Compound annual growth rate is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the time period. CAGR is not an accounting term, but it is often used to describe some element ofthe business, for example revenue, units delivered, registered users, etc. CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant. It is particularly useful to compare growth rates from various data sets of common domain such as revenue growth of companies in the same industry or sector. CAGR is equivalent to the more generic exponential growth rate when the exponential growth interval is one year.
Formula
CAGR is defined as: where is the initial value, is the end value, and is the number of years. Actual or normalized values may be used for calculation as long as they retain the same mathematical proportion.
Example
In this example, we will compute the CAGR over three periods. Assume that the year-end revenues of a business over a three-year period,, have been:
Therefore, to calculate the CAGR of the revenues over the three-year period spanning the "end" of 2004 to the "end" of 2007 is: Note that this is a smoothed growth rate per year. This rate of growth would take you to the ending value, from the starting value, in the number of years given, if growth had been at the same rate every year. Verification: Multiply the initial value by three times. The product will equal the year-end revenue for 2007. This shows the compound growth rate: For n = 3: For comparison:
In contrast to CAGR, you cannot obtain by multiplying the initial value,, three times by .
the arithmetic return or simple return would be the ending value minus beginning value divided by the beginning value:
Applications
These are some of the common CAGR applications:
Calculating and communicating the average returns of investment funds
Demonstrating and comparing the performance of investment advisors
Comparing the historical returns of stocks with bonds or with a savings account
Forecasting future values based on the CAGR of a data series. As every forecasting method, this method has a calculation error associated.
Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.
