunker, ($24,000 – $8,000) / 120 =$133.3 3 for the new car, and ($19,800 –$7,000) / 96 = $133.33 for the used car. Since we account for these costs as the acquisition and liquidation values, they are not included in our monthly costs. We note, however, that one significant advantage of the clunker is its lower monthly depreciation. Table Q13.1. A summary of per mile and monthly costs of driving a clunker, a new car, and a used car. Clunker New Car Used Car V0$3,000 $24,000$19,800
Miles driven per month 1,000 1,000 1,000
Repair costs per mile $0.14$0.035 $0.05 Maintenance costs per mile$0.025 $0.025$0.025
Miles per gallon 17 27 25
Fuel cost per mile ($3 / gal)$3 / 17 = $0.176$3 / 27 = $0.111$3 / 25 = $0.12 Insurance cost per mile$0.10 $0.12$0.11
Total operating cost per mile $0.441$0.291 $0.325 Operating cost per month (1000 miles/month * cost/mile)$441 $291$325
Economic life (months) 24 120 96
Salvage Value (Vn) V24 = $375 V120 =$8,000 V96 = \$7000
Interest rate per year / month 12% / 1% 12% / 1% 12% / 1%
Net present cost (NPC). Your goal is to select the least cost transportation option. What makes this problem especially interesting is that the term is different for each car option requiring that we compare car transportation costs using their annuity equivalent (AE) cost per month. Your assignment is to find the NPC, AE, and IRR for the useful life of each car using the template that corresponds to equation 13.21 with T set equal to zero. Then describe your rankings. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/13%3A_Homogeneous_Investment_Types.txt |
Learning Objectives
After completing this chapter, you should be able to: 1. Learn how to measure an investment’s liquidity. 2. Learn how to compare liquidity for a firm versus liquidity for an investment. 3. Learn how to rank investments according to their liquidity using cash flow measures.
To achieve your learning goals, you should complete the following objectives:
• Learn to distinguish between two types of returns earned by an investment: time dated cash flow and capital gains (losses).
• Learn how to distinguish between a firm’s liquidity and an investment’s liquidity.
• Learn how to describe an investment’s liquidity at a point in time by using its current-to-total returns (CTR) ratio.
• Learn how to describe an investment’s liquidity over time by using its inter temporal CTR ratio.
• Learn how to connect CTR ratios to price-to-earnings (PE) ratios.
• Learn how PE ratios can be used to infer the liquidity of an investment.
• Learn how coverage (C) ratios can be used to infer the liquidity of an investment.
Introduction
An investment may earn two types of returns (losses) for investors: (1) time-dated cash flow called current returns, and (2) capital gains (losses). This chapter demonstrates that capital gains earned on an investment depend on the investment’s pattern of future cash flow.
This chapter also demonstrates that the combination of current returns versus capital gains (losses) has important liquidity implications for investors, especially when an investment is financed with debt capital. Debt-financed investments whose earnings are expected to grow over time may experience a cash shortfall called a financing gap, in which the cash returns are less than the scheduled payments of principal plus interest. This gap is most likely to occur early in the investment’s life and is exacerbated by inflation. As time passes and the cash returns grow in size, they will eventually exceed the repayment obligation, and the liquidity problem is solved.
The term liquidity is used to describe “near-cash investments” because of the similarity between liquids and liquid investments. A liquid such as water can fill the shape of its container and is easily transferred from one container to another. Similarly, liquid funds easily meet the immediate financial needs of their owners. Illiquid investments such as land and buildings, like solids, are not easily accessed to meet financial needs because their ownership and control are not easily transferred.
A firm’s liquidity reflects its capacity to generate sufficient cash to meet its financial commitments as they come due. A firm’s failure to meet its financial commitments results in bankruptcy, even though the firm might be profitable and have positive equity. Consequently, firms must account for an investment’s liquidity in addition to earning positive net present value (NPV).
There are several measures that reflect a firm’s or an investment’s liquidity. One measure used to reflect the liquidity of the firm is the current ratio, the ratio of current assets divided by current liabilities. Because current assets can be quickly converted to cash, they are an important source of liquidity for the firm.
While the current ratio measures the liquidity of the firm, we want a liquidity measure specific to an investment, and one that describes the liquidity of an investment over time—what we will refer to as a periodic liquidity measure. The liquidity measure that provides investment-specific liquidity information over time is the current-to-total returns (CTR) ratio. The CTR ratio is derived from market equilibrium conditions where NPV is zero and represents the ratio of current (cash) returns to total returns. The price-to-earnings (PE) ratio is a commonly reported ratio reflecting the price of an investment reflected by its current earnings. A liquidity measure related to the CTR ratio is the coverage (C) ratio. A C ratio is the ratio of cash returns to loan payments or other debt obligations in any particular period.
Current-to-Total-Returns (CTR) Ratio
The current-to-total returns (CTR) ratio is a periodic liquidity measure derived from the relationship in a given period between an investment’s current (cash) returns, its capital gains (losses), and its total return, or the sum of current returns and capital gains (losses). To derive the CTR measure, we begin with an expression of an investment’s total returns:
Total investment returns = current returns + capital gains (losses)
The above relationship is expressed symbolically as follows. Let the investment’s total return equal the investment’s internal rate of return r times the value of the investment at the beginning of the period V0 or rV0. Meanwhile, let R1 be defined as the asset’s net cash, or current returns earned at the end of the first period. In addition, let V0 and V1 equal the investment’s beginning and end-of-period values respectively, while their difference (V1V0) is equal to the investment’s capital gains (losses) in the first period. Summarizing, we write the investment’s total returns as:
(14.1)
Next we solve for the investment’s internal rate of return earned in each period, r. We solve for this measure by dividing the investment’s total returns by the investment’s value at the beginning of the period V0:
(14.2)
A useful measure obtained from Equation \ref{14.2} is the ratio of current returns R1 divided by total returns rV0. This ratio indicates the percentage of total returns the firm receives as cash. The higher this ratio, the greater the likelihood that the firm has the liquidity required to meet its debt obligations in the current period. Rearranging the previous equation yields the ratio of current to total returns in the first period, equal to CTR1:
(14.3)
where is the capital gains (loss) rate in period one.
To illustrate the CTR ratio, we now derive the CTR ratio for the geometric series of cash flow. Consider an investment that is expected to generate a perpetual series of cash flow that grow at average geometric rate of g percent per period. If R0 is the initial net cash flow, and r is the IRR of the investment, then the PV of the growth model can be expressed as:
(14.4a)
One year later:
(14.4b)
and in general
(14.4c)
and the capital gains rate for the geometric growth model is found to equal:
(14.4d)
Using our results from Equation \ref{14.3} we can find our CTR ratio as:
(14.5)
To illustrate, if an investment earns cash flow in perpetuity described by R0, r = 10% and g = 5%, the investment’s CTR ratio can be found equal to:
(14.6)
It is left as an exercise to demonstrate that if the CTR ratio is constant over time, the CTR ratio is 1. Namely, that:
(14.7a)
To illustrate equation (14.7a), if in period one, r = 10% and g = 5%, then 50% of the investment’s returns will be earned in the form of capital gains. On the other hand, if the geometric mean of changes in future cash flow was negative, (g < 0), the current returns to total returns would exceed total returns. If g = –5%, the CTR1 ratio would equal:
(14.7b)
In words, equation (14.7b) informs us that 150% of the investment’s return in period one will be received as current returns in order to compensate for the 50% capital losses experienced by the investment.
So what does this mean? It means that the investments with increasing cash flow are less liquid than those with decreasing cash flow. A less (more) liquid investment means that a part of its return in each period is earned in capital gains (losses) that are not converted to cash until the investment is liquidated.
Liquidity, Inflation, and Real Interest Rates
Prices reflect the ratio of money exchanged for a unit of a good. For example, assume that the price for gasoline is $3.00 per gallon. If you purchased 10 gallons of gasoline, you would pay$30.00 ($3.00 x 10). Conversely, the ratio of$30.00 expended for gas divided by the gallons of gas purchased is the price of gas: $30.00/10 equal to$3.00.
Now suppose that last year you purchased roughly $50,000 worth of goods. For convenience, let pj be the price of good j where j = 1, …, n. Furthermore, let qj represent the quantity of good j purchased. Multiplying the price times the quantity of each good purchased equals your total expenditures of$50,000. To summarize, equals the sum of price times quantity of all of the goods you purchased.
In case you had not noticed, prices for goods and services change over time. Consider the price of a dozen large eggs. The price of a dozen of large eggs over the past 38 years is graphed in Figure 14.1 ranging from less than $1 per dozen in 1980 to almost$3 per dozen in 2016.
Figure 14.1. The price of a dozen large eggs over the period 1980 to 2016.
(Bureau of Labor Statistics, 2016)
Prices over time for an individual good can change for several reasons. The demand for eggs can rise—more people wanting to consume more eggs will likely cause egg prices to rise. Or the cost of supplying eggs may change—chicken have become more efficient at producing eggs making them cheaper or chicken feed may become more expensive making eggs more expensive to produce.
The quantity theory of money
There is another reason why prices may change over time—there is more money in circulation. This explanation for why prices rise we call the quantity theory of money (QTM). The quantity theory of money states that there is a direct relationship between the quantity of money in an economy and the level of prices of goods and services sold. What constitutes the money supply is a complicated subject that we can avoid here and still make our point.
Returning to our earlier discussion, let the total of goods and services sold times their prices equal the amount of money M in the economy times its velocity (V) or the number of times the same unit of money is used during a time period. We write this relationship as
(14.8)
According to the QTM, if people purchased the same goods in the same quantity and if V were held constant and M increased by i percent, then the price of each individual good must also increase by i percent.
(14.9)
Finally, if we measured the prices times the same goods in each year and calculated the ratio of the current year by the previous year we could obtain an estimate of the how prices in general have changed or the rate of inflation. Adding a superscript t to the price variable, we find the inflation rate plus one in year t is equal to:
(14.10)
An index (1 + i) can be computed for all different bundles of purchased goods. One popular inflation index is called the Consumer Price Index (CPI) that measures the rate of increase in prices holding the bundle of goods constant or at least as far as it is possible. Consider how inflation has affected consumer purchases over time. The vertical axis measures the CPI. The horizontal axis measures time. All indices select one year at their base in which the index is one. In Figure 14.2, the base year is somewhere between 1982-1984.
Figure 14.2. The consumer price index for all the U.S. letting average prices between 1982-84 equal 100.
According to Figure 14.2, in 2018 you paid on average two and one-half times as much money to purchase the same good as you did in 1982-1984.
So why is inflation important to our discussion of PV models and profit measures? If your income increases by i percent and the cost of everything you purchase increases by the same percent i, then in real terms what you can actually purchase is the same as before since your income and costs increased by the same rate.
Real interest rates. Let say that your after-tax cash flows increased by rate g% but that g is influenced by the rate of inflation. Then after accounting for inflation, what is left is attributed to other factors besides an increase in the money supply. Let this real growth in after-tax cash flow (ATCF) be g*. Then we can write:
(14.11)
Interest rates, discount rates, and inflation. Inflation also influences interest rates paid to borrow money and the discount rate that reflects the opportunity cost for one’s resources. To motivate this discussion intuitively, assume you lent a friend $1000 for one year. Also assume that inflation is 5% so that when your friends repays the loan, to make the same purchases at the time the loan was made, they would have to pay back$1,000 * (1.05) = $1,050. But they would have to pay more than 5% for being able to rent your money for a year—let’s call this rate the real interest rate and denote it as r*. To account for both the reduced purchase price of your money because an increase in prices by inflation i and the cost of postponing the use of one’s money, the interest rate (and opportunity cost of resources invested in a defender) is r equal to: (14.12) We graph real interest rates r* over time in Figure 14.3. Figure 14.3. 10-year Treasury constant maturity interest rate, U.S., 1988 – 2018 So what does all this mean? It mean that real interest rates have been falling since 1988 and have recently started to increase. Increasing real interest rates will make long-term investments less liquid because it increases interest rate changes on loans and also increases the rate of growth g that we already demonstrated increases capital gains relative to current earnings. Liquidity Implications The mix of capital gains (losses) versus current returns depends directly on the average rate of growth (g > 0) or decline (g < 0) in future cash flow. As inflation increases the average rate of growth g, then inflation also reduces an investment’s liquidity, especially during the investment’s initial years. For geometric decay in earnings (g < 0), current returns are more than 100% of total earnings—and current returns have increased in importance relative to capital loss or depreciation. These results clearly show the paradoxical conditions that growth in projected earnings can weaken the liquidity of the investment due to the increasing relative importance of capital gains. In contrast, a decline in projected earnings can strengthen the liquidity due to the increasing relative importance of current returns (See Table 14.1). Also note in Table 14.1 that increases in the capital gains rate g holding r constant always leads to a reduction in CTR ratio. This is easily explained. Since the total rate of return r is fixed and composed of current rate of returns and capital gains rate of returns, increases in the capital gains rate of return must necessarily decrease the current rate of returns. Table 14.1. Values of CTR ratios where CTRt = (rg) / r r% g% 10 8 6 4 2 –5 150% 163% 183% 225% 350% –3 130% 138% 150% 175% 250% 0 100% 100% 100% 100% 100% 3 70% 63% 50% 25% 5 50% 38% 17% Price-to-earnings (PE) Ratios Related to the CTR ratio is the price-to-earnings (PE) ratio equal to: (14.13) If we describe the investment using the PV expression in equation (14.4a), then we can write: (14.14) Next we substitute R0(1 + g) for R1, and the right-hand side of Equation \ref{14.9} for V0 into the PE expression in Equation \ref{14.8}, and obtain: (14.15) But from equation (14.7a) we know that rCTR = (rg), which allows us to connect CTR and PE ratios, namely: (14.16) In words, what we learn from Equation \ref{14.16} is that, in general, higher CTR ratios imply lower PE ratios and lower CTR ratios imply higher PE ratios. These results may at first appear to be somewhat counter intuitive—that, for liquidity purposes, we prefer investments with lower PE. Upon reflection, it makes sense—assets whose returns are mostly capital gains will be earning a lower percentage of current returns compared to their values than assets that earn little or no capital gains. To make the point that CTR and PE ratios are inversely related, we construct Table 14.2 for PE ratios. Compare the results with those found in Table 14.1 to confirm in your minds the implications of Equation \ref{14.16}. Note that PE ratios uniformly increase with increases in g and the rate of return earned in the form of capital gains. Table 14.2. Values of PE ratios where PEt = 1/(rg) = 1 / (rCTRt) r% g% 10 8 6 4 2 –5 6.67% 7.67% 9.11% 11.11% 14.29% –3 7.69% 9.06% 11.11% 14.29% 20.00% 0 10% 13.50% 16.67% 25.00% 50.00% 3 14.29% 20.00% 33.33% 100.00% 5 20.00% 33.33% 100.00% PE ratios are frequently used to describe the financial condition of an asset. Generally speaking, high PE ratios reflect an expectation of income growth for an asset. Unfortunately, high levels of PE ratios may reflect bubbles or unrealistic expectations for income growth for a particular investment—and high PE ratios are often followed with a market adjustment in which the earnings expectation of an investment are adjusted downward, which reduces the investment’s PE ratio. For example, in 1929 for stocks (see Figure 14.4), and 2010 for housing (see Figure 14.5), expected income growth was unrealistic, and in both cases, PE ratios fell when earnings expectations were adjusted downward. Figure 14.4. Historic PE ratios for stocks described on the Standard and Poor’s Stock Exchange. (Earnings are estimated based on a lagged 10-year average.) Figure 14.5. Historic PE ratios for UK housing stock. Compare the value of the PE ratios in Figures 14.4 and 14.5. PE values for stocks that reflect depreciable assets (g < 0) have average values around 20. PE values for housing stock that reflect non-depreciable assets (g > 0) have recently averaged around 5. (See Table 14.2.) Coverage (C) Ratios Investments can be evaluated according to both profitability and periodic liquidity criteria. Profitability analysis focuses on whether the acceptance of an investment will increase the investor’s present wealth. Periodic liquidity measure analysis considers whether an investment will generate cash flow consistent with the terms of financial capital, especially debt capital, that are used to finance the investment. Is an investment capable of generating sufficient net cash flow in each period to satisfy the requirements for repayment of the loan’s principal plus interest? If not, then the investment is illiquid because liquid funds drawn from other sources are required to meet cash flow requirements associated with the investment. Thus, a simple test of investment liquidity is to compare the net cash flow generated by the investment in a given period with the debt-servicing requirement. The ratio of net cash flow in a period t, Rt, divided by the loan plus principal payment in the same period, At, is called the coverage ratio, Ct: (14.17) If the coverage ratio is equal to or exceeds 1.0, the investment is liquid in that period. If coverage is less than one, the investment is illiquid in that period. In most cases, the loan payment that includes principal plus interest is a constant “A,” that depends on the price of the purchased asset, V0; the financed proportion of the purchase price ; the term of the loan n; and the interest rate charged on the loan rf. Using our previous notation, we can express the relationship between the amount financed, the fixed loan payment, the interest rate on the loan, and the term of the loan as: (14.18) We solve Equation \ref{14.18} for A and substitute the result for At in Equation \ref{14.19}. In the same equation,we also substitute R0(1 + g)t for Rt, and obtain: (14.19) Replacing V0 with [R0 (1 + g)]/(rg), we can rewrite Equation \ref{14.19} as: (14.20) We illustrate Equation \ref{14.20} as follows. Assume r = 8%, g = 2%, n = 20, and rf = 7%. Also assume the investment is 80% financed. Using an Excel spreadsheet, we find that US0(7%, 20) = 10.59. Table 14.3. Calculating US0(rf=7%, n=20) Open Table 14.3 in Microsoft Excel B6 Function: =PV(B3,B4,B5,,0) A B C 1 Calculating US0(rf = 7%, n=20) 2 3 rate 7% 4 nper 20 5 payment -1 6 NPV$10.59 “=PV(rate,nper,payment,,0)
Then we find the coverage value for the first year of the investment to equal:
(14.21a)
Interpreted, in year one, the investment described above will only pay for 79 percent of the loan payment due. However, 10 years later and half way into the term of the loan, the coverage ratio has increased to:
(14.21b)
Finally, in the last year of the loan, the coverage ratio is:
(14.21c)
In other words, in year 20, the last year of the loan, the investment cash flow not only repays the loan but 16 percent more than the required loan payment. Of course, after the loan is repaid, the periodic cash flow is available to the firm to meet its cash flow requirements.
One word about the term of the investment, it is assumed to be infinite. However, for any one investor, the term may be finite, but since the terminal value for any one owner is simply the present value of the continued cash flow, we can express the investment as having an infinite life. Therefore, we are justified in ignoring the term of the infinite-life investment.
When is the coverage equal to 100 percent? There is another way to approach the issue of coverage. It is to ask in what year is the coverage equal to 1? To answer this question for the geometric growth model with an infinite life and using the already established notation, we set:
(14.22)
and solving for t we find:
(14.23a )
And after making substitutions for A and R0 and simplifying, we can write:
(14.23b )
We illustrate equation using numbers from the previous example where: = .8, r = .08, g = .02, rr = .07, and n = 20. We find:
(14.24 )
In words, what we have found that the 12th payment will be the first period that more than pays for its financing.
So what does this mean? As the previous example demonstrates, it means that for investments with increasing cash flow, its liquidity increases over time.
Summary and Conclusions
An investment may earn two types of returns: time dated cash flow and capital gains (losses). Moreover, these returns can be earned over the lifetime of the asset. The relative importance of the two forms of returns, cash flow versus capital gains (losses), will determine the inter temporal liquidity of the asset. The greater the portion of the return is earned as cash, the more liquid will be the investment.
This chapter demonstrated whether an investment earns capital gains (losses) is determined in PV models by its pattern of expected future cash flow. Expected increases (decreases) in the number, frequency, or amount of the expected future cash flow will produce capital gains (losses). Inflation causes long-term investments to become less liquid because they increase the rate of growth in the investment’s cash flow.
Investments that earn capital gains are called appreciating investments. Investments that experience capital losses or depreciation are referred to as depreciating investments.
Perhaps paradoxically, investments that earn capital gains are less liquid than investments that experience capital losses. Assuming investments earn similar total rates of return, the greater the cash returns are compared to total returns, the greater are the liquid funds available to meet liquidity needs including repayment of funds and interest required to maintain control of the asset.
In this chapter we developed current-to-total returns (CTR) measures to indicate an investment’s liquidity over time. Furthermore, CTR measures were shown to be related to price-to-earnings (PE) ratios which also depended on an investment’s liquidity. Finally, one feature of an investment, is its coverage, its ability in any one period to repay principal and interest payments due in any one period. If funds borrowed to purchase an appreciating investment are repaid with a constant loan payment,then initially, it is likely that cash flow generated by the investment will not cover the interest and principal payments. This pattern is very likely during periods of inflation. Coverage ratios will also indicate the liquidity of investments over their productive lives.
In summary, the periodic liquidity of an investment is an important characteristic that should influence the capital decisions of financial managers along with the impact of an investment on the firm’s solvency, profitability, efficiency, and leverage.
Questions
1. Please describe three possible appreciating and three depreciating investments that are available for most farm financial managers.
2. Describe the connections between capital gains (losses) with an investment’s periodic liquidity.
3. Describe the connection between the inflation rate i and an investment’s CTR ratio.
4. How is an investment’s periodic liquidity related to its CTR (current-to-total returns) ratio and its C (coverage) ratio? How are the two periodic liquidly measures related to each other?
5. Compare the firms current (CT) ratio and its debt-to-service (DS) ratio with an investment’s CTR ratio and C ratio. In what ways are they similar? How do they differ?
6. Consider the CTR ratio described in Equation \ref{14.3}. Find the CTR ratio for the investment whose anticipated cash flow is a constant R in perpetuity described below:
(Q14.1)
(Hint: Observe the CTR ratio described in Equation \ref{14.3}. Then derive capital gains (losses) measures for the PV model described in this question.)
1. Find the CTR ratio for an investment whose defender’s IRR is 8% and its anticipated growth rate is 2%. Then find the PE ratio for the same investment.
2. Assume that PE ratios can be approximated using Equation \ref{14.10}. What would account for the large swings in PE ratios described in housing stock described in Figure 14.2—changes in expected r or g? Or due to some other influence on the value of housing stock?
3. Find the coverage (C) ratio for year 5 for the investment described in the text where: = .7, r = .08, g = .02, rr = .07, and n = 20. Call the result, the result for the base model.
1. Recalculate the base model C ratio where n = 20 is changed to n = 15. Describe how reducing n changed the coverage compared to the base model. Then provide an explanation for the change in coverage.
2. Recalculate the base model C ratio where g = .02 is changed to g = –.02. Describe how reducing g changed the coverage compared to the base model. Then provide an explanation for the change in coverage.
3. Recalculate the base model C ratio when = .8 is changed to = .6. Describe how increasing γ changed the coverage compared to the base model. Then provide an explanation for the change in coverage.
4. In this chapter we derived Equation \ref{14.18} which solved for the time period in which the coverage was 100%. Find the time period in which coverage is 100% when = .7, r = .08, g = .02, rf = .06, and n = 20. Call the result, the base model result. Then use Equation \ref{14.18} to find how t associated with 100 percent coverage changes for the following cases:
1. Recalculate the base model and find a new t value associated with 100% coverage where n = 20 is changed to n = 15. Describe how reducing n changed t and then provide an explanation for the change in t.
2. Recalculate the base model and find a new t value associated with 100% coverage where rf = .06 is changed to rf = .08. Describe how increasing the interest rate rf changed t associated with 100% coverage. Then provide an explanation for the change in t.
3. Recalculate the base model and find a new t value associated with 100% coverage where r = .08 is changed to r = .06. Describe how decreasing the discount rate r changed t associated with 100% coverage. Then provide an explanation for the change in t.
5. Suppose the firm you managed was facing financial stress due to falling prices. Moreover, the stress is reflected in low liquidity and solvency measures for the firm. It appears that there is no way the firm can survive its current crises without liquidating not only short-term assets, but also long-term investments. Based on what you have learned about investment liquidity, propose a plan for the firm to meet it liquidity crisis. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/14%3A_Homogeneous_Liquidity.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) define and measure risk; (2) understand how a person’s risk aversion affects his/her resource allocation; (3) distinguish between direct and indirect outcome variables; and (4) evaluate alternative risk response strategies available to financial managers including sharing risky outcomes, purchasing insurance, diversifying investments, purchasing risk reducing investments, and choosing an optimal capital structure.
To achieve your learning goals, you should complete the following objectives:
• Learn how to describe risky events by assigning a random variable to their outcomes and by assigning a probability density function (pdf) to the random variable.
• Learn how measure the variability and central tendencies of random variables using the expected values and variances of their probability density functions.
• Learn how risk premiums can be used to measure the cost of risk.
• Learn how to describe the risky choice set facing firm managers using expected value-variance (EV) efficient sets.
• Learn about the normal probability density function and understand why it is so important when describing risky events.
• Learn how sharing risk with others can be a useful response to risk.
• Learn how purchasing insurance can be a useful response to risk.
• Learn how diversification can be a useful response to risk.
• Learn how purchasing risk-reducing inputs can be a useful response to risk.
• Learn how leverage affects the level of risk facing the firm.
Introduction
The adjective “uncertain” describes an event (such as a hurricane or a football game) whose outcomes are not known with certainty. An uncertain event must have at least two possible outcomes, and it usually has more. In an earlier time, a distinction was made between risky events and uncertain events based on the information available for identifying an event’s possible outcomes and predicting the probabilities of those outcomes. For example, the flip of a coin is a familiar event with two outcomes: heads (H) and tails (T). Based on past trials or logic, we can infer that the probability of a heads (tails) appearing when a fair coin is tossed is about 50 percent. Some may call this event risky because we have good information about the possible outcomes and the probability of their occurrence.
Now consider a different event: the toss of a thumbtack.[1] What is the probability that the thumbtack will land on its side versus landing on its head? Because we are not familiar with this event and cannot assign probabilities to its outcomes based on our past experience or logic, this event might be called uncertain.
For many, the distinction between risky events and uncertain events is no longer important, and most researchers assign the adjectives uncertain and risky to events interchangeably. One reason many do not distinguish between risky and uncertain events is because the assignment of probabilities to event outcomes is subjective (we never have enough information to be absolutely certain about either possible outcomes or their probabilities) and may be based on other factors besides logic and past observations including hunches, omens, experiences of others in irrelevant circumstances, and advice from unqualified persons to name a few.
A distinction between risky and uncertain events may still be useful. People appear to refer to events as uncertain when the event’s outcomes are not known with certainty. It also appears popular to refer to uncertain events as risky when they are uncertain and their occurrence alters the decision maker’s well-being. Thus, only risky events matter, regardless of one’s confidence in the probabilities of various outcomes (e.g. the toss of a coin versus the toss of a thumbtack).
The study of risky events, of course, has application to capital budgeting problems. When we estimate future cash flow used in analyzing capital budgeting decisions, we are estimating risky outcomes associated with a risky event. Thus, we are faced with the challenge of satisfying the homogeneous measures principle applied to risk by adjusting future cash flow projections of a challenger and the cash flow predictions used to find the IRR of the defender to their certainty equivalent value that we will define in this chapter.
Statistical Concepts Useful in Describing Risky Events and Risky Outcomes
Probability density function. A probability density function (pdf) is a function that assigns probabilities to outcomes of risky events. For example, the toss of a fair coin is an event with outcomes showing a heads (H) or a tails (T). The pdf for this event may assign to H the probability of 50% occurrence and 50% to the occurrence of T. A pdf may be discrete or continuous. If the outcomes of an event are finite, then their likelihood of occurring is described by a discrete pdf. If the outcomes of an event are infinite, then their likelihood of occurring is described by a continuous pdf.
Random variables. A random variable is a numerical value assigned by a function or rule to outcomes of risky events. The probability of a particular value described by a random variable is the same as the probabilities of its underlying event outcome. For example, suppose that an event were the toss of a coin. We might assign the outcome of heads the number one, and the outcome of tails the value of zero. Then the probability of a random variable taking on the value one is the same probability as H occurring when tossing a coin.
Expected values. An expected value is one measure used to describe the properties of a pdf. It is sometimes called the first moment of the pdf because it measures the center of a pdf’s mass (like the fulcrum of a teeter totter).
The expected value of a pdf is determined by calculating a weighted average of the possible values of the random variable values times their likelihood of occurring. To illustrate, consider two possible investments A and B. The event is the operation of the economy with three possible outcomes: a recession with 20% likelihood, a stable economy with 60% likelihood, and a growth economy with 20% likelihood. The value of the random variables describing the three outcomes for investments A and B are described in Table 15.1 and represent alternative rates of return on the investments.
Table 15.1. pdfs and Random Variables Associated with Investments A and B
Economic outcomes pdf associated with economic outcomes Returns on investment A (a random variable) Returns on investment B (a random variable)
Recession 20% –20% –40%
Stable 60% 20% 20%
Growth 20% 40% 60%
Expected values of investments A and B 16% 16%
Variances (standard deviations) of investments A and B .039 (19.6%) .103 (32.0%)
The expected value operator is expressed as E( ). The expected value of investment A is the sum of A’s random variables weighted by their respective probabilities and is written as:
$E(\text {Investment } A)=(.2)(-.20)+(.6)(.20)+(.2)(.4)=16 \% \label{15.1}$
The expected value of investment B is written as:
$E(\text {Investment } B)=(.2)(-.40)+(.6)(.20)+(.2)(.60)=16 \% \label{15.2}$
In general, the expected value of random variable yj which occurs with discrete probability pj with j = 1, …, n outcomes is expressed as:
$\label{15.3} E(y)=\sum_{j=1}^{n} p_{j} y_{j}$
and where the sum of all probabilities of yj occurring equal 1:
$\label{15.4} \sum_{j=1}^{n} p_{j}=1$
A special kind of expected value is the mean. A mean is calculated for n observations from an unknown pdf where every observation is equally likely. Suppose we observed five draws from an unknown distribution equal to 8, 4, 0, 2, and 6. Since we assume each observation was equally likely, 1/n , or 1/5, in this case the expected value is equal to the mean calculated as
\begin{align} \bar{x}=\frac{\sum x_{i}}{n} \label{15.5a} \ =\frac{8+4+0+2+6}{5}=\frac{20}{5}=4 \label{15.5b} \end{align}
Variance and standard deviation. Even though the expected values of investments A and B described above are equal, most investors would not consider them equally attractive because of the wide differences in the variability of the values assumed by their random variables. One approach to measuring the variability of a random variable is to calculate its variance or the square root of its variance equal to its standard deviation. We can find the variance of a random variable yj with n possible outcomes by summing yj minus E(y) quantity squared weighted by the probability of random variable occurring. We write the variance formula for random variable yj as:
$\operatorname{Variance}(y)=\sigma_{y}^{2}=\sum_{j=1}^{n} p_{j}\left[y_{j}-E(y)\right]^{2} \label{15.6}$
We illustrate the variance formula by calculating the variances and standard deviations for investments A and B. The variance for investment A is calculated as:
$\sigma_{A}^{2}=.2(-.2-.16)^{2}+.6(.2-.16)^{2}+.2(.4-.16)^{2}=.039 \label{15.7}$
Meanwhile the standard deviation for investment A can be found by calculating the square root of the variance of investment A and is equal to:
$\sigma_{A}=\sqrt{\sigma_{A}^{2}}=\sqrt{.039}=.196 \text { or } 19.6 \% \label{15.8}$
The variance for investment B is calculated as:
(15.9)
Meanwhile the standard deviation for investment B is found to equal:
$\sigma_{B}=\sqrt{\sigma_{B}^{2}}=\sqrt{.320}=.320 \text { or } 32 \% \label{15.10}$
One reason for measuring the variability of the random variable by squaring its deviations from its expected value is because were we to find the average of the deviation of the random variable from their expected values, they would always sum to zero. They would sum to zero because probability weighted deviations above the expected value exactly equal probability weighted deviations below the expected value. Taking the square root of the variance of returns converts the deviation measure to units comparable with those of the original random variable. Thus, from the standard deviations calculated above, we can infer that, on average, the random variable representing investment A will deviate 19.6% from its expected value while the random variable representing investment B will deviate 32.0% from its expected value. Clearly, risky outcomes for investment B are more variable—and some would say more risky—than outcomes associated with investment A. We add to the descriptions in Table 15.1 of investments A and B their respective variances (standard deviations).
The variance of the sample is found as before by summing and squaring the deviations from the mean weighted by their probability of occurrence. However, for reasons not discussed here, the variance of the sample of observations is divided by n–1 instead of n where n is the number of observations. Thus the standard deviation from a sample distribution is denoted Sx for observations on the random variable x. Otherwise the variance of the random variable x drawn from the true population is divided by n. Therefore in our example, the sample standard deviation, the square root of the variance is:
$S=\sqrt{\frac{\left(\sum x_{i}-\bar{x}\right)^{2}}{n-1}} \label{15.11a}$
(15.11b)
Risk premiums and certainty equivalent incomes. While not properties of pdfs, important concepts connected to pdfs describing investments are risk premiums and certainty equivalent incomes. While these concepts are related to pdf properties, they also depend on risk preferences of individual decision makers for the variance and expected return inherent in the investment. Risk premiums, certainty equivalent incomes, and risk preferences can be easily explained.
Suppose an investor faced investment A described in Table 15.1 and had the opportunity to receive its expected value with certainty in exchange for paying a risk premium. What is the largest risk premium the investor would pay to receive the investment’s expected value with certainty? The answer would depend on the investor’s risk preferences. If the investor would pay a positive risk premium to receive investment A’s expected value with certainty, then the investor is risk averse. If the investor would pay nothing to receive investment A’s expected value with certainty, the investor is risk neutral. If the investor would pay to keep the variability (the investor enjoys gambling), we would say the investor is risk preferring.
