CAGR - Compounding Average Growth Rate

 This is a very simple, but easily forgetting formula that many people in finance or research use. The goal of the CAGR (compounding average growth rate) is to figure out the exact percentage that a beginning value must grow at per period in order to reach a final value in a given number of periods.

Free CAGR calculator: Example Google Sheet

Here are all the inputs you need:

  • Beginning value
  • Ending value
  • Number of periods in-between the beginning and ending value

Here is the formula:
(ending value / beginning value) divided by (1/number of periods) - 1

Be sure to use the parenthesis as seen above. Also, it is correct that the ending value is divided by the beginning value even through it seems kind of backwards.

Remember, when you are figuring out the number of periods in-between, be sure to count only the number of times the beginning value grows, not the total periods you see. For example, if the beginning value starts in period 1 and the ending value is in period 10, there are 9 total growth periods and 9 is what you would input into the CAGR formula.

This is most commonly used in financial modeling when one wants to figure out the average growth in revenue, EBITDA, or some other key metric over time. In a 5-year model, there will always be 4 annual periods and 59 monthly periods assuming everything starts in period 1 and ends in period 5 (or 1/60 for monthly).

The rate is a highlight of the compounded growth that must happen (the same growth rate) each period in order to end up at the final value.

This could also be used to figure out average inflation rates in the same sense because you can see the average compounded rate of change required to get from a beginning value to an ending value. For example, how much did the value of $1.00 change from 1920 to 2020? The buying power of $1.00 in 1920 is $1.00 and in 2020 the same buying power equivalent (what amount of money is able to buy the same relative amount of foods / services / goods that $1.00 could have bought in 1920) may be $30 or $50 or whatever the number is. CAGR plays a big part here in figuring out the average periodic change.