## What is the 'Average Annual Growth Rate - AAGR'

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%