Once we know the investor’s risk premium for a particular investment’s pdf, we can find his/her certainty equivalent income by subtracting it from the investment’s expected value. We can describe the relationship between the ith investor’s risk premium, certainty equivalent income, risk attitudes, and the expected value and variance of the random variable in the following expression:
$y_{C E}^{i}=E(y)-\frac{\lambda^{i}}{2} \sigma_{y}^{2} \label{15.12}$
In Equation \ref{15.12}, the ith investor’s certainty equivalent income for an investment whose possible values are represented by the random variable y is equal to the expected value of y less a risk premium. In Equation \ref{15.13}, we can solve for the largest insurance premium the investor would be willing to pay to receive the investment’s expected value with certainty.
$\label{1\frac{\lambda^{i}}{2} \sigma_{y}^{2}=E(y)-y_{C E}^{i}5.13}$
The ith’s investor’s risk premium is equal to the decision maker’s risk preference measure λi divided by 2 times the variance of the random variable y. The investor’s risk aversion coefficient λi/2 is best understood as a slope coefficient that indicates the response on the investor’s certainty equivalent income by an increase in a unit of variance of the random variable y.
Expected value-variance criterion. Suppose we had a set of pdfs each representing the likelihood of m alternative random variables. Furthermore, suppose each of the m investments were described using their expected values and variances. Then, assuming that all investors were risk averse and without knowing each investor’s risk aversion coefficient, we know that for every two investments with equal expected values (variances) and unequal variances (expected values) the investor would prefer the investment with the smaller variance (largest expected value). On the other hand, we could not rank two investments in which one had a larger expected value and variance than the other. The set of investments and ranked preferred for risk averse decision makers is called the expected value-variance (EV) efficient set. The graph of a particular EV set follows.
Figure 15.1. An Efficient Expected Value-Variance Frontier of Investments Represented by their Expected Values E(y) and Variances σ2.
Suppose that we were to draw a line tangent to the relevant section of the EV at point A, representing an investment A. Then the slope of the line at point A would equal the decision maker’s risk coefficient at the point. Furthermore, were we to extend the tangent line to intersect with the vertical axis, the point of intersection would equal the certainty equivalent of the investment.
The Normal Probability Density Function (pdf)
If you have a large enough sample of outcomes from a normal distribution, the distribution will look like a bell-shaped curve.
Figure 15.2. A normal probability distribution that describes probability in areas divided to standard deviations from the mean.
The normal distribution is symmetric about its expected value. The numbers in the graph correspond to standard deviations measured from the mean of the normal distribution. All of the characteristics of the normal distribution are completely described by the mean and variance (or equivalently, the standard deviation). The mean specifies the average value of the rate of return. The probability of getting a return above or below the mean by a certain amount is determined by the size of the standard deviation.
If the returns are normally distributed, there is a 68% chance that the return for any given period will be within one standard deviation of the expected value; a 95% probability that any particular observed return will be within 2 standard deviations of the expected value; and a 99.74% probability that any return will be within 3 standard deviations of the mean. Clearly, the larger the standard deviation, the more spread out the actual returns that occur will be. Suppose the common stock returns we looked at earlier were generated by a normal distribution. We estimated the expected value of the distribution to be r = 18.92% and the standard deviation to be σ(r) = 16.18%. If we were interested in predicting what next year’s return on common stocks will be, we could say that the expected value will be about 18.92%, but, in addition, there is a 68.26% probability that returns will be between 2.74% and 35.1%; a 95.44% probability that returns will be between –13.44% and 51.28%; and a 99.74% chance that the returns will be between –29.62% and 67.46%. The smaller the standard deviation, the less spread out the returns will be and the more accurate the mean will be as a predictor of future returns.
Sampling error. The normal distribution is an important distribution from both a theoretical and a practical standpoint. It is important to note that if you are looking at a small sample of data, its empirically based pdf is likely not to have the shape of a normal distribution even if it is actually generated from a normal distribution. In a small sample, the distribution will have gaps and holes in it and is unlikely have a shape that looks like the true distribution that generated the data. If you keep adding observations from the distribution, eventually the gaps will fill in, and it will start to look like the true distribution that generated the data. The point here is, even if the sample pdf generated by a normal distribution does look like a normal distribution, this may be because the sample size is too small. Therefore, because of its usefulness and tractability, we often assume that our sample pdfs are normally distributed.
Direct and Indirect Outcome Variables
Typically, we connect a risky event ϵ to a random variable y(ϵ). For example, ϵ may represent uncertain prices and y(ϵ) may represent income which depends on uncertain prices ϵ. We will refer to ϵ as the direct outcome variable and y(ϵ) as the indirect outcome variable over which the firm’s utility is defined.
In most risk models, the relationship between ϵ and y(ϵ) is monotonic, if the direct outcome variable goes up (down) so does the indirect outcome variable. If prices increase, so does income; if the variance of ϵ increases, so does the variance of y(ϵ). However, one can easily construct examples in which the linkage is not so direct. For example, suppose the firm faces financial stress and that only very favorable outcomes will permit the firm to meet its cash flow obligations and survive. Under such circumstances, the firm may increase its expected income and its probability of surviving by choosing a strategy that increases its variance of direct outcomes. Consider such a problem by defining an indirect outcome variable w = 0 if the firm fails to survive and w = 1 if the firm survives. In this model the direct outcome variable is y. Then we connect the indirect outcome variable w to the direct outcome variable y by defining a survival income yd and defining w in terms of y as follows:
$w=\left\{\begin{array}{ll}{0} & {\text { for } \quad y<y_{d}} \ {1} & {\text { for } \quad y \geq y_{d}}\end{array}\right. \nonumber$
The ad hoc decision rule can be expressed as:
$V(y)=\left\{\begin{array}{lll}{U(0)} & {\text { for }} & {y<y_{d}} \ {U(1)} & {\text { for }} & {y \geq y_{d}}\end{array}\right. \nonumber$
Since U(0) and U(1) are arbitrarily assigned values, let U(0) = 0 and U(1) = 1. Then, the ad hoc decision rule to be maximized is:
(15.14)
which calls for minimizing Pr(y < yd). This rule is known as Roy’s safety-first rule. When direct outcomes are defined in terms of winning or losing, Roy’s safety-first rule is consistent with an expected utility model.
Of course, one can think of other direct and indirect outcome variable relationships. For example, y could represent uninsured income and w could represent insured income, or y could represent unhedged income and w could represent hedged income, or y could represent income produced without risk reducing inputs and w could represent income produced with risk reducing inputs.
So what have we learned? We learned that risk responses are defined over direct outcome variables. Failure to distinguish between indirect and direct outcome variables may lead us to view responses to indirect outcome variables as risk preferring when they are indeed risk averting.
Firm Responses to Risk
Individuals and businesses all face risky events, including the possibility of losses that leave them less well off than before the outcome associated with the risky event occurred. These outcomes may include you or someone you care about becoming ill or unemployed. Business also face the possibility of losing customers, production failures, declining prices, and loss of financial support.
The next section describes alternative responses to risky events available to firms and individuals. If firms and individuals limit their risk responses described by alternatives on an EV frontier and select risky alternatives consistent with their underlying risk preferences, then they will maximize their certainty equivalent income. Higher risk-averse decision makers will select investments with lower expected values and variances. Less risk-averse decision makers will select investments with higher expected values and variances. If the firm’s current risk position is an expected value-variance combination off the frontier, then the firm’s risk responses may be designed to move the firm closer to a position on the EV frontier.
More to the point, moving up or down its EV frontier involves paying another unit to absorb part or all of its risk (e.g. buying insurance) or changing the relative amount of safe and risky investments in its portfolio.
Someone once claimed that economists can predict the past correctly only 50% of the time. Imagine how successful economists are at predicting future outcomes for risky events? This should suggest that even though we present risk response solutions in closed forms, we should be cautious and explore alternative assumptions and predictions to explore the robustness of our estimates. With that caution in mind, we proceed to explore external risk responses (pay others to absorb our risk) and internal risk responses (change the firm’s holdings of risky and safe investments).
Our discussion of risky and uncertain events and how to measure the probabilities of their outcomes has prepared us to evaluate alternative risk responses including: (1) sharing risk with others through various arrangements including forming partnerships and cooperatives, (2) buying insurance, (3) diversifying one’s holdings of risky investments, (4) purchasing risk reducing inputs, and (5) choosing optimal capital structure. In addition, we will introduce the expected value-variance criterion for ranking alternative risky investments. Finally we will explore how converting risky cash flow to their certainty equivalents can provide the means for introducing risk into PV models so that the homogeneous measures principle applied to risk is satisfied.
Sharing Risky Outcomes
One way to mitigate the impact of adverse outcomes associated with risky events is by forming risk sharing arrangements with others even when they are facing similar risks. The key to successful risk reduction combinations with others is to combine operations that are statistically independent of each other. Statistical independence has a precise meaning, but essentially it means that the expected value of the product of two random variables equals the product of their expected values. In a later section we will discuss combining firms’ operations within other firms whose returns tend to move together.
To make the point that combining units experiencing independent risky outcomes can mitigate risk, consider the following. Let x be a random variable with expected value and variance respectively. Let “a” and “b” equal numerical constants. Then, define a new random variable:
(15.15)
The variance of y, , is equal to:
(15.16)
The explanation for Equation \ref{15.16} is that the variance of the constant “a” or any constant is always zero while the variance of a constant times a random variable is the constant squared times the variance of the random variable.
In Equation \ref{15.15} we created a new random variable y by linearly transforming the random variable x. Now consider another way to create a new random variable—by taking the average of two (or more random variables). For example, suppose two businesses were facing independently distributed risky earnings. One business owner faced the random variable x1 and the second business owner faced the random variable x2. Also suppose that the two business owners decided to combine their businesses and agreed that each would receive half of the average earnings. In this process we define a new random variable.
(15.17)
First, recognize that each random variable is multiplied by the constant (1/2). Then each partner would earn on average the expected value
(15.18)
and the variance each owner would face would be the variance of the expected return multiplied by the constant (1/2) squared. The variance of the average earnings each firm would receive, σy2, is equal to:
(15.19)
n the case that the distributions were identically distributed with expected value and variance of and , each partner would face the same expected value as before, . But, the variance of their individual earnings would be , half of what it was before without combining their businesses. Furthermore, the standard deviation of the earnings each partner would face would be:
(15.20)
And if n partners joined together, then they would each face the same expected value as before, but the variance each partner would receive is . We now illustrate these important results.
Assume that business one’s earnings are determined by outcomes associated with the toss of a fair coin. If the outcome of the coin toss is tails, the firm pays (loses) $5,000. If the toss is a heads, the firm wins$8,000. Thus, the firm wins either $8,000 or loses$5,000 and earns on average (.5) (–5,000) + (.5) (8,000) = $1500. The standard deviation of this risky outcomes is: (15.21) Furthermore, assuming a normal distribution, 68% of the time, the average outcome will be between the mean and plus or minus one standard deviation: ($1,500 + $6,500) =$8,000 and ($1,500 –$6,500) = –$5,000. Now suppose that two persons decide to combine their operations and share the average of the outcomes. Then the possible outcomes of two coin tosses are two heads (H, H) which earns on average$16,000 / 2 = $8,000 and occurs with a probability of .25; two tails (T, T) which earns on average –$10,000 / 2 = –$5,000 and occurs with a probability of .25, and one head and one tail (H, T) or one tail and one head (T, H) which both earn on average$3,000 / 2 = $1,500 and each occurs with a probability of .25. The expected value for each of the two players can now can be expressed as: (15.22) The two players now receive on average the same as before,$1,500, but consider the standard deviation of the average outcome:
(15.23)
Furthermore, assuming a normal distribution, 68% of the time, the average outcome will be between the mean and plus or minus one standard deviation: ($1,500 +$4,596) = $6,096 and ($1,500 – $4,596) = –$3,096. Note that even though the expected value did not change when outcomes were averaged over two persons, the standard deviation was reduced almost 30%. Also note that the results are in accord with Equation \ref{15.24}:
(15.24)
Now imagine ten persons each facing independent and identical distributed earnings outcomes, then the standard deviation each would face would equal:
(15.25)
Furthermore, assuming a normal distribution, 68% of the time, the average outcome will range between ($1,500 –$2,055) = –$555.48 and ($1,500 + $2,055) =$3,555. Note that even though the expected value did not change when outcomes were averaged over ten persons, the standard deviation was reduced almost over 70%. Reducing the variability for each person by over 70% by combining ten independent risky events (facing each of 10 independent firms) illustrates the power of reducing risk by sharing independent risky events.
In the previous example we assumed that each partner contributed an equal share. Now assume two persons decided to form a partnership and share the risk and expected returns weighted by their shares contributed to the business. Assume partner 1 contributed w1 = 30% of the assets and partner 2 contributed w2 = 70% of the business. Each partner’s business rate of return can be described by random variable y1 and y2 with expected values and variances for partner one of and for the first partner and and for the second partner. We want to find expected value of the partnership and each partner’s share of the expected value. Then, we want to find the variance of the partnership and the variance of returns each partner would face.
First, to find the expected value of the partnership, we weight each partner’s contribution by the percentage of their contributions. Call the expected return of the partnership E(yp):
(15.26)
Meanwhile, the variance of expected return from the partnership is the sum of the individual variances multiplied by the partners’ shares squared:
(15.27)
Furthermore, the standard deviation of the portfolio is 4.5%. Thus, the partnership earns 11.4% on its investments and faces a standard deviation of returns equal to 4.5% which is less than their standard deviation of returns faced alone equal to 5.0% or 6.0%. Of course, they would have to agree on how to distribute profits, but we assume it would be based on the shares they contributed.
Reducing Risk by Purchasing Insurance
It may be difficult for an individual firm to agree with other independent firms on how to share profits and risk. However, an insurance company that absorbs individual firms’ risk in exchange for an insurance premium can reduce the overall risk by combing the risk facing large numbers of individual firms. Furthermore, by carefully selecting businesses from different geographic areas and of different types, the risk absorbed by individual firms can be close to negligible.
For most individuals and businesses, insurance offers a way to reduce their risk when other measures are not available. Insurance is a practical arrangement by which a company or government agency provides compensation for a wide variety of losses and adverse outcomes. For example, we can purchase health insurance in case we become ill, fire insurance in case of a fire, term and whole life insurance for our heirs if we die, revenue insurance in case our expenses exceed income, trip insurance in case our flight gets canceled, and almost any other adverse outcome as long as we are willing to pay someone to assume the possibility of loss. This kind of insurance, discrete disaster event insurance, is described next.
Discrete disaster event insurance. Consider a firm with wealth comprised of a risky asset, whose value is W in the best state of nature and zero in the worst state of nature, and risk-free assets valued at W0 regardless of the state of nature. An insurance company is willing to absorb the risk of possible losses of wealth in exchange for an insurance premium . The firm must determine the maximum insurance premium it can pay to avoid a disaster without reducing the level of its certainty equivalent wealth below the level attained with no insurance coverage. The firm can increase its certainty equivalent income by purchasing insurance if .
Suppose the firm is considering a comprehensive fire insurance policy and W represents the value of the firm’s flammable property being insured. To the find the maximum insurance premium that the firm can pay without reducing its certainty equivalent income, we form the decision matrix displayed in Table 15.2.
The matrix has two possible states of nature, two choices, and four different possible outcomes. The states of nature are (1) a fire state s1, and (2) a no-fire state s2 . The choices are buy insurance (choice A1) and remain uninsured (choice A2). If choice A1 is selected, the outcome in both states s1 and s2 is initial wealthy W + W0 less an insurance premium . This result is obtained because if a fire does occur, the insurance company reimburses the firm for its losses and receives a risk premium. If there is no fire, the insurance company pays for no losses while still earning the insurance premium. In both states the firm purchasing insurance pays a premium. If, on the other hand, the firm decides to remain uninsured (choice A2) and no fire occurs, the firm will be left with both its safe wealth W0 and its risky wealth W and will have saved the insurance premium because it didn’t purchase insurance. However, if a fire does occur, the firm will lose its risky wealth W. These results are summarized below.
Table 15.2. Decision Matrix for Insurance Versus No Insurance with a Discrete Disaster Outcome.
Choices
States of nature Probability of outcomes A1 (buy insurance) outcomes A2 (Don’t buy insurance) outcomes
(s1) fire 0 < p < 1
(s2) no fire 1 – p
If the probability of fire is p and the probability of no fire is 1 – p, the expected values of the two choices E(A1) and E(A2) are:
(15.28)
And
(15.29)
The difference between E(A1) and E(A2) can be expressed as:
(15.30)
If the decision maker was risk neutral and decided between options based on their expected value, the maximum the client would pay for the fire insurance would be , and as long as the client would be better off purchasing insurance than not purchasing insurance.
To illustrate, suppose that the flammable property was W = $100,000 and p = 1%. Then, the most a client could pay and break-even based on his or her expected values would be pW = (.01)($100,000) = $1,000. If an insurance policy was available for less than$1,000, the client would be advised to purchase the insurance. Suppose the client is risk averse and lays awake at night worrying about the possibility of a fire, and perhaps the client is willing to pay an additional insurance premium based on some function of p and W equal to U(p,W) $150 to know that, no matter what, the outcome will be . Revenue insurance. One for the most important forms of insurance available to individual and firms is revenue insurance. The general principles of revenue insurance can be complicated. We describe a simplified version of revenue insurance with discrete outcomes. Suppose an outcome from a crop operation is a risky event with three possible outcomes: normal income y, reduced income where is a percentage between one and zero, or a failed crop resulting in y = 0. Let the probability of y be p1. Let the probability of be p2. And let the probabilities of a failed crop and zero income be (1 – p1p2). The insurance provided does not fully compensate farmers for their losses for moral hazard reasons; they want the farmers to experience some losses for not producing a normal crop. As a result, lost revenues are only compensated by percent. Furthermore, there is a complicated process to determine what is a normal yield that produces y. If a failed crop outcome occurs, the firm receives or percent of what it normally earns. If a partial crop outcome occurs, then the firm also earns because the insurance company pays of the firm’s lost earnings equal to To describe the revenue insurance program described above we construct Table 15.3. Table 15.3. Decision Matrix for Revenue with Insurance Versus no Insurance with Discrete Outcomes. Choices States of nature Probability of outcomes A1 (buy insurance) outcomes A2 (Don’t buy insurance) outcomes (s1) full crop p1 (s2) partial crop p2 (s3) crop failure (1 – p1p2) 0 To solve for we equate the expected value for the two choice options: (15.31) And solving for the insurance premium we find: (15.32) To illustrate, suppose and so that Assume that the probability of a normal income is 60%, the probability of a partial crop and a reduced income is 30%, and the probability of a complete crop failure and no income is 10%. Finally, assume that your revenue insurance policy covers = 80% of lost revenue. We restate these conditions in Table 15.4 and then solve for the break-even insurance premium Table 15.4. Decision Matrix for Revenue Insurance Versus No Insurance with Discrete Outcomes. Choices States of nature Probability of outcomes A1 (buy insurance ) outcomes A2 (Don’t buy insurance) outcomes (s1) full crop p1 = 60% (s2) partial crop p2 = 30% (s3) crop failure (1 – p1p2) = 10% 0 Finally, we solve for the break-even insurance premium (15.33) In other words, a manager could afford to pay up to 17% of its normal income as revenue insurance under the conditions described in Table 15.3. Diversification of Firm Investments Investors rarely hold investments in isolation. Indeed, holding a single investment by itself may be very risky. Most investors attempt to reduce risk by holding a portfolio of (two or more) investments. Adding a risky investment to a portfolio of investments may actually decrease the risk of the portfolio without adversely affecting the expected return on the portfolio. We illustrate the point that adding risky investments to one’s portfolio may decrease risk with an example. Umbrellas and sunglasses. Suppose that on any given day there are three possible weather outcomes: there may be rain, there may be a mix of clouds and sun, and there may be bright sunny skies. For simplicity, assume that the probability of each outcome is 1/3. A firm whose outcomes depend on the weather state can invest in umbrellas or sunglasses or a mix of the two. Both investments in umbrellas and sunglasses earn an expected rate of return equal to 10%. These results are summarized in Table 15.5 below: Table 15.5. Expected Returns and Variances on Investments in Sunglasses and Umbrella Weather states i = 1,2,3: Probability of weather states Random Returns on Sunglasses in the ith weather state: riS Random Returns on Umbrellas in the ith weather state: riW Return on portfolio Rain 1/3 0% 20% .5(0) +.5(20%) = 10% Mix clouds and sunshine 1/3 10% 10% .5(10) +.5(10%) = 10% Sunny 1/3 20% 0% .5(20) +.5(0%) = 10% Expected return on investments: E(riS) = (1/3)(0% + 10% + 20%) = 10% E(riW) = (1/3)(20% + 10% + 0%) = 10% .5E(riS) + .5E(riS) = (1/3)(10% + 10% + 10%) = 10% Standard deviation of returns: 8.16% 8.16% 0% Notice that when it rains, return on umbrellas is favorable (20%) but the return on sunglasses is low, 0%. The reverse is true when there are bright sunny skies; the return on umbrellas is low (0%) while the return on sunglasses is favorable, 20%. The standard deviation for both investments equals: (15.34a) Now assume that the firm diversified and created a portfolio in which 50% of its investments were in sunglasses and the other 50% were in umbrellas. The results are described in the last column of Table 15.5. Notice that the return in each state is 10% because when returns on low on sunglasses, return on umbrellas are favorable and vice versa. Note also that while each individual investment has a standard deviation of returns equal to 8.16%, the return on the portfolio is constant and the standard deviation of portfolio returns is zero. (15.34b) This is an extreme example of how adding a risky investment may actually decrease the firm’s risk. However, this favorable result occurred because the returns on umbrellas and sunglasses were perfectly and negatively correlated. Covariance measures. To be perfectly and negatively correlated means that returns on one investment is above its mean by exactly same amount as the other investment is below its mean in the same state. One measure of correlation between two random variables is the covariance measure. Using the notation from the umbrellas and sunglasses example, we define the covariance as: (15.35) Notice that the covariance is similar to a variance measure except that instead of a deviation from the expected value being squared, the deviation for both variables in the same state are multiplied, so the covariance measures whether the two variables are moving in opposite directions from their means (negative covariance) or whether the two variables are moving in the same direction from their means (positive covariance). To emphasize the difference between variance and covariance measures, when calculating variance, we squared deviations from the mean, and as a result all variances are positive. In contrast, deviation in covariance measures are not squared which allows them to be positive or negative. Note that the first and third term in the covariance calculation in Equation \ref{15.35} were negative while the second term was zero. Thus, the covariance of investments in sunglasses and umbrellas is negative. Obviously the sunglasses and umbrellas example is simplified to illustrate a point, that risk is completely eliminated because the returns from the two investments have perfect negative correlation. The level of correlation between returns is measured by the correlation coefficient defined as: (15.36) Thus, in our example, the correlation coefficient is negative one: (15.37) Obviously, other things being equal, we would prefer to add investments to our portfolio that are negatively correlated with our overall portfolio returns. Let’s return to our investigation of the partnership, only this time allow for a single firm to consider its rate of return on its portfolio of investments. Assume that it has two investments and the percent of the total portfolio invested in each investment is indicated by a weight w1 and w2 that sum to one. The expected value for the firm’s portfolio can be expressed as before: (15.38) Now consider the variance of the investor’s portfolio. If the investments are represented by independent random variables, the portfolio variance is as before—the weighted sum of the individual variances. When the investments are not independent, the portfolio variance also includes a covariance term. We can write the variance of the portfolio allowing for dependence between the two investments as: (15.39) We now apply our portfolio approach to the umbrellas and sunglasses example. Recall that both investments earned an expected rate of return of 10% and their standard deviations were both equal to 8.16%. If the firm divided their portfolio between the two investments, then we would write the expected value and variance of the portfolio as: (15.40) And we write the portfolio variance as: (15.41) In this special example, that the returns on sunglasses and umbrellas moved in perfectly opposite direction means that combining investments in both eliminated the variability of returns on the firm’s portfolio. Beta coefficients and risk diversification. An important risk concept applied to securities markets but which also has application to the firm is the beta coefficient (β). The beta coefficient is a measure associated with an individual investment which reflects the tendency of an investment’s returns to move with the average return in the market. Applied to the individual firm, the beta coefficient measures the tendency of an individual investment’s returns to move with the average return on the firm’s portfolio of investments. To explain beta coefficient, suppose we have past rate of return observations rtj on a potential new investment and on the firm’s portfolio of returns rtp in time period t. Table 15.6 summarizes our observations: Table 15.6. Observations of Returns on the Firm’s Portfolio of Investments rtp and on a Potential New Investment (a Challenger). Time t Observed returns on the firm’s portfolio over time rtp Observed returns on a potential new investment for the firm’s rtj 2012 10% 7% 2013 6% 8% 2014 7% 5% 2015 3% 2% 2016 5% 3% Another way to represent the two rates of return measures and their relationship to each other is to represent them in a two dimensional scatter graph. We may visually observe how the two sets of rates of return move together by drawing a line through the points on the graph in such a way as to minimize the squared distance from the point to the line. Our scatter graph is identified as Figure 15.3. Figure 15.3. Scatter Graph of Returns on the Firm’s Portfolio of Investments and Returns on the Potential New Investment The relationship between the returns on the new investment and the firm’s portfolio can be expressed as: (15.42) Notice that the equation above describes the straight line drawn through the point plus the vertical distance from the line to each point. The slope of the line is the beta coefficient β and tells us how the returns on the portfolio and potential new investment have moved together in the past. We can find the equation for this line using a statistical method called “least squares” regression analysis. The method essentially finds a line so that the average squared deviations from the line, εt2, are minimized. The formula for beta is equal to the covariance between the returns on the new investment rtj and the returns on the firm’s portfolio rtp over some time period divided by the variance of portfolio returns: (15.43) Fortunately, the calculations for the beta coefficient as well as the coefficients in Equation \ref{15.16} can be found using Excel.[2] We find the beta coefficient and the coefficients for Equation \ref{15.16} using the data in Table 15.6. The estimated equation for the line is: (15.44) So what have we learned? We learned that, in particular, a beta coefficient of .48 means that a 10% change in the return on the firm’s portfolio will likely be accompanied by an increase of 4.8% in the expected returns on the potential new investment. Furthermore, a decrease of 10% in the returns on the firm’s portfolio of investments will likely be accompanied by a 4.8% decrease in the expected returns on the potential new investment. It also means that the variability of the returns on the potential investment are less than the variability of returns on the firm’s portfolio of returns. It also says that adding the potentially new investment will not diversify all of the firm’s risk. There will still be 48% that is not diversified; it varies with the returns on the firm’s overall rate of return. It reduces some of the risk faced by the firm, but not all of it—only about 52%. Diversifiable and non-diversifiable risk. Assume a beta coefficient of minus one (–1). This would mean that for a 10% increase (decrease) in the firm’s overall rate of return, that the expected rate of return on the potentially new investment decreases (increases) by 10%. Like investments in sunglasses and umbrellas, a sufficient investment in the new investment would eliminate the firm’s risk. Thus, a beta of –1 means that all of its risk can be diversified. In contrast, assume a beta coefficient of one. This would mean that for a 10% increase (decrease) in the firm’s overall rate of return, that the expected rate of return on the potentially new investment increases (decreases) by 10%. Unlike investing in sunglasses and umbrellas, adding the potentially new investment to the firm’s portfolio of investment only accentuates its risk, and the new investment has no potential to diversify the firm’s overall risk. Purchase Risk Reducing Investments It is useful to distinguish between two primary reasons for investing: first, to increase expected earnings for the firm and second, to reduce the variability of earnings. If one can increase expected returns without increasing variance of return, certainty equivalent income has increased. If one can reduce variance of returns without also reducing expected returns, certainty equivalent income has increased. See Equation \ref{15.12}. Of course if from one’s current expected value-variance position, one could increase one’s expected value of returns without increasing the variance of returns—or if one could reduce one’s variance without also reducing one’s expected value—then the firm would be in an inefficient expected value-variance position off the EV frontier. However, we can identify investments whose primary purpose is to reduce variability even though they alter expected incomes. We call these risk reducing investments. We analyze risk reducing inputs using the certainty equivalent income model described in Equation \ref{15.12} that accounts for both variance and expected value in the ranking criterion. We will illustrate risk reducing investments with a case study involving an irrigation investment. Consider a firm facing five moisture states with an equally likely chance of occurring: normal, low stress, moderate stress, high stress, and drought. The returns per acre with and without the irrigation system are reported in Table 15.7. The annualized cost of the irrigation system, which is expected to have a 20 year life and no liquidation value, is per acre. We assume the defender’s IRR associated with the certainty equivalent cash flow stream to be 8%. Table 15.7. Returns per Acre under Alternative Moisture States with and without an Irrigation System. Moisture states Probability of moisture states Return per acre without the irrigation investment riw/0 Return per acre with the irrigation system riw minus irrigation costs per acre π Normal 20%$128.00 $113– π Low stress 20%$105.00 $100 – π Moderate stress 20%$90.00 $80 – π High stress 20%$75.00 $75 – π Drought 20%$50.00 $70– π Expected returns$89.60 $87.60 Standard deviation of returns$26.43 $16.28 Assume that is$15 per acre. Then the expected value of the crop production per acre without irrigation is still $89.60 and greater than$87.60. If the decision maker were risk neutral, he or she would not invest in the irrigation system. Allow that the decision maker is risk averse and chooses between investments based on their certainty equivalent incomes rather than the difference in their expected values. If this were the case, then the certainty equivalent income without irrigation is:
(15.45)
In contrast, the certainty equivalent income with the irrigation system is:
(15.46)
We cannot decide between the two systems because one has a higher expected value and the other has a lower variance. It all depends on how risk averse the decision maker is. Recall that reflects the decision maker’s preferred trade-off between expected return for variance. The break-even λ in this case is found by equating the two certainty equivalent incomes:
(15.47)
and solving for :
(15.48)
Thus, all decision makers more risk averse than is reflected by the risk aversion coefficient of = .009 will be earning a lower expected value on average than would be earned without the irrigation system.
Choosing an Optimal Capital Structure
Leverage and risk. In an earlier chapter, we used leverage as a measure of the firm’s risk without explicitly stating the connection. We now make the connection explicit by reconsidering equation 8.5 and making one adjustment. The adjustment is that since we only consider realized capital gains when finding ROA–IRR, we ignore unrealized capital gains (V1V0) which allows us to rewrite equation 8.5 as:
(15.49)
In Equation \ref{15.49}, note the leverage ratio D/E and that it multiplies the difference between the ROA and the average interest rate i. And now we return to a risk principle introduced earlier—that multiplying a random variable by a constant, in this case the leverage ratio, increases the variance of the random variable by the constant squared. Consider the application of this principle.
Suppose the random variable ROA is described by pdf f(rROA) with expected value rROA and variance σ2. Now suppose that we were to multiply the random variable ROA by some scalar, say 2. Then the expected value of the random variable would be 2rROA and the variance would be 22σ2, or 4σ2.
In Equation \ref{15.49}, the debt-to-equity ratio is the scaler that multiplies and exaggerates the difference between rROA and i. To illustrate, suppose that ROA can take on values of –8%, –3%, 3%, 5%, and 12% and i = 3%. Then in Table 15.8 we find ROE for leverage ratios of 0, 2, 5, and 10.
Table 15.8. ROEs whose Expected Values and Standard Deviations depend on Leverage Ratios.
Values of the random variable ROA (i = 3%) ROE values for alternative Leverage Ratios (L = D/E) and values of the random variable ROA
L = 0 L = 2 L = 5 L = 10
–8% –8% –30% –63% –118%
–3% –3% –15% –33% –63%
3% 3% 3% 3% 3%
5% 5% 9% 15% 25%
12% 12% 30% 57% 102%
Standard deviations for ROEs associated with each leverage ratio L
Expected values 1.8 % –.6% –4.2% –10.2%
Standard deviation σ .077 .23 .460 .843
The first thing to note about the outcomes in Table 15.8 is that whenever the ROA exceeds the average interest rate i, that ROE > ROA. For example, for a leverage ratio of 2 and an ROA of 5%, ROE is 9%. The second point to observe is that even though the E(ROA) > 0, as the leverage ratio increased, the E(ROE) was mostly less than zero. In other words, the effect of leverage was more pronounced when the ROA < i than when ROA > i. Another thing to note is that if the ROA outcome is –8% and the firm has a leverage ratio of 10, it loses 118% of its equity. In other words, one unfavorable outcome with a high leverage ratio can destroy the firm. Finally, due to the cost of debt that must be paid regardless of ROA outcomes, ROA’s less-than-average cost of debt with high leverage ratios have significant adverse effects on the firm’s equity. Thus, we conclude that a high leverage ratio, even though it can exaggerate unusually high ROA outcomes, is still a risky state for the firm. For that reason, many firms view leverage reduction as an important strategy for reducing the riskiness of the outcomes they face.
Capital structure. A firm’s capital structure is its combination of debt and equity used to finance its overall operations and growth. The small to medium-size firm may finance its overall operations and growth by using long-term debt, equity, and notes payable. We will discuss the small to medium-size firm’s optimal capital structure using a simplified expected value-variance (EV) profit model.
In our simplified model, we let the firm’s assets A be funded by a combination of debt D and equity E. We let be the stochastic rate of return on the firm’s assets whose variance is and whose expected rate of return is ra. We let the average non-stochastic cost of debt per dollar be represented by the variable iD. The firm decision maker’s risk-return trade-off is measured by
We represent the firm’s stochastic profits to equal the stochastic rate of return on assets times assets less the firm’s average cost of debt times the firm’s debt. Then we substitute for assets A the sum of debt D plus equity E and collect like terms and express the stochastic results in Equation \ref{15.50}.
(15.50)
We write the expected value of stochastic profits as:
(15.51)
We write the variance of profits as:
(15.52)
Finally, we substitute the expected value and variance of profits into Equation \ref{15.51} to find the firm’s certainty equivalent of profits that we refer to as the EV model.
(15.53)
Finding the firm’s optimal capital structure.[3] Having our EV model defined over the expected value and variance of profits and accounting for the decision maker’s risk attitudes, we use calculus to find the optimal debt level by differentiating the certainty equivalent function with respect to D.
