# How to Compute the Compound Annual Growth Rate

We know that the compound annual growth rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

Let us consider Disney’s (NYSE: DIS) 10 year book value per share from 2002 - 2011 and compute its CAGR over that period:

Year Book Value
2002 $11.61 2003$11.82
2004 $13.05 2005$13.06
2006 $15.42 2007$15.67
2008 $17.73 2009$18.55
2010 $19.78 2011$21.21

our present value starting 2002 is $$PV=\11.61$$. Our future value (measure in 2011) is $$FV=\21.21$$. We know that:

$$FV=PV (1 + r)^n$$

where $$r$$ is the annual rate of return and $$n$$ is the number of periods over which we are compounding our value.

So in order for us to calculate the compound annual growth rate, $$r$$, we need to divide the value of an investment at the end of the period, $$FV$$, by its value at the beginning of that period, $$PV$$, and raise the result to the power of one divided by the period length $$n$$ (or n-th root), and subtract one from the subsequent result:

$$r=(\frac{FV}{PV})^{(\frac{1}{n})} - 1$$

For our Disney example this would be:

$$(\frac{21.21}{11.61})^{(\frac{1}{9})} - 1=0.0692$$ or $$6.92\%$$
Written on August 15, 2021