Kaplan CAGR vs. geometric return issue

So on page 123 of book 1 there’s a TVM question about CAGR that says in the last 5 years there’s been sales (all in euros) of 4.5, 5.7, 5.3, 6.9, and 7.1. the question asks what the compound annual growth rate of sales over the period is.

the answer is that the 5 years of sales represent 4 years of growth and the CAGR of sales is (7.1/4.5)^(1/4)-1=12.1%. the interem sales figures don’t matter

Contrast this with the later discussion of the geometric mean return of equity returns, which in one example were -9.34%, 23.45%, and 8.92%. the question asks what the compound annual rate of return over the 3 year period is. for this one it’s 1+ each of the returns, then all the returns multiplied together which is 1.21903. then the cube root of that which gives a CAGR of 6.825.

My question is what’s the differnce between these two? Why the totally different methods and different results?

To get a growth rate you need a beginning and an end value.

The first example gives you 5 values (not growth rates). You could calculate the growth in each year (add 1), multiply them and then take the fourth root of the final result. However, since they gave you beginning and ending values, just divide final by initial and take the _n_th root, where n is the number of growth periods (here it is 4).

The second example doesn’t give you values of an asset (for example), just growth (return/etc.) rates. Remember you need 2 points in time to get one growth rate. So time 0 to time 1, time 1 to time 2, and time 2 to time 3 gives three growth periods. If you had a dollar at time 0, it would be worth 9.34% less at time 1 ( 0.9066), then this would grow by 23.45% so .9066*1.2345= 1.1192… until you get the final value of 1.21903. Take the 3rd root to get the geometric growth rate. Here, you need the interim growth rates, because you don’t know the final and initial (asset) values.

There really aren’t any differences (sure one is a growth rate and the other is a rate of return, but the investment grew to give a return), they just gave you slightly different information to start with, so your approach is slightly different. Mathematically, same idea, though.