(15.54)
The second order conditions are satisfied allowing us to solve for the optimal debt D* (assuming fixed equity). We find the optimal debt D* to equal:
(15.55)
Equation (15.55) reveals an interesting detail. If the cost of debt equals the expected return on assets, the firm holds negative debt—preferring to lend out its equity at a safe rate iD rather than earning a stochastic return on firm assets.
Dividing Equation \ref{15.55} by the firm’s equity E, we can find its optimal leverage ratio l* equal to:
(15.56)
We illustrate Equation \ref{15.56} using HQN’s data. We substitute for ra the ROA value equal to 6.5% (equation 5.13), the average cost of debt iD equal to 6% (equation 5.21), equity E equal to $8,000 (Table 4.1), the risk aversion coefficient calculated in Equation \ref{15.48} equal to .009, and finally, we let the standard deviation—the amount that returns on assets vary on average—equal 1.25% or .0125 that we square to find the variance of profits equal to .000156. Making the substitutions for the variables in Equation \ref{15.56} we find the firm’s optimal leverage ratio equal to: (15.57) compared to the firm’s actual leverage ratio of 4.0. Changing variables affecting the optimal capital structure. We can imagine how the optimal leverage would change in response to changes in the value of the variables included in Equation \ref{15.57}. In other words, we ask: how would the optimal leverage change if the value of one of the variables in Equation \ref{15.57} changed? We can infer the answer to this question by looking at changes in the optimal leverage ratio in response to a change in one of the variables holding the other variables constant. Increasing the expected value of asset returns ra makes it more profitable to use borrowed funds and increases the optimal leverage ratio. Increasing the average cost of debt iD makes using debt less profitable and reduces the optimal leverage ratio. As a decision maker becomes more risk averse, represented by an increase in the risk aversion coefficient , the decision maker is less willing to risk losing equity with an unfavorable outcome and reduces leverage. As the firm’s equity increases, it can achieve the same risk return combination with less debt and the optimal leverage ratio decreases. Finally, as the variance of return on firm assets increases, the firm reduces its leverage ratio to return to its preferred trade-off between equity and debt. In addition to describing how the firm’s finds its optimal capital structure in response to changes in the value of the variables that determine the optimal capital structure, we create Table 15.9. Columns in Table 15.9 include the list of variables, their original values for HQN, a column showing increased values of the variables, the revised optimal leverage ratio, and the change in the optimal leverage ratio compared to the original optimal leverage ratio of 3.45. Table 15.9 Optimal leverage ratios and changes in the optimal leverage ratio in response to increases in one of the variables in Equation \ref{15.57} holding the other variables constant. Variable Original value Increased value Revised optimal leverage ratio Change in the optimal leverage ratio ra 6.5% 7.0% 7.903134 4.45 iD 6% 6.5% (1) (4.45) .009 .001 3.01 (.44) 0.000156 .000175 2.97 (.48) E$8,000 $9,000 2.96 (.49) So what have we learned? We learned that firms generally dislike risk (however it is defined) and prefer expected earnings. Generally, we are willing to assume some risk if the increase in expected returns is sufficient. The firm selects its optimal combination of debt and equity to achieve its preferred expected profits and variance of profits. Increases in the value of variable that increase the firm’s expected profits increase the firm’s optimal leverage ratio. Increases in the value of variables that increase the firm’s variance of profits reduce the firm’s optimal leverage ratio. Summary and Conclusions Some sage is reported to have said that only death and taxes are certain. If that statement is anywhere close to being true, then risk and uncertainty fill the world we live in and try to manage. One important step toward managing the outcomes of risky events is to understand the tools that have been developed to report and measure it. In this effort, precision is not expected. It is best to explore the influence of risk in a variety of settings and assumptions. The second thing to note about risk, emphasized in the irrigation example, is that individual risk preferences may have significant effects. As a result, two individuals facing the same investment opportunities may make different choices because of the different risk preferences. As a result, it is important for managers to explore their own risk preferences and apply them when making risky decisions. Questions 1. This question has several parts. 1. What is the difference between a sample of observations and the population of possible values? 2. Explain the difference between an expected value and variance (standard deviation) calculated from a sample and the expected value and variance (standard deviation) of a population. 3. Find the expected value and variance (standard deviation) for the numbers 5, 8, –3, 9, and 0. Assume each number has an equally likely chance of being observed. 4. Find the expected value and population variance (standard deviation) for the numbers 5, 8, –3, 9, and 0 if their probability of occurring were .1, .2, .4, .2, and .1 respectively. 5. Compare the results obtained in parts c and d. 2. Return to Table 15.1 in the text. Suppose that the investor decided to invest half of her assets in investment A and half in investment B. Describe the random variable for the combined investment. Then describe its pdf, expected value, and variance (standard deviation). Based on the respective expected values and variances for investment A, investment B, and the combined investment—which would you prefer, assuming you are risk averse? 3. Assume two people decide to form a partnership and share the risk and expected returns based on their shares contributed to the business. Assume partner 1 contributed 40% of the assets and partner 2 contributed 60% of the assets. Each partner’s business can be described by random variables y1 and y2 with expected values and variances of μ1 = 8% and σ12 = 0.006 for the first partner and μ2 = 12% and σ22 = .007 for the second partner. Find the expected value standard deviation of the partnership. 4. Assume that Kelly wants to provide for her heirs in case she dies during the coming year. Therefore, she purchases a term life insurance policy that pays$1,000,000 in case she dies in return for an insurance premium of \$800. Assuming Kelly is risk neutral, what must Kelly assume is the probability of her death in order for her to purchase the insurance policy?
5. Assume the conditions described in Table 15.3 except allow for the insurance coverage δ to increase from 80% to 85%. Find the increase in the break-even insurance premium.
6. Assume the conditions described in Table 15.4. Also assume that instead of purchasing revenue insurance the investor could purchase an irrigation system that would increase the probability of a normal revenue income year from 60% to 75%, reduce the probability of a reduced income year from 30% to 20%, and reduce the probability of zero income from 10% to 5%. What would be the most that the manager could pay to reduce its risk through the purchase of an irrigation system and still be as well as he was before? (Hint: compare the value provided by the irrigation system less the cost of the irrigation system compared to the outcomes without an irrigation system.)
7. One of the differences between the purchase of an irrigation system and revenue insurance is that one has to purchase revenue insurance each year while the irrigation system continues to provide risk reduction services during its useful life. If the irrigation system described in the previous question were available for 10 years and the discount rate were 8%, what is the NPV of the irrigation system?
8. Use the data in Table 15.5 to find the beta coefficient for the investment in umbrellas and sunglasses.
9. A firm has two investments in its portfolio. The historical rates of return on the two investments are reported below. Find the expected rate of return for the firm’s portfolio, the covariance between the two investments, and the variance of the portfolio returns. Rank investment 1, investment 2, and the combined investment using the EV criterion.
Table Q15.1. Observations of Returns on the Firm’s Two Investments
Time t Observed returns on investment one. Observed returns on investment two.
2012 10% 7%
2013 6% 8%
2014 7% 5%
2015 3% 6%
2016 5% 4%
1. The authors thank Jack Meyer for the thumbtack example of an uncertain event.
2. The linear regression equation that includes the Beta coefficient is found in Excel by first plotting a scatter diagram and then hovering over a data point in the graph. A complete discussion of linear regression models is outside the scope of this class.
3. This section uses calculus to find the firm’s optimal debt level and its optimal capital structure or leverage ratio (D/E). Those not interested in the derivation may skip to the next section without loss of continuity in the discussion. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/15%3A_Homogeneous_Risk_Measures.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) understand the different ways interest can be calculated on a loan; (2) recognize the different kinds of interest rates that are used to calculate interest costs on loans; (3) computer comparable interest rates by finding a loan’s effective interest rate; (4) use Excel worksheets to calculate the loan payment, interest rate, term, elasticity of term, and amortization schedule for a particular loan; and (5) evaluate alternative loans using present value (PV) models developed earlier.
To achieve your learning goals, you should complete the following objectives:
• Learn the differences between the following interest rates: the annual percentage rate (APR), the actuarial rate, and the effective rate.
• Learn how to compute the APR, the actuarial rate, and the effective rate on alternative loans.
• Learn how to use the loan equality equation to find a loan’s effective interest rate, its constant payment, its term, and its original loan amount.
• Learn how to find the elasticity relationship between interest rates, loan payments, and the term of the constant payment loan.
• Learn how to create an amortization table for constant payment loans.
• Learn how to find break-even points for refinancing loans.
• Learn how to find the effective rate for several disguised interest rate loans including discount loans and points added loans.
Introduction
Loan formulas and PV models have many similarities. Interest rates on loans are like opportunity costs, the loan amount is like an investment, and loan payments are like an investment’s cash flow. These and other similarities between PV models and loan formulas allow us to use PV tools to analyze different types of loans. The next section focuses on alternative interest rate definitions. This chapter will also identify the relationship between the term of a loan and the size of the loan payment. Finally, this chapter finds break-even points when refinancing loans and effective interest rates for a variety of disguised interest rate loans.
Comparing the Actuarial Rate, Annual Percentage Rate (APR), and Effective Interest Rate
Loans charge interest rates of which there are at least three kinds that are closely related to each other. These rates and their commonly used synonyms are listed below. The interest rate name used in this chapter is italicized. They are: (1) actuarial rate, compound rate, true rate, or periodic rate; (2) Annual Percentage Rate (APR), annual rate, or nominal rate; and (3) effective interest rate or effective annual rate.
Actuarial Rate. In financial transactions, interest may be computed and charged more than once a year. For example, interest on savings deposits is usually calculated on a daily basis while many corporate bonds pay interest on a semiannual basis. The interest rate used in computations for periods of less than one year is called an actuarial interest rate. The actuarial rate is defined as the interest rate per compounding period or the interest rate per period of conversions. It is the actuarial rate used to charge interest on the principal sum during each successive conversion period. For example, consider a 1% actuarial rate charged monthly on $1,000. In this case, in the first month of the loan, 1% of$1,000 or $10 of interest is charged. In the second month, interest is charged on$1,010 equal to $10.10, etc. Annual Percentage Rate (APR). Let rf represent the APR. Let m stand for the number of times during the year the interest is calculated or charged. Thus, m equals the number of compounding periods per year. The ratio of rf / m is the actuarial rate, the compound rate, the true rate, or the periodic rate. We find the APR from actuarial rates by expressing the actuarial rate on an annual basis. To convert the actuarial rate to an APR, we multiply the actuarial rate by m. In the previous example, we multiply the actuarial rate of 1% per month by 12 to yield an APR of 12%. When the compound period or conversion period is one year in length, then the actuarial rate and the APR are equal. Consider two savings institutions, both offering the same APR. The only difference is that institution A offers monthly compounding of interest, while institution B offers annual compounding. Which one should the saver prefer? Obviously, monthly compounding is preferred because the saver earns interest on the interest earned during the same year. With institution B, interest is earned during the year only on the principal saved and on interest earned in previous years. Effective interest rates. Effective interest rates are the actual interest charged measured on an annual basis. When APRs have different numbers of compound periods per year, the different actuarial rates should be converted to their effective interest rates for comparison. The effective rate is obtained by compounding the actuarial rate for a period of one year. As the number of compounding periods per year increases, the difference between the APR and the effective rate increases. Relationship between interest rates. The relationships between an actuarial rate, an APR, and an effective rate can be easily summarized. Let m be the number of compounding periods per year, let rf be the APR, let rf/m be the actuarial rate, and let re be the effective rate. The relationship between the effective rate re, the APR rate rf, and the actuarial rate rf/m can be expressed as: $r^{e}=\left[\left(1+\frac{r^{f}}{m}\right)^{m}-1\right] \label{16.1}$ Note that when m = 1, the effective interest rate, the APR rate, and the actuarial rate are equal. However, when m is not 1, the rates are no longer equal. For example, suppose we wish to find the re assuming rf were compounded quarterly. To solve this problem let m = 4, and rf = 12. Substituting .12 for rf and 4 for m in Equation \ref{16.1}, we obtain the results described in Table 16.1 using Microsoft Excel. In cell B3 we enter the function fx = ((1 + (B1 / B2))^B2) – 1 which returns 12.55%. Table 16.1. Finding an effective interest rate compounded quarterly. Open Table 16.1 in Microsoft Excel. B4 Function: =(1+B2/B3)^B3 -1 A B C 1 Finding an effective interest rate 2 APR 0.12 3 m 4 4 effective rate 12.55% “=(1 + APR/m)^m – 1 If m is increased to 12, or monthly compounding periods, the effective rate is found as before. Let m = 12, and rf = 12 in Equation \ref{16.1}. Then $\left[\left(1+\frac{.12}{12}\right)^{12}-1\right] \label{16.2}$ To solve this equation in Excel, we change cell B3 to 12 and find the effective interest rate to equal 12.68% as shown in Table 16.2. Table 16.2. Finding an effective interest rate compounded monthly. Open Table 16.2 in Microsoft Excel. B4 Function: =(1+B2/B3)^B3 -1 A B C 1 Finding an effective interest rate 2 APR 0.12 3 m 12 4 effective rate 12.68% “=(1 + APR/m)^m – 1 A special compounding formula is obtained by allowing the number of periods compounded to be very large. This idea is expressed as: (16.3) which means that as m approaches infinity the effective rate re equals: (16.4) To solve this problem using Excel, we use the EXP function. In Excel, Euler’s number “e” is found as the function EXP(1) and 12% compounded continuously can be calculated as fx = EXP(.12) – 1 = 12.75. Using the previous cell designation, to find the value of continuously compounding of 12% we would enter the formula in B4 as: fx = EXP(B2) – 1 = 12.75. Table 16.3. Finding an effective interest rate compounded continuously. Open Table 16.3 in Microsoft Excel B4 Function: =EXP(B2) – 1 A B C 1 Finding an effective interest rate 2 APR 0.12 3 m Infinite 4 effective rate 12.75% “=EXP(APR) – 1 Constant Payment Loans Having defined interest rates in financial models, we now use PV models to analyze the most common type of loan, the constant payment loan. Constant payment loans are repaid with a series of equal payments A at equal time intervals. These payments may occur m times during a year over n years, yielding a total of mn payments. The fundamental equality is that the sum of the loan payments discounted at the actuarial interest rate must equal the amount loaned. The relationship between loan amount, , received in time-period zero, with payment A, made for mn periods, at actuarial interest rate (rf/m) beginning in period one, is: $L_{0}=\frac{A}{1+\frac{r^{f}}{m}}+\frac{A}{\left(1+\frac{r^{f}}{m}\right)^{2}}+\dots+\frac{A}{\left(1+\frac{r^{f}}{m}\right)^{m n}} \label{16.5}$ In this formula, the actuarial rate (rf/m) is the IRR for the PV model, and since loan payments are constant, it is unique. A sum that will prove useful in several calculations is the following: (16.6) The notation US0(rf/m, mn) stands for the present value of a uniform series of$1 payments discounted at the actuarial rate (rf/m) for (mn) periods. This shorthand notation allows us to rewrite Equation \ref{16.2} as:
(16.7)
Recall that with one equation we can solve for at most one unknown variable. From Equation \ref{16.7} if we know A and US0(rf/m, mn) we can find loan amount L0 that mn payments of amount A discounted at actuarial rate (rf/m) will repay.
Suppose we solve for A in Equation \ref{16.7}. The result is:
(16.8)
From Equation \ref{16.8} if we know L0 and US0(rf/m, mn), we can find constant loan payment A, that, if discounted at actuarial rate (rf/m) for mn periods, will repay loan amount L0.
Suppose we solve for US0(rf/m, mn) in Equation \ref{16.7}. The result is:
(16.9)
If we know A and loan amount L0 in Equation \ref{16.9} we can find rf, m, or n, that constant loan payment A discounted at actuarial rate (rf/m) for mn periods will repay.
Fortunately, the calculations described in equations (16.7), (16.8), and (16.9) can be easily performed using Excel.
Example $1$: Loan amount supported by a constant payment loan
Suppose a borrower can make constant payments of $150 per month for 48 months (four years). The borrower wants to know what size loan can be repaid if the APR interest rate is 5% and the actuarial rate is .05/12 = 0.42%. Using Equation \ref{16.8} we can solve for the loan amount supported by the constant loan payment of$150 using the formula below:
(16.10)
We solve the equation above using Excel’s PV function in Table 16.4.
Table 16.4. Finding the Loan Amount in a Constant Payment Loan. Open Table 16.4 in Microsoft Excel
B7 Function: =PV(B3/B4,B4*B5,B6,,0)
A B C
1 Finding the loan amount in a constant payment loan
2
3 rate .05
4 m 12
5 n 4
6 pmt -150
7 PV $6,513.44 “=PV(rate/m,mn,pmt,,0) The answer displayed is:$6,513.44. In other words, 48 monthly payments of $150 on a loan charging a 5% APR interest rate and a monthly actuarial interest rate of .42% will repay a loan in the amount of$6,513.44.
Example $2$: Constant Payment Loan Annuities
Suppose $5,000 is borrowed from a lending institution for five years at an APR of 12% or a monthly actuarial rate of 1%. The loan is to be repaid with 60 equal monthly installments. What is the payment or annuity necessary to retire the loan? Using Equation \ref{16.4} we can solve for the payment that repays the$5,000 loan:
(16.11)
We solve for the loan payment using Excel’s PMT function in Table 16.5. The answer displayed is: –$111.22 which means that 60 payments of$111.22 on a loan charging 12% APR interest and a monthly actuarial interest rate of 1% will repay a loan in the amount of $5,000. Table 16.5. Finding the Constant Loan Payment. Open Table 16.5 in Microsoft Excel B6 Function: =PV(B3/B4,B4*B5,B7,,0) A B C 1 Finding the loan amount in a constant payment loan 2 3 rate 0.12 4 m 12 5 n 5 6 pmt ($111.22) “=pmt(rate/m,mn,PV,,0)
7 PV $5,000.00 Example 16.3. Loan term required to retire a constant payment loan. Suppose a borrower can make constant payments of$150 per month. The borrower wants to know how many monthly payments will be required to retire a loan of $8,000 if the APR interest rate is 6% and the monthly actuarial rate is .5%. Using Equation \ref{16.9} we can solve for the term of the loan required to retire the loan. (16.12) We solve the equation using Excel’s NPER function shown in Table 16.6. The answer displayed is 62.19 which means that 62 regular payments and one partial payment will be required to retire a loan of$8,000 if the APR interest rate charged on the loan is 6%.
Table 16.6. Finding the Number of Payments required to Retire a Loan
Open Table 16.6 in Microsoft Excel
B8 Function: =NPER(B3/B4,B6,B7,,0)
A B C
1 Finding the number of payments required to retire a loan
2
3 rate 0.06
4 m 12
5 n
6 pmt -150
7 PV $8,000.00 8 nper 62.18593 “=NPER(rate/m,pmt,PV,,0) Comparing Interest Paid, Loan Term, and Payment Amounts for Constant Payment Loans An important relationship exists between the loan’s term and total interest paid. To illustrate, consider a$30,000 loan at 15% APR to be repaid in monthly payments over 30 years. The monthly payment for this loan is $379.33. Total interest TI paid on a constant payment loan is found by multiplying the constant loan payment A times the term of the loan mn, minus the amount of the loan L0: (16.13) In this case, the total interest paid is$106,560.
Increasing the payment amount by 10% to $417.27 reduces the term of the loan by 48% to just over 15.36 years (verify the results above using Excel). Meanwhile, total interest paid is reduced by 56% to$46,961.
The term reduction in response to an increased loan payment is not always so significant. For example, if the above loan had an 8% APR, the monthly payment would equal $220.13 instead of$379.22. Increasing the payment by 10% would decrease the term of the loan by only 27% from 30 years to 21.93 years, and the total interest paid would be decreased by 32% from $49,247 to$33,722.
It would be useful to know how changing the term of the loan affects payment size and total interest paid. It can be shown that as mn becomes large, the payment A approaches the interest cost per period, i.e., the smallest payment possible equals the interest charged on the outstanding loan balance. If the borrower wished to minimize his or her payment, the appropriate term is the one that permits the borrower to repay only interest. The shortest repayment period, on the other hand, is one. Obviously, there is a trade-off between the size of the loan payment and the length of the loan.
The point elasticity of term, measured in years n with respect to the payment A, measures the percentage change in the term n in response to a 1% change in the loan payment. The term elasticity, E(n,A), has been calculated as:
(16.14)
For example, a 30-year loan and an APR of 15% would have an elasticity of term equal to:
(16.15)
In other words, increasing the payment by 1% would decrease the term by approximately 19.78%. In contrast, the arc elasticity, rather than the point elasticity, compares the percentage change in the loan term to a 10% increase in the loan payment and finds the percentage change in the term to equal 48%, or an arc elasticity of term equal to 4.8%. Note that a point elasticity of 19.78% versus an arc elasticity of 48% is the result of comparing large changes in loan payments of 10% versus comparing tiny changes in loan payments (e.g. .00001%). See Table 16.7 of point elasticities below.
Table 16.7. Point elasticity measures for loans of alternative terms and interest rates.
n / r % 1% 5% 7.5% 10% 15% 20%
1 1.01 1.03 1.04 1.05 1.08 1.11
5 1.08 1.14 1.21 1.30 1.49 1.72
10 1.17 1.30 1.49 1.72 2.32 3.19
15 1.26 1.49 1.85 2.32 3.77 6.36
20 1.37 1.72 2.32 3.19 6.36 13.40
25 1.49 1.99 2.94 4.47 11.07 29.48
30 1.49 2.32 3.77 6.36 19.78 67.07
60 2.99 6.36 19.78 67.07 900.23 13,563.00
Example 16.4.Term and Loan Payment Trade-Offs. Lucy Landlord is financing the renovation of a property. She needs a loan for $28,000. Her lender offers her a loan for 20 years at the current interest rate of 15%. She calculates her annual payment to be$4,473.32. If she increases her payment by 1% to $4,518.05, her term is reduced to 19 years, or a reduction of 5%. This percentage reduction is nearly equal to the tabled value of 6.36 in the Table 16.1, found at the intersection of the row labeled 20 and the column labeled 0.15. Large percentage increases in A, such as 10%, may not be accurately reflected in the table of point elasticities. This is because the percentage changes in n with respect to A are large compared to the very small changes in n with respect to A used to calculate the table. Creating an Amortization Table for Constant Payment Loans The word “amortize” originally meant “to kill.” Thus when we amortize a loan, we kill or extinguish it by making regular payments—killing the loan if you will. One feature of the constant payment loan is that, while the loan payment is constant, the amount of the payment devoted to paying off the loan—the principal portion of the payment—and the amount of the payment devoted to paying the interest on the loan are constantly changing. As the loan principal is reduced or killed off, the amount of the payment devoted to interest charges is reduced and the amount of the payment devoted to reducing the loan is increased. Lending institutions, when asked, will provide amortization tables that detail the amount of interest and principal paid on each payment during the life of the loan. Fortunately, Excel provides us the tools needed to create our own amortization tables. Finding principal portion of the tth loan payment using Excel. The Excel PPMT function can be used to find the principal portion of the tth loan payment. The function is expressed as: (16.16) To illustrate the PPMT function, consider at$25,000 loan to be repaid in monthly installments for four years. The APR for the loan is 5%. We want to know what portion of the 5th payment (period) will be applied to the loan’s principal. The Excel solution is represented in Table 16.8.
Table 16.8. Finding the Loan Principal Paid on the tth Payment
Open Table 16.8 in Microsoft Excel
B8 Function: =PPMT(B3/B4,B6,B4*B5,B7,,0)
A B C
1 Finding the loan principal paid on the tth payment
2
3 rate 0.05
4 m 12
5 n 4
6 period 5
7 PV $25,000 8 Principal paid ($479.47) “=PPMT(rate/m,period,m*n,PV,,0)
It turns out that $479.47 of the 5th payment is applied to the outstanding loan principal. In addition, students may verify that the principal portion of the 25th payment is$521.05. This is because the outstanding principal on which interest is charged decreases over the life of the loan. As interest decreases, more of the loan payment can be applied to the outstanding loan principal.
Finding interest payment IP(t) on the tth loan payment using Excel. The Excel IPMT function can be used to find the interest portion of a loan payment in the tth period and is expressed as:
(16.17)
To illustrate the IPMT function, we return to the earlier example: a loan amount of $25,000, a term of 48 monthly payments, at 5% APR, and a desire to find the interest paid on the 5th loan payment. We illustrate the Excel solution for finding interest paid on the tth period. The solution is entered in cell B8 as$54.68. Table 16.9 describes the solution in more detail.
Table 16.9. Finding the Loan Interest Paid on the tth Payment
Open Table 16.9 in Microsoft Excel.
B8 Function: =IPMT(B3/B4,B6,B4*B5,B7,,0)
A B C
1 Finding the loan interest paid on the tth payment
2
3 rate 0.05
4 m 12
5 n 4
6 period 5
7 PV $25,000 8 Interest paid ($96.26) “=IPMT(rate/m,period,m*n,PV,,0)
Together, the interest payment of $96.26 and the principal payment of$479.47 equals the constant loan payment of $575.73. PVs of Special Loans Loans and credit (one’s borrowing capacity) make possible a modern economy and successful firms. Sometimes sellers offer special loan arrangements to encourage the potential buyers to purchase their products. These may include concessionary interest rate loans, skip payment loans, skip principal payment loans, variable interest rate loans, and balloon payment loans. Other times firms may want to expand their investment base and need to refinance their loans, or decreases in interest rates may provide them an incentive to refinance. Fortunately, all of these special loans can be analyzed using PV models developed earlier. We consider the benefits and costs of several special loans in what follows. Concessionary interest rate loans. Assume that Jane Doe’s IRR = r is 10%. Recall that an IRR is the opportunity cost of the defender and is the appropriate rate to use when discounting investment cash flow. Jane is considering an investment loan for$50,000 to be repaid in monthly installments over 15 years (mn = 180). The APR for the loan is 7%, while the actuarial rate is 7% / 12 = .58%.
To find Jane’s NPV for this loan, we first determine her loan payment A. This we can do using the Excel function PMT(rate,nper,PV,,0) = PMT(.58,180,$50,000,,0). The payment A for this loan is:$449.41.
The next step is to treat the loan payment as a cash flow in an investment problem and discount the payments using the borrower’s IRR = r of 10%, or the borrower’s actuarial opportunity cost rate of 10%/12=.83%. Using Equation \ref{16.3}, we find:
(16.18)
Some interpretation of the above results may be helpful. The first important fact is that the borrower’s IRR(r = 10%) was more than the interest rate on the loan (rf = 7%). Therefore the borrower can borrow at a rate less than what she will earn by investing the loan. The borrower’s actual cost of the loan, what is paid back after adjusting for what the loan earns as an investment, is $41,916.34, not$50,000. Another way to express this result is that present value of the loan was $41,916.34. The Net Present Value (NPV) of the$50,000 loan is:
(16.19)
In other words, the borrower received in the form of a loan $50,000 in present value dollars. What the borrower paid back in present value dollars was$41,916.34. The difference—the NPV—was $8,083.66. Refinancing a Constant Payment Loan. A common financial transaction is the refinancing of a constant payment loan. What complicates this transaction is loan closing costs or points charged as a percentage of the loan required to close. If the current interest rate is less than one’s interest rate on the existing loan, a reasonable borrower would prefer to refinance. What if refinancing requires a fee, percentage points charged as a percentage of the new loan, to be paid at the loan closing? We want to know what the borrower can afford to pay as a refinancing cost, or points of the loan to break even. Finding break-even points is what we do next. We will use as our starting point the numbers introduced into the previous example. The refinance problem is clearly an NPV problem. Its solution requires that we identify which is the defending and which is the challenging investment. The defender in this case is the loan the borrower now holds. The challenger is the new loan with its reduced interest rate and points charged to close the loan. What the borrower will earn on the loan is not relevant here because we assume that those earnings will be the same regardless of whether they are financed with the new loan or continue to be financed with the old loan. To solve this problem, we recognize that if the PV of loan payments on the new loan plus points charged to close the loan is the same as the PV of loan payments on the old loan (and ignoring taxes), points charged are break-even. So using Equation \ref{16.8}, we find break-even points charged to refinance as: (16.20a) where pL0 is the cost the borrower pays to refinance the loan, p percent of the new loan must be paid as a refinance cost, and rN is the interest rate on the new loan. The loan payment on the old loan is: (16.20b) where rO is the interest rate on the old or original loan. Finally, equating equation (16.20a) to (16.20b) and solving for p, we find the break-even points to refinance the loan; that is, we find the percentage of the loan p that could be paid as a refinancing charge by the borrower to obtain a loan with a lower interest rate and still break-even. The formula for p is: (16.21) To illustrate, let rO = 8%, rN = 6%, and let mn = 180. We first solve for p using Excel: (16.22) by keying in PV(rate,nper,PMT,,0) = PV(.66,180,1,,0) and find: (16.23) We follow the same procedures to find: (16.24) Finally, we find p by making the appropriate substitutions into Equation \ref{16.21}: (16.25) So what have we learned? We learned that we could afford to pay 13% of the loan as a closing fee to acquire the same loan at a lower interest rate and still be as well off as we would have been keeping the old loan. A variation of the problem would be the following: Suppose that we knew what points would be charged to refinance the loan, and we wanted to know what APR would be required to be indifferent between the new and old loan. In other words, we want to find the break-even rN given that we know p, the points charged to refinance the loan. The solution is found by rearranging Equation \ref{16.9} so that: (16.26) To illustrate, suppose that p is known to be 10%, and the conditions attached to the old loan are as before, so that: (16.27) To find the break-even APR on the new loan we equate: (16.28) We now solve this problem using Excel RATE function: (16.29) Displayed is the break-even actuarial rate, .53, which when multiplied by 12 equals the break-even loan rate of 6.38%. Compared with our earlier results, if points paid to refinance the loan were reduced from 13% to 10%, the borrower could afford to pay 6.38% on the new loan and still break even. Consider another example with p = 15% in the previous example. First equate: (16.30) To find the corresponding interest rate for US0(rN/12, 180) =$120.92, we key into Excel’s RATE function:
(16.31)
The answer displayed is: .47 which, when multiplied by 12, equals the break-even loan rate of 5.69%. Before, a new interest rate of rN = 6% corresponded to break-even points of 13%. If points charged were 15% instead of 13%, the new interest rate would need to equal 5.69% to be indifferent between continuing with the old loan versus paying closing costs and taking out a new loan.
Practical refinance problems facing agricultural firms. Agricultural firms in particular face cash receipts variability. This means that firm’s liquidity measures such as the current ratio (CT) or the times-interest-earned (TIE) ratio may also face significant variability over time making mortgage payments problematic. And sometimes, the original mortgage for an investment was written for a much shorter period than the investment’s productive life. Whatever the case, liquidity concerns may require the firm to renegotiate the terms of their loans with their lenders. To illustrate, consider the payment calculated in Example 16.2. In this case the required payment was found to equal $111.22. Suppose the lender were willing to increase the term of the loan by 12 monthly payments. What would be the new loan payment? Resolving the Excel PMT function returns: (16.32) The solution is the loan payment that will retire a loan of$5,000 with 72 payments rather than 60 payments at an actuarial rate of 1%. The loan payment is reduced from $111.22 to$97.75.
Disguised Interest Rates and Effective Interest Rates
One of the challenges financial managers face when considering borrowing decisions is knowing the actual cost of borrowing—or, stated another way, knowing the effective APR interest rate. Sometimes lenders offer loans designed to disguise the real cost of their loans. We call their loans disguised interest rate loans. Disguised interest rate loans have effective interest rates increased by methods other than increasing the interest rate on the loan. For example, interest costs can be subtracted in the initial period, reducing the actual loan amount received by the borrower (a discount loan). Interest can be charged as though the original loan balance was outstanding throughout the life of the loan (an add-on loan). Alternatively, the lender can charge a loan closing fee, reducing the actual loan balance received by the borrower. Additionally, the interest can compound more frequently than loan payments occur. Each of these methods will increase the effective interest rate above the stated interest rate. Consider several types of disguised interest rate loans.
The Discount Loan: A borrower approaches his lender for a loan of L0 for mn periods. The borrower learns that the stated interest rate or disguised interest rate is rd. When the borrower picks up the check for his loan, the amount he receives equals only:
(16.33)
the amount of the loan requested less the stated interest rate times the term of the loan. Meanwhile, the constant loan payment is calculated as:
(16.34)
To calculate the APR associated with this loan, treat payments of amount A as if they were associated with a constant payment loan that retires a principal amount of Ld. The relationship is expressed as:
(16.35)
Next, substituting for A, L0/mn, we find:
(16.36)
To illustrate the discount loan, assume a consumer obtains an installment loan for $10,000, from which$2,500 is deducted for interest costs. The loan is to be repaid over 2 years, with monthly payments equal to $416.67 = ($10,000/24). To solve this example, we first must find the stated rate rd:
(16.37)
Normally, the stated rate is given, but it is advisable to confirm the rate as we have done above. Now we enter our numbers into Equation \ref{16.36} and obtain:
(16.38)
To find the actuarial rate, we key into our Excel RATE function:
(16.39)
Displayed is the actuarial monthly rate of 2.44% or, after multiplying by 12, we find the corresponding APR rate of 29.3%. The effective rate re is: re = (1.0244)12 – 1 = 33.55%.
This is quite a difference compared to the stated interest rate of 12.5%. Hence, the discount loan effectively disguises its true APR.
