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: Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002.
A)-.259
B)-.139
C)-.181
D).861
E).741

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:  Calculate the geometric mean growth rate increase or decrease over the period from 1998 to 2002.
A)-.259 
B)-.139 
C)-.181 
D).861 
E).741

Quizplus · Accepted Answer

To find the geometric mean growth rate increase or decrease, we need to first calculate the average annual percentage growth rate across the 5 years. Using the formula for geometric mean = [(1 + r1)*(1 + r2)*...*(1 + rn)]^(1/n) - 1, where r1, r2...rn are the annual percentage growth rates, we get:

[(1 + 0.2)*(1 - 0.2)*(1 - 0.35)*(1 + 0.15)*(1 - 0.1)]^(1/5) - 1
= [1.2*0.8*0.65*1.15*0.9]^(1/5) - 1
= 0.771 - 1
= -0.229 (rounded to three decimal places)

Therefore, the geometric mean growth rate increase or decrease over the period from 1998 to 2002 is -0.229 or -22.9%. The closest choice is B) -0.139, so that is the best answer.

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