Investopedia: What is the 'Compound Annual Growth Rate - CAGR'?

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Compound Annual Growth Rate - CAGR
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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:

Formula for Compound Annual Growth Rate (CAGR)

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 true return rate, but rather a representational figure. It is essentially a 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 of CAGR as a way to smooth out an investment’s returns so that they may be more easily understood.
CAGR Example

Don't worry if this concept is still fuzzy to you – CAGR is one of those terms best explained through an example. Suppose you invested $10,000 in a portfolio on Jan 1, 2014. Unsurprisingly, your portfolio would likely grow at an inconsistent rate. Let us assume that by Jan 1, 2015, your portfolio had grown to $13,000. Let us also assume that it then grew to $14,000 at the same time in 2016, and spiked during that year, ending up at $19,500 by Jan 1, 2017.

To calculate the CAGR of your portfolio from the period from Jan 1, 2014 to Jan 1, 2017, you would divide the final value of your portfolio by the portfolio’s initial value ($19,500 / $10,000 = 1.95). Next, you would  raise the result to the power of 1 divided by the number of years (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 – 1

= 1.950.3333 – 1

= 1.2493 – 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, assuming your investment was compounding over the three-year time period.
Uses of the Compound Annual Growth Rate (CAGR)

CAGR is a relatively simple metric, since it merely measures the average rate of an investment’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. Due to 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 investment’s progress.

CAGR may also be used to compare investments of different types with one another. For example, suppose in 2014 you put $10,000 into a savings account with a fixed annual interest rate of 1%, growing to a value of $10,100 in 2015, $10,201 in 2016 and $10,303.01 in 2017. Say that in 2014, 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 2015, dropped to a value of $5,098 in 2016 and grew to $5,437 in 2017. Although the portfolio grew at an inconsistent rate and even lost value in 2016, the investment’s CAGR between 2014 and 2017 was

(5,437 / 5,000)1/3 - 1 = 1.08740.3333 – 1 = 1.0283 – 1 = 0.0283 = 2.83%

Since 2.83% is substantially higher than the 1% interest rate of the savings account, the portfolio investment 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 Stores’ 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 the company’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-Sale’s customer satisfaction CAGR might not seem so low if compared with SuperFast Cable’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 fundamentals 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 — 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 investment’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 investment’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 2012, $71,000 in 2013, $44,000 in 2014, $81,000 in 2015 and $126,000 in 2016. If the fund managers told you in 2017 that the fund’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 fund’s history, including the fact that the fund’s CAGR over the past five years was a much more modest 4.73%.

For more on the Compound Annual Growth Rate (CAGR), see: Compound Annual Growth Rate: What You Should Know.
Average Annual Growth Rate - AAGR
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The average annual growth rate (AAGR) is the average increase in the value of an individual investment, portfolio, asset or cash stream over specific interval of time. It is calculated by taking the arithmetic mean of the growth rate over the time periods in question. The average annual growth rate can be calculated for any investment, but will not include any measure of the investment's overall risk, as measured by its price volatility.

!--break--The AAGR measure the average rate of return or growth over a series of equally spaced time periods. As an example, assume an investment has the following values over the course four years:

Beginning value = $100,000

End of year one value = $120,000

End of year two value = $135,000

End of year three value = $160,000

End of year four value = $200,000

The formula to determine the percentage growth for the year is:

Percentage growth = (Ending value / Beginning value) -1

Thus, the growth rates for each of the years is as follows:

Year one growth = $120,000 / $100,000 - 1 = 20%

Year two growth = $135,000 / $120,000 - 1 = 12.5%

Year three growth = $160,000 / $135,000 - 1 = 18.5%

Year four growth = $200,000 / $160,000 - 1 = 25%

To find the AAGR, and analyst simply needs to find the average of these growth rates:

AAGR = (20% + 12.5% + 18.5% + 25%) / 4 = 19%

In the financial and accounting settings, typically the beginning and ending prices are used, but some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed
Average Annual Growth Rate vs. Compound Annual Growth Rate

AAGR is a linear measure that does not take into account the effect of compounding. The above example shows that the investment grew 19% per year on average over the course of the year. This gives an analyst some useful information, but often it is not enough. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR). The CAGR shows how much an investment needs to grow each year to get from the initial value to the ending value, assuming that compounding occurs. This is often the case with investments.

The formula for the CAGR is:

CAGR = (Ending value / Beginning value) ^ (1/n) - 1

Using the above example, the CAGR equals:

CAGR = ($200,000 / $100,000) ^ (1/4) - 1 = 1.1892 - 1 = 18.92%
BREAKING DOWN 'Average Annual Growth Rate - AAGR'

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