Compound annual growth rate

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Please improve this article if you can. (May 2008)

Compound Annual Growth Rate (CAGR) is a business and investing specific term for the geometric mean growth rate on an annualized basis.

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

Where,

     V(t_0)     = start value, 
     V(t_n)     = finish value, and
     t_n - t_0  = number of years.

Note (1): The actual values may be used for calculation, or normalized values that retain the same mathematical proportion. Note (2): You can use the following formula to calculate CAGR in Excel:

  • XIRR function
  • "=((lastnumber/firstnumber)^(1/numberofyears))-1"

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 or to compare the growth rates of two investments because CAGR dampens the effect of volatility of periodic returns that can render arithmetic means irrelevant.

[edit] Example

Where:

    V(t_0) = 100,
    V(t_1) =  95,
    V(t_2) = 115,
    V(t_3) = 150,
    V(t_4) = 200, and
    
    t_n - t_0 = 4;
{CAGR} = \left( \frac{200}{100} \right)^\frac{1}{4} - 1 = 0.1892 = 18.92%

Whereas,

The Arithmetic Mean Return would be the sum of annual returns divided by number of years or:

\bar{x} = \frac{1}{n}\sum_{i=1}^n x_i = \frac{1}{n} (x_1+\cdots+x_n) = \frac{-5% + 21% + 30% + 25%}{4} = 20.25%.

Whereas,

The Arithmetic Return or simple return would be the ending value - beginning value divided by the beginning value:

\text{Arithmetic Return}=\frac{V_f - V_i}{V_i} = \frac{200-100}{100} = 100%.

[edit] See also

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