Chapter 7, Problem 28QP

Summary Introduction

To determine: The high and low target stock prices over the next year.

Introduction:

Target stock price is a price in which the investor wants to exit from the current position to attain the maximum earnings.

Answer to Problem 28QP

The high target stock prices over the next year are $160.96 andthe low target stock prices over the next year are $112.41.

Explanation of Solution

Given information:

Refer QP 28 in the text for high price, low price and EPS details.

Formula:

The formula to calculate the next year’s earnings per share:

${\text{EPS}}_1={\text{EPS}}_o\left(1+\text{g}\right)$

Where,

EPS₁refers to the earnings per share of the next year,

EPS_o refers to the current year’s earnings per share,

g refers to the expected growth rate.

The formula to calculate high or low price-to-earnings ratio:

$\text{High or low price-to-earnings ratio}=\frac{\text{High or low price of stock of the year}}{\text{Earnings per share of the year}}$

The formula to determine average high or lowprice-to-earnings:

$\text{Average high or low price-to-earnings ratio}=\frac{\begin{array}{l}\text{Sum of each year's high }\\ \text{or low price to earnings ratio}\end{array}}{\text{Total number of years}}$

The formula to calculate the price of a share of stock:

${\text{P}}_1=\text{Benchmark price-to-earnings ratio }\times {\text{EPS}}_1$

Where,

EPS₁ refers to the earnings per share of the next year,

P₁ refers to the price of stock per share.

Note:

The current stock price is often called as high or low target stock prices over the next year.

Compute the next year’s earnings per share:

$\begin{array}{c}{\text{EPS}}_1={\text{EPS}}_o\left(1+\text{g}\right)\\ =\$11.40\times \left(1+\frac{6}{100}\right)\\ =\$11.40\times 1.06\\ =\$12.084\end{array}$

Hence, the next year’s earnings per share are $12.084.

Compute the high price to earnings ratio of Year 1:

$\begin{array}{c}\text{High price-to-earnings ratio of Year 1}=\frac{\text{High price of stock of Year 1 }}{\text{Earnings per share of Year 1}}\\ =\frac{\$97.90}{\$7.18}\\ =\$13.64\end{array}$

Hence, the high price-to-earnings ratio of Year 1 is $13.64.

Compute the high price to earnings ratio of Year 2:

$\begin{array}{c}\text{High price-to-earnings ratio of Year 2}=\frac{\text{High price of stock of Year 2 }}{\text{Earnings per share of Year 2}}\\ =\frac{\$121.50}{\$8.93}\\ =\$13.61\end{array}$

Hence, the high price-to-earnings ratio of Year 2 is $13.61.

Compute the high price-to-earnings ratio of Year 3:

$\begin{array}{c}\text{High price-to-earnings ratio of Year 3}=\frac{\text{High price of stock of Year 3 }}{\text{Earnings per share of Year 3}}\\ =\frac{\$130.90}{\$10.01}\\ =\$13.08\end{array}$

Hence, the high price-to-earnings ratio of Year 3 is $13.08.

Compute the high price-to-earnings ratio of Year 4:

$\begin{array}{c}\text{High price-to-earnings ratio of Year 4}=\frac{\text{High price of stock of Year 4 }}{\text{Earnings per share of Year 4}}\\ =\frac{\$147.53}{\$11.40}\\ =\$12.94\end{array}$

Hence, the high price-to-earnings ratio of Year 4 is $12.94.

Compute the average high price-to-earnings ratio :

$\begin{array}{c}\text{Average high price-to-earnings ratio}=\frac{\text{Sum of each year's high price-to-earnings ratio}}{\text{Total number of years}}\\ =\frac{\$13.64+\$13.61+\$13.08+\$12.94}{4}\\ =\frac{\$53.27}{4}\\ =\$13.32\end{array}$

Hence, the average high price-to-earnings ratio is $13.32.

Compute the high price of a share of stock:

$\begin{array}{c}{\text{P}}_1=\text{Benchmark price-to-earnings ratio}\times {\text{EPS}}_1\\ =\$13.32\times \$12.084\\ =\$160.96\end{array}$

Hence, high price of a share of stock is $160.96.

Compute the low price-to-earnings ratio of Year 1:

$\begin{array}{c}\text{Low price-to-earnings ratio of Year 1}=\frac{\text{Low price of stock of Year 1 }}{\text{Earnings per share of Year 1}}\\ =\frac{\$72.73}{\$7.18}\\ =\$10.13\end{array}$

Hence, the low price-to-earnings ratio of Year 1 is $10.13.

Compute the low price-to-earnings ratio of Year 2:

$\begin{array}{c}\text{Low price-to-earnings ratio of Year 2}=\frac{\text{Low price of stock of Year 2 }}{\text{Earnings per share of Year 2}}\\ =\frac{\$88.84}{\$8.93}\\ =\$9.95\end{array}$

Hence, the low price-to-earnings ratio of Year 2 is $9.95.

Compute the low price-to-earnings ratio of Year 3:

$\begin{array}{c}\text{Low price-to-earnings ratio of Year 3}=\frac{\text{Low price of stock of Year 3 }}{\text{Earnings per share of Year 3}}\\ =\frac{\$69.52}{\$10.01}\\ =\$6.95\end{array}$

Hence, the low price-to-earnings ratio of Year 3 is $6.95.

Compute the low price-to-earnings ratio of Year 4:

$\begin{array}{c}\text{Low price-to-earnings ratio of Year 4}=\frac{\text{Low price of stock of Year 4 }}{\text{Earnings per share of Year 4}}\\ =\frac{\$116.05}{\$11.40}\\ =\$10.18\end{array}$

Hence, the low price-to-earnings ratio of Year 4 is $10.18.

Compute the average low price-to-earnings ratio:

$\begin{array}{c}\text{Average low price-to-earnings ratio}=\frac{\text{Sum of each year's low price-to-earnings ratio}}{\text{Total number of years}}\\ =\frac{\$10.13+\$9.95+\$6.95+\$10.18}{4}\\ =\frac{\$37.21}{4}\\ =\$9.3025\end{array}$

Hence, the average low price-to-earnings ratio is $9.3025.

Compute the low target price (price of a share of stock):

$\begin{array}{c}{\text{P}}_1=\text{Benchmark price-to-earnings ratio}\times {\text{EPS}}_1\\ =\$9.3025\times \$12.084\\ =\$\text{112}\text{.41}\end{array}$

Hence, the low price of a share of stock is $112.41.