Points-added loans. Sometimes lenders charge points p to close a loan. The fee has the effect of increasing the interest rate on the loan since the lender earns more than the stated rate suggests. The APR rate for such a loan can be calculated by first computing the payment which retires the loan, plus the points added. The payment equals:
(16.40)
Next, express the relationship between the payment A in Equation \ref{16.40}, APR rate rf, and the actual amount of the loan received as:
(16.41)
Equating equations (16.40) and (16.41), we find rf from the equality:
(16.42)
To illustrate how to find the effective interest rate for a points-added loan, consider the following problem. A bank offers a loan rate of 12% with monthly payments for three years, with a 3% loan-closing fee. What is the APR interest rate rf? Using Equation \ref{16.42} we first find:
(16.43)
To find the true actuarial rate, we key into our Excel RATE function:
(16.44)
Displayed is the actuarial monthly rate of 1.15%, or after multiplying by 12, we find the corresponding APR rate of 13.83%. The effective rate re is: re = (1.0115)12 – 1 = 14.71%. This is quite different compared to the stated interest rate of 12%.
Summary and Conclusions
In this chapter we demonstrated the versatility of PV models by using them to analyze loans. For constant payment loans, we used PV models to solve for constant loan payments, terms, loan amounts, and interest rates—remembering that one PV equation can solve for at most one unknown.
Using PV models to analyze loans required that we identify the various kinds of interest rates. This was an important exercise because we discovered the difference between stated interest rates and effective interest rates—the interest rate actually paid on the loan funds made available.
Another important exercise was discovering the sensitivity of the relationship between the size of the loan payment and the term of the loan. In most cases, the relationship is not one-to-one. In other words, a 1% increase in the size of the loan payment rarely leads to a 1% drop in the term. The corresponding percent decline in the term of the loan is usually much, much more. Hence, we discovered that, when applying for loans, it pays to explore various terms and sizes of loan payments and find the best match—the one with the optimal trade-off between term and liquidity.
A common problem is that existing loans often need to be refinanced. Such may be the case when interest rates drop or a project currently financed is expanded and additional funds are required. In the text we considered refinancing existing loans and found break-even loan closing points. In the supplemental materials at the end of this chapter, we will find the more general formula for refinancing when the term, interest rate, and size of the new loan may be different than on the existing loan.
Lastly, we demonstrated how some loans may disguise the true interest rate. While we only illustrated the solution for the discount loan and the points-added loan, there are several other kinds of loans that disguise the true interest rate.
Questions
1. Which would you prefer to earn on your savings? An APR rate of 12.5% or a 1% actuarial rate compounded monthly? Given an APR of r percent, what is the most that the effective rate can earn above the APR rate if it is compounded continuously?
2. Consider a loan of $80,000 at an APR of 13%. What is the loan payment that would retire the loan if repaid in monthly payments for 10 years? If repaid in monthly installments for 9 years? Compare the percentage change in the term versus the percentage change in the loan payment (the arc elasticity). Finally, find the point elasticity E(n,A) on the original loan. 3. Assume a loan of$54,000 with a remaining term of 21 years. The existing loan requires monthly payments at an APR of 11.25%. For a 3% closing fee, the borrowers could refinance their loan at an APR rate of 10% for the same term. What is the effective interest rate on the new loan? What are the break-even points for refinancing the loan? What is the total interest paid on the two loans?
4. A consumer obtains an installment loan of $12,000 from which$2,700 is deducted for interest costs. The loan is to be repaid over two years with monthly payments equal to $500 ($12,000/24). Please determine the effective interest rate re on this loan.
5. A farm supply store offers its customers 30 days same-as-cash arrangements. That is, for bills paid within 30 days after purchases are made, no interest is charged. On the other hand, to encourage early payments, the supply store offers a 2% discount on bills paid with 10 days. Please calculate the effective interest rate the store offers its buyers for giving up 20 days of free credit.
6. Suppose you borrowed $5,000 for 3 years at an APR rate of 8%. Create an amortization table for this loan. 7. Home Depot mailed to some of its customers a coupon entitling them to either a 10% discount on their next purchase or two years of free credit. Under what conditions would you be indifferent between the two options? (Hint: the answer does not depend on the amount purchased.) 8. A farm firm has a mortgage loan for$150,000 at an APR rate of 5%. The term of the loan is 15 years and the payments equal $14,451. Cash flow problems from reduced farm income leaves the firm only able to pay$10,000 on this loan. What would the new term equal if the lender allowed the borrower to repay over a longer term?
Supplemental Materials
The refinancing problem described in this chapter can be more complicated. What if not only the new and old APR loan rate were different but also the term and the amount refinanced? Let rO and rN equal the APR on the old and new loans respectively. Let’s assume that the new loan included not only the refinanced loan L0 but also an additional amount equal to L0. Also assume that the term on the old loan is mnO compared to the term on the new loan, mnN. We want to know if the borrower should refinance. The IRR used for calculating the NPVs for the new and old loans is r.
Recall that if the IRR is also the reinvestment rate, then an investment’s NPV is not affected by changing its size and term. Therefore, we can determine if the borrower should refinance by comparing the NPVs on the old and new (refinanced) loan.
Assume for the moment that we know the points charged to refinance a loan and we want to know our loan payment for the refinanced loan. Using the notation already defined, we solve the problem by revising equation (16.21a) and write the revised equation as:
(16.i)
The loan payment for the original (old) loan, for which there are no points charged, can be written as:
(16.ii)
At this point,we make a critical assumption; namely, that funds are reinvested at the defender’s IRR, which allows us to write the NPVs for the new and old loans as:
(16.iii)
and
(16.iv)
If the points charged make the two loans equal in NPV, then we can equate equations (16.iii) and (16.iv) and solve for the break-even points:
(16.v)
Where . Note that if = 0" title="Rendered by QuickLaTeX.com" height="18" width="174" style="vertical-align: -5px;"> and nO = nN, equation (16.v) reduces to Equation \ref{16.22}. Therefore, equation (16.v) allows us to find break-even points in general, even if the interest rates, term, and size of the refinanced loans are different compared to the loan being refinanced. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/16%3A_Loan_Analysis.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) describe land’s unique investment characteristics; (2) understand how land’s endurable nature affects its price variability; (3) recognize how transaction costs reduce the liquidity of land investments; and (4) evaluate land investments using present value (PV) models developed earlier.
To achieve your learning goals, you should complete the following objectives:
• Learn what makes land distinct from other types of investments.
• Learn why land prices are so volatile compared to other investments.
• Learn how to distinguish between real and nominal discount rates.
• Learn how to distinguish between inflationary and real growth in earning rates.
• Learn how expected growth rates in earnings from land are capitalized into land values.
• Learn how to find the real growth rate for land.
• Learn how to calculate the maximum bid (minimum sell) price for land.
• Learn how transaction costs associated with buying and selling land influence land’s liquidity.
• Learn how taxes influence the maximum bid (minimum sell) price for land.
• Learn how to find the tax adjustment coefficient for investments in land.
• Learn how to use land price-to-earnings ratios to predict adjustments in the price of land.
Introduction
Land’s immobility and durability make it unique among investments and deserving of special attention in PV analysis. Land’s immobility means that it cannot be moved and its services must be extracted by those physically on site. Durability means that land has the capacity to provide services over time without significant change in its service provision capacity.
Earlier, an asset’s liquidity was defined as it nearness to cash. One dimension of an asset’s liquidity depends on the form of its earnings—cash versus capital gains (see Chapter 13). In this chapter we discuss a different dimension of liquidity—the cost of converting an asset to cash through its sale. Land’s immobility makes land less liquid than assets that can be moved because land cannot be moved to meet the convenience of the buyer. Land’s immobility also limits the potential buyers to those near enough to the land to extract its services. Another reason that land is illiquid is because buyers and sellers pay fees to complete its purchase and sale, including Realtor fees, legal costs of changing and recording its title, and other related fees—but not to each other. Evidence of farmland’s low liquidity is its infrequent transfer. On average, only 2% to 3% of the privately owned farmland in the United States is sold each year.
On the other hand, lenders prefer land as collateral for loans for the same reason that makes land illiquid—its immobility. Land’s immobility reduces the riskiness of it being stolen, hidden, or moved. Lenders also prefer land as collateral for loans because of its durability, which reduces the riskiness of it losing its value as security for loans. To offset some of land’s illiquidity, special institutions and programs have developed for financing residential and farm real estate.
The immobility and durability of land also make it a popular object on which to assess taxes. Taxing agencies have easy and indisputable records of the amount of land subject to tax and who owns the land. Thus, most land-owners pay property taxes on land and buildings but pay no similar tax on more mobile and less durable investments. Consequently, land is one of the few investments for which taxes are based on the market value of the investment at the beginning of the period as well as on the earnings of the investment during the period.
This chapter develops PV models to estimate maximum bid (minimum sell) prices for land investments, to describe how transaction costs contribute to land’s illiquidity, to understand how land’s durability increases its price volatility, and to demonstrate the influence of taxes on maximum bid (minimum sell) prices. We begin by describing the connection between land’s durability and its price volatility and why land and other durables are subject to inflationary bubbles and crashes.
Why are land prices so volatile?
Durable price volatility. One interesting feature of farmland prices, and other durables prices such as housing stock, is their historically high swings in values. Figure 17.1 describes year-to-year changes in Michigan farmland values over the 2000 to 2010 period. Figure 17.2 describes changes year-to-year changes in housing values over the same period. Part of these changes can be attributed to capital gains (losses). But there is another explanation for changes in the value of land and other durables, and it has to do with changes in real interest rates and real growth rates.
Figure 17.1. Year-to-year changes in farmland values.
Figure 17.2. Year-to-year changes in housing prices.
Inflationary, nominal, and real interest rates. To understand price volatility of durables, it is necessary to describe inflationary, nominal, and real interest rates. Recall from your earlier training that the inflation rate i is equal to the rate of change in average prices, changes often linked to monetary or fiscal policies of governments. The nominal interest rate r depends on the rate of inflation and a real component that is dependent on factors other than the rate of inflation such as changing market conditions or changes in productivity. To describe the effects of inflation on the nominal interest, let one plus the nominal interest rate r equal one plus the real rate r* times one plus the inflation rate i so that:
(17.1)
We solve for the real interest rate in Equation \ref{17.1} as:
(17.2)
Historically, real interest rates vary by sectors but are highly correlated. Real interest rates on home loans are described graphically in Figure 17.3:
Figure 17.3. Real home loan interest rates.
We can describe the effects of changes in the real growth rate on durable asset prices by letting the nominal growth rate g equal one plus the real growth rate g* times one plus the inflation rate i, so that:
(17.3)
We solve for the real growth rate in Equation \ref{17.3} as:
(17.4)
To understand the volatility of farmland prices, we build a general PV model where V0 is land’s present value, g is the average nominal growth (decay) rate of net cash flow, r is the nominal interest rate, and R0 represents initial cash flow. For the moment we ignore taxes and write the relationship between the variables just described in a growth model as:
(17.5)
We call the result the value in use model because there are no sales or purchases implied. Suppose we replace (1 + r) with the right-hand side of Equation \ref{17.1} and (1 + g) with the right-hand side of Equation \ref{17.3}. After the substitution, we obtain the result:
(17.6)
Notice that the inflationary effects on the discount rate and the growth (decay) rate cancel, so that we can write Equation \ref{17.6} as a function of only real rates and initial cash flow:
(17.7)
Suppose that in Equation \ref{17.7}, r* changes. To measure the impact of a change in r*, we differentiate V0 with respect to r* and obtain:
(17.8)
The percentage change in V0, with respect to a change in r*, equals the change in the asset’s value in response to a change in the real interest rate, Equation \ref{17.8}, divided by the asset’s initial value V0, the right-hand side of Equation \ref{17.7}:
(17.9)
Now suppose that g* changes. To measure the impact of a change in g* we differentiate V0 with respect to g* in Equation \ref{17.7} and obtain:
(17.10)
The percentage change in V0 with respect to a change in g* equals the change in the asset’s value in response to a change in the real interest rate, Equation \ref{17.10} divided by the asset’s initial value V0 described in Equation \ref{17.7}.
The percentage change in V0 with respect to a change in g* equals:
(17.11)
We now describe the percentage changes in asset values in response to changes in the real discount rate and the real growth rate for alternative real interest rates and real capital gains (capital loss) rates. In the previous chapter we described changes in asset values over time. This analysis is different (and static or timeless). We consider what happens to an asset’s value at a point in time if one of the underlying variables that determines its value is changed.
In Table 17.1 calculations are based on Equation \ref{17.11}. In the calculations we set the percentage change in asset values for alternative values of r* and g*. We set r* equal to 2%, 4%, 6%, 8%, and 10%. We set g* equal to –20%, –10%, –5%, 0%, 2% and 4%. Negative values for g* correspond to depreciable durable assets such as buildings and machinery. Positive values of g* are harder to justify and may reflect speculative bubbles in which asset earnings are expected to grow in real terms in perpetuity—an assumption which is hard to justify.
Table 17.1. Percentage changes in asset values corresponding to small changes in real interest rates for alternative values of r* and for assets with various degrees of durability characterized by the variable g*.
g* = –20% g* = –10% g* = –5% g* = 0% g* = 2% g* = 4%
r* = 2% –4.5% –8.3% –14.3% –50% n.a. n.a.
r* = 4% –4.1% –7.1% –11.1% –25% –50% n.a.
r* = 6% –3.8% –6.3% –9.1% –16.7% –25% –50%
r* = 8% –3.6% –5.6% –7.7% –12.5% –16.7% –25%
r* = 10% –3.3% –5% –6.7 –10% –12.5% –16.7%
Consider Table 17.1. Note that an asset’s durability is reflected by its real growth (decay) rate—an asset’s durability decreases with its g* value. Also note that the percentage change in asset values in response to increases in real interest rates decreases with an asset’s durability. For example, if the real interest rate were 4%, a small increase in the real interest rate would cause a 4.1% decrease in the value of a depreciable asset with a negative real growth rate of –20%. Meanwhile, a small increase in the real interest rate for a durable asset with a 4% real growth rate would result in a 50% decrease in the value of an asset.
Now consider Table 17.2, which examines the effect of small increases in the real growth rate for the same scenarios described in Table 17.1 and also based on Equation \ref{17.11}. The difference between Table 17.1 and Table 17.2 is that the signs within the body of the tables are reversed. An increase in the real interest rate reduces asset values because future dollars are worth less with a higher discount rate. In contrast, an increase in the real growth rates means there are more future cash flows to discount—making the change in the value of the assets positive in response to a small increase in the real growth rate.
Table 17.2. Percentage changes in asset values corresponding to 1% changes in real growth rate for alternative values of r*and for assets with various degrees of durability characterized by the variable g*.
g* = –20% g* = –10% g* = –5% g* = 0% g* = 2% g* = 4%
r* = 2% 4.5% 8.3% 14.3% 50% n.a. n.a.
r* = 4% 4.1% 7.1% 11.1% 25% 50% n.a.
r* = 6% 3.8% 6.3% 9.1% 16.7% 25% 50%
r* = 8% 3.6% 5.6% 7.7% 12.5% 16.7% 25%
r* = 10% 3.3% 5% 6.7 10% 12.5% 16.7%
One interesting feature of Table 17.2 is that the percentage change in asset values in response to small increases in the real growth rate are dampened by higher real interest rates. For that reason, when the economy is “overheated” and prices are rising, one response is to reduce the money supply, increasing the real interest rate and slowing price increases. For example, suppose the real growth rate were zero% and the real interest rate was 2%. If the real growth rate increased slightly, the asset value would increase by 50%. If, instead, the real interest rate were 10% and the real growth rate increased slightly, the asset value would increase by only 10%.
So what have we learned? We learned that durable assets such as land and houses are subject to significant percentage changes in value in response to changes in real interest rates and real growth rates—much more so than depreciable assets. In addition, changes in the asset’s real growth rate in earnings have less effect when real interest rates are high.
To test your understanding of the material just covered, demonstrate that a 1% increase in the real growth rate produces the same percentage changes in asset values as those described in Table 17.1, except opposite in sign.
Maximum Bid (Minimum Sell) Price Models and Transaction Costs
Maximum bid (minimum sell) price models. We now deduce maximum bid price models for buyers and minimum sell price models for sellers. At least two costs differentiate maximum bid price models for buyers and minimum sell price models for sellers: taxes and transactions costs. Let c equal the percentage of land’s sale price paid by the buyer to purchase the land—but not paid to the seller. These may include loan closing fees, title examination and registration fees, attorney’s costs, and closing points paid by the buyer. Let s equal the percentage of the land’s sale price paid by the seller to sell the land—but not paid to the buyer. This may include loan closing fees, Realtor fees, advertising, and other fees.
Denote as the buyer’s maximum bid price and as the seller’s minimum sell price. Ignoring taxes, and assuming that the land will never be sold again, the expression for can be written as:
(17.12)
Expression represents the maximum bid price, including the effect of closing costs. To isolate the maximum bid price, we solve for.
(17.13)
In the maximum bid price model, the discounted stream of future cash flow represents the challenging investment—the present value of earnings the buyer will receive if the land is purchased.
Example 17.1: Finding the Maximum Bid Price for Land. What is the maximum bid price of a parcel of land if the buyer pays 6% of the acquisition price as a closing fee? To solve the problem, assume last year’s net cash flow was $22,000, which is expected to grow in perpetuity at 4.5%. Assume that the buyer’s opportunity cost of capital is 12%. The maximum bid price is calculated using Equation \ref{17.13}: (17.14) If closing costs, as a percentage of the price, increase from 6% to 9%, decreases to$281,223.
Minimum sell price models. Realtor fees and other closing costs paid by the seller are now introduced into the minimum sell price model. To build the minimum sell price model, let be subtracted from the seller’s proceeds. Ignoring taxes and assuming that the land will only be sold one time, we can write the minimum sell price model as:
(17.15)
Solving for , we find the minimum sell price equal to:
(17.16)
In the minimum sell price model, the discounted stream of future cash flow represents the defending investment—it represents the earnings the seller would not earn if the land were sold.
Example 17.2: Finding the Minimum Sell Price. Letting s = 2% and using the data from Example 17.1, we find the minimum sell price using Equation \ref{17.13}:
(17.17)
Now, suppose s increases from 2% to 3%. In turn, increases to $316,014. In contrast to the effects of an increase in c that reduced the maximum bid price, an increase in s increases the minimum sell price: Land Values, Transaction Costs, and Liquidity Suppose a buyer and a seller had the same earnings expectations and opportunity costs for a durable such as farmland. It must follow that their present-value for the durable in use would be the same. But if the buyer had to pay closing fees to acquire the durable, his maximum bid price would be reduced. And if the seller received only a portion of the present value after the sale, her minimum sell price would increase. Therefore, transaction costs that increase the seller’s minimum sell price and reduce the buyer’s maximum bid price reduce the liquidity of the durable, even when the buyer and seller have the same earnings expectations and opportunity costs. In other words, an asset is illiquid if its value in use (V0) is bounded below by a buyer’s maximum bid price () and bounded above by the seller’s minimum sell price (). We can easily show that assets for individuals with identical expectations of land’s value in use are illiquid when transaction costs are imposed on its sale and purchase. Substitute the value in use from Equation \ref{17.5} into the maximum bid price model in Equation \ref{17.13}, and the result is: (17.18) It should be clear that for c > 0, Next, substitute the value in use from Equation \ref{17.5} into the minimum sell price model in Equation \ref{17.16} and the result is: (17.19) V_0 \end{equation*}" title="Rendered by QuickLaTeX.com"> It should be clear that for s > 0, Finally combining these results allows us to express the effects of transaction costs on the maximum bid, minimum sell, and value-in-use models: (17.20) Despite equal earning expectations, as a result of transaction costs, the maximum bid price is less than the minimum sell price making land illiquid. To make this point another way, suppose that we formed the ratio of the maximum bid price and the minimum sell price for land and assumed that c = 5% and s = 6%. Then the buyer in this example would only be willing to offer 89.2% of the seller’s minimum sell price, and a sale would not occur. (17.21) Other Factors Contributing to Asset Liquidity Differences in financing costs for buyers and sellers may also contribute to an asset’s illiquidity. For example, a loan tied to the ownership of durables at below-market interest rates may create a wedge between the maximum bid price and the minimum sell price. If the loan has a due-on-sale clause, the seller gives up something of value that is not received by the buyer when the investment is sold. Thus, concessionary interest rate loans with due-on-sale clauses may create illiquidity. Differences in information between the buyer and seller may also contribute to an asset’s illiquidity. When two trusted friends exchange a durable, the information costs are insignificant—they freely exchange information. However, when two strangers exchange a durable, the buyer must commit resources to discover the quality of the information provided by the seller. If an investment’s service capacity is easily observed, as with certified seed or fertilizer, then the information cost is small and the investment will be more liquid. Durables like used cars or tractors, whose remaining service capacity is not easily observed, will be less liquid. The issuance of a warranty is a signal of higher quality, and thus a warranty is an attempt to reduce information costs for the prospective buyer and to increase the liquidity of the asset. The cost of gathering information about the asset’s service capacity may also contribute to its liquidity. To illustrate, a new asset’s service capacity may be well known. Once the durable is used, however, the uncertainty associated with the intensity of use and care of the durable creates an immediate decline in the value of the durable. On the other hand, a used durable whose service extraction is nearly depleted is more liquid, because there is nearly perfect information about the durable’s remaining capacity. The liquidity of durables is also affected by disposal costs. Disposal cost is the cost of removing durables from service paid by its current owner. Most durables are mobile. Buildings, however, must be disassembled at considerable costs. In some cases, the investment is so valuable that assembly and disassembly are warranted. An example is the London Bridge. Most durables with high disposal costs become completely illiquid and remain in service to the first owner until destroyed. Often it is easier to transfer the owner rather than the investment itself. Examples of durables with high disposal costs are land and houses. Durables whose value increases with time and use are called appreciating durables. Durables whose values decrease with time and use are called depreciating durables. A durable whose value increases with time and use will be more liquid than one whose value declines with time and use, with all other liquidity attributes held constant. Appreciating durables provide greater security for lenders than depreciating durables because their value and the lender’s security are increasing. Finally, liquidity is affected by whether or not time or use determines the durables’ service capacity. Durables whose service capacity is determined by time have a fixed pattern of changes in service capacity and cannot adjust to changes in the market. Durables whose change in service capacity is determined by use can adjust to changes in the marketplace for the value of its services. Thus, durables whose service capacity is tied to use are more liquid than those whose service capacity is linked to time. The liquidity of a durable is also influenced by the number of services the durable can provide. Durables become more liquid if the buyer has opportunities for the durables’ services that are not available to the seller. A durable is more likely to have multiple uses when it is not fixed geographically. Multiple use capability is also tied to the acquisition characteristics of the durable. If the durable is lumpy in acquisition, potential buyers must take it or leave it. Durables divisible in acquisition, on the other hand, provide options for prospective buyers. They can buy a gallon or a tankful of gas, a sack of seeds or a truckload. Finally, durables whose service extraction rate is fixed, and hence irreversible, are less liquid than durables whose service extraction rate is variable. Variations in service capacity provide greater adjustment potentials, and thus reduce the differences in perceptions between buyers and sellers. Moreover, durables whose service extraction rates vary tend to have multiple uses, while those with fixed service extraction rates tend to be single-use durables. Maximum Bid (Minimum Sell) Land Price Models with Taxes Taxes are now introduced into our maximum bid (minimum sell) price for land models. As mentioned earlier, land is subject to a wide variety of taxes, not all of which are imposed on other assets. Four kinds of taxes must be considered in our maximum bid (minimum sell) price for land models: First, the cash flow stream is taxed at the average income tax rate T. Second, the opportunity cost of capital r is expressed on an after-tax basis. Since the discount rate may reflect the opportunity cost of capital associated with investments that earn both capital gains and cash, the tax rate is . Third, property taxes (Tp) are another tax charged against the market price of land in each period. Thus, land’s maximum bid price in future periods must be included in each period. The study of capital gains indicated that land prices should increase at the same rate as land earnings. Finally, one tax not included in the land price models is tax-savings rate Tg, resulting from durable depreciation. The reason is simple—land is not considered a depreciable investment. The Maximum Bid Price Model with Taxes. The expanded maximum bid price model with taxes is written as: (17.22) The cash flow stream contains two geometric series. In both series, the geometric factor is and the sums of the two series are equal to: (17.23) while (17.24) Finally, setting equal to the sum of S1 and S2 and solving for , the maximum bid price with taxes of land can be written as: (17.25) It is still the case that the challenging investment in Equation \ref{17.16} is represented by the discounted after-tax cash flow stream while the defender is the maximum bid price plus closing fees, which earns the discount rate r given up to acquire the income earning durable. Example 17.3:Maximum Bid Price with Taxes. An investor is interested in buying a crop farm. According to the financial statements, last year the farm generated a net cash receipts of$48,000. Past data indicated that net cash returns have been growing at 6% per year. The investor’s opportunity cost of capital is 11%, and closing fees for the transaction are 3%. The investor’s income tax bracket is 30%, the property tax is 2%, and we assume that = .75" title="Rendered by QuickLaTeX.com" height="18" width="186" style="vertical-align: -5px;">. Using Equation \ref{17.25}, the maximum bid price for the farm is
(17.26)
The Value in Use model. It will be convenient later on to find the value of what the seller will sacrifice instead of selling his or her land and continuing to extract services from it. In this case there are no transaction costs, and property taxes are associated with its use value as opposed to its maximum bid price. We can derive the value in use with taxes model, , by setting c = 0 in Equation \ref{17.25}. The result is:
(17.27)
To illustrate, the value in use model for the previous example is:
(17.28)
One way to interpret the value in use with taxes model is that it represents the defending asset for the seller of land—the present value of future earnings it would receive, provided the land isn’t sold.
The Minimum Sell Price Model with Taxes. The minimum sell price model with taxes is similar to the maximum bid price model with taxes, with a few exceptions: First, assume the seller originally bought his or her land t periods earlier at a price of -t}^b" title="Rendered by QuickLaTeX.com" height="24" width="113" style="vertical-align: -9px;">. Then, if -t}^b" title="Rendered by QuickLaTeX.com" height="24" width="113" style="vertical-align: -9px;"> is less than (more than) the current selling price of , the seller pays (earns) capital gains taxes (credits) at a rate of α times the average income tax rate of or .
Another difference is the transaction costs. These costs affect taxable capital gains because the capital gains tax is only paid on the net gain from the sale of land. Like the maximum bid price model, however, the property tax rate is assessed against the inflating value in use since there is no benchmark sell price to calibrate its tax value.
The value in use with taxes is the challenging investment for the seller. We equate the after-tax sale price to the value in use with taxes in Equation \ref{17.29}. We summarize these results in Equation \ref{17.29}:
(17.29)
Solving for the minimum sell price with taxes we find:
(17.30)
Example 17.4:Minimum Sell Price with Taxes. ABC Corporation wants to sell a large farm. They want to know their minimum sell price to accept—or the price a buyer would need to offer in order for them to be as well off selling as they would be continuing to farm the land. ABC has already calculated the farmland’s value in use is equal to $913,230 (see equation 17.27). This is the present value of their defender. Recognizing its minimum sell price adjusted for transaction costs and capital gains taxes (credits) as its challenger, ABC equates the two, and solves for its minimum sell price with taxes. The result is expressed in Equation \ref{17.30}. Summarizing the information needed to find ABC’s minimum sell price: and s = 5%. The result is: (17.31) Clearly, the buyer and seller in Examples 17.3 and 17.4 would never exchange land—the minimum sell price of$1,003,672 exceeds the buyer’s maximum bid price of $890,400. What would have to change for land to become liquid—for the buyer to offer the seller at least his or her minimum sell price? Well, for one thing, the buyer would have to expect initial earnings greater than$48,000. Or the buyer could find means of reducing its property tax rate. Or the buyer could reduce its transaction costs. Or the buyer may have a lower opportunity cost than the seller. Other changes, such as changes in g and T, have ambiguous effects on the maximum bid price .
Finding the Tax Adjustment Coefficient
The homogeneity of measures principle requires that after-tax cash flow be discounted by an after-tax discount rate—in most cases the IRR of the defender. The question is, how do we find the after-tax IRR that corresponds to the after-tax cash flow of the defender? First, we specify the defender’s cash flow stream and PV and solve for the discount rate or the IRR of the investment. We are guaranteed that we have found the IRR of the defender in a maximum bid (minimum sell) price model and value in use model because the NPV in these models is always zero. We demonstrate how to find the defender’s IRR first for the simple geometric growth model and then for more complicated models that include taxes.
Now we introduce taxes into Equation \ref{17.5}, holding V0 constant, and express the after-tax geometric growth model as:
(17.32)
To summarize, because Equation \ref{17.32} describes a defender’s after-tax cash flow stream, then is the defender’s after-tax IRR—because NPV in Equation \ref{17.32} is zero. Another way to summarize the results above is to note that taxes in Equation \ref{17.32} are neutral—meaning that they are introduced so that NPV remains zero. Since V0 is the same in both equations (17.5) and (17.32), we can equate their right-hand sides and write:
(17.33)
Up to this point, we have not specified the value of . However, we do require that its value be chosen in such a way that is the after-tax IRR of the defender’s after tax cash described using a geometric growth model. We find such a for the geometric cash flow model using Equation \ref{17.32}, which equals:
(17.34)
The above results are intuitive. For g ≠ 0 in Equation \ref{17.34}, capital gains (losses) are earned (lost) without creating any tax consequences. If the before-tax IRR is r, an after-tax rate of r(1 – T) implies cash and capital gains (losses) are taxed at the average income tax rate T, which is not true because only cash receipts are taxed. Since capital gains (losses) are earned (lost) at rate g, subtracting from r%, g%, makes taxes neutral in the geometric growth model described above. To confirm that coefficient makes taxes neutral, the right-hand side of Equation \ref{17.34} is substituted into Equation \ref{17.33} to obtain the result:
(17.35)
Following a similar procedure, we can find the value for in the value in use model for land. In this case, we equate the right-hand side of the value in use land model to the right hand side of the geometric growth model. This new equality can be written as:
(17.36)
As before, in Equation \ref{17.36} is the coefficient that makes taxes neutral in the land value in use model because it ensures that the effects of taxes on the defender’s cash flow are equally offset by changes in the discount rate. Therefore, the discount rate continues to equal the defender’s IRR. We can find such a for a value in use land model by solving for in Equation \ref{17.36}:
(17.37)
Clearly, property taxes increase the tax adjustment coefficient and the effective tax rate.
Non-neutral taxes. When we calculated the tax-adjustment coefficient, we assumed tax-neutrality. This was an appropriate assumption for finding the after-tax IRR of the defender. In other PV models, there is no reason to assume that the after-tax IRR of the defender used to calculate the maximum bid (minimum sell) price or NPV will be tax-neutral. For example, assume the challenger’s cash flow is represented by a geometric growth equation and assume that the tax adjustment coefficient of the defender is one—an assumption consistent with a defender’s whose returns are only cash. In this case, we find the value in use as:
(17.38)
To test for tax-neutrality, we differentiate V0 with respect to T and find:
(17.39) 0 \end{equation*}" title="Rendered by QuickLaTeX.com">
In this particular case, taxes are not neutral, and increasing the tax rate makes the defender less attractive relative to the challenger because the challenger’s capital gains are shielded from income taxes.
Price-to-earnings Ratios for Land
An interesting ratio can be derived from the value in use with taxes model, Equation \ref{17.32}. It is the ratio of land’s value in use, divided by the previous period’s cash flow, approximated by cash rents. We write the ratio as:
(17.40)
Note that the value-to-earnings ratio for land depends on specific tax rates, opportunity costs, and expected growth rates, and these vary from location to location. Figure 17.4 below describes land values to rent ratios for land in Iowa, Illinois, and Indiana since 1967. Suppose that in Equation \ref{17.40} we were to ignore taxes and assume a real growth rate of zero. Then Equation \ref{17.40} reduces to the traditional capitalization ratio of:
(17.41)
This is how the traditional capitalization ratio is derived. As an earlier graph demonstrated, however, the ratio has not been constant over time.
Figure 17.4. Land values to rent ratios for land in Iowa, Illinois, and Indiana since 1967.
An interesting exercise would be to approximate the discount rate in Equation \ref{17.41} with the real interest rate described in an earlier figure and then compare the results with the ratios described above.
Summary and Conclusions
Land’s immobility and durability make it an important asset for securing loans. Its immobility means that lenders know where to find it, and its durability means that it will have the capacity to supply services and earn a return almost undiminished into the future. Both of these characteristics provide assurances to lenders that if they loan money to buy land, they will be able to recover their loans even if the borrowers fail to meet their obligations. On the other hand, land’s immobility and durability also mean that its owners’ can be easily identified and taxed. Land sales are carefully recorded to establish its value. Thus, land is a favorite source of tax revenue not only for its market value but also at the time of sale if capital gains (losses) are incurred.
Land has another feature. Land is infrequently traded, and transfers of ownership are costly for both buyers and sellers—often requiring the help of outside agents who must be paid for their services. As a result, both buyers and sellers pay funds they do not receive when buying and selling land. These transaction costs, including tax payments, mean that land exchange will likely not occur unless the buyer expects to earn more from land’s services than currently earned by sellers. As a result, land is illiquid and its purchase and sale is a very infrequent occurrence.
In this chapter, PV models were used to model three types of prices: maximum bid prices, the most a buyer could offer to purchase the land; minimum sell prices, the least a seller would accept to sell the land; and value in use prices, the value of the land assuming continued use. These models accounted for three different types of taxes (property tax, income tax, and capital gains tax) as well as cash flow. These models provide helpful tools for assisting buyers and sellers in determining investment strategies.
Questions
1. Describe the features that make land an illiquid investment.
2. Why do lenders seem to prefer land to secure their loans? Compare the loan security provided by land compared to that offered by used equipment or breeding livestock?
3. Figures 17.1 and 17.2 compare year-to-year changes in farmland and housing prices. What is similar between those forces contributing to the variability in the prices of land and housing stock?
4. Commodities are nondurable goods and are likely used up in a single period. Meanwhile, land and houses are durables and last for many years. Can you describe how these differences between durable and nondurable goods may contribute to differences in the variability of their prices? Does the fact that the supply of land is relatively fixed versus the supply of commodities that can vary from year to year influence their variability?
