how to calculate growth rates
growth rates can be calculated in several ways depending on what the figure is intended to convey a simple growth rate simply divides the difference between the ending and starting value by the beginning value or ev bv bv the economic growth rate for a country s gdp can thus be computed as economic growth gdp2 gdp1gdp1where gdp gross domestic product of nation begin aligned text economic growth frac text gdp 2 text gdp 1 text gdp 1 textbf where text gdp text gross domestic product of nation end aligned economic growth gdp1 gdp2 gdp1 where gdp gross domestic product of nation this approach however may be overly simplistic the compound annual growth rate cagr is a variation on the growth rate that is often used to assess an investment s or company s performance the cagr which is not a true return rate but rather a representation that describes the rate at which an investment would have grown if it had grown at the same rate every year and the profits were reinvested at the end of each year the formula for calculating cagr is cagr evbv 1n 1where ev ending valuebv beginning valuen number of years begin aligned cagr left frac ev bv right frac 1 n 1 textbf where ev text ending value bv text beginning value n text number of years end aligned cagr bvev n1 1where ev ending valuebv beginning valuen number of years the cagr calculation assumes that growth is steady over a specified period of time cagr is a widely used metric due to its simplicity and flexibility and many firms will use it to report and forecast earnings growth financial theory suggests that a company s shares can be fairly valued using a dividend discount model ddm based on the hypothesis that present day price is worth the sum of all of its future dividend payments when discounted back to its present value as a result dividend growth rates are important for valuing stocks the gordon growth model ggm is a popular approach used to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate this dividend growth rate is assumed to be positive as mature companies seek to increase the dividends paid to their investors on a regular basis knowing the dividend growth rate is thus a key input for stock valuation using growth ratesgrowth rates are utilized by analysts investors and a company s management to assess a firm s growth periodically and make predictions about future performance most often growth rates are calculated for a firm s earnings sales or cash flows but investors also look at growth rates for other metrics such as price to earnings ratios or book value among others when public companies report quarterly earnings the headline figures are typically earnings and revenue along with the growth rates quarter over quarter or year over year for each for example amazon reported full year revenue of 232 89 billion for 2018 this represented growth of 30 93 from 2017 revenue of 177 9 billion amazon also reported that its earnings totaled 10 07 billion in 2018 compared to 3 03 billion in 2017 so the firm s growth rate for earnings on a year over year basis was a whopping 232 1the internal growth rate igr is a specific type of growth rate used to measure an investment s or project s return or a company s performance it is the highest level of growth achievable for a business without obtaining outside financing and a firm s maximum igr is the level of business operations that can continue to fund and grow the company investors often look to rate of return ror calculations to compute the growth rate of their portfolios or investments while these generally follow the formulae for growth rate or cagr investors may wish to also know their real or after tax rate of return thus growth rates for investors will net out the impact of taxes inflation and transaction costs or fees because stock prices are thought to reflect the discounted value of a firm s future cash flows a rising stock market implies improving forecasted growth rates for the company specific industries also have growth rates each industry has a unique benchmark number for rates of growth against which its performance is measured for instance companies on the cutting edge of technology are more likely to have higher annual rates of growth compared to a mature industry such as retail industry growth rates can be used as a point of comparison for firms seeking to gauge their performance relative to their peers the use of historical growth rates is one of the simplest methods of estimating the future growth of an industry however historically high growth rates do not always indicate a high rate of growth looking into the future as industrial and economic conditions change constantly and are often cyclical for example the auto industry has higher rates of revenue growth during periods of economic expansion but in times of recession consumers are more inclined to be frugal and not spend disposable income on a new car in addition to gdp growth retail sales growth is another important growth rate for an economy because it can be representative of consumer confidence and customer spending habits when the economy is doing well and people are confident they increase spending which is reflected in retail sales when the economy is in a recession people reduce spending and retail sales decline for example second quarter q2 2016 retail sales growth for ireland was reported in july 2016 revealing that domestic retail sales flatlined through the quarter it is believed that political instability within the country combined with the results of the brexit vote in june 2016 caused ireland s sales to stall while some industries such as agriculture and garden showed positive growth other industries within the retail sector counteracted that growth fashion and footwear had negative growth for the quarter 2example of a growth ratesay that we are comparing the annual growth rates of two countries gdp first we can look at the annual growth rates of each country for the first two years country a is growing at a modest rate that is declining over the three years country b is growing rapidly and at an increasing rate this is not unusual for large mature countries and emerging markets economies respectively but also notice that in year 3 the size of country a s economy is still more than 36 larger than it we can also consider the cagr of the two countries over the two year period taking place between years 1 and 3 we then get note that the cagr annualized rates are slightly lower than the arithmetic average of the two years individual growth rates limitations of growth rateswhile growth rates are important for understanding how things change over time they do come with some important limitations first the growth rate only considers the net change between two points in time but it says nothing about the price movements or volatility that may have occurred in between for instance if some variable has a value of 10 00 today and 10 00 as well a year from now the growth rate is zero however it could have fluctuated wildly or not at all during those 12 months the annual growth rate in this case cannot tell us anything about that growth rates also ignore the nominal amounts involved for instance company a s earnings may grow from 100 000 per year to 150 000 per year representing 50 growth but only a 50 000 change a much larger company b s earnings may only grow at say 5 a year 10 less in terms of the growth rate but amount to several millions of dollars in the company s coffers finally growth rates are hard to compare across industries or other unlike variables a 5 rate of growth for a company may be relatively good or bad depending on if it is a growth oriented tech startup vs a large incumbent consumer staples manufacturer likewise a 4 decline in unemployment does not necessarily carry the same impact as a 4 increase in gdp 