how investors use the cagr
understanding the formula used to calculate cagr is an introduction to many other ways that investors evaluate past returns or estimate future profits the formula can be manipulated algebraically into a formula to find the present value or future value of money or to calculate a hurdle rate of return for example imagine that an investor knows that they need 50 000 for a child s college education in 18 years and they have 15 000 to invest today how much does the average rate of return need to be to reach that objective the cagr calculation can be used to find the answer to this question as follows required return 50 000 15 000 1 18 1 100 6 90 text required return left frac 50 000 15 000 right frac 1 18 1 times 100 6 90 required return 15 000 50 000 181 1 100 6 90 this version of the cagr formula is just a rearranged present value and future value equation for example if an investor knew that they needed 50 000 and they felt it was reasonable to expect an 8 annual return on their investment they could use this formula to find out how much they needed to invest to meet their goal modifying the cagr formulaan investment is rarely made on the first day of the year and then sold on the last day of the year imagine an investor who wants to evaluate the cagr of a 10 000 investment that was entered on june 1 2013 and sold for 16 897 14 on sept 9 2018 before the cagr calculation can be performed the investor will need to know the fractional remainder of the holding period they held the position for 213 days in 2013 a full year in 2014 2015 2016 and 2017 and 251 days in 2018 this investment was held for 5 271 years which is calculated by the following the total number of days that the investment was held was 1 924 days to calculate the number of years divide the total number of days by 365 1 924 365 which equals 5 271 years the total number of years that the investment was held can be placed in the denominator of the exponent inside cagr s formula as follows investment cagr 16 897 14 10 000 1 5 271 1 100 10 46 text investment cagr left frac 16 897 14 10 000 right frac 1 5 271 1 times 100 10 46 investment cagr 10 000 16 897 14 5 2711 1 100 10 46 smooth rate of growth limitationthe most important limitation of the cagr is that because it calculates a smoothed rate of growth over a period it ignores volatility and implies that the growth during that time was steady returns on investments are uneven over time except for bonds that are held to maturity deposits and similar investments also the cagr does not account for when an investor adds funds to a portfolio or withdraws funds from the portfolio over the period being measured for example if an investor had a portfolio for five years and injected funds into the portfolio during the five year period then the cagr would be inflated the cagr would calculate the rate of return based on the beginning and ending balances over the five years and would essentially count the deposited funds as part of the annual growth rate which would be inaccurate other cagr limitationsbesides the smoothed rate of growth the cagr has other limitations a second limitation when assessing investments is that no matter how steady the growth of a company or investment has been in the past investors cannot assume that the rate will remain the same in the future the shorter the time frame used in the analysis the less likely it will be for the realized cagr to meet the expected cagr when relying on historical results a third limitation of the cagr is a limitation of representation say that an investment fund was worth 100 000 in 2016 71 000 in 2017 44 000 in 2018 81 000 in 2019 and 126 000 in 2020 if the fund managers represented in 2021 that their cagr was a whopping 42 01 over the past three years they would be technically correct they would however be omitting some very important information about the fund s history including the fact that the fund s cagr over the past five years was a modest 4 73 cagr vs irrthe cagr measures the return on an investment over a certain period of time the internal rate of return irr also measures investment performance but is more flexible than the cagr the most important distinction is that the cagr is straightforward enough that it can be calculated by hand in contrast more complicated investments and projects or those that have many different cash inflows and outflows are best evaluated using irr to back into the irr a financial calculator excel or portfolio accounting system is ideal those interested in learning more about cagr and other financial topics may want to consider enrolling in one of the best investing courses currently available 