5. Equation (17.9) describes the percentage change in the price of a long term asset (in this case land) in response to a change in the real interest rate r*. Assume that the real growth rate is 3% and the real interest rate is 4%. Find the percentage increase in V0 if r* increases by 1%. Find the percentage increase in V0 if g* decreases by 1%.
6. Consider the maximum bid price and minimum sell price models. Consider the following data: the closing fee for the buyer is 3%, the closing fee for the seller is 4%, and in the last period land rented for $150 per period. Land is liquid if the maximum bid price is greater than the minimum sell price. Using this data, please answer the following questions. Calculate the ratio of the maximum bid price to the minimum sell price. Is land liquid or illiquid? What must occur for the land to become liquid? 7. An investor is interested in buying a crop farm. According to the financial statements last year, the farm generated a net cash flow of$52,000. Past data indicates that net cash returns have been growing at 3% per year. The investor’s opportunity cost of capital, the IRR on its defender, is 8%, and closing fees for the transaction are 4%. The property is taxed at 1.5%, and the investor is in the 35% tax bracket. The tax adjustment coefficient is assumed to equal 75%. Find the maximum bid price for the parcel of land using maximum bid price with taxes model.
8. Farmland owners Rob and Ruthie Bell want to retire and sell their farm. They purchased their farm over 30 years ago for \$325,000. They recognize that their minimum sell price must leave them as well off as they would be if they continued to operate their farm. They estimate that closing fees will equal 3%, they are in the 30% tax bracket, and their capital gain tax rate αT is 12%. Finally, they realize that their closing fees will be 5%. Find the minimum sell price for Rob and Ruthie Bell. (Hint: first find the value in use with taxes for the farmland. Then using the value in use with taxes and data described in this question, calculate the minimum sell price using the minimum sell price with taxes model.)
9. In previous problems, the tax adjustment coefficient was assumed to be 75%. Using the data supplied for calculating the maximum bid price for land with taxes, find the tax adjustment coefficient using Equation \ref{17.37}.
10. Use Equation \ref{17.41} and land value to cash rent data described in Figure 17.4 to approximate real interest rates over time for Iowa, Indiana, or Illinois. If you believe that real interest rates are constant, what other explanations can you offer for time varying land value to rent ratios? | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/17%3A_Land_Investments.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) understand how leasing can provide an alternative method for gaining control of and access to capital resources; and (2) evaluate leases using present value (PV) models developed earlier.
To achieve your learning goals, you should complete the following objectives:
• Learn how leasing arrangements offer a different method for gaining control of and access to capital resources.
• Distinguish between the different forms of leases including the sale and leaseback lease, the operating lease, and the financial or capital lease.
• Learn the differences between leases and rental agreements.
• Learn how lease agreements are taxed.
• Learn the advantages and disadvantages of entering a lease agreement versus owning a capital resource.
• Learn how to find the break-even purchase price when compared to a leasing option.
Introduction
Control of a durable can be transferred between parties in several ways. A lease agreement is one important way. A lease is a contract through which control over the right to use a durable is transferred from one party, the lessor, to another party, the lessee who acquires control of the durable. In exchange for the right to use or control a durable for a specified time period, the lessee pays the lessor a rental payment or share in the output produced by the leased durable. The lease payment or shared output must cover the opportunity cost of funds invested in the leased item, depreciation of the durable, and other incidental ownership costs incurred by the lessor. Thus, leasing is a method of financing the control of a durable that separates its use from its ownership.
There are several kinds of lease arrangements and several kinds of durables that are leased. Farmland is frequently leased as are machines, houses, cars, computers, coping equipment, buildings, breeding livestock, and many kinds of management services. In this chapter, we describe various types of leases, evaluate their advantages and disadvantages, and apply present value (PV) tools to analyze leasing benefits for both the lessor and the lessee.
Types of Lease Agreements
Sale and leaseback. Under the sale-and-leaseback agreement, a firm owning a durable to be leased sells the durable to a financial institution and simultaneously executes an agreement to lease the durable back. Thus, the lease becomes the alternative to a purchase with a specific advantage to the lessee: namely, he or she is allowed to write off the entire lease payment as an expense instead of just interest costs and depreciation. The lessor will not enter into this type of lease agreement unless the lease payments are sufficient to return the full purchase price plus a return on the investment to the lessor.
Operating leases. Operating leases, sometimes called service leases, provide for both financing and maintenance. These leases ordinarily call for the lessor to maintain the leased equipment. The cost of the maintenance is built into the lease payment. Computers and office copiers, together with cars and trucks, are the primary types of equipment involved in operating leases.
In the case of operating leases, lease payments are often insufficient to recover the full cost of the equipment. To offset this feature, the lease is written for a time period considerably less than the expected life of the leased equipment, leaving the lessor to recover his or her investment in renewal payments of the lease or through disposal of the leased equipment.
One of the main advantages of the operating lease for lessees is the cancellation of the short lease period which allows them to adopt and bring into use more advanced equipment. Thus, for durables subject to rapid changes in technology, an operating lease is often a preferred method for gaining control of a durable.
Financial or capital leases. A financial lease is a fully amortized lease whose PV of the lease payments equals the full price of the leased equipment. It does not provide for maintenance service nor may it be canceled. The financial lease begins with a lessee selecting the specific items it requires and agreeing with the lessor about the price and the delivery of the item. The lessor arranges with a bank or another financial institution to purchase the equipment and simultaneously executes a financial lease with the lessee intending to use the equipment. The purchase of the equipment builds into the lease payments a rate of return equivalent to what would be charged on a loan, and the lease is canceled when the purchase price of the durable plus a return for the lessor is paid.
Under financial leases, lessees generally pay property taxes and insurance and, in many cases, can acquire ownership of the durable at the end of the lease. The significant difference between the sale-and-leaseback lease and the financial lease is that the lessee purchases the durable directly from the manufacturer rather than from the lessor under the terms of the financial lease.
Lease Agreements and Taxes
One of the major effects of the lease is to alter the tax obligations of the lessee and lessor. Therefore, special attention is required to make sure that lease agreements are acceptable under current tax codes as interpreted in the United States by the Internal Revenue Service. There is an important distinction between a lease agreement and a loan for tax purposes. If the lease agreement cannot be distinguished from an ordinary loan agreement, then any special tax provisions associated with the lease agreement are lost.
To distinguish a lease from a sale agreement, the term over which the investment durable is leased must be less than 75 percent of the economic life of the durable. Nor should the lessee be granted any special repurchase option not available to others not involved in the lease. There are other conditions as well; tax codes are evolving documents that are constantly being updated.
Lease Liquidity and Risk
Normally, the decision to acquire the durable is not at issue in the typical lease analysis. The issue at hand is whether to acquire control of the durable through a lease or by purchasing it—often by borrowing funds to finance the purchase. The decision requires a careful examination of the advantages of leasing. Leasing offers several possible advantages relative to owning a durable that we describe next.
Release of cash and credit. When a firm leases or sells a durable on a leaseback arrangement, the lessee avoids the cash down payment required to purchase the investment. More generally, the liquidity of a lease versus the liquidity of a purchase depends on which option requires the most accelerated payments.
Some texts discuss in detail the effect on the firm’s credit reserve as a result of leasing. If leasing uses up credit at a slower rate than borrowing, there may be credit incentives for leasing rather than borrowing. However, lenders are likely to recognize that long-term lease agreements place the same requirements on the firm’s future cash flow as loans do.
Obsolescence risk. Investments may experience significant obsolescence risks. In addition, there is some risk that the need for durables’ services will change before the durables’ service capacity is exhausted. Part of this obsolescence and use risk may be reduced through a lease arrangement for a short time period, especially if the lessor is less subject to obsolescence risk than the lessee. This is likely the case where the leased equipment has alternative uses in other firms or industries and where the risk can be spread over many lessees.
Idle capacity risk. Another risk that can often be reduced through lease arrangement is the risk of holding idle equipment. If the demand for services from a durable is not sufficient to employ the durable full time, the lessee can reduce idle capacity risk by leasing rather than owning the durable. From the lessor’s point of view, the durable can be completely employed because many lessees will use the equipment.
Foreclosure risk. In many respects, leasing is similar to borrowing because it represents an obligation of the firm to a series of future cash payments. There is one significant difference between agreeing to lease and borrowing to purchase the durable. In the case of financial difficulties, the lessor simply takes back the equipment because he or she holds the legal title. In the case of a loan, inability to meet loan payments may result in more complex foreclosure proceedings.
Tax advantages. A tax advantage may be gained when the term of the lease is shorter than the allowable tax depreciation period for ownership. However, tax incentives for the lessee must be a result of a lower total tax burden for the lessee and lessor. This situation implies that the lease arrangement has legitimately allowed for a reduction in the total amount of taxes paid. Needless to say, the Internal Revenue Service imposes conditions on what does and does not constitute a legal lease.
Net Present Cost of Leasing versus Purchasing
The decision to lease or to buy a durable depends on the net present cost (NPC) of leasing versus NPC of purchasing the durable. Since the size and timing of the cash flow, influence of taxes, and risks associated with buying and leasing are different, they represent two different investment opportunities which are amenable to analysis using PV models. In the following discussion, the after-tax cash flow is considered risk-adjusted, and the problem is treated as riskless.
To compare the lease with the purchase option, the firm considers itself in both roles—that of a lessee and lessor—and finds the maximum lease payment it could pay and be indifferent between purchasing or leasing the durable. We begin by describing the NPC of the lease (NPCL). Because we are describing the NPC of the lease, cash costs are treated as positive flow, and income that reduces the cost of leasing is treated as negative cash flow. For simplicity, we will assume a maximum constant lease payment equal to C. Then we assume the lease payment at age t is Ct, the lessee’s constant marginal tax rate is T, the lessee’s before-tax opportunity cost of capital is r, and the lessee’s tax adjustment coefficient is θ as described in Chapter 11. With these definitions in place, the net present cost of a lease for n periods, NPCL, can be expressed as:
$-N P C^{L}=C(1-T)+\frac{C(1-T)}{[1-r(1-\theta T)]}+\cdots+\frac{C(1-T)}{[1-r(1-\theta T)]^{n-1}} \label{18.1}$
Notice in Equation \ref{18.1} that the first lease payment is made at the beginning of the lease payment rather than at the end of the lease period, which would be the case of a loan. Therefore, leases can be viewed as an annuity due type of financial arrangement. Multiplying both sides of Equation \ref{18.1} by and summing the resulting geometric series, we write the result as:
$N P C^{L}=C(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\} \label{18.2}$
where:
$U S_{0}[r(1-\theta T), n-1]=\frac{C(1-T)}{[1-r(1-\theta T)]}+\cdots+\frac{C(1-T)}{[1-r(1-\theta T)]^{n-1}} \label{18.3}$
We now consider the net present cost of a cash purchase, NPCP, for the same financial manager who previously considered the lease option. We begin by assuming that the market value of the durable leased or purchased is equal to V0. We also assume that is the book value of the depreciable durable at age t. We continue to assume that the purchaser’s opportunity cost of capital is r, the average tax rate is T, and is the percentage of the investment’s value allowed to be deducted in year t where t = 1, …, n, and the tax adjustment coefficient is . Of course, the sum of the amount deducted cannot exceed the value of the investment so that . All these assumptions allow us to write the NPCP as:
\begin{align} N P C^{P}=V_{0}-\frac{T \gamma_{1} V_{0}}{[1+r(1-\theta T)]}-\cdots \[4pt] -\frac{T \gamma_{n} V_{0}}{[1+r(1-\theta T)]^{n}}-\frac{V_{n}-T \gamma_{n} V_{n}}{[1+r(1-\theta T)]^{n}} \label{18.4} \end{align}
The purchaser’s cost on the right-hand side of Equation \ref{18.4} is the purchase price V0, less n periods of tax savings from depreciation equal to in the period discounted to the present period. The liquidation value Vn minus a tax adjustment term reduces the purchaser’s cost. The adjustment term accounts for the tax consequences of a difference between the liquidation value and the book value of the investment. If the investment is completely depreciated by the nth period, and the liquidation value is zero, then the NPCP can be written as:
$N P C^{P}=V_{0}-\frac{T \gamma_{1} V_{0}}{[1+r(1-\theta T)]}-\cdots-\frac{T \gamma_{n} V_{0}}{[1+r(1-\theta T)]^{n}} \label{18.5}$
Finally, if the NPCL, expressed as the right-hand side of Equation \ref{18.2}, is equated to NPCP, expressed as the left-hand side of Equation \ref{18.5}, we can solve for the lease payment C, a maximum bid lease, which equates the two alternatives for controlling the services from the durable.
$C=\frac{N P C^{p}}{(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\}} \label{18.6}$
Consider an example. Go Green is a lawn service that requires a new truck to service its customers. It wants to know the largest lease payment it could afford and still be as well off as it would be if it purchased the truck. The truck in question has a new sticker price of $30,000 and can be depreciated using a straight-line method over five years. At the end of the lease, the truck has a liquidation value of$5,000. To find the maximum bid payment, the following assumptions are used: T = 32%, for t = 1, …, 5, r = 14%, = 1, n = 5, Vn = $5,000, and . Finally, the after-tax discount rate is r(1 – T) = .14(1 – .32) = .095 To find the maximum bid payment, we first find NPCP by substituting numerical values into Equation \ref{18.6}: $N P C^{P}=\ 30,000-(.32)(\ 6,000) U S_{0}(0.095,5)-\frac{\ 5,000(1-.32)}{(1.0952)^{5}} \label{18.7}$ We record the solution to this problem using Excel in Table 18.1 below. Table 18.1. Finding the NPC of the Purchase. Open Table 18.1 in Microsoft Excel C10 Function: =NPV(C3,C4:C9) A B C D 1 Finding the NPC of the Purchase 2 Purchase Price$30,000.00
3 rate .095
4 Depreciation tax savings period 1 ($1,920) 5 Depreciation tax savings period 2 ($1,920)
6 Depreciation tax savings period 3 ($1,920) 7 Depreciation tax savings period 4 ($1,920)
8 Depreciation tax savings period 5 ($1,920) 9 After-tax salvage value period 6 ($3,100)
10 NPV of depreciation tax savings + after-tax salvage ($9,170.60) “=NPV(rate, value1:value6) 11 NPC: purchase price – (PV of tax-savings + salvage value)$20.829.40 “=NPV of depreciation tax savings + after-tax salvage plus the purchase price (C10+C2)
In cell C10 we enter the function: = NPV(rate,values) = NPV(C3,C4:C9) which returns the value ($9,170.60). In cell C11 we add the purchase price of$30,000 to the NPC of after-tax depreciation savings plus the liquidation value which returns the NPC of the purchase equal to $20,829.36. Having found equal to$20,829.40, we can find C using Equation \ref{18.6}.
We solve this problem using Excel in Table 18.2 by finding the present value of Annuity Due with 5 payments of –1. We enter the arguments of the PV function and label the terms in adjacent cells. Excel’s PV function has the following arguments listed in column A: rate (rate), number of payments (nper), annuity (pmt), future value (FV), annuity type (type). For this problem, the discount rate is 9.5% = .095, the number of payments equals 5, the payments are –1, the future value FV is zero, and the type of annuity is an annuity due which requires we enter 1.
Table 18.2. Finding the PV of the Annuity Due
Open Table 18.2 in Microsoft Excel
B6 Function: =PV(B1,B2,B3,B4,B5)
A B C
1 rate .095
2 nper 5
3 pmt -1
4 FV 0
5 type 1
6 PV $4.20 “=PV(rate,nper,pmt,FV,type) In cell B6 we type in the PV function: = PV(B1,B2,B3,B4,B5). The result returned is PV =$4.20. Then we multiply by (1 – T) as required in Equation \ref{18.6}. Finally we find C:
$C=\frac{N P C^{P}}{(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\}}=\frac{\ 20,829.40}{.68(4.2)}=\ 7,283.01 \label{18.8}$
Now suppose that we wanted to know the number of periods required to reach a future value of $2,000. With the data already entered, we turn to the “goal seek” option in Excel. To access goal seek from the main menu, press the [Data] tab, then on the ribbon menu press the [What-if Analysis] button, and on the drop down menu press [Goal Seek…]. The goal seek menu allow us to identify a target value for a particular cell and a variable to change. In our case the target cell is B6 and the target amount is$2,000. The cell we allow to vary is the number of periods cell, B2. Then entering these into Excel’s solver, the solution returned is 18.57. Thus, by continuing to invest for 8.57 periods, we obtain a future value of $2,000 compared to the future value of$1,005.18 reached after 10 years of investing.
Alternatively, we could have asked what is the payment amount required to reach a future value of $2,000 during the original term. In this case we vary the annuity in cell is B3, and the solver returns the value of$182.65. Thus, by increasing our annuity due from $90 to$182.65, we reach a future value amount of $2,000 in the same term required to reach a future value of$1,005.18 with $90 annuity due payments. What we have found in this example is that we would be indifferent between purchasing the truck for$30,000 and making five lease payments of 7,283.01. Obviously, the high discount rate of 14% and making the payment for the truck up front contributes to the high lease payment. In the questions at the end of this chapter, students will be asked to repeat the problem assuming the same values except that the opportunity cost of capital is 5%. Comparative Advantages for Leasee and Leasor So far, we have described the technical properties of leases and how a financial manager may decide between gaining control of a durable through a lease or purchase arrangement. In this section, we allow the lessee and the lessor to be two different persons whose comparative advantages lead them into an exchange arrangement in which one party purchases an asset and then leases it to another party. The solution in this case considers the NPC from the lessee’s (lessor’s) position, assuming that the lessor (lessee) pays their maximum bid purchase price (lease payment). What makes this an interesting problem is that differences in the lessee’s and lessor’s tax rates, as well as opportunity costs of capital, can create incentives to exchange. Comparative advantage. A fundamental principle of economics is that firms should specialize in tasks for which nature, institutions, or luck has granted them an advantage. To illustrate, suppose two farmers, A and B, can both produce dry edible beans and carrots. Also assume A can grow dry edible beans and carrots more profitably than B, and B can grow carrots more profitably than it can grow dry beans. If both beans and carrots must be produced, then A should produce beans, and B should grow carrots. They could then trade to obtain what they did not produce, and both would be better off. Even though A produced both beans and carrots more profitably than B, it would still be to A’s and B’s advantage to specialize. They should decide in which product A had the greatest advantage in production, or B had the least comparative disadvantage, and then specialize and trade as before. An application of the law of comparative advantage explains why two firms may lease. Suppose firm A is able to purchase a durable at a lower price than firm B. But firm B, not firm A, has need of the services of the durable. In this case, firm A’s advantage is in purchasing while B’s advantage is in using the durable. Thus, A might purchase the durable and either sell or lease to B. Another reason why A and B might both agree to lease has to do with relative tax rates. Suppose A, the purchaser of a durable, pays taxes at an average rate TP, which is higher than TL, the average rate at which B, the lessee, pays taxes. As the durable is depreciated, the depreciation creates a tax shield of greater value to the purchaser than to the lessee. Thus, we might say that A, the purchaser, has a comparative tax advantage over B, the lessee, in claiming tax depreciation. The lease allows the purchaser, A, and the lessee, B, to benefit from their comparative advantages associated with the tax shields created by depreciation. Still further reasons why A and B might purchase and lease a durable are that they face different opportunity costs of capital, have different opportunities for using the durable’s services, or face different marginal costs of credit. Comparative advantages for lessee and lessor created by different tax rates and opportunity costs of capital. To demonstrate the idea of comparative advantage with a lease agreement, consider that person B, the lessee, will not lease for more than it would cost to control the durable through a purchase agreement. We want to find B’s NPC if the durable were purchased. To simplify, assume the purchase price of the durable is V0, the book value depreciation rate in year t is where t = 0, …, n – 1, rB is B’s opportunity cost of capital, TB is B’s average tax rate, and assume the lessee tax adjustment coefficient is 1. The NPCP of the purchase for B is: $N P C^{L}(\text {purchase})=V_{0}-\frac{T^{B} \gamma V_{0}}{\left[1+r^{B}\left(1-T^{B}\right)\right]}-\frac{T^{B} \gamma V_{0}(1-\gamma)}{\left[1+r^{B}\left(1-T^{B}\right)\right]^{2}} -\frac{T^{B} \gamma V_{0}(1-\gamma)^{2}}{\left[1+r^{B}\left(1-T^{B}\right)\right]^{3}}-\cdots \label{18.9}$ Equation \ref{18.9} is equivalent to Equation \ref{18.4} except that it is expressed in a form that makes it analytically tractable. Obviously, more detailed expressions with finite time horizons could easily be calculated. What makes Equation \ref{18.9} tractable is that it is expressed as an infinite series whose solution can be written as: $N P C^{L}(\text {purchase})=V_{0}-\frac{T^{B} \gamma V_{0}}{r^{B}\left(1-T^{B}\right)+\gamma} \label{18.10}$ Now consider what happens to B’s NPC resulting from the purchase if B’s tax rate increases. We find the change in B’s NPC associated with the purchase of the durable by differentiating NPCP with respect to TB. (This operation in essence examines the change in NPCP with respect to a small change in TA. The results is that NPCP decreases with an increase in TB. Thus, a firm in a higher tax bracket can buy a durable at a lower after-tax cost than someone in a lower tax bracket. Next, we find B’s NPCL associated with leasing the durable which, after summing geometrically, can be expressed as: \begin{align} N P C^{L}(\text {lease}) &=\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]}+\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]^{2}} +\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]^{3}}+\cdots \[4pt] &=\frac{C\left[1+r^{L}\left(1-T^{B}\right)\right]}{r^{L}} \label{18.11} \end{align} To illustrate Equation \ref{18.10} consider the following example: Suppose Affordable Assets (AA) buys durables and leases them to other firms. As a well-to-do established firm, AA’s tax rate, TA is high—45 percent. On the other hand, the Unendowed User (UU) lacks capital and prefers to lease rather than own in order to protect its limited credit. Because of its lower earnings, UU’s average tax rate TU is 21 percent. In addition, assume that the leased durable wears out at the rate of = 10 percent, and assume the market rate of return for both AA and UU is 14 percent. Finally, assume that the purchase price of the durable is4,000.
Making the appropriate substitutions into Equation \ref{18.10}, we find the NPC of purchasing the durable for UU is:
$N P C^{U U}=\ 4,000-\frac{[(.21)(.1)(\ 4,000)]}{[(0.14)(1-0.21)+0.1]}=\ 3,600 \label{18.12}$
In other words, the after-tax purchase price of the durable for UU is $3,600. Now consider the after-tax NPC of the purchase for firm AA. Making the appropriate substitutions into Equation \ref{18.10}, we find the NPC of purchasing the durable for AA is: $N P C^{A A}=\ 4,000-\frac{[(0.45)(0.1)(\ 4,000)]}{[(0.14)(1-0.45)+0.1]}=\ 3,000 \label{18.13}$ In other words, the after-tax cost of the durable purchase for AA was only$3,000 compared to $3,600 for UU. Having calculated NPC for purchasing the durable for firms UU and AA, we can find their respective maximum bid lease prices. Making the appropriate substitutions into Equation \ref{18.11}, we find $NPC^{UU} (leasing) = \dfrac{C^{UU}[1 + (0.14)(1 – 0.21)]}{0.14} = \3,600.$ Solving for $C^{UU}$ we find $C^{UU} = \453.81$. Similarly we find $NP^{AA} (leasing) = \dfrac{C^{AA}[1 + (0.14)(1 – 0.45)]}{0.14} = \3,000.$ Solving for $C^{AA}$ we find $C^{AA} = \389.97$. Reflections on comparative advantages for firms UU and AA. Because of their differences in tax rates, firms UU and AA have different effective after-tax cost of the durable even though the market price of the durable is the same for each firm. In this case, the effective cost for AA is less than for firm UU—$3,000 versus $3,600. On the other hand and as a result of the differences in the effective after tax cost of the durable, the maximum bid lease price for firm UU is greater than for firm AA:$453.81 versus $389.97. These results provide opportunities for firms AA and UU to take advantage of their comparative advantages: firm AA purchases the durable at a lower effective cost than is available to UU. UU, on the other hand, is quite willing to pay a higher lease price than AA’s maximum bid lease price. Under these arrangements, both firms AA and UU are made better off. Leases and NPV. Assume that firm AA buys the durable and UU leases the durable from AA. Now the lease price in an expense for firm UU but an income for AA. We may want to ask: what is the minimum lease payment AA could accept from UU and still break even? To find this amount we set AA’s NPV as: $N P V^{A A}=\frac{C\left[1+r\left(1-T^{A A}\right)\right]}{r-N P C^{A A}(\text {purchase})} \label{18.14}$ After making the appropriate substitutions we find $C=\frac{N P C^{A A}(\text {purchase})\left(r^{A A}\right)}{\left[1+r^{A A}\left(1-T^{A A}\right)\right]}=\frac{\ 3,000(.14)}{[1+(.14)(1-.45)]}=\ 389.97 \label{18.15}$ Thus, any arrangement with UU which generates a lease payment more than$389.97 will result in a positive NPV for AA.
Summary and Conclusions
Trades occur when each party to the exchange gives up something of value in return for something of greater value. In most trades, a physical object or service is exchanged for an agreed-on amount of cash. Moreover, in most cases, ownership is transferred along with the good or service.
This chapter has considered leasing, a different kind of trade, in which the control over the use of a durable is transferred, but ownership of the durable is not. Leasing exists because it provides benefits to the lessee and lessor that might not be realized if control of a durable also required ownership.
Different types of leases described in this chapter include sale-and-leaseback agreements, operating leases, and financial or capital leases. Leases offer particular advantages for lessees including the avoidance of capital requirements associated with a purchase. As a result, lessees may use their limited credit for other purchases or as a credit reserve. Obsolescence risk of ownership is also reduced for lessees. Additionally, leasing offers the chance to better match service requirements to the delivery of services. Ownership of durables may require holding idle capacity—less likely when services of a durable are leased.
Tax considerations are critical in the decision to lease or to purchase. Ownership allows for tax depreciation shields; leasing allows the entire lease payment to be claimed as an expense.
An important principle of comparative advantage is involved in the lease decision. If the tax depreciation from ownership is greater for one firm than for another, leasing permits the firm which can benefit the most from the depreciation shield to claim it by purchasing the asset and leasing it to another firm. Not only can comparative tax advantages be optimally used through leasing, there can also be comparative advantages in acquiring financing. Comparative advantage and the incentive to lease may also result from differences in opportunity costs, access to credit, and use for the durables’ services. In essence, leasing is a critical tool that allows firms to benefit from their comparative advantages.
Questions
1. Describe three different lease types and their essential differences.
2. For every lease agreement, there is a lessor and a lessee who both believe they will be better off by executing the lease. Describe how a sale and leaseback agreement might make both the lessor and lessee better off.
3. Assume a lease agreement that requires $100 payments at the beginning of each period for 15 years. The lessee’s marginal tax bracket is 25% and opportunity cost of capital is 8%. The tax adjustment coefficient is assumed to equal 80%. Find the NPC of this lease. Now assume that the lessor agreed to accept payments at the end of each period instead of the beginning. What would be the NPC of the lease agreement under the new arrangement? 4. Resolve the Go Green lease problem assuming that the firm’s opportunity cost of capital is 5% rather than 14%. Compare your solution with the previous one. Did the lease payment go up or down? Can you explain why? 5. Resolve the Go Green lease problem by assuming that the lessee will lease the durable for an extra period. The lessee will make 6 lease payments instead of 5, but the depreciation schedule will not change. In other words, find the maximum lease payment and explain your results. 6. Explain in your own words the concept of comparative advantage. Provide one example of how the concept of comparative advantage has influenced your choice or the choice of others. 7. Explain how the principle of comparative advantage might explain why two firms may agree to a lease arrangement. 8. In the example of a lessee UU and a lessor AA, the lessee and lessor are in different average tax brackets (45 versus 21 percent) but were assumed to face the same opportunity cost of capital. Resolve the example by assuming UU’s opportunity cost of capital is 7% instead of 14%. Find the effective after-tax purchase price of the durable for the two firms. Then find the maximum bid lease price for the two firms. Do the results allow for the two firms to take advantage of the principle of comparative advantage? Please explain. 9. Consider the case of firms UU and AA described in the text. Since AA has the lowest NPC for purchasing the durable, it should do so. Meanwhile the maximum bid lease price for UU is higher than for AA, so UU should lease rather than purchase the durable. Suppose that UU agrees to pay AA a lease price of$410.00. What is AA’s NPV from buying the durable and leasing it back to UU? (Hint: In this arrangement, the lease cost for UU is an income for AA.) | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/18%3A_Leases.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) distinguish between financial investments and capital investments; (2) recognize the different kinds of financial investments; and (3) evaluate the different kinds of financial investments using present value (PV) models developed in earlier chapters.
To achieve your learning goals, you should complete the following objectives:
• Distinguish between financial investments and nonfinancial investments.
• Learn how PV tools can be used to analyze financial investments using methods similar to those used when comparing nonfinancial investments.
• Learn to distinguish between financial and nonfinancial objectives.
• Learn the role of brokers, dealers, and financial intermediaries in the securities markets.
• Learn how to value riskless securities such as time deposits.
• Learn why Albert Einstein called compounding interest “the greatest mathematical discovery of all time”.
• Learn the nature of bonds and the variables that determine their value.
• Learn how tax rates affect the value of financial investments.
Introduction
In its broadest meaning, to invest means to give up something in the present for something of greater value in the future. Investments, what we invest in, can differ greatly. They may range from lottery tickets and burial plots to municipal bonds and corporate stocks. It is helpful to organize these investments into two general categories: real and financial. Capital, or real, investments involve the exchange of money for nonfinancial investments that produce services such as storage services from buildings, pulling services from tractors, and growing services from land. Financial investments involve the exchange of money in the present for a future money payment. Financial investments include time deposits, bonds, and stocks.
This chapter applies PV models developed earlier to financial investments. Large corporations and other business organizations require financial investments from a large number of small investors to provide funds for operation and growth. The collection of these funds would be impossible if each investor were required to exercise a managerial role over them. Moreover, the collection of investment funds from a large number of small investors would be impossible unless the investors could be assured of investment safety and limited liability. A number of financial investments have been designed to overcome these and other investment obstacles.
The market in which financial investments are traded is called the securities market or financial market. Activities in the financial markets are facilitated by brokers, dealers, and financial intermediaries. A broker acts as an agent for investors in the securities markets. The securities broker brings two parties together to obtain the best possible terms for his or her client and is compensated by a commission. A dealer, in contrast to a broker, buys and sells securities for his or her own account. Thus, a dealer also becomes an investor. Similarly, financial intermediaries (e.g. banks, investment firms, and insurance companies) play important roles in the flow of funds from savers to ultimate investors. The intermediary acquires ownership of funds loaned or invested by savers, modifies the risk and liquidity of these funds, and then either loans the funds to individual borrowers or invests in various types of financial assets.
Numerous books discuss the institutional arrangements associated with securities trading. In this chapter, the focus in not on the details of trading in the securities market but on how to value financial investments or securities.
Valuation of Riskless Securities
The prices of financial investments, like other prices, are determined in markets—financial markets. The characteristics of financial markets, however, may differ significantly depending on the type of financial investment traded. Common to all financial markets, though, is that prices are established by matching the desires of buyers and sellers. Moreover, in equilibrium there is neither excess demand nor excess supply. However, equilibrium does not mean that all prospective buyers and sellers agree that an investment’s price is equal to its value. It only means that a price has been found that, in a sense, balances the different goals of buyers and sellers.
Time deposits. Time deposits are money deposited at a banking institution for a specified period of time. The main difference between different kinds of time deposits is their liquidity. Generally speaking, the less liquid the time deposits are, the greater their yield is.
The most liquid form of time deposits are sometimes known as “on call” deposits. On call deposits can be withdrawn at any time and without any notice or penalty. Examples of on call deposits include money deposited in a savings or checking account in a bank. Another kind of time deposit is a certificate of deposit (CDs). When CDs mature, they can be withdrawn or they can be held for another term. CDs are generally considered to be liquid because they are negotiable and can be re-discounted when the holder needs some liquidity.
Some time deposits must be held until maturity or suffer penalties for early withdrawal. The rate of return for these time deposits is higher than on call deposits because the requirement that the deposits be held for a designated term gives the bank the ability to invest in financial products that earn greater returns. In addition, the return on time deposits is generally lower than the average return on long-term investments in riskier products like stocks and some bonds. Some banks offer market-linked time deposit accounts which offer potentially higher returns while guaranteeing principal.
Investments in time deposits may consist of a one-time investment or a series of deposits. What all time deposits have in common is that the payment(s) is compounded until some ending date at which time they are partially or totally withdrawn. Thus, our interest is not in the present value of the payments but in their future value. The market determined price in the case of financial investments is the compound rate at which time deposits earn interest. Typically, the compound rate of interest earned on time deposits is low—partly because they provide nearly perfect liquidity—especially for time deposits for which there is no penalty nor transaction cost associated with withdrawal of funds.
Ordinary annuities and annuities due. Previously we described an annuity as a time series of constant payments made or received at the end of each period. Annuities paid and received at the end of a period are referred to as ordinary annuities. Annuities paid (or received) at the beginning of each period are referred to as annuity due payments.
To illustrate an annuity due, consider a series of deposits R made every period, the first one occurring in the present. We write the future value Vn of the time series of deposits R compounded at rate r̂ for withdrawal in period n as:
(19.1)
Note that the first time deposit R is compounded for n periods—and is equal in value to its compounded value at the beginning of period n. Similarly, the second payment is compounded for n – 1 period and is equal to its compounded value at the beginning of period n. Finally, the last payment is made at the beginning of period n – 1 and is compounded once to find its compounded value at the beginning of period n.
