# Compound Annual Growth Rate - CAGR

## What is the 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.

This can be written as follows:

Â

CAGR can also be calculated using Investopedia's own Compound Annual Growth Rate Calculator.

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## BREAKING DOWN 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate isn't a trueÂ return rate, but rather a representational figure. It is essentially an imaginary number that describes the rate at which an investment would have grown if it had grown at a steady rate, which virtually never happens in reality. You can think ofÂ CAGRÂ as a way to smooth out an investmentâ€™s returns so that they may be more easily understood.

Don't worry if this concept is still fuzzy to you â€“Â CAGRÂ is one of those terms best explained through example. Suppose you invested \$10,000 in a portfolio on Jan 1, 2005. Unsurprisingly, your portfolio would likely grow at an inconsistent rate. Let us assume that by Jan 1, 2006, your portfolio had grown to \$13,000. Let us also assume that it then grew to \$14,000 by the same time in 2007, and spiked during that year, ending up at \$19,500 by Jan 1, 2008.

To calculate the CAGRÂ of your portfolio from the period from Jan 1, 2005 to Jan 1, 2008, you would divide the final value of your portfolio by the portfolioâ€™s initial value (\$19,500 / \$10,000 = 1.95). Next, you wouldÂ  raise the result to the power of 1 divided by the number of years (1 / 3 = 1/3 or 0.3333). Finally, you would subtract 1 from the resulting value.

Doing the math, you would calculate:

[(19,500 / 10,000)^(1 / 3)] â€“ 1

= (1.95 ^ 0.3333) â€“ 1

= 1.2493 â€“ 1

= 0.2493, or 24.93%.

Thus, the compound annual growth rate of your three-year investment is equal to 24.93%, representing the smoothed annualized gain you earned over your investment time horizon.

## Uses of theÂ Compound Annual Growth Rate (CAGR)

CAGR is a relatively simple metric, since it merely measures the average rate of an investmentâ€™s growth over a variable period of time. Because of this simplicity, this metric is a flexible one and thus has a variety of uses.

Most simply, CAGR can be used to calculate the average growth of a single investment. Because of market volatility, the year-to-year growth of an investment may be difficult to interpret. For example, an investment may increase in value by 8% in one year, decrease in value by 2% the following year and increase in value by 5% in the next. With inconsistent annual growth, CAGR may be used to give a broader picture of an investmentâ€™s progress.

CAGR may also be used to compare investments of different types with one another. For example, suppose in 2010 you put \$10,000 into a savings account with a fixed annual interest rate of 1%, growing to a value of \$10,100 in 2011, \$10,201 in 2012 and \$10,303.01 in 2013. Say that in 2010, you wanted to pursue other investment options but, fearing market volatility, you only invested \$5,000 this time, into a portfolio with a varying growth rate. Suppose that the portfolio grew in value to \$5,114 in 2011, dropped to a value of \$5,098 in 2012 and grew to \$5,437 in 2013. Although the portfolio grew at an inconsistent rate and even lost value in 2012, the investmentâ€™s CAGR between 2010 and 2013 was 2.83% ((5,437/5,000)^(1/3) - 1 = 1.0874^0.3333 â€“ 1 = 1.0283 â€“ 1 = 0.0283 = 2.83%), substantially higher than the interest rate of the savings account. The portfolio, then, proved to be the more profitable investment.

CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another. For example, over a five-year period Big-Sale Storesâ€™ market share CAGR may be 1.82% but its customer satisfaction CAGR over the same period might be -0.58%. In this way, comparing the CAGRs of measures within a single company may reveal that companyâ€™s strengths and weaknesses. However, comparing those CAGRs with those tracking the same measures in other companies may help situate this data within the scope of the market. For example, Big-Saleâ€™s customer satisfaction CAGR might not seem so low if compared with SuperFast Cableâ€™s customer satisfaction CAGR of -6.31% during the same period.

## Limitations of 'Compound Annual Growth Rate - CAGR'

Like any metric, CAGR should not be used alone, but rather should be used alongside other metrics as well. This is because, like any metric, CAGR is not without its drawbacks.

The simplest limitation of CAGR is that because it calculates the smooth average of growth over a period, it ignores volatility and implies that the growth during that time was steady. Yet, this is never actually the case. As such, you should never take CAGR at face value â€” also check the values each year that go into calculating CAGR.

Another limitation of using CAGR in assessing investments is that, no matter how steady the growth of a company or investment has been over a period of time (even if you have checked the individual annual values), CAGR is a purely historical metric. What this means is that even if an investmentâ€™s growth has been very consistent over a five-year period, you cannot safely use CAGR to assume that the investment will continue to grow at the same rate during the following year or years, as market volatility and other factors may come into play and affect that investmentâ€™s rate of growth.

A third limitation of CAGR is a limitation of representation. Say that an investment fund had values of \$100,000 in 2010, \$71,000 in 2011, \$44,000 in 2012, \$81,000 in 2013 and \$126,000 in 2014. If the fund managers told you in 2015 that the fundâ€™s CAGR was a whopping 42.01% over the past three years, they would not be lying. They would, however, be omitting some very important information about the fundâ€™s history, including the fact that the fundâ€™s CAGR over the past five years was a much more modest 4.73%.

For more on the Compound Annual Growth Rate (CAGR), see:Â Compound Annual Growth Rate: What You Should Know.

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