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. $\begin{array} { c c c }
\text { Year } & \text { P/E Ratio } & \text { Growth rate } \% \
1998 & 12.4 & \
1999 & 14.6 & 17.74 \% ( 1998 - 1999 ) \
2000 & 11.1 & - 23.97 \% ( 1999 - 2000 ) \
2001 & 8.2 & - 26.13 \% ( 2000 - 2001 ) \
2002 & 6.8 & - 17.07 \% ( 2001 - 2002 )
\end{array}$
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. $\begin{array} { c c c } 
\text { Year } & \text { P/E Ratio } & \text { Growth rate } \% \
1998 & 12.4 & \
1999 & 14.6 & 17.74 \% ( 1998 - 1999 ) \
2000 & 11.1 & - 23.97 \% ( 1999 - 2000 ) \
2001 & 8.2 & - 26.13 \% ( 2000 - 2001 ) \
2002 & 6.8 & - 17.07 \% ( 2001 - 2002 )
\end{array}$
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 find out the geometric mean growth rate over the period, we can use the formula:
Geometric mean = [(1+g1)(1+g2)...(1+gn)]^(1/n) - 1
where g1, g2, ..., gn are the annual growth rates.
Using the given values, we can calculate:
Geometric mean = [(1+17.74/100)(1-23.97/100)(1-26.13/100)(1-17.07/100)]^(1/4) - 1
Geometric mean = (0.9176)^(1/4) - 1
Geometric mean = -0.1397
Therefore, the answer is B.

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