To illustrate, suppose a saver deposits a $90 payment (PMT) at the beginning of each period for n = 10 periods. If the deposits are compounded at a rate of r = 2%, what amount is available for withdrawal at the beginning of period 10? We solve this problem using Excel in Table 19.1. Note that to indicate annuity due payments at the beginning of the period, “type” in the Excel future value FV function is changed from its default of zero to 1. In place of PV in the equation, we enter a blank closed with a comma. Table 19.1. The Future Value of 10 Annuity Payments of$90 Compounded at 2%
Open Table 19.1 in Microsoft Excel
B6 Function: =FV(B4,B5,B3,,B2)
A B C
1 The Future Value of 10 Annuity Due Payments of $90 Compounded at 2% 2 type 1 3 PMT ($90.00)
4 rate 0.02
5 n 10
6 FV $1,005.18 “=FV(rate,nper,pmt,[pv],type) 7 PV 0 What our calculations determine is that at the beginning of the 10th period, we have$1,005.18 available. However, there are several other interesting questions that we might answer using our Excel formulas. For example, we might want to know how many periods would be required to have $2,000 available at some future date. Continuing with the entries already made in Excel, we add the following: Table 19.2. Finding the Number of Annuity Due Payments Required to Earn a Future Value of$2,000
Open Table 19.2 in Microsoft Excel
B5 Function: =NPER(B4,B3,B6,B2)
A B C
1 Number of Annual $90 Annuity Due Payments Compounded at 2% Required to Earn a FV of$2,000
2 type 1
3 PMT ($90.00) 4 rate 0.02 5 n 29.69347722 “=NPER(rate,pmt,FV,type) 6 FV$2,000
7 PV 0
We might be interested in knowing the periodic investment required to have $2,000 available in 10 years if the investments were compounded at 2%. The required Excel formula is represented in Table 19.3. Table 19.3. Finding the Annuity Due Payment Required to Earn a Future Value of$2,000 in 10 Years
Open Table 19.3 in Microsoft Excel
B3 Function: =PMT(B4,B5,B7,B6,B2)
A B C
1 Annual Annuity Due Payment Compounded at 2% Required to Earn a FV of $2,000 in 10 years. 2 type 1 3 PMT ($179.07) “=PMT(rate,nper,PV,FV,type)
4 rate 0.02
5 n 10
6 FV $2,000 7 PV 0 To reach one’s savings goal of$2,000 in 10 years at a compound rate of 2% would require a periodic payment into a time deposit at the beginning of each period equal to $179.07. Compound Interest The magic of compounding. It is claimed that Albert Einstein called compound interest “the greatest mathematical discovery of all time”. It is probable that no other concept in finance has more importance for investors than what is sometimes called the “wonder of compound interest.” Compounding interest creates earnings not only on the original amount saved or invested but also creates earning on the interest on earnings, and it does so period after period. Another way to describe this process is to say that compounding interest generates earnings on the investment and reinvested earnings from the investment. To realize the power of compound interest requires two things: the re-investment of earnings and time. Our previous calculations confirm the importance of compound interest. In 10 payments of$90 we accumulated a future value of $1,005.18. By making an additional 8.57 payments, we doubled our future value. We found a similar effect when we increased loan payments and observed significant decreases in term. When finding the effect of increased loan payments on loan terms, we calculated the elasticity of the term of the loan with respect to the size of the loan payment. Similarly, we can find the impact of an increase in the term of periodic savings on future values (FV). We refer to this elasticity as the FV elasticity with respect to term. The derivation of the FV elasticity with respect to term is found in Derivation 19.1 at the end of this chapter. The discrete approximation to the FV elasticity with respect to n is: (19.2) Table 19.4 provides elasticity estimates for alternative reinvestment rates and terms. Table 19.4. Tabled Values of elasticity EFV,n = n/US0(r,n) n r = .01 r = .03 r = .05 r = .08 r = .10 r = .15 1 1.00% 1.03% 1.05% 1.08% 1.10% 1.15% 3 1.02% 1.06% 1.10% 1.16% 1.21% 1.31% 5 1.03% 1.09% 1.15% 1.25% 1.32% 1.49% 10 1.05% 1.17% 1.30% 1.49% 1.63% 1.99% 20 1.08% 1.34% 1.60% 2.04% 2.35% 3.20% 30 1.16% 1.53% 1.95% 2.66% 3.18% 4.57% 60 1.34% 2.17% 3.17% 4.85% 6.02% 9.00% A related question with a more intuitive answer is how long does it take to double, triple, or quadruple one’s investment? The derivation for the equation that answers this question can be found in Derivation 19.2 at the end of this chapter. Let m be the number of times one wants to multiply his or her FV obtained at period n. Let nm equal the period in which the last deposit is made. Then we can find the number of periods (nmn) required to increase the original FV by m times. The formula found in Derivation 19.2 is provided below: (19.3) To illustrate, let r = .1, n = 5, and m = 2. The number of periods required to double the FV of one’s original investment equals: (19.4) In this example, an investment consisting of 5 equal payment compounded at 10% could be doubled in additional 3.3 payments. And the investment could be tripled in: (19.5) The second example illustrates the power of compounding interest. Starting after 5 periods of investing, in 3.3 more periods the FV of the investment doubled and in 5.8 additional periods the FV of the original investment tripled. Finally, we conclude this section by constructing Table 19.5 demonstrating the power of compounding interest. The cells of the table indicate the time required to double, triple, and quadruple an initial investment for reinvestment rates of 1%, 3%, 5%, and 10%. Table 19.5. Periods required to double, triple, or quadruple the FV of an investment consisting of 5 equal payments assuming alternative reinvestment rates. Alternative re-investment rates Number of time periods required to increase the FV of the original investment m times m = 2 (double the original FV) m = 3 (triple the original FV) m = 4 (quadruple the original FV) 1% 4.8 9.3 13.7 3% 4.4 8.2 11.6 5% 4.0 7.3 10.2 10% 3.3 5.8 7.8 The rule of 72 approximates the amount of time it takes to double your investment at a given rate of return. To apply the rule, you divide the rate of return by 72. For example, assume you invest$1000 at an interest rate of 5%. It would take 14.4 years (72/5) to double your investment to $2000. Bonds A bond is a financial asset frequently traded in financial markets. Bonds represent debt claims on the assets and income of the entity issuing the bond. A bond’s value is equal to the present value of its future cash flow (interest and principal) discounted at an appropriate interest rate. Bonds usually have a known maturity date at which time the bond holder receives the bond’s face or par value. Bonds are unique because their redemption or liquidation value is fixed. Typical redemption amounts are$1,000 or $10,000. Consider the following example. Suppose a bond can be purchased at a price of V0 (an initial cash outflow) and redeemed n periods later at a cash value of Vn, a cash inflow to the bond holder. Moreover, suppose that the bond generates no cash return except when it is sold. Further, assume that the before-tax discount rate is r percent. Ignoring any tax consequences, the NPV of this bond is the sum of the cash outflow plus the present value of the cash inflow. (19.6) Those who purchase bonds may want to calculate the “yield” on a bond, which is the discount rate that equates the present value of the bond’s cash flow to its present market value—the bond’s internal rate of return (IRR). If, for example, the bond’s market value is$321.97 and its cash flow of $1,000 occurs at the end of year 10, then the bond’s yield, or its IRR, is 12 percent. (19.7) Now consider the effect of taxes. First, assume capital gains taxes are paid by the bond purchaser at rate Tg and income taxes are paid at rate T. The after-tax NPV of the bond is calculated by adjusting the discount rate to its after-tax equivalent and by subtracting from the liquidation value of the bond, the capital gains tax: (19.8) where is the tax adjustment coefficient defined in Chapter 11. If the NPV in Equation \ref{19.5} is zero then is the bond’s after-tax IRR. To find the effective tax rate we set NPV equal to zero in equations (19.8) and (19.6) so that before-tax cash flow discounted by the before-tax IRR in Equation \ref{19.6} is equal to the after-tax cash flow discounted by the after-tax IRR in Equation \ref{19.8}. Then we solve for that makes the two equations equal. The result is: (19.9) To illustrate using the numbers from our previous example, let the before-tax IRR equal 12%, let V0 equal$321.97, let Vn equal $1,000, and let the income tax and the capital gains tax T and Tg both equal 15 percent. Next making the appropriate substitutions into Equation \ref{19.6} we find equal to: (19.10) For the effective tax rate is reduced from 0.15 to (.66)(0.15) = 0.10. In the example, just completed, we were able to deduce a closed form solution for . In most cases, closed form solutions are very difficult to obtain. Nevertheless, in most practical cases involving numerical estimates, we can still find estimates for the effective tax rate and after-tax IRRs. We will demonstrate the empirical approach to finding effective tax rates in the next section. Coupons and Bonds Most bonds, in addition to capital gains (or losses), provide “coupon” (interest) payments. The number and amount of the coupon payments will alter the NPV as well as the price of the bond. Usually, the coupon rate rc is a percentage of the redemption value of the bond. The before-tax NPV of a bond with n coupon payments is: (19.11) To illustrate, suppose an investor wants to find the maximum bid price for a three-year$1,000 bond if it offers coupon payments of rcVn = (.05)(1,000) = $50, and r = 10%. Then using Equation \ref{19.11} and setting NPV equal to zero, find the maximum bid price equal to: (19.12) Taxes, of course, affect the NPV of bonds with coupon payments. Only now, taxes may or may not be paid on the coupon payments and capital gains. For example, coupon payments of many municipal bonds are not taxed but their capital gains are taxed. Tax exemptions, of course, raise the maximum bid price and NPVs of the bonds for all investors but especially for higher tax bracket investors. The after-tax present value of the bond with tax-exempt coupon payments is written as: (19.13) To illustrate, suppose an investor wants to find the maximum bid price for a three-year$1,000 bond if it offers coupon payments of rcVn = (.05)(1,000) = $50 and r = 10% and pays capital gains and income taxes at the rate of 10%. Then using Equation \ref{19.13} and setting NPV equal to zero, we find the maximum bid price for the bond whose earlier maximum bid price was calculated equal to$875.65:
(19.14)
In the application of Equation \ref{19.13}, the discount rate was the IRR—because it was the discount rate that resulted in NPV equal to zero. We introduced taxes into the cash flow, but we don’t know the effective after-tax discount rate that would set NPV equal to zero. We have to solve for that will adjust the discount rate for taxes in the same magnitude as were the cash flow adjusted for taxes. For Equation \ref{19.13}, we find the after-tax IRR using Excel:
Table 19.6. Finding the After-tax IRR
Open Table 19.6 in Microsoft Excel
B6 Function: =IRR(B2:B5)
A B C
1 Finding the After-tax IRR
2 Bond’s max bid price -875.65
3 first coupon payment 50
4 second coupon payment 50
5 Salvage value (1000) + coupon payment 1037.6
6 IRR 9.59% “=IRR(B2:B5)
The IRR calculation of 9.59% equals the after-tax IRR of 9.59% compared to the before tax IRR of 10%. We can find and the effective tax rate by setting
(19.15)
From the above equation we find = .41. Thus the effective tax rate is (.2) (.41) = 8%—far less than the actual income tax rate of 20%.
To review the process, we began by solving for the maximum bid price of the bond. This required that the stated discount rate was the before-tax IRR for the bond. Then we reasoned as follows. If the maximum bid price is the same whether calculated on a before-tax or after-tax basis, then the effect of taxes on the cash flow—in this case the capital gains tax—must have the same effect on the discount rate. Thus, we required that the maximum bid price in the after-tax model be the same maximum bid determined in the before-tax model and solved for the after-tax IRR and the tax adjustment coefficient .
Common Stocks
In contrast to bonds, common stocks have neither a fixed return nor a fixed cost. The terminal value of bonds is usually fixed, but the terminal value of stocks depends on the market value of the stock at the time of sale. The equity capital generated by the sale of stock is an alternative to debt capital generated by the sale of bonds. It also is a means of sharing risk among numerous investors.
Stocks offer significant benefits for stockholders as well as the companies issuing the stocks. Stockholders have the opportunity for ownership in the major businesses of the world with the consequent share in profits while their liability is limited to their investments. Moreover, stock ownership frees them from decision-making responsibilities in the management of the company, although common stock allows its owners to vote for directors and sometimes other matters of significance facing the company.
Stock owners receive dividend payments on their stocks, usually on a quarterly basis. The amount of dividends paid on stocks is determined by a corporation’s board of directors. The board of directors’ dividend policies may influence the kinds of stock they issue and the kinds of investors they attract.
The relevant question for a potential stock purchaser is what is the maximum bid price for a particular stock? If r is the nominal discount rate, and R1, R2, ⋯ are projected dividends paid on the stock in periods 1, 2, ⋯, the maximum bid price for the stock is:
(19.16)
The model above assumes an infinite life. This assumption is consistent with the “life of the investment” principle discussed in Chapter 8 because to know the terminal value of the stock, Vn, we must know the value of the dividends in periods (n + 1), (n + 2), ⋯. Knowing all future dividends converts the problem to one in which the number of periods equals the life of the firm.
A simplified form of Equation \ref{19.16} is possible if expected dividends R1, R2, ⋯ are replaced by their expected annuity equivalent R. Then we can write:
(19.17)
And r, the stock’s IRR, is R/V0. Thus, with long-term constant dividends of $100 and the stock valued at$1000, the rate of return is 10%. Another important ratio derived from Equation \ref{19.16} is what is commonly referred to as the price-to-earnings ratio, V0 / R = 1 / r which is often viewed as the bellwether of financial irregularities in the financial market. Higher than usual price-to-earnings ratios may signal what has been called “irrational exuberance” for the investment. Lower than usual price-to-earnings ratios may signal that the investment is undervalued.
Finally, debt capital must be repaid regardless of the financial fortunes of the business. However, the return to stockholders depends critically on the performance of the company. This makes NPV analysis of stock investments subject to considerable uncertainty.
Figure 19.1. S&P 500 PE ratio peaks at record highs.
So what have we learned? We learned to distinguish between real and financial investments. Earlier chapters in this book focused on real investments. Our focus in this chapter was on financial investments including time deposits, certificates of deposits, bonds, and stocks. The important point is that we can examine both real and financial investments using PV tools.
Summary and Conclusions
This chapter has introduced concepts related to financial investments which involve exchanges of money over time. In relation to financial investments, the focus is on the amount of one’s investment available at some future period of time. We find the FV of a financial investment by compounding interest. As we demonstrated in Table 19.1, the power of compounding is truly amazing. Therefore, the advice for most investors is to invest early and continuously, and then let one’s investment grow.
Time deposits represent an important financial investment opportunity. These differ mostly in their liquidity—those that are least liquid are also the ones with the higher yields. Bonds are an important class of financial investment. In contrast to most other financial investments, their liquidation value is fixed. What is not fixed is their purchase price which is established in the market and depends on their yield—their expected IRR.
One of the interesting aspects of bonds is the way they are taxed. Often when bonds are issued by municipalities and some other institutions, they receive special tax considerations. In the extreme neither their coupon payments nor their capital gains are taxed. In other circumstances, capital gains are taxed and coupon payments are not. Regardless, an important question is how do special tax provisions provided with some bonds affect their after-tax IRRs. While the effective after-tax IRR can sometimes be found in a formulaic expression, often they are too complicated to be expressed in a closed form solution but can be found numerically by calculating the before and after-tax IRRs.
Finally, we only introduced the concept of common stocks. Investments in common stocks are most often discussed in the context or risk analysis and include discussions of many alternative of risk response strategies. A more complete discussion of investments in stocks is beyond the scope of this financial management text.
Questions
1. To invest means to give up something in the present for something of value in the future. Can you describe three of your most important personal investments? Describe what you sacrificed including money and time, and describe your expected future returns.
2. Describe the difference between real and financial investments. Also describe how the investment settings for real and financial investments may differ.
3. Describe the main characteristics of alternative types of time deposits? What are the rates of return currently offered by major banks or credit unions on alternative types of time deposits?
4. Suppose a saver invests $65 in a time deposit at the beginning of each period for 10 periods. If the deposits are compounded at a rate of 4%, what amount is available for withdrawal at the beginning of period 11? 5. Suppose a young couple now renting an apartment wants to invest in their own home. The average price range of their desired home is approximately$250,000. If they make monthly deposits in a time deposit account at the beginning of the period for 5 years and their deposits earn an APR compound rate of 3%, what would be the required size of their monthly deposit to pay for the 20% required down payment of the price of their home ($50,000)? If they desired to save the required down payment in three years, what would be the required size of their monthly deposits? 6. It is claimed that Albert Einstein called compound interest “the greatest mathematical discovery of all time.” What is it about compounding that is so important that he would make such a claim? Do you agree? If so, why? If you disagree, what would be an alternative mathematical discovery of greater importance? 7. Describe in words the meaning of the elasticity of the future value of an investment with respect to its term. Then calculate the elasticity of the future value of an investment compounded at an APR rate of 4% for 12 periods. How would the elasticity measure change if the compound rate were increased to 7%? Can you explain the direction of the change? 8. Find the number of periods required to double the future value of an investment compounded for 5 periods at alternative reinvestment rates of 2%, 4%, and 8%. 9. An investor desires to save$10,000. If the compound rate is 3% per month and the investor plans on saving $200 at the beginning of each month, how many months will be required for the investor to reach her savings goal of$10,000? Once the saving goal is reached, how many addition months will be required for the saver to double the amount saved if she saves at the same rate?
10. Consider an 8-year bond with a par value of $10,000. If the purchase price of the bond is$4,250, what is the yield on the bond? (Ignore the influence of taxes.)
11. What is the relationship between the bond’s yield (its IRR) and the bond’s purchase price? What would you expect to happen to the bond’s purchase price if the expected yield on the bond increased? Please explain.
12. In the example illustrating Equation \ref{19.8}, the effective tax rate for a bond purchaser was found to equal θT = .66(.15) = 10%. Please recalculate the effective tax rate in the example assuming the capital gains tax rate is only 50% of the income tax rate. In other words, if the capital gains tax rate is 7.5%, what is the bond purchaser’s effective tax rate? How does lowering the effective tax rate change the firm’s effective after-tax IRR?
13. Consider the equation:
(Q19.1)
where is the after-tax IRR of a bond.
Next consider the equation:
(Q19.2)
where r is the before-tax IRR of the bond.
Then assume that V0 = $500, Vn =$1000, rcVn = .04($1,000) =$40, T = 20%, and Tg = 10%. Find the before-tax and after-tax IRRs using the two equations described in this question and the values listed. Then use the before-tax and after- tax IRRs to find the value of the tax-adjustment coefficient .
1. Compare the rule of 72 with the actual time required to double your investment.
Derivation 19.1.
The derivation of the elasticity of future value (FV) with respect to term:
The elasticity of FV with respect to n is defined as:
(19.i)
The future value of n payments compounded at rate r is equal to:
(19.ii)
And the derivative of FV with respect to n is:
(19.iii)
Substituting into the elasticity formula we find:
(19.iv)
The discrete approximation of the elasticity of FV with respect to n is:
(19.v)
Derivation 19.2.
Deriving the formula for calculating the number of periods to double the FV of an n period investment reinvested at an interest rate of r%.
To begin, the future value (FV) of an n period investment R compounded at rate r is equal to:
(19.vi)
Now m times the FV of the original investment is set equal to the same investment compounded for nm periods:
(19.vii)
and simplifying by equating the two integrated equations above we find:
(19.viii)
Then solving for the difference between (nmn), we find the time it takes to increase the FV of the original investment at period n by m times.
(19.ix) | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/19%3A_Financial_Investments.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) understand how interest and earning rates on a variety of debt and investments instruments are related to yield curves and periodic interest rates; (2) describe how yield curves and periodic interest rates defined over future time periods can be used to predict market participants’ expectation of future opportunities and threats; and (3) use yield curves and periodic interest rates to better understand and predict future financial opportunities and threats.
To achieve your learning goals, you should complete the following objectives.
• Learn how to calculate single period discount rates from investments of varying terms.
• Understand the relationship between yield curves and single period discount rates.
• Learn how yield curves can be used to predict future financial opportunities and threats.
Introduction
In most present value (PV) models, the discount rate is a constant even when the term of the model has changed. In reality, each period’s discount rate may be different because factors that influence the discount rate are not constant. These factors include the level of economic growth in the economy, the inflation rate, national and international events likely to influence our economy, activities in the stock and bond market, housing and land markets, the unemployment rate, and election outcomes.
One way to observe the difference in period discount rates is to observe the interest rates on loans with different terms. They are not constant. To demonstrate, note the changes in variable interest rate loans. They aren’t constant either. Or, relevant to this discussion, notice the difference in average yields on bonds with different maturities even in the same risk class. Alternatively, notice the change in the internal rate of return (IRR) of a bond as its time to maturity changes over times.
In what follows, we pursue two objectives. The first objective is to demonstrate how to calculate the periodic discount rate for no-coupon bonds. The approach we describe can also be used to find periodic discount rates implied by bonds that are more complicated as well as other financial instruments. Our second objective is to connect the shapes and patterns of periodic interest rate curves and their corresponding yield curves patterns to predict future economic activity and opportunities and threats. Yield curves, as we will explain in more detail later, are the geometric means of periodic interest rates at a point in time with various maturities.
Geometric Means and Periodic Discount Rates
Geometric means and long-term discount rates. Suppose we have information that allows us to predict n future periodic discount rates r1, r2, ⋯, rn. The geometric mean for the n periodic rates satisfies the following equation:
(20.1)
In words, one plus the geometric mean multiplied by itself n times would equal the product of 1 plus n periodic discount rates. We can solve for the geometric mean of the n periodic discount rates in Equation \ref{20.1} by finding the nth root of the products of the n periodic discount rates and subtracting one:
(20.2)
To demonstrate, suppose that periodic discount rates for period one through three were r1 = .07, r2 = .03, and r3 = .075. We can solve for the geometric mean of the three periodic interest rates as:
(20.3)
How to calculate periodic discount rates. Consider a zero coupon bond that can be purchased for at the beginning of the period and redeemed at the end of the period for its par value of $1,000. The periodic rate of return r1 for the one-period bond satisfies the PV model: (20.4) Solving for the one-period discount rate r1 we find: (20.5) For example if then (20.6) In the case of a one-period bond, the one-period discount rate is also the geometric mean. Now consider a zero-coupon bond that matures in two periods with similar risk and tax provisions as the one-period bond described in Equation \ref{20.4}. Assume the zero-coupon two-period bond can be purchased for at the beginning of the period and redeemed at the end of the period for its par value of$1,000. The periodic rate of return r2 for the two-period bond satisfies the PV model:
(20.7)
Solving for the second period discount rate r2 we find:
(20.8)
For example if then
(20.9)
When we purchase a two period bond, we acquire a financial instrument with a single yield for two periods. The yield is the geometric mean of the product of the single period discount rates. In our example, the yield or geometric mean is equal to:
(20.10)
Continuing our example, if then
(20.11)
Finally, consider a zero-coupon n period bond that can be purchased for at the beginning of the period and redeemed at the end of the period for its par value of $1,000. The periodic rate of return rn for the n period bond satisfies the PV model equal to: (20.12) Solving for the one-period discount rate rn we find: (20.13) Periodic rates of return and geometric means. When we purchase a three-period bond, we acquire a single yield for three periods. Consistent with the PV model, the yield is the geometric mean of the product of the single-period discount rates. In our example, the yield or geometric mean for the three-period bond is equal to: (20.14) While one could expect to earn the bond’s yield to maturity if the investor held the bond to maturity, a three-year bond becomes a two-year bond after one year, and if sold, the bond’s price would reflect the yield on a two-year bond. Graphing the geometric means of bonds against their varying time to maturity produces the bond’s yield curve. In Figure 20.1, we graph the periodic discount rates and the corresponding yield curves for one, two, and three period bonds. Figure 20.1. A comparison of periodic interest rates and the corresponding yield curves of bonds of varying maturities Predicting Future Economic Activities and Opportunities and Threats Marginal periodic rates and average geometric mean yield curves. The periodic rate is a marginal rate while the yield rate is an average or mean—in this case a geometric mean. In our example, the periodic rate is increasing. As a result, the yield curve is also increasing but at a slower rate because previous and lower values of the periodic rate influence the yield. Therefore, if the yield curve is increasing, it is because the marginal periodic rates added to the series are greater than the geometric mean of the previous values included in the calculation. Moreover, if the yield curve were decreasing, it would require that periodic rates added were less than the geometric mean. To be complete, if the yield curve were constant, it would suggest that the marginal periodic rate were equal to the geometric mean. Of course, there are many bond yield curves depending on the type of bond considered. When producing a yield curve, it is essential that bonds used to produce the yield curve belong to a similar risk class—even though this may be difficult because term differences produce different risks. To do the best we can to hold risk constant when producing yield curves, government backed debt is often considered. The most frequently reported yield curve compares three-month, two-year, five-year and thirty-year U.S. Treasury debt. We present graphs of U.S. Treasury yield curves at two points in time in Figure 20.2 below Figure 20.2. Yield curves using U.S. Treasury debt calculated on January 3, 2017 and June 20, 2017 Interpreting the shapes of yield curves. In the previous section, we described the relationship between the period or marginal interest rates and the yield curve that, according to our PV model, is the geometric mean of the periodic rates. We now suggest some interpretations of the yield curves. Figures of periodic rate calculated from yield curves are not generally available. • Positively sloped yield curves. To invest or lend one’s financial capital to another person or entity requires a sacrifice on the part of the lender. Furthermore, the longer the funds are committed to another person or entity, the greater is the sacrifice. As a result, many economists claim that upward sloping yield curves predict a healthy economy in the future where borrowers have a bright view of future earnings and are willing to pay increased interest rates for the privilege of investing in the future. Another explanation is that borrowers expect periodic interest rates in the future to rise that in turn will produce an increasing yield curve. One reason for periodic rates to rise is expected increases in inflation and subsequent response to inflation by the Federal Reserve to increase interest rates on government debt instruments to offset inflationary pressures. • Flat or humped yield curves. A flat yield curve is consistent with constant periodic interest rates so that all bond maturities have similar yields. A humped yield curve implies that periodic interest rates for a period lie above then fall below the yield curve and are constant before and after the hump. Economists generally view constant or humped yield curves as uncertain indicators of the future well-being of the economy. • Negatively sloped or inverted yield curves. During periods when financial market participants expect periodic rates of return to decrease, yield curves have been downward sloping or inverted. Some financial economist connect inverted yield curves with pending downturns in the economy or recessions. In support of this connection, an inverted yield curve has indicated a worsening economic situation in the future 7 times since 1970 (Adrian, 2010). See Table 20.1. Summary and Conclusions Previous chapters have treated the multi-period discount rate in PV models (including IRR) as constants. This chapter has emphasized that these constant discount rates are composed of time varying periodic discount rates. Many time-varying factors would prevent periodic discount rates from being constant. Such forces acting on periodic interest rates include monetary and fiscal policies, inflation rates, unemployment rates, and national and international trade and treaties to name a few. So what have we learned? We learned that rate of return expectations built into periodic discount rates and reflected in yield curves of bonds (and interest rates) of varying maturities reflect expected future economic conditions. While there is not universal agreement on how to interpret yield curves, and indeed different yield curves may be subject to varying interpretations, there is support for interpreting downward sloping or inverted yield curves as foreshadowing a slow-down in future economic activities. The goal of this chapter has been to acquaint students with another resource for predicting future opportunities and threats. Table 20.1. The connection between inverted yield curves and future recessions (1970-2009). Event Date of Inversion Start Date of the Recession Start Time from Inversion to Recession Start Duration of Inversion Duration of Recession Months Months Months 1970 Recession Dec-68 Jan-70 13 15 11 1974 Recession Jun-73 Dec-73 6 18 16 1980 Recession Nov-78 Feb-80 15 18 6 1981–1982 Recession Oct-80 Aug-81 10 12 16 1990 Recession Jun-89 Aug-90 14 7 8 2001 Recession Jul-00 1-Apr 9 7 8 Questions 1. Compare geometric means and periodic discount rates. 2. Find the geometric mean of three periodic discount rates equal to . 3. Suppose the geometric mean of two periodic discount rates was 6%, and the periodic discount rate in the second period was 7%. Find the periodic discount rate in the first period. 4. Suppose a one-year zero-coupon bond with a par value of$1,000 was selling for \$962. Find the bond’s yield.
5. Suppose the yield curve was decreasing. Some economics would view this as a sign the economy is slowing down. Do you agree or disagree? Defend your answer.
6. Find data on the yield curve in the economy and discuss what it portends. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/20%3A_Yield_Curves.txt |
Learning Objectives
After completing this chapter, you should be able to: (1) understand that, as humans, our needs include socio-emotional goods as well as those goods that can be purchased with money; and (2) that our needs motivate us to allocate resources to achieve both economic as well as socio-emotional goals.
To achieve your learning goals, you should complete the following objectives:
• Learn the difference between “econs” and “humans”.
• Be reminded of the five distinct motives for pursuing a goal.
• Learn why humans exchange on different terms and levels than econs.
• Learn why humans exchange goods on terms and levels that econs view as irrational.
• Learn the difference between commodities and relational goods.
• Learn how including relational goods in our models explains exchanges that many econs would call irrational.
Introduction
The famous Beatles singing group titled one of their hit songs, “Can’t Buy Me Love.” While coming from an unlikely source of philosophical insight, their song title did proclaim an important truth: money can’t buy love nor most any other goods whose value depends on relationships. So, the purpose of this chapter is to remind us that relationships and the intangible goods produced in relationships may be our most important resources that need careful managing.
Econs versus humans. The behavioral economist Richard Thaler (2008) described two types of decision makers: “econs” and “humans.” Econs, according to Thaler, make decisions like persons described in graduate school economic textbooks. They are perfectly selfish, possess perfect information about the outcome of their choices, and their will power is absolute. Humans, on the other hand, fail to satisfy any of those assumptions. Their choices are influenced by relationships with other humans that lead them to unselfish choices. They lack complete information about the outcomes of their choices and about alternative choices. Finally, they sometimes overeat, drink too much, and also often don’t follow through on their choices.
Motives. A homework question at the end of Chapter 1 asked you what are your motives for wanting a college degree? The list of possible motives are reported below.
• I want a college degree so I can increase my lifetime earnings and get a better job.
• I want a college degree so important people in my life will be pleased with my achievements.
• I want a college degree to live up to the expectations I have for myself.
• I want a college degree so I will feel part of groups to which I want to belong.
• I want a college degree so that, in the future, I will be better able to help others.
An econ would have said that 100% of his or her motive was to increase lifetime earnings. Assuming your responses were not those of an econ, then you undoubtedly make decisions like a human. Your selection of motives can be used to infer that you care about and are motivated by other considerations than your desire to obtain a college degree to increase your potential income. The evidence from past surveys supports the conclusion that we are all human.
Anomalies
One outcome of managers behaving like humans instead of econs is that we observe behavior that is inconsistent with the prediction of profit and net present value (NPV) maximizing behavior associated with econs. One such example occurs regularly in the sale and purchase of farmland. Some of the anomalies we observe in the farmland market include terms and level of trade and selection of trading partners that depend on relationships, unselfish exchanges where sellers sacrifice higher prices for lower ones, and prefer to sell to friends and family rather than strangers and unfriendly neighbors.
To illustrate anomalies in the U.S. farmland markets, consider the minimum sell price of land. Compared to the arm’s length market price, fifteen hundred farmland owner-operators in Illinois, Michigan, and Nebraska were surveyed. They reported discounting farmland prices to friends and family members by 5.57% and 6.78% respectively. These same owner-operators reported that they would require a minimum sell price premium of 18.4% to sell their land to their unfriendly neighbors (Siles, et. al., 2000).
Another farmland market study found that strangers entering the Linn County, Oregon, farmland market were at a decided disadvantage because they were forced to rely on public advertisements and Realtors to gain access to farmland sales information. Friendly neighbors and family of sellers accessed farmland purchase opportunities directly from the sellers. One consequence of this differential information access was that a stranger buying an 80-acre parcel of Class II non-irrigated farmland though a Realtor was projected to pay \$2,535 per acre while a neighbor of the seller buying the same land was projected to pay 20% less (Perry and Robison, 2001).
Finally, as a result of premiums and discounts and preferential access to farmland markets that depend on relationships, farmland sellers reported that less than 2% of their sales were to unfriendly neighbors while up to 70% of land sales were to friendly neighbors and family. Others reported similar observations in which relationships altered the terms and level of farmland trades. Indeed, terms and level of trade and selection of trading partners in farmland exchanges that are not influenced by relationships have a special name, “arm’s length sales.”
How do we explain the regular anomalies we observe in farmland markets? One explanation follows. Econs trade and consume only commodities. Humans trade and consume both commodities and relational goods. When we ignore relational goods in human exchanges and consumption, the results appear as anomalies. Consider next the nature of relational goods.
Commodities and Relational Goods
Expanding the decision maker’s choice set. For the most part, economic theory focuses on physical goods and services that decision makers obtain for themselves and whose values do not depend on their connection to a particular person(s). We call these goods commodities. Describing this focus on commodities, Becchetti, Pelloni and Rossetti (2008) wrote: “in mainstream economics agents are mostly considered in isolation as they impersonally interact through markets, and consumption goods and leisure are assumed to be ‘sufficient statistics’ of their utility.”
Nothing in economic theory, however, prevents us from expanding the set of properties used to describe goods in decision makers’ choice sets. For example, we could add the goods’ relational properties to the description of those goods. Relational properties of goods include the identity of persons who produce, exchange, consume, and store goods in the choice set. Furthermore, this added description of goods could be justified if it were shown that decision makers’ preference ordering depended on the relational properties of goods.
Social scientists in the past have connected a good’s relational properties to its preference orderings (Bruni and Stanca, 2008). Indeed, Adam Smith may have foreshadowed the concept of relational goods when he described fellow-feeling or sympathy as essential for human happiness.
Emphasizing that the identity of exchange partners matters when defining relational goods, Uhlaner (1989) wrote, “goods which arise in exchanges where anyone could anonymously supply one or both sides of the [exchange] are not relational”. Luigino and Stanca (2008) concluded in their review of relational goods that “genuineness” is foundational, and the identity of the other person is essential for the value, and in some cases even for the existence, of the relational good. Gui and Sugden (2005) defined relational goods as “the affective components of interpersonal relations [that] are usually perceived as having value through their sincerity or genuineness”.
