The following table shows the Price-to-Earnings ratio for a Stereo equipment manufacturing...

Question:

The following table shows the Price-to-Earnings ratio for a Stereo equipment manufacturing company between 1998 and 2002. The annual percentage growth rate of the P/E ratios are also calculated and given below:

Year/ P-E Ratio/ Growth rate %

1998/ 12.4/ -

1999/ 14.6/ 17.74% (1998-1999)

2000/ 11.1/ -23.97% (1999-2000)

2001/ 8.2/ -26.13% (2000-2001)

2002/ 6.8/ -17.07% (2001-2002)

Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002. Please show ALL work

Geometric Average:

The formula for a geometric average return is ((1 + Return1) * (1 + Return2) * ... (1 + Returnn))1/n - 1. It is considered a better estimate for the average return than the arithmetic average.

Answer and Explanation:

The geometric average return is:

{eq}\bar {g}=\sqrt[n]{\prod_{1}^{n}(1+g_{i})}-1\\ \bar {g}=\sqrt[4]{(1+0.1774)*(1-0.2397)*(1-0.2613)*(1-0.1707)}-1\\ \bar {g}=-13.95\%\\ {/eq}


Learn more about this topic:

Geometric vs. Arithmetic Average Returns

from Finance 101: Principles of Finance

Chapter 11 / Lesson 6
2.2K

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