Compounded annual growth rate - CAGR

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The compound annual growth rate (CAGR) is the rate at which something (e.g., revenue, savings, population) grows over a period of years, taking into account the effect of annual compounding.

A compound is composed of two or more parts. In the case of compound growth, the two parts are principal and the amount of change in the principal over a certain time period, which is called “interest” in some circumstances.

This is sometimes called “growth on growth” because it measures periodic growth of a value that is itself growing periodically. If we are calculating the annual compound growth rate, then each year the new basis is the previous basis plus the growth over the previous period.

In looking at an investment, the CAGR is a measure that is commonly used to show how quickly the investment, or certain aspects of it, such as gross sales, have been growing. Investment analysts often look at five-year periods to discern a trend. A specific company’s rate of growth is often then compared with that of competitors or with the industry as a whole.

For example, Company A had a revenue CAGR of 8.5% over the past five years. One of its direct competitors has grown by 9.4% and two others have seen slower growth. The industry as a whole has seen revenues grow by 7.3% per year, compounded annually. On this basis one would conclude that Company A is doing well and in fact might be gaining market share. Of course, other factors need to be looked at, such as debt and the outlook for the industry.

The formula for compound annual growth rate is:

((Ending Value/Beginning Value)^(1/# of Years))-1

(A financial calculator may be useful for performing this calculation.)

There are five variables in a compound growth rate calculation:

  • Beginning value
  • Ending value
  • Length of time between the values
  • Periodic scale (days?, months? years?)
  • Periodic rate of change

You need to know four of these values to make the calculation of the fifth.

For example, Company A had revenues of $1.35 billion in 2002. Revenues grew by a CAGR of 8.5% through 2007, a period of five years. We know the beginning value, the length of time, the periodic scale (years) and the periodic rate of change. Now we can determine what the revenue was in 2007.

Related concepts:

Average annual change is not to be confused with compound annual change. Average annual change is simply the growth rate over a period, say 50% over ten years, divided by the number of years, which yields 5.0% in this case. That is higher than the CAGR, which is 4.1%.

Compound interest. Useful when there is a set interest rate, as in a savings account. The interest rate is applied to the beginning principal and also to all accumulated interest. Sometimes there is an annual interest rate compounded monthly. Say you deposit $10,000 at an annual interest rate of 12% (you wish!), compounded monthly. At the end of the first month your $10,000 has grown by 1.0% (12%/12), or $100. During the next month the basis is $10,100 and it grows another 1%, or $101, making the balance $10, 201. At the end of one year the balance grows to $11,268. Compare that with $10,000 invested at a simple annual interest rate of 12%, which yields $11,120, which is $148 less.