Defining relational goods. Relational goods are those goods whose value depends at least in part on their connections to people who produce, exchange, consume, and store them. Three concepts describe relational goods. The flow of relational goods is called socio-emotional goods (SEG). The stock or inventory of relational goods is called attachment value goods (AVG). SEG embedded in persons are said to create investments in social capital (Robison and Flora, 2003). Finally, social capital is required to produce SEG. We describe these, SEG, AVG, and social capital, in more detail in what follows.
SEG are intangible goods that satisfy socio-emotional needs. While there is no universally accepted list of socio-emotional needs that relational goods are expected to satisfy, generally accepted needs include the need for internal validation or self-actualization, the need for external validation, the need for connectedness (belonging, love and friendship), and the need for knowing (Robison, Schmid, and Siles, 2002). SEG differ from other intangible goods and services because they are produced by social capital—sympathy (empathy), regard, or trust that one person has for another person or group.
SEG like other intangible goods can become attached to, associated with, or embedded in durable goods and change the meaning and value of the durable goods they act on. Durable goods embedded with SEG are called attachment value goods (AVG) and represent a stock of SEG. Since SEG and AVG “spring out of interpersonal relationships, and comprise the often intangible, interpersonal side of economic interactions”, they qualify as relational goods (Robison and Ritchie, 2010).
In mainstream economics, the production of commodities employs manufactured capital (tools and implements), natural capital, human capital, and financial capital. All of these contribute to the creation of a good or service valued for its mostly observable physical properties. In contrast, relational goods are produced in sympathetic (empathetic), trusting, and high regard relationships referred to here and by others as social capital. While there are other definitions of social capital, many of these do not satisfy the requirement of being capital or social. Instead they focus on where social capital lives (networks), what it can produce (cooperation), the rules that organize its use (institutions) and how to produce it (Robison, Schmid and Siles, 2002).
Human needs are satisfied by commodities and relational goods. The distinguishing properties of commodities and relational goods are described next.
Distinguishing properties of commodities. The properties that describe commodities have little or no connection to people or relationships among people and are described next. (1) Commodities are exchanged in impersonalized markets. (2) The terms and level at which commodities are exchanged are determined by the aggregate of market participants and apply generally. (3) Commodities are standardized goods of uniform quality which makes them perfect substitutes for each other so that little or no connection exists between their value and those who produce, exchange, consume, and store them. (4) The value of commodities can be inferred from their (mostly) observable properties. (5) Manufactured, natural, human, and financial capital may all play an important role in the production of commodities. (6) The value of commodities can be altered by changing their form, function, location, or other physical properties. (7) Commodities satisfy mostly physical needs and wants. (8) Commodities are mostly nondurable goods not likely to become embedded with SEG because of their short useful lives. (9) Commodities are most likely to have their quantity and quality certified by arm’s length agencies established for that purpose.
Distinguishing properties of relational goods. The properties that describe relational goods are wholly or partially dependent on the good’s connection to people who produce, exchange, consume, and store them and are described next. (1) Relational goods are exchanged in personalized settings in which either the buyer or the seller or both are known to each other. (2) The terms and level of relational goods exchanged are influenced by the social capital inherent in the relationships of those producing, exchanging, consuming, and storing them. (3) Relational goods are poor substitutes for each other because they are produced in unique relational settings. (4) The value of relational goods depend on their mostly unobservable intangible properties. (5) While other forms of capital may be used in their production, relational goods cannot be produced without social capital. (6) The value of relational goods can be altered by changing their connections to people who produce, exchange, consume, or store them. (7) Relational goods satisfy mostly socio-emotional needs and wants. (8) Relational goods are mostly durable goods likely to become embedded with SEG because of their extended useful lives. (9) Relational goods are not likely to have their quantity or quality value certified by arm’s length agencies established for that purpose.
We summarize the differences between commodities and relational goods in Table 21.1.
Table 21.1. Properties of commodities and relational goods.
Property Commodities Relational goods
1. Exchange setting. Impersonal setting in which buyer and seller are not known to each other. Personalized setting in which buyer and seller are connected through a social relationship.
2. How terms and level of exchange are determined. Terms and level of goods exchanged are determined by the aggregate influence of market participants. Terms and level of goods exchanged are uniquely determined by the social capital inherent in the persons engaged in the exchange.
3. Substitutability of goods. Standardized goods with uniform quality which allows one commodity to substitute for another. Unique good with few substitutes because its value is uniquely determined by the social capital involved in its exchange.
4. Value determining properties. Mostly observable, physical properties. Mostly unobservable intangible SEG exchanged directly or embedded in an AVG.
5. Capital used in their production. Manufactured, natural, human, and financial capital may all be important in the production of commodities. While other forms of capital may be used, social capital is required in the production of relational goods.
6. How the value of the good is changed. Value is altered by changing the physical properties of the good including its form, function, location, taste, color, and other physical properties. Value is altered by humanistic acts that produce SEG that may lead to increased investments in social capital or that may become embedded objects creating AVG.
7. Needs satisfied. Mostly physical Mostly socio-emotional including the need for validation, belonging, and knowing.
8. Durability. Mostly nondurable or used infrequently. Mostly durable or if nondurable, used frequently.
9. Certification. Arm’s length agencies empowered with regulatory and inspection duties. Within the relationships associated with the good’s production, consumption, or exchange.
Two setting for exchanging relational goods
There are two types of relational good exchanges. In the first type of exchange, the focus is on the relationships, and goods exchanged are mostly SEG. In the second type of exchange, the focus is on the good exchanged that is almost always an AVG, a tangible thing embedded with SEG.
Exchanges focused on relationships. In relationship focused exchanges, SEG are exchanged directly between persons in social capital rich relationships and require no object besides the persons involved in the exchange to complete the transaction. For example, two persons with strong feelings of affection for each other may express those feelings, SEG, in any number of settings including meals, cultural events, conferences, religious gatherings, or work settings. And if there is an object exchanged, it is incidental to the exchange of SEG.
Exchanges focused on objects. In object focused exchanges, AVG are exchanged, things or objects embedded with SEG. AVG result from prior or anticipated connections between social capital rich persons in which SEG are produced and embedded in objects. AVG are most likely a durable. However, AVG may sometimes be non durables that are often exchanged repeatedly such as a meal prepared to celebrate special occasion or a song or dance performed to mark milestones.
Anomalies and Isoutilities
At the beginning of this chapter, we claimed that econs and humans made decisions differently. Sometimes these differences are called anomalies. Furthermore, because many human decisions differ from econ choices, human choices are sometimes called irrational. The claim here is that human choices can appear irrational because relational goods are excluded from the analysis.
To illustrate how including relational goods in exchanges can resolve important economic anomalies, consider the following example. Suppose a seller has the option of exchanging his farmland with a stranger for a commodity (the market price) or exchanging his farmland with a friend or family member for a combination of commodities and relational goods. If the seller prefers the combination of relational goods and commodities offered by friends and family members to the commodities only offered by a stranger even though the commodities offered by the stranger exceed those offered by friends and family members, we might consider that an economic exchange anomaly has occurred. The seller accepted a lower commodity price from a friend or family member when a higher commodity price was available from a stranger. This is only an anomaly if the relational goods included in the exchange are ignored.
To explain further how including relational goods in exchanges can resolve anomalies, we consider the concept of an isoutility line. Suppose that a decision maker is offered alternative combinations of two goods, a commodity and a relational good. Furthermore, allow that the amounts of the commodity and relational good can be exchanged at some rate that leaves the well-being of the decision maker unaffected. The combinations of relational goods and commodities that leave the decision maker’s well-being unaltered are referred to isoutility combinations and are represented in Figure 21.1 as PbuyerPbuyer. Curve PsellerPseller represents the seller’s isoutility combinations of relational goods and commodity prices.
Figure 21.1. Combinations of Commodity Prices and Relational Goods that Leave Buyers’ and Sellers’ Well-Being Unchanged.
The implication of the graph in Figure 21.1 is that as more of a relational good is received, the seller (buyer) would be willing to accept (offer) a lower (higher) commodity price without suffering a loss in well-being. Furthermore, as relational goods are included in the transaction, the range of commodity prices acceptable to both buyers and sellers increases which also increases the likelihood that persons rich in social capital will exchange. For example, in Figure 21.1 persons without social capital would not trade since, with no relational goods exchanged, the minimum sell price is above the maximum bid price.
In one of the first studies designed to test the influence of relationships on terms and level of exchange, Robison and Schmid (1989) asked faculty and graduate students what would be their minimum sell price of a used car to people who offered them various levels of social capital. Since the Robison and Schmid article was published, the essence of the study has been repeated multiple times with similar results. A recent unpublished survey by Richard Winder found the results reported in Table 21.2. The mode of the distributions of responses by relationship are in bold.
Table 21.2. Average minimum sell price for a used car with a market value of \$3,000 reported by 600 survey respondents.
Nasty neighbor Stranger Friend Family
> \$3,500 65
\$3,500 263 39 2
\$3,250 21 33 5 1
\$3,000 236 476 122 29
\$2,750 11 30 135 24
\$2,500 4 22 298 199
< \$2,500 38 348
Notice that in the absence of social capital (exchanges with a stranger), the distribution of minimum sell prices centers around the commodity exchange price of \$3,000. However, when the exchange is conducted with a social capital rich partner such as a friend or family member, the minimum sell price is significantly below the market price with a mode of \$2,500 for a friend and a mode price below \$2,500 for a family member.
Summary and Conclusions
The material covered in this book is intended to provide instructions about how to behave like an econ. We hope you don’t always follow our advice. There are times and places and circumstances when commodity considerations should be softened by social capital and the importance of relational goods. Learning how to make the appropriate trade-offs between commodities and investments in social capital and relational goods, when to behave like an econ versus a human, may be our most important management task. Good luck.
Questions
By 2013 Bill and Melinda Gates had donated 38 billion dollars to various charities and especially to fight hunger in Africa. They have donated billions more to these causes since. If Bill and Melinda Gates were to have taken the same survey you took at the beginning of the class where “I want a college degree” is replaced with “We donated billions of dollars…”, how do you think they would have answered? To better speak for them, read a brief interview of Bill Gates by Neil Tweedie at: http://www.telegraph.co.uk/technolog...Gods-work.html. Now answer the survey that follows as though you were channeling either Bill or Melinda Gates by writing the relative importance of each motive using percentages in the blank besides each motive. The sum of the motives must equal 100%.
• We have donated billions of dollars so that we could increase our lifetime earnings and get a better job.
• We have donated billions of dollars so that important people in our lives would be pleased with our achievements.
• We have donated billions of dollars to live up to the expectations we have for ourselves.
• We have donated billions of dollars so we will feel part of different groups to which we want to belong.
• We have donated billions of dollars to help others.
Consider a hypothetical gas purchase.
You gas tank holds 15 gallons and is nearly empty. You normally fill up your car with gas at a station on your way home. How many additional miles would you drive to fill up your car with gas if you could save 10 cents per gallon? I would drive an additional ____ miles to save 10 cents per gallon.
You gas tank holds 15 gallons and is nearly empty. You normally fill up your car with gas at a station on your way home. How many additional miles would you drive to fill up your car with gas at a gas station owned and operated by your favorite uncle? I would drive an additional ____ miles to purchase gas at a gas station owned and operated by my favorite uncle.
If your answer to parts a) and b) were different from zero, can you explain why?
Summarize the difference between relational goods and commodities as discussed in this chapter. Please list two commodities and two relational goods that you own.
An isoutility line describes different combinations of two different goods that provide equal satisfaction. Use the concept of isoutility to explain why you might sell your used car at different prices to a friend, a stranger, a family, member, and someone you disrespect.
Commodities are sold in the market place, and their prices are determined by anonymous market forces. The terms of trade of relational goods depend on the relationship between persons exchanging them. Give an example in which you have exchanged relational goods in which relationships altered the terms and level of trade. Then give another example in which you have exchanged commodities in which relationships had no influence on the terms and level of trade.
One could donate one’s blood or blood plasma at a local Red Cross and receive in return a small amount of juice served in a paper cup and possibly a cookie. One could also sell one’s blood at a number of places (the current price is \$25 to \$60 per bag). Since some people sell their blood for money and others donate it for free, explain the difference in the way these two groups of people dispose of their blood.
Suppose you needed a medical procedure that required a skilled physician. Assume that a number of equally skilled physicians were available to perform the procedure. Would your choice of a physician to perform the procedure depend on your relationship to the physician? If he were a family friend? If he were a stranger? If you knew the physician only by reputation—that he performed volunteer work in developing countries? If he was rude to his/her patients, inconsiderate to his/her assistants, and lived a lavish life style? For each of the physicians, answer the questions that follow using the scale included in each question:
If the physician were skilled and a family friend, the likelihood I would select this physician to perform my procedure is:
Not likely 1 3 5 7 Very likely (circle one)
If the physician were skilled and a stranger, the likelihood I would select this physician to perform my procedure is:
Not likely 1 3 5 7 Very likely (circle one)
If the physician were skilled and someone I knew only by reputation—that he performed volunteer work in developing countries, the likelihood I would select this physician to perform my procedure is:
Not likely 1 3 5 7 Very likely (circle one)
If the physician were skilled and someone I knew only by reputation—that he was rude to his/her patients, impatient with his assistants, and lived a lavish lifestyle, the likelihood I would select this physician to perform my procedure is:
Not likely 1 3 5 7 Very likely (circle one)
If you were equally likely to select one of the physicians described in question 7, explain why. If you were not equally likely to select one of the physicians described above, explain why. | textbooks/biz/Finance/Book%3A_Financial_Management_for_Small_Businesses__Financial_Statements_and_Present_Value_Models_(Robinson_et_al)/21%3A_One_Thing_More.txt |
Economics is a social science whose purpose is to understand the workings of the real-world economy. An economy is something that no one person can observe in its entirety. We are all a part of the economy, we all buy and sell things daily, but we cannot observe all parts and aspects of an economy at any one time.
For this reason, economists build mathematical models, or theories, meant to describe different aspects of the real world. For some students, economics seems to be all about these models and theories, these abstract equations and diagrams. However, in actuality, economics is about the real world, the world we all live in.
For this reason, it is important in any economics course to describe the conditions in the real world before diving into the theory intended to explain them. In this case, in a textbook about international finance, it is very useful for a student to know some of the values of important macroeconomic variables, the trends in these variables over time, and the policy issues and controversies surrounding them.
This first chapter provides an overview of the real world with respect to international finance. It explains not only how things look now but also where we have been and why things changed along the way. It describes current economic conditions and past trends with respect to the most critical international macroeconomic indicators. In particular, it compares the most recent worldwide economic recession with past business cycle activity to put our current situation into perspective. The chapter also discusses important institutions and explains why they have been created.
With this overview about international finance in the real world in mind, a student can better understand why the theories and models in the later chapters are being developed. This chapter lays the groundwork for everything else that follows.
01: Introductory Finance Issues- Current Patterns Past History and International Institutions
Learning objectives
1. Learn past trends in international trade and foreign investment.
2. Learn the distinction between international trade and international finance.
International economics is growing in importance as a field of study because of the rapid integration of international economic markets. Increasingly, businesses, consumers, and governments realize that their lives are affected not only by what goes on in their own town, state, or country but also by what is happening around the world. Consumers can walk into their local shops today and buy goods and services from all over the world. Local businesses must compete with these foreign products. However, many of these same businesses also have new opportunities to expand their markets by selling to a multitude of consumers in other countries. The advance of telecommunications is also rapidly reducing the cost of providing services internationally, while the Internet will assuredly change the nature of many products and services as it expands markets even further.
One simple way to see the rising importance of international economics is to look at the growth of exports in the world during the past fifty or more years. Figure 1.1 shows the overall annual exports measured in billions of U.S. dollars from 1948 to 2008. Recognizing that one country’s exports are another country’s imports, one can see the exponential growth in outflows and inflows during the past fifty years.
Source: World Trade Organization, International trade and tariff data, http://www.wto.org/english/res_e/statis_e/statis_e.htm.
However, rapid growth in the value of exports does not necessarily indicate that trade is becoming more important. A better method is to look at the share of traded goods in relation to the size of the world economy. Figure 1.2 shows world exports as a percentage of the world gross domestic product (GDP) for the years 1970 to 2008. It shows a steady increase in trade as a share of the size of the world economy. World exports grew from just over 10 percent of the GDP in 1970 to over 30 percent by 2008. Thus trade is not only rising rapidly in absolute terms; it is becoming relatively more important too.
Source: IMF World Economic Outlook Database, http://www.imf.org/external/pubs/ft/weo/2009/02/weodata/index.aspx.
One other indicator of world interconnectedness can be seen in changes in the amount of foreign direct investment (FDI). FDI is foreign ownership of productive activities and thus is another way in which foreign economic influence can affect a country. Figure 1.3 shows the stock, or the sum total value, of FDI around the world taken as a percentage of the world GDP between 1980 and 2007. It gives an indication of the importance of foreign ownership and influence around the world. As can be seen, the share of FDI has grown dramatically from around 5 percent of the world GDP in 1980 to over 25 percent of the GDP just twenty-five years later.
Source: IMF World Economic Outlook Database, http://www.imf.org/external/pubs/ft/weo/2009/02/weodata/index.aspx; UNCTAD, FDI Statistics: Division on Investment and Enterprise, www.unctad.org/Templates/Page.asp?intItemID=4979&lang=1.
The growth of international trade and investment has been stimulated partly by the steady decline of trade barriers since the Great Depression of the 1930s. In the post–World War II era, the General Agreement on Tariffs and Trade, or GATT, prompted regular negotiations among a growing body of members to reciprocally reduce tariffs (import taxes) on imported goods. During each of these regular negotiations (eight of these rounds were completed between 1948 and 1994), countries promised to reduce their tariffs on imports in exchange for concessions—that means tariff reductions—by other GATT members. When the Uruguay Round, the most recently completed round, was finalized in 1994, the member countries succeeded in extending the agreement to include liberalization promises in a much larger sphere of influence. Now countries not only would lower tariffs on goods trade but also would begin to liberalize the agriculture and services markets. They would eliminate the many quota systems—like the multifiber agreement in clothing—that had sprouted up in previous decades. And they would agree to adhere to certain minimum standards to protect intellectual property rights such as patents, trademarks, and copyrights. The World Trade Organization (WTO) was created to manage this system of new agreements, to provide a forum for regular discussion of trade matters, and to implement a well-defined process for settling trade disputes that might arise among countries.
As of 2009, 153 countries were members of the WTO “trade liberalization club,” and many more countries were still negotiating entry. As the club grows to include more members—and if the latest round of trade liberalization talks, called the Doha Round, concludes with an agreement—world markets will become increasingly open to trade and investment.Note that the Doha Round of discussions was begun in 2001 and remains uncompleted as of 2009.
Another international push for trade liberalization has come in the form of regional free trade agreements. Over two hundred regional trade agreements around the world have been notified, or announced, to the WTO. Many countries have negotiated these agreements with neighboring countries or major trading partners to promote even faster trade liberalization. In part, these have arisen because of the slow, plodding pace of liberalization under the GATT/WTO. In part, the regional trade agreements have occurred because countries have wished to promote interdependence and connectedness with important economic or strategic trade partners. In any case, the phenomenon serves to open international markets even further than achieved in the WTO.
These changes in economic patterns and the trend toward ever-increasing openness are an important aspect of the more exhaustive phenomenon known as globalization. Globalization more formally refers to the economic, social, cultural, or environmental changes that tend to interconnect peoples around the world. Since the economic aspects of globalization are certainly the most pervasive of these changes, it is increasingly important to understand the implications of a global marketplace on consumers, businesses, and governments. That is where the study of international economics begins.
What Is International Economics?
International economics is a field of study that assesses the implications of international trade, international investment, and international borrowing and lending. There are two broad subfields within the discipline: international trade and international finance.
International trade is a field in economics that applies microeconomic models to help understand the international economy. Its content includes basic supply-and-demand analysis of international markets; firm and consumer behavior; perfectly competitive, oligopolistic, and monopolistic market structures; and the effects of market distortions. The typical course describes economic relationships among consumers, firms, factory owners, and the government.
The objective of an international trade course is to understand the effects of international trade on individuals and businesses and the effects of changes in trade policies and other economic conditions. The course develops arguments that support a free trade policy as well as arguments that support various types of protectionist policies. By the end of the course, students should better understand the centuries-old controversy between free trade and protectionism.
International finance applies macroeconomic models to help understand the international economy. Its focus is on the interrelationships among aggregate economic variables such as GDP, unemployment rates, inflation rates, trade balances, exchange rates, interest rates, and so on. This field expands basic macroeconomics to include international exchanges. Its focus is on the significance of trade imbalances, the determinants of exchange rates, and the aggregate effects of government monetary and fiscal policies. The pros and cons of fixed versus floating exchange rate systems are among the important issues addressed.
This international trade textbook begins in this chapter by discussing current and past issues and controversies relating to microeconomic trends and policies. We will highlight past trends both in implementing policies that restrict trade and in forging agreements to reduce trade barriers. It is these real-world issues that make the theory of international trade worth studying.
Key Takeaways
• International trade and investment flows have grown dramatically and consistently during the past half century.
• International trade is a field in economics that applies microeconomic models to help understand the international economy.
• International finance focuses on the interrelationships among aggregate economic variables such as GDP, unemployment, inflation, trade balances, exchange rates, and so on.
exerCise
1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
• The approximate share of world exports as a percentage of world GDP in 2008.
• The approximate share of world foreign direct investment as a percentage of world GDP in 1980.
• The number of countries that were members of the WTO in 2009.
• This branch of international economics applies microeconomic models to understand the international economy.
• This branch of international economics applies macroeconomic models to understand the international economy. | textbooks/biz/Finance/Book%3A_International_Finance__Theory_and_Policy/01%3A_Introductory_Finance_Issues-_Current_Patterns_Past_History_and_International_Institutions/1.01%3A_The_International_Economy_and_International_Economics.txt |
Learning Objective
1. Learn current values for several important macroeconomic indicators from a selected set of countries, including GDP, GDP per capita, unemployment rates, inflation rates, national budget balances, and national debts.
When someone reads the business and economics news it is common to see numerous values and figures used to describe the economic situation somewhere. For example, if you read a story about the Philippines you might read that the gross domestic product (GDP) is \$167 billion or that the GDP per person is \$3,500 per person, or that its unemployment rate is 7.1 percent and its inflation rate is now 2.8 percent. You might read that it has a government budget deficit of 3.7 percent of the GDP and a trade deficit of 5.2 percent of the GDP. But what does this all mean? How is someone supposed to interpret and understand whether the numbers indicate something good, bad, or neutral about the country?
One way to make judgments is to compare these numbers with other countries. To this end, the next few sections will present some recent data for a selected set of countries. Although memorizing these numbers is not so important, especially since they will all soon change, it is helpful to have an idea about what the values are for a few countries; or if not that, to know the approximate normal average for a particular variable. Thus it is useful to know that GDP per person ranges from about \$500 per year at the low end to about \$50,000 to \$75,000 per person at the high end. It is also useful to know that unemployment rates are normally less than 10 percent. So when you read that Zimbabwe recently had unemployment of 75 percent, a reader will know how unusually large that is. Once you also recognize that inflation rates are normally less than 10 percent, a rate of 10,000 percent will strike you as extraordinary.
Thus the values for some of these numbers will be helpful to make comparisons across countries today and to make comparisons over time for a particular country. Therefore, it can be very helpful to know the numbers for at least a few countries, or what may be deemed a set of reference countries. The countries in Table 1.1 were selected to provide a cross section of countries at different levels of economic development. Thus the United States, the European Union, and Japan represent the largest economies in the world today. Meanwhile, countries like Brazil, Russia, India, and China are watched so closely today that they have acquired their own acronym: the BRIC countries. Finally, countries like Indonesia, Kenya, Ghana, and Burundi are among the poorest nations of the world. Note that in later tables other countries were substituted for the African countries because data are less difficult to obtain.
Gross Domestic Product around the World
Macroeconomics is the study of the interrelationships of aggregate economic variables. The most important of these, without question, is a country’s gross domestic product (GDP). GDP measures the total value of all goods and services produced by a country during a year. As such, it is a measure of the extent of economic activity in a country or the economic size of a country.
And because the consumption of goods and services is one way to measure an individual’s economic well-being, it is easy to calculate the GDP per capita (i.e., per person) to indicate the average well-being of individuals in a country.
Details about how to measure and interpret GDP follow in subsequent chapters, but before doing so, it makes some sense to know a little about how economy size and GDP per person vary across countries around the world. Which are the biggest countries, and which are the smallest? Which countries provide more goods and services, on average, and which produce less? And how wide are the differences between countries? Table 1.1 provides recent information for a selected group of countries. Note that reported numbers are based on purchasing power parity (PPP), which is a better way to make cross-country comparisons and is explained later. A convenient source of the most recent comprehensive data from three sources (the International Monetary Fund [IMF], the World Bank, and the U.S. CIA) of GDP (http://en.Wikipedia.org/wiki/List_of_countries_by_GDP_%28PPP%29) and GDP per person (http://en.Wikipedia.org/wiki/List_of_countries_by_GDP_%28PPP%29_per_capita) is available at Wikipedia.
Country/Region (Rank) GDP (Percentage in the World) GDP per Capita (Rank)
World 68,997 (100) 10,433
European Union (1) 15,247 (22.1)
United States (2) 14,265 (20.7) 47,440 (6)
China (3) 7,916 (11.5) 5,970 (100)
Japan (4) 4,354 (6.3) 34,116 (24)
India (5) 3,288 (4.8) 2,780 (130)
Russia (7) 2,260 (3.3) 15,948 (52)
Brazil (10) 1,981 (2.9) 10,466 (77)
South Korea (14) 1,342 (1.9) 27,692 (33)
Indonesia (17) 908 (1.3) 3,980 (121)
Kenya (82) 60 (nil) 1,712 (148)
Ghana (96) 34 (nil) 1,518 (152)
Burundi (158) 3 (nil) 390 (178)
Figure \(1\): Table 1.1 GDP and GDP per Capita (PPP in Billions of Dollars), 2009
Table 1.1 displays several things that are worth knowing. First, note that the United States and European Union each make up about one-fifth of the world economy; together the two are 42 percent. Throw Japan into the mix with the European Union and the United States and together they make up less than one-sixth of the world’s population. However, these three developed nations produce almost one-half of the total world production. This is a testament to the high productivity in the developed regions of the world. It is also a testament to the low productivity in much of the rest of the world, where it takes another five billion people to produce the remaining half of the GDP.
The second thing worth recognizing is the wide dispersion of GDPs per capita across countries. The United States ranks sixth in the world at \$47,440 and is surpassed by several small countries like Singapore and Luxembourg and/or those with substantial oil and gas resources such as Brunei, Norway, and Qatar (not shown in Table 1.1). Average GDP per capita in the world is just over \$10,000, and it is just as remarkable how far above the average some countries like the United States, Japan, and South Korea are as it is how far below the average other countries like China, India, Indonesia, and Kenya are. Perhaps most distressing is the situation of some countries like Burundi that has a GDP of only \$370 per person. (Other countries in a similar situation include Zimbabwe, Congo, Liberia, Sierra Leone, Niger, and Afghanistan.)
Unemployment and Inflation around the World
Two other key macroeconomic variables that are used as an indicator of the health of a national economy are the unemployment rate and the inflation rate. The unemployment rate measures the percentage of the working population in a country who would like to be working but are currently unemployed. The lower the rate, the healthier the economy and vice versa. The inflation rate measures the annual rate of increase of the consumer price index (CPI). The CPI is a ratio that measures how much a set of goods costs this period relative to the cost of the same set of goods in some initial year. Thus if the CPI registers 107, it would cost \$107 (euros or whatever is the national currency) to buy the goods today, while it would have cost just \$100 to purchase the same goods in the initial period. This represents a 7 percent increase in average prices over the period, and if that period were a year, it would correspond to the annual inflation rate. In general, a relatively moderate inflation rate (about 0–4 percent) is deemed acceptable; however, if inflation is too high it usually contributes to a less effective functioning of an economy. Also, if inflation is negative, it is called deflation, and that can also contribute to an economic slowdown.
Country/Region Unemployment Rate (%) Inflation Rate (%)
European Union 9.8 (Oct. 2009) +0.5 (Nov. 2009)
United States 10.0 (Nov. 2009) +1.8 (Nov. 2009)
China 9.2 (2008) +0.6 (Nov. 2009)
Japan 5.1 (Oct. 2009) −2.5 (Oct. 2009)
India 9.1 (2008) +11.5 (Oct. 2009)
Russia 7.7 (Oct. 2009) +9.1 (Nov. 2009)
Brazil 7.5 (Oct. 2009) +4.2 (Nov. 2009)
South Korea 3.5 (Nov. 2009) +2.4 (Nov. 2009)
Indonesia 8.1 (Feb. 2009) +2.4 (Oct. 2009)
Spain 19.3 (Oct. 2009) +0.3 (Nov. 2009)
South Africa 24.5 (Sep. 2009) +5.8 (Nov. 2009)
Estonia 15.2 (Jul. 2009) −2.1 (Nov. 2009)
Figure \(2\): Table 1.2 Unemployment and Inflation Rates
Source: Economist, Weekly Indicators, December 17, 2009.
The unemployment rates and inflation rates in most countries are unusual in the reported period because of the economic crisis that hit the world in 2008. The immediate effect of the crisis was a drop in demand for many goods and services, a contraction in GDP, and the loss of jobs for workers in many industries. In addition, prices were either stable or fell in many instances. When most economies of the world were booming several years earlier, a normal unemployment rate would have been 3 to 5 percent, while a normal inflation rate would stand at about 3 to 6 percent.
As Table 1.2 shows, though, unemployment rates in most countries in 2009 are much higher than that, while inflation rates tend to be lower with several exceptions. In the United States, the unemployment rate has more than doubled, but in the European Union, unemployment was at a higher rate than the United States before the crisis hit, and so it has not risen quite as much. Several standouts in unemployment are Spain and South Africa. These are exceedingly high rates coming very close to the United States unemployment rate of 25 percent reached during the Great Depression in 1933.
India’s inflation rate is the highest of the group listed but is not much different from inflation in India the year before of 10.4 percent. Russia’s inflation this year has actually fallen from its rate last year of 13.2 percent. Japan and Estonia, two countries in the list, are reporting deflation this year. Japan had inflation of 1.7 percent in the previous year, whereas Estonia’s rate had been 8 percent.
Government Budget Balances around the World
Another factor that is often considered in assessing the health of an economy is the state of the country’s government budget. Governments collect tax revenue from individuals and businesses and use that money to finance the purchase of government provided goods and services. Some of the spending is on public goods such as national defense, health care, and police and fire protection. The government also transfers money from those better able to pay to others who are disadvantaged, such as welfare recipients or the elderly under social insurance programs.
Generally, if government were to collect more in tax revenue than it spent on programs and transfers, then it would be running a government budget surplus and there would be little cause for concern. However, many governments oftentimes tend to spend and transfer more than they collect in tax revenue. In this case, they run a government budget deficit that needs to be paid for or financed in some manner. There are two ways to cover a budget deficit. First, the government can issue Treasury bills and bonds and thus borrow money from the private market; second, the government can sometimes print additional money. If borrowing occurs, the funds become unavailable to finance private investment or consumption, and thus the situation represents a substitution of public spending for private spending. Borrowed funds must also be paid back with accrued interest, which implies that larger future taxes will have to be collected assuming that budget balance or a surplus is eventually achieved.
When governments borrow, they will issue Treasury bonds with varying maturities. Thus some will be paid back in one of two years, but others perhaps not for thirty years. In the meantime, the total outstanding balance of IOUs (i.e., I owe you) that the government must pay back in the future is called the national debt. This debt is owed to whoever has purchased the Treasury bonds; for many countries, a substantial amount is purchased by domestic citizens, meaning that the country borrows from itself and thus must pay back its own citizens in the future. The national debt is often confused with a nation’s international indebtedness to the rest of the world, which is known as its international investment position (defined in the next section).
Excessive borrowing by a government can cause economic difficulties. Sometimes private lenders worry that the government may become insolvent (i.e., unable to repay its debts) in the future. In this case, creditors may demand a higher interest rate to compensate for the higher perceived risk. To prevent that risk, governments sometimes revert to the printing of money to reduce borrowing needs. However, excessive money expansion is invariably inflationary and can cause long-term damage to the economy.
In Table 1.3, we present budget balances for a selected set of countries. Each is shown as a percentage of GDP, which gives a more accurate portrayal of the relative size. Although there is no absolute number above which a budget deficit or a national debt is unsustainable, budget deficits greater than 5 percent per year, those that are persistent over a long period, or a national debt greater than 50 percent of GDP tends to raise concerns among investors.
Country/Region Budget Balance (%) National Debt (%)
European Union −6.5
United States −11.9 37.5
China −3.4 15.6
Japan −7.7 172.1
India −8.0 56.4
Russia −8.0 6.5
Brazil −3.2 38.8
South Korea −4.5 24.4
Indonesia −2.6 29.3
Spain −10.8 40.7
South Africa −5.0 31.6
Estonia −4.0 4.8
Figure \(3\): Table 1.3 Budget Balance and National Debt (Percentage of GDP), 2009
Source: Economist, Weekly Indicators, December 17, 2009, and the CIA World Factbook.
Note that all the budget balances for this selected set of countries are in deficit. For many countries, the deficits are very large, exceeding 10 percent in the U.S. and Spain. Although deficits for most countries are common, usually they are below 5 percent of the GDP. The reason for the higher deficits now is because most countries have increased their government spending to counteract the economic recession, while at the same time suffering a reduction in tax revenues also because of the recession. Thus budget deficits have ballooned around the world, though to differing degrees.
