Compound annual growth rate

Compound Annual Growth Rate (CAGR) or cumulative annual growth rate is another term for the rate of return or interest rate variable in the formula Present value of a dollar and Future value of a dollar discussed at time value of money. It measures the rate of change in a value between two points in time(t and t0). These equations are basic to the concept of compound interest.


 * $$\mathrm{CAGR}(t_0,t) = \left( \frac{V(t)}{V(t_0)} \right)^\frac{1}{t-t_0} - 1 $$

Where V(t0) = the start value, V(t) = the finish value and t-t0 is the time span.

In business, CAGR is used to describe the growth over a period of time of some element of the business, usually revenue, although other measures may be used (such as the number of units delivered, registered users, etc.). CAGR is not an accounting term, but remains widely used, particularly in growth industries. CAGR is preferable to applying more simplistic terms, such as "business doubled in three years", as it properly accounts for the effect of compounding.

Example
A company may double its sales (an increase of 100%) over a period of four years. Applying the formula above, the CAGR is approximately 18.9% (not 25% per year):
 * $$ {CAGR} = \left( \frac{200}{100} \right)^\frac{1}{4} - 1 = 0.1892 = 18.92%$$

Note (1): The actual sales figures may be used for calculation, or (as above) normalized values that retain the same mathematical proportion.

Note (2): You can use the following formule to calculate CAGR in Excel:
 * "=((lastnumber/firstnumber)^(1/numberofperiods))-1"

Note (3): A quicker way to calculate the CAGR with Excel is to use the RATE function as follows:
 * =RATE(A3,,-A1,A2)
 * A1 is the starting number
 * A2 the ending ammount
 * A3 is the number of periods.