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 is also calculated and given below. Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002.
A)-.2592
B)-.1397
C)-.1816
D).8616
E).7417

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 is also calculated and given below.  Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002.
A)-.2592 
B)-.1397 
C)-.1816 
D).8616 
E).7417

Quizplus · Accepted Answer

To calculate the geometric mean growth rate, we need to use the formula: (P/E ratio end / P/E ratio start)^(1/n) - 1, where n is the number of years.

Using the given table, we can calculate the P/E ratios and growth rates as follows:

- 1998: P/E ratio = 18.7, growth rate = N/A
- 1999: P/E ratio = 22.5, growth rate = (22.5/18.7)^(1/1) - 1 = 0.2038
- 2000: P/E ratio = 28.0, growth rate = (28.0/22.5)^(1/1) - 1 = 0.2444
- 2001: P/E ratio = 21.2, growth rate = (21.2/28.0)^(1/1) - 1 = -0.2429
- 2002: P/E ratio = 17.1, growth rate = (17.1/21.2)^(1/1) - 1 = -0.1925

To calculate the geometric mean growth rate, we multiply all the growth rates and take the nth root, where n is the number of years:

(1 + 0.2038) x (1 + 0.2444) x (1 - 0.2429) x (1 - 0.1925) = 0.5304
4th root of 0.5304 = 0.8603
Subtracting 1, we get -0.1397.

Therefore, the answer is B, -0.1397, as this represents the geometric mean growth rate over the period from 1998 to 2002.

The Following Table Shows the Price-To-Earnings Ratio for a Stereo