As budget deficits rise and as GDP falls due to the recession, national debts as a percent of GDP are also on the rise in most countries. In the United States, the national debt is still at a modest 37.5 percent, but recent projections suggest that in a few years it may quickly rise to 60 percent or 70 percent of the GDP. Note also that these figures subtract any debt issued by the government and purchased by another branch of the government. For example, in the United States for the past decade or more, the Social Security system has collected more in payroll taxes than it pays out in benefits. The surplus, known as the Social Security “trust fund,” is good because in the next few decades as the baby boom generation retires, the numbers of Social Security recipients is expected to balloon. But for now the surplus is used to purchase government Treasury bonds. In other words, the Social Security administration lends money to the rest of the government. Those loans currently sum to about 30 percent of GDP or somewhat over \$4 trillion. If we include these loans as a part of the national debt, the United States debt is now, according to the online national debt clock, more than \$12 trillion or about 85 percent of GDP. (This is larger than 37.5 + 30 percent because the debt clock is an estimate of more recent figures and reflects the extremely large government budget deficit run in the previous year.)
Most other countries’ debts are on a par with that of the U.S. with two notable exceptions. First, China and Russia’s debts are fairly modest at only 15.6 percent and 6.5 percent of GDP, respectively. Second, Japan’s national debt is an astounding 172 percent of GDP. It has arisen because the Japanese government has tried to extricate its economy from an economic funk by spending and borrowing over the past two decades.
Key Takeaways
• GDP and GDP per capita are two of the most widely tracked indicators of both the size of national economies and an economy’s capacity to provide for its citizens.
• In general, we consider an economy more successful if its GDP per capita is high, unemployment rate is low (3–5 percent), inflation rate is low and nonnegative (0–6 percent), government budget deficit is low (less than 5 percent of GDP) or in surplus, and its national debt is low (less than 25 percent).
• The United States, as the largest national economy in the world, is a good reference point for comparing macroeconomic data.
• The U.S. GDP in 2008 stood at just over \$14 trillion while per capita GDP stood at \$47,000. U.S. GDP made up just over 20 percent of world GDP in 2008.
• The U.S. unemployment rate was unusually high at 10 percent in November 2009 while its inflation rate was very low at 1.8 percent.
• The U.S. government budget deficit was at an unusually high level of 11.9 percent of GDP in 2009 while its international indebtedness made it a debtor nation in the amount of 37 percent of its GDP.
• Several noteworthy statistics are presented in this section:
• Average world GDP per person stands at around \$10,000 per person.
• The GDP in the U.S. and most developed countries rises as high as \$50,000 per person.
• The GDP in the poorest countries like Kenya, Ghana, and Burundi is less than \$2,000 per person per year.
• U.S. unemployment has risen to a very high level of 10 percent; however, in Spain it sits over 19 percent, while in South Africa it is over 24 percent.
• Inflation is relatively low in most countries but stands at over 9 percent in Russia and over 11 percent in India. In several countries like Japan and Estonia, deflation is occurring.
• Due to the world recession, budget deficits have grown larger in most countries, reaching almost 12 percent of GDP in the United States.
• The national debts of countries are also growing larger, and Japan’s has grown to over 170 percent of GDP.
Exercises
1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
• The approximate value of world GDP in 2008.
• The approximate value of EU GDP in 2008.
• The approximate value of U.S. GDP in 2008.
• The approximate value of world GDP per capita in 2008.
• The approximate value of EU GDP per capita in 2008.
• The approximate value of U.S. GDP per capita in 2008.
• The approximate value of South Africa’s unemployment rate in 2009.
• The approximate value of India’s inflation rate in 2009.
• The approximate value of the U.S. budget balance as a percentage of its GDP in 2009.
• The approximate value of Japan’s national debt as a percentage of its GDP in 2009.
1. Use the information in Table 1.1 and Table 1.3 to calculate the dollar values of the government budget balance and the national debt for Japan, China, Russia, South Korea, and Indonesia. | textbooks/biz/Finance/Book%3A_International_Finance__Theory_and_Policy/01%3A_Introductory_Finance_Issues-_Current_Patterns_Past_History_and_International_Institutions/1.02%3A_GDP_Unemployment_Inflation_and_Government_Budget_Balances.txt |
Learning Objective
1. Learn current values for several important international macroeconomic indicators from a selected set of countries, including the trade balance, the international investment position, and exchange rate systems.
Countries interact with each other in two important ways: trade and investment. Trade encompasses the export and import of goods and services. Investment involves the borrowing and lending of money and the foreign ownership of property and stock within a country. The most important international macroeconomic variables, then, are the trade balance, which measures the difference between the total value of exports and the total value of imports, and the exchange rate, which measures the number of units of one currency that exchanges for one unit of another currency.
Exchange Rate Regimes
Because countries use different national currencies, international trade and investment requires an exchange of currency. To buy something in another country, one must first exchange one’s national currency for another. Governments must decide not only how to issue its currency but how international transactions will be conducted. For example, under a traditional gold standard, a country sets a price for gold (say \$20 per ounce) and then issues currency such that the amount in circulation is equivalent to the value of gold held in reserve. In this way, money is “backed” by gold because individuals are allowed to convert currency to gold on demand.
Today’s currencies are not backed by gold; instead most countries have a central bank that issues an amount of currency that will be adequate to maintain a vibrant growing economy with low inflation and low unemployment. A central bank’s ability to achieve these goals is often limited, especially in turbulent economic times, and this makes monetary policy contentious in most countries.
One of the decisions a country must make with respect to its currency is whether to fix its exchange value and try to maintain it for an extended period, or whether to allow its value to float or fluctuate according to market conditions. Throughout history, fixed exchange rates have been the norm, especially because of the long period that countries maintained a gold standard (with currency fixed to gold) and because of the fixed exchange rate system (called the Bretton Woods system) after World War II. However, since 1973, when the Bretton Woods system collapsed, countries have pursued a variety of different exchange rate mechanisms.
The International Monetary Fund (IMF), created to monitor and assist countries with international payments problems, maintains a list of country currency regimes. The list displays a wide variety of systems currently being used. The continuing existence of so much variety demonstrates that the key question, “Which is the most suitable currency system?” remains largely unanswered. Different countries have chosen differently. Later, this course will explain what is necessary to maintain a fixed exchange rate or floating exchange rate system and what are some of the pros and cons of each regime. For now, though, it is useful to recognize the varieties of regimes around the world.
Figure \(1\): Table 1.4 Exchange Rate Regimes. Source: International Monetary Fund, De Facto Classification of Exchange Rate Regimes and Monetary Policy Framework, 2008.
Country/Region Regime
Euro Area Single currency within: floating externally
United States Float
China Crawling peg
Japan Float
India Managed float
Russia Fixed to composite
Brazil Float
South Korea Float
Indonesia Managed float
Spain Euro zone; fixed in the European Union; float externally
South Africa Float
Estonia Currency board
Table 1.4 shows the selected set of countries followed by a currency regime. Notice that many currencies—including the U.S. dollar, the Japanese yen, the Brazilian real, the South Korean won, and the South African rand—are independently floating, meaning that their exchange values are determined in the private market on the basis of supply and demand. Because supply and demand for currencies fluctuate over time, so do the exchange values, which is why the system is called floating.
Note that India and Indonesia are classified as “managed floating.” This means that the countries’ central banks will sometimes allow the currency to float freely, but at other times will nudge the exchange rate in one direction or another.
China is listed and maintaining a crawling peg, which means that the currency is essentially fixed except that the Chinese central bank is allowing its currency to appreciate slowly with respect to the U.S. dollar. In other words, the fixed rate itself is gradually but unpredictably adjusted.
Estonia is listed as having a currency board. This is a method of maintaining a fixed exchange rate by essentially eliminating the central bank in favor of a currency board that is mandated by law to follow procedures that will automatically keep its currency fixed in value.
Russia is listed as fixing to a composite currency. This means that instead of fixing to one other currency, such as the U.S. dollar or the euro, Russia fixes to a basket of currencies, also called a composite currency. The most common currency basket to fix to is the Special Drawing Rights (SDR), a composite currency issued by the IMF used for central bank transactions.
Finally, sixteen countries in the European Union are currently members of the euro area. Within this area, the countries have retired their own national currencies in favor of using a single currency, the euro. When all countries circulate the same currency, it is the ultimate in fixity, meaning they have fixed exchange rates among themselves because there is no need to exchange. However, with respect to other external currencies, like the U.S. dollar or the Japanese yen, the euro is allowed to float freely.
Trade Balances and International Investment Positions
One of the most widely monitored international statistics is a country’s trade balance. If the value of total exports from a country exceeds total imports, we say a country has a trade surplus. However, if total imports exceed total exports, then the country has a trade deficit. Of course, if exports equal imports, then the country has balanced trade.
The terminology is unfortunate because it conveys a negative connotation to trade deficits, a positive connotation to trade surpluses, and perhaps an ideal connotation to trade balance. Later in the text, we will explain if or when these connotations are accurate and when they are inaccurate. Suffice it to say, for now, that sometimes trade deficits can be positive, trade surpluses can be negative, and trade balance could be immaterial.
Regardless, it is popular to decry large deficits as being a sign of danger for an economy, to hail large surpluses as a sign of strength and dominance, and to long for the fairness and justice that would arise if only the country could achieve balanced trade. What could be helpful at an early stage, before delving into the arguments and explanations, is to know how large the countries’ trade deficits and surpluses are. A list of trade balances as a percentage of GDP for a selected set of countries is provided in Table 1.5.
It is important to recognize that when a country runs a trade deficit, residents of the country purchase a larger amount of foreign products than foreign residents purchase from them. Those extra purchases are financed by the sale of domestic assets to foreigners. The asset sales may consist of property or businesses (a.k.a. investment), or it may involve the sale of IOUs (borrowing). In the former case, foreign investments entitle foreign owners to a stream of profits in the future. In the latter case, foreign loans entitle foreigners to a future repayment of principal and interest. In this way, trade and international investment are linked.
Because of these future profit takings and loan repayments, we say that a country with a deficit is becoming a debtor country. On the other hand, anytime a country runs a trade surplus, it is the domestic country that receives future profit and is owed repayments. In this case, we say a country running trade surpluses is becoming a creditor country. Nonetheless, trade deficits or surpluses only represent the debts or credits extended over a one-year period. If trade deficits continue year after year, then the total external debt to foreigners continues to grow larger. Likewise, if trade surpluses are run continually, then credits build up. However, if a deficit is run one year followed by an equivalent surplus the second year, rather than extending new credit to foreigners, the surplus instead will represent a repayment of the previous year’s debt. Similarly, if a surplus is followed by an equivalent deficit, rather than incurring debt to foreigners, the deficit instead will represent foreign repayment of the previous year’s credits.
All of this background is necessary to describe a country’s international investment position (IIP), which measures the total value of foreign assets held by domestic residents minus the total value of domestic assets held by foreigners. It corresponds roughly to the sum of a country’s trade deficits and surpluses over its entire history. Thus if the value of a country’s trade deficits over time exceeds the value of its trade surpluses, then its IIP will reflect a larger value of foreign ownership of domestic assets than domestic ownership of foreign assets and we would say the country is a net debtor. In contrast, if a country has greater trade surpluses than deficits over time, it will be a net creditor.
Note how this accounting is similar to that for the national debt. A country’s national debt reflects the sum of the nation’s government budget deficits and surpluses over time. If deficits exceed surpluses, as they often do, a country builds up a national debt. Once a debt is present, though, government surpluses act to retire some of that indebtedness.
The key differences between the two are that the national debt is public indebtedness to both domestic and foreign creditors whereas the international debt (i.e., the IIP) is both public and private indebtedness but only to foreign creditors. Thus repayment of the national debt sometimes represents a transfer between domestic citizens and so in the aggregate has no impact on the nation’s wealth. However, repayment of international debt always represents a transfer of wealth from domestic to foreign citizens.
Figure \(2\): Trade Balances and International Investment Positions GDP, 2009. Sources: Economist, the IMF, and the China State Administration of Foreign Exchange. See Economist, Weekly Indicators, December 30, 2009; IMF Dissemination Standards Bulletin Board at http://dsbb.imf.org/Applications/web/dsbbhome; IMF GDP data from Wikipedia at http://en.Wikipedia.org/wiki/List_of..._%28nominal%29; and China State Administration of Foreign Exchange at www.safe.gov.cn/model_safe_en/tjsj_en/tjsj_detail_en.jsp?ID=30303000000000000,18&id=4.
Country/Region Trade Balance (%) Debtor (−)/Creditor (+) Position (%)
Euro Area −0.9 −17.5
United States −3.1 −24.4
China +6.1 +35.1
Japan +2.7 +50.4
India −0.3 −6.8
Russia +2.2 +15.1
Brazil −0.8 −26.6
South Korea +3.8 −57.9
Indonesia +1.2 −31.4
Spain −5.7 −83.6
South Africa −5.4 −4.1
Estonia +5.8 −83.1
Table 1.5 shows the most recent trade balances and international investment positions, both as a percentage of GDP, for a selected set of countries. One thing to note is that some of the selected countries are running trade deficits while others are running trade surpluses. Overall, the value of all exports in the world must equal the value of all imports, meaning that some countries’ trade deficits must be matched with other countries’ trade surpluses. Also, although there is no magic number dividing good from bad, most observers contend that a trade deficit over 5 percent of GDP is cause for concern and an international debt position over 50 percent is probably something to worry about. Any large international debt is likely to cause substantial declines in living standards for a country when it is paid back—or at least if it is paid back.
The fact that debts are sometimes defaulted on, meaning the borrower decides to walk away rather than repay, poses problems for large creditor nations. The more money one has lent to another, the more one relies on the good faith and effort of the borrower. There is an oft-quoted idiom used to describe this problem that goes, “If you owe me \$100, you have a problem, but if you owe me a million dollars, then I have a problem.” Consequently, international creditor countries may be in jeopardy if their credits exceed 30, 40, or 50 percent of GDP.
Note from the data that the United States is running a trade deficit of 3.1 percent of GDP, which is down markedly from about 6 percent a few years prior. The United States has also been running a trade deficit for more than the past thirty years and as a result has amassed a debt to the rest of the world larger than any other country, totaling about \$3.4 trillion or almost 25 percent of U.S. GDP. As such, the U.S. is referred to as the largest debtor nation in the world.
In stark contrast, during the past twenty-five or more years Japan has been running persistent trade surpluses. As a result, it has amassed over \$2.4 trillion of credits to the rest of the world or just over 50 percent of its GDP. It is by far the largest creditor country in the world. Close behind Japan is China, running trade surpluses for more than the past ten years and amassing over \$1.5 trillion of credits to other countries. That makes up 35 percent of its GDP and makes China a close second to Japan as a major creditor country. One other important creditor country is Russia, with over \$250 billion in credits outstanding or about 15 percent of its GDP.
Note that all three creditor nations are also running trade surpluses, meaning they are expending their creditor position by becoming even bigger lenders.
Like the United States, many other countries have been running persistent deficits over time and have amassed large international debts. The most sizeable are for Spain and Estonia, both over 80 percent of their GDPs. Note that Spain continues to run a trade deficit that will add to it international debt whereas Estonia is now running a trade surplus that means it is in the process of repaying its debt. South Korea and Indonesia are following a similar path as Estonia. In contrast, the Euro area, South Africa, and to a lesser degree Brazil and India are following the same path as the United States—running trade deficits that will add to their international debt.
Key takeaways
• Exchange rates and trade balances are two of the most widely tracked international macroeconomic indicators used to discern the health of an economy.
• Different countries pursue different exchange rate regimes, choosing variations of floating and fixed systems.
• The United States, as the largest national economy in the world, is a good reference point for comparing international macroeconomic data.
• The United States maintains an independently floating exchange rate, meaning that its value is determined on the private market.
• The United States trade deficit is currently at 3.1 percent of GDP. This is down from 6 percent recently but is one of a string of deficits spanning over thirty years.
• The U.S. international investment position stands at almost 25 percent of GDP, which by virtue of the U.S. economy size, makes the United States the largest debtor nation in the world.
• Several other noteworthy statistics are presented in this section:
• China maintains a crawling peg fixed exchange rate.
• Russia fixes its currency to a composite currency while Estonia uses a currency board to maintain a fixed exchange rate.
• Japan is the largest creditor country in the world, followed closely by China and more distantly by Russia.
• Spain and Estonia are examples of countries that have serious international debt concerns, with external debts greater than 80 percent of their GDPs.
Exercises
1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
• The de facto exchange rate regime implemented in China in 2008.
• The de facto exchange rate regime implemented in the United States in 2008.
• The de facto exchange rate regime implemented in Indonesia in 2008.
• The de facto exchange rate regime implemented in Estonia in 2008.
• The name for the exchange rate regime in which a fixed exchange rate is adjusted gradually and unpredictably.
• The name for the exchange rate regime in which the exchange rate value is determined by supply and demand for currencies in the private marketplace.
• The term for the measure of the total value of foreign assets held by domestic residents minus the total value of domestic assets held by foreigners.
• This country was the largest creditor country in the world as of 2008.
2. Use the information in Table 1.1 and Table 1.5 to calculate the dollar values of the trade balance and the international investment position for Japan, China, Russia, South Korea, and Indonesia. | textbooks/biz/Finance/Book%3A_International_Finance__Theory_and_Policy/01%3A_Introductory_Finance_Issues-_Current_Patterns_Past_History_and_International_Institutions/1.03%3A_Exchange_Rate_Regimes_Trade_Balances_and_Investment_Positions.txt |
Learning Objectives
1. Understand the distinctions between an economic recession and a depression.
2. Compare and contrast the current recession in the United States with previous economic downturns.
3. Recognize why the economic downturn in the 1930s is called the Great Depression.
In 2009 the world was in the midst of the largest economic downturn since the early 1980s. Economic production was falling and unemployment rising. International trade fell substantially everywhere in the world, while investment both domestically and internationally dried up.
The source of these problems was the bursting of a real estate bubble. Bubbles are fairly common in both real estate and stock markets. A bubble is described as a steady and persistent increase in prices in a market, in this case, in the real estate markets in the United States and abroad. When bubbles are developing, many market observers argue that the prices are reflective of true values despite a sharp and unexpected increase. These justifications fool many people into buying the products in the hope that the prices will continue to rise and generate a profit.
When the bubble bursts, the demand driving the price increases ceases and a large number of participants begin to sell off their product to realize their profit. When these occur, prices quickly plummet. The dramatic drop in real estate prices in the United States in 2007 and 2008 left many financial institutions near bankruptcy. These financial market instabilities finally spilled over into the real sector (i.e., the sector where goods and services are produced), contributing to a world recession. As the current economic crisis unfolds, there have been many suggestions about similarities between this recession and the Great Depression in the 1930s. Indeed, it is common for people to say that this is the biggest economic downturn since the Great Depression. But is it?
To understand whether it is or not, it is useful to look at the kind of data used to measure recessions or depressions and to compare what has happened recently with what happened in the past. First, here are some definitions.
An economic recession refers to a decline in a country’s measured real gross domestic product (GDP) over a period usually coupled with an increasing aggregate unemployment rate. In other words, it refers to a decline in economic productive activity. How much of a decline is necessary before observers will begin to call it a recession is almost always arguable, although there are a few guidelines one can follow.
In the United States, it is typical to define a recession as two successive quarters of negative real GDP growth. This definition dates to the 1970s and is little more than a rule of thumb, but it is one that has become widely applied. A more official way to define a recession is to accept the pronouncements of the National Bureau of Economic Research (NBER). This group of professional economists looks at more factors than just GDP growth rates and will also make judgments about when a recession has begun and when one has ended. According to the NBER, the current recession began in December 2007 in the United States. However, it did not proclaim that until December 2008. Although the U.S. economy contracted in the fourth quarter of 2007, it grew in the first two quarters of 2008, meaning that it did not fulfill the two successive quarters rule. That wasn’t satisfied until the last two quarters of 2008 both recorded a GDP contraction. As of January 2010, the U.S. economy continues in a recession according to the NBER.See the National Bureau of Economic Research, http://www.nber.org/cycles.html.
A very severe recession is referred to as a depression. How severe a recession has to be to be called a depression is also a matter of judgment. In fact in this regard there are no common rules of thumb or NBER pronouncements. Some recent suggestions in the press are that a depression is when output contracts by more than 10 percent or the recession lasts for more than two years. Based on the second definition and using NBER records dating the length of recessions, the United States experienced depressions from 1865 to 1867, 1873 to 1879, 1882 to 1885, 1910 to 1912, and 1929 to 1933. Using this definition, the current recession could be judged a depression if NBER dates the end of the contraction to a month after December 2009.
The opposite of a recession is an economic expansion or economic boom. Indeed, the NBER measures not only the contractions but the expansions as well because its primary purpose is to identify the U.S. economy’s peaks and troughs (i.e., high points and low points). When moving from a peak to a trough the economy is in a recession, but when moving from a trough to a peak it is in an expansion or boom. The term used to describe all of these ups and downs over time is the business cycle.
The business cycle has been a feature of economies since economic activity has been measured. The NBER identifies recessions going back to the 1800s with the earliest listed in 1854. Overall, the NBER has classified thirty-four recessions since 1854 with an average duration of seventeen months. The longest recession was sixty-five months from 1873 to 1879, a contraction notable enough to be called the Great Depression until another one came along to usurp it in the 1930s. On the upside, the average economic expansion in the United States during this period lasted thirty-eight months, with the longest being 120 months from 1991 to 2001. Interestingly, since 1982 the United States has experienced three of its longest expansions segmented only by relatively mild recessions in 1991 and 2001. This had led some observers to proclaim, “The business cycle is dead.” Of course, that was until we headed into the current crisis. (See here for a complete listing of NBER recessions: http://www.nber.org/cycles/cyclesmain.html.)
The Recession of 2008–2009
Next, let’s take a look at how the GDP growth figures look recently and see how they compare with previous periods. First, growth rates refer to the percentage change in real GDP, which means that the effects of inflation have been eliminated. The rates are almost always reported in annual terms (meaning the growth rate over a year) even when the period is defined as one quarter. In the United States and most other countries, GDP growth rates are reported every quarter, and that rate represents how much GDP would grow during a year if the rate of increase proceeded at the same pace as the growth during that quarter. Alternatively, annual growth rates can be reported as the percentage change in real GDP from the beginning to the end of the calendar year (January 1 to December 31).
Table 1.6 presents the quarterly real GDP growth rates from the beginning of 2007 to the end of 2009 and the corresponding unemployment rate that existed during the middle month of each quarter. Note first that in 2007, GDP growth was a respectable 2 to 3 percent and unemployment was below 5 percent, signs of a healthy economy. However, by the first quarter in 2008, GDP became negative although unemployment remained low. Growth rebounded to positive territory in the second quarter of 2008 while at the same time unemployment began to rise rapidly. At this time, there was great confusion about whether the U.S. economy was stalling or whether it was experiencing a temporary slowdown. By late 2008, though, speculation about an impending recession came to an end. Three successive quarters of significant GDP decline occurred between the second quarter of 2008 and the end of the first quarter in 2009, while the unemployment rate began to skyrocket. By the middle of 2009, the decline of GDP subsided and reversed to positive territory by the third quarter. However, the unemployment rate continued to rise, though at a slower pace. What happens next is anyone’s guess, but to get a sense of the severity of this recession it is worth analyzing at least two past recessions: that of 1981 to 1982 and the two that occurred in the 1930s, which together are known as the Great Depression.
Year.Quarter Growth Rate (%) Unemployment Rate (%)
2007.1 1.2 4.5
2007.2 3.2 4.5
2007.3 3.6 4.7
2007.4 2.1 4.7
2008.1 −0.7 4.8
2008.2 1.5 5.6
2008.3 −2.7 6.2
2008.4 −5.4 6.8
2009.1 −6.4 8.1
2009.2 −0.7 9.4
2009.3 2.2 9.7
2009.4 10.0
Figure \(1\): Table 1.6 U.S. Real GDP Growth and Unemployment Rate, 2007–2009
Sources: U.S. Bureau of Economic and Analysis and U.S. Department of Labor.
The Recession of 1980–1982
At a glance the current recession most resembles the recessionary period from 1980 to 1982. The NBER declared two recessions during that period; the first lasting from January to July 1980 and the second lasting from July 1981 to November 1982. As can be seen in Table 1.7, GDP growth moved like a roller coaster ride. Coming off a sluggish period of stagflation in the mid-1970s, unemployment began somewhat higher at around 6 percent, while growth in 1979 (not shown) was less than 1 percent in several quarters. Then in the second quarter of 1980, GDP plummeted by almost 8 percent, which is much more severe than anything in the current recession. Note that the largest quarterly decrease in the U.S. GDP in the post–World War II era was −10.4 percent in the first quarter of 1958. In the same quarter, unemployment soared, rising over a percentage point in just three months. However, this contraction was short-lived since the GDP fell only another 0.7 percent in the third quarter and then rebounded with substantial growth in the fourth quarter of 1980 and the first quarter of 1981. Notice that despite the very rapid increase in the GDP, unemployment hardly budged downward, remaining stubbornly fixed around 7.5 percent. The rapid expansion was short-lived, as the GDP tumbled again by over 3 percent in the second quarter of 1981 only to rise again by a healthy 5 percent in the third quarter. But once again, the economy plunged back into recession with substantial declines of 5 percent and over 6 percent for two successive quarters in the GDP in late 1981 and early 1982. Meanwhile, from mid-1981 until after the real rebound began in 1983, the unemployment rate continued to rise, reaching a peak of 10.8 percent in late 1982, the highest unemployment rate in the post–World War II period.
Year.Quarter Growth Rate (%) Unemployment Rate (%)
1980.1 +1.3 6.3
1980.2 −7.9 7.5
1980.3 −0.7 7.7
1980.4 +7.6 7.5
1981.1 +8.6 7.4
1981.2 −3.2 7.5
1981.3 +4.9 7.4
1981.4 −4.9 8.3
1982.1 −6.4 8.9
1982.2 +2.2 9.4
1982.3 −1.5 9.8
1982.4 +0.3 10.8
1983.1 +5.1 10.4
1983.2 +9.3 10.1
1983.3 +8.1 9.5
1983.4 +8.5 8.5
Figure \(2\): Table 1.7 U.S. Real GDP Growth and Unemployment Rate, 1980–1983
Sources: U.S. Bureau of Economics and Analysis (http://www.bea.gov) and U.S. Department of Labor (http://www.dol.gov).
If indeed the current recession turns out like the 1980 to 1983 episode, we might expect to see substantial swings in the GDP growth rates in future quarters in the United States. The ups and downs are analogous to a bicycle smoothly traversing along a smooth road when the rider suddenly hits a large obstruction. The obstruction jolts the bike to one side while the rider compensates to pull the bike upright. However, the compensation is often too much, and the bike swings rapidly to the opposite side. This too inspires an exaggerated response that pushes the bike again too quickly to the original side. In time, the rider regains his balance and directs the bike along a smooth trajectory. That is what we see in Table 1.7 of the last quarters in 1983, when rapid growth becomes persistent and unemployment finally begins to fall.
The other lesson from this comparison is to note how sluggishly unemployment seems to respond to a growing economy. In late 1980 and early 1981, unemployment didn’t budge despite the rapid revival of economic growth. In 1983, it took almost a full year of very rapid GDP growth before the unemployment rate began to fall substantially. This slow response is why the unemployment rate is often called a lagging indicator of a recession; it responds only after the recession has already abated.
The Great Depression
During the current recession there have been many references to the Great Depression of the 1930s. One remark often heard is that this is the worst recession since the Great Depression. As we can see in Table 1.7, this is not quite accurate since the recession of the early 1980s can easily be said to have been worse than the current one…at least so far.
It is worth comparing numbers between the current period and the Depression years if only to learn how bad things really were during the 1930s. The Great Depression was a time that transformed attitudes and opinions around the world and can surely be credited with having established the necessary preconditions for the Second World War.
So let’s take a look at how bad it really was. Once again, we’ll consider the U.S. experience largely because the data are more readily available. However, it is worth remembering that all three of the economic downturns described here are notable in that they were worldwide in scope.
First of all, there is no quarterly data available for the 1930s as quarterly data in the United States first appeared in 1947. Indeed, there was no formal organized collection of data in the 1930s for a variable such as GDP. Thus the numbers presented by the U.S. Bureau of Economic and Analysis (BEA) were constructed by piecing together available data.
A second thing to realize is that annual GDP growth rates tend to have much less variance than quarterly data. In other words, the highs are not as high and the lows not as low. This is because the annual data are averaging the growth rates over the four quarters. Also, sometimes economic downturns occur at the end of one year and the beginning of the next so that the calendar year growth may still be positive in both years. For example in 2008, even though GDP growth was negative in three of four quarters, the annual GDP growth that year somehow registered a +0.4 percent. Also in 1980, despite an almost 8 percent GDP drop in the second quarter, the annual GDP growth that year was −0.3 percent. The same is true for 1982, which registered two quarters of negative GDP growth at −6.4 percent and −1.5 percent but still the GDP fell annually at only −1.9 percent.
With this caveat in mind, the U.S. GDP growth rates for the 1930s are astounding. From 1930 to 1933, the United States registered annual growth rates of −8.6 percent, −6.5 percent, −13.1 percent, and −1.3 percent. The unemployment rate, which is estimated to have been around 3 percent in the 1920s, rose quickly in 1930 to 8.9 percent and continued to rise rapidly to a height of almost 25 percent in 1933. Although growth returned with vigor in 1934 and for another four years, the unemployment rate remained high and only slowly fell to 14.3 percent by 1937.
Year Growth Rate (%) Unemployment Rate (%)
1930 −8.6 8.9
1931 −6.5 15.9
1932 −13.1 23.6
1933 −1.3 24.9
1934 +10.9 21.7
1935 +8.9 20.1
1936 +13.0 17.0
1937 +5.1 14.3
1938 −3.4 19.0
1939 +8.1 17.2
1940 +8.8 14.6
Figure \(3\): Table 1.8 U.S. Real GDP Growth and Unemployment Rate, 1930–1940
Sources: U.S. Bureau of Economics and Analysis and U.S. Department of Labor.
The NBER dated the first part of the Depression as having started in August 1929 and ending in March 1933. But a second wave came, another recession beginning in May 1937 and ending in June 1938. This caused GDP to fall by another 3.4 percent in 1938 while unemployment rose back above 15 percent for another two years.
The Great Depression is commonly used to refer to the economic crisis (or crises) that persisted for the entire decade of the 1930s, only truly coming to an end at the start of World War II. Even then it is worth mentioning that although GDP began to grow rapidly during World War II, with GDP growth from 1941 to 1943 at 17.1 percent, 18.5 percent, and 16.4 percent, respectively, and with U.S. unemployment falling to 1.2 percent in 1944, these data mask the fact that most of the extra production was for bullets and bombs and much of the most able part of the workforce was engaged in battle in the Atlantic and Pacific war theaters. In other words, the movement out of the Great Depression was associated with a national emergency rather than a more secure and rising standard of living.
Although the data presented only cover the United States, the Great Depression was a worldwide phenomenon. Without digging too deeply into the data or just by taking a quick look at Wikipedia’s article on the Great Depression, it reveals the following: unemployment in 1932 peaked at 29 percent in Australia, 27 percent in Canada, and 30 percent in Germany. In some towns with specialized production in the United Kingdom, unemployment rose as high as 70 percent.
Needless to say, the Great Depression was indeed “great” in the sense that it was the worst economic downturn the world experienced in the twentieth century. In comparison, the current recession, which is coming to be known as the Great Recession, comes nowhere close to the severity of the Great Depression…at least for the moment (as of January 2010). A more accurate description of the current recession is that it is the worst since the 1980s in the United States. However, we should always be mindful of a second downturn as was seen in the late 1930s. Even after things begin to improve, economies can suffer secondary collapses. Hopefully, demands will soon rebound, production will sluggishly increase, and unemployment rates will begin to fall around the world. We will soon see.
Key takeaways
• The business cycle refers to the cyclical pattern of economic expansions and contractions. Business cycles have been a persistent occurrence in all modern economies.
• The current recession, sometimes called the Great Recession, is comparable in GDP decline and unemployment increases in the United States to the recessions in the early 1980s.
• The Great Depression of the 1930s displayed much greater decreases in GDP, showed much larger increases in unemployment, and lasted for a longer period than any economic downturn in the United States since then.
• The largest annual decrease in the U.S. GDP during the Great Depression was −13.1 percent while the highest unemployment rate was 24.9 percent.
• The largest quarterly decrease in the U.S. GDP during the current recession was −6.4 percent while the highest unemployment rate was 10.1 percent.
• The largest quarterly decrease in the U.S. GDP since World War II was −10.4 percent in the first quarter of 1958, while the highest unemployment rate was 10.8 percent in 1982.
• Of the thirty-four U.S. recessions since 1854 classified by the NBER, the longest was sixty-five months in the 1870s, whereas the average length was seventeen months.
• Of all the U.S. expansions since 1854 classified by the NBER, the longest was 120 months in the 1990s whereas the average length was thirty-eight months.
exercise
1. Jeopardy Questions. As in the popular television game show, you are given an answer to a question and you must respond with the question. For example, if the answer is “a tax on imports,” then the correct question is “What is a tariff?”
• Approximately the worst U.S. quarterly economic growth performance between 2007 and 2009.
• Approximately the worst U.S. quarterly economic growth performance between 1980 and 1983.
• Approximately the worst U.S. annual economic growth performance between 1930 and 1940.
• Approximately the best U.S. annual economic growth performance between 1930 and 1940.
• Approximately the period of time generally known as the Great Depression.
• Approximately the highest unemployment rate in the U.S. during the Great Depression.
• Approximately the highest unemployment rate in Germany during the Great Depression.
• Approximately the best U.S. annual economic growth performance in the midst of World War II.
• The longest economic recession (in months) in the United States since 1854 as classified by the NBER.
• The longest economic expansion (in months) in the United States since 1854 as classified by the NBER.
• The term used to describe the cyclical pattern of economic expansions followed by economic contractions. | textbooks/biz/Finance/Book%3A_International_Finance__Theory_and_Policy/01%3A_Introductory_Finance_Issues-_Current_Patterns_Past_History_and_International_Institutions/1.04%3A_Business_Cycles-_Economic_Ups_and_Downs.txt |
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