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 maximum earnings.

Answer to Problem 28QP

The high target stock prices over the next year are $76.95.

The low target stock prices over the next year are $60.79.

Explanation of Solution

Given information:

The high price of Year 1, Year 2, Year 3, and Year 4 is $48.60, $57.34, $69.46, and $74.85 respectively. The low price of Year 1, Year 2, Year 3, and Year 4 is $37.25, $42.18, $55.85, and $63.18 respectively. The earnings per share of Year 1, Year 2, Year 3, and Year 4 are $2.35, $2.48, $2.63, and $2.95. The projected earnings growth rate for next year is 9%.

Formulae:

The formula to calculate 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 next year,

EPS_orefers 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 low price to earnings:

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

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 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:

$\begin{array}{c}{\text{EPS}}_1={\text{EPS}}_o\left(1+\text{g}\right)\\ =\$2.95\times \left(1+\frac{9}{100}\right)\\ =\$2.95\times 1.09\\ =\$3.22\end{array}$

Hence, the next year’s earnings per share are $3.22.

Compute the high price to earnings ratio of Year 1:

$\begin{array}{c}\text{High price to earnings ratio of Year 1}=\frac{\text{High price of stock of Year 1 }}{\text{Earnings per share of Year 1}}\\ =\frac{\$48.60}{\$2.35}\\ =\$20.68\end{array}$

Hence, the high price to earnings ratio of Year 1 is $20.68.

Compute the high price to earnings ratio of Year 2:

$\begin{array}{c}\text{High price to earnings ratio of Year 2}=\frac{\text{High price of stock of Year 2 }}{\text{Earnings per share of Year 2}}\\ =\frac{\$57.34}{\$2.48}\\ =\$23.12\end{array}$

Hence, the high price to earnings ratio of Year 2 is $23.12.

Compute the high price to earnings ratio of Year 3:

$\begin{array}{c}\text{High price to earnings ratio of Year 3}=\frac{\text{High price of stock of Year 3 }}{\text{Earnings per share of Year 3}}\\ =\frac{\$69.46}{\$2.63}\\ =\$26.41\end{array}$

Hence, the high price to earnings ratio of Year 3 is $26.41.

Compute the high price to earnings ratio of Year 4:

$\begin{array}{c}\text{High price to earnings ratio of Year 4}=\frac{\text{High price of stock of Year 4 }}{\text{Earnings per share of Year 4}}\\ =\frac{\$74.85}{\$2.95}\\ =\$25.37\end{array}$

Hence, the high price to earnings ratio of Year 4 is $25.37.

Compute the average high price to earnings:

$\begin{array}{c}\text{Average high price to earnings ratio}=\frac{\text{Sum of each year's high price to earnings ratio}}{\text{Total number of years}}\\ =\frac{\$20.68+\$23.12+\$26.41+\$25.37}{4}\\ =\frac{\$95.58}{4}\\ =\$23.90\end{array}$

Hence, the average high price to earnings ratio is $23.90.

Compute the high price of a share of stock:

$\begin{array}{c}{\text{P}}_1=\text{Benchmark price to earnings ratio}\times {\text{EPS}}_1\\ =\$23.90\times \$3.22\\ =\$76.95\end{array}$

Hence, high price of a share of stock is $76.95.

Compute the low price to earnings ratio of Year 1:

$\begin{array}{c}\text{Low price to earnings ratio of Year 1}=\frac{\text{Low price of stock of Year 1 }}{\text{Earnings per share of Year 1}}\\ =\frac{\$37.25}{\$2.35}\\ =\$15.85\end{array}$

Hence, the low price to earnings ratio of Year 1 is $15.85.

Compute the low price to earnings ratio of Year 2:

$\begin{array}{c}\text{Low price to earnings ratio of Year 2}=\frac{\text{Low price of stock of Year 2 }}{\text{Earnings per share of Year 2}}\\ =\frac{\$42.18}{\$2.48}\\ =\$17.01\end{array}$

Hence, the low price to earnings ratio of Year 2 is $17.01.

Compute the low price to earnings ratio of Year 3:

$\begin{array}{c}\text{Low price to earnings ratio of Year 3}=\frac{\text{Low price of stock of Year 3 }}{\text{Earnings per share of Year 3}}\\ =\frac{\$55.85}{\$2.63}\\ =\$21.24\end{array}$

Hence, the low price to earnings ratio of Year 3 is $21.24.

Compute the low price to earnings ratio of Year 4:

$\begin{array}{c}\text{Low price to earnings ratio of Year 4}=\frac{\text{Low price of stock of Year 4 }}{\text{Earnings per share of Year 4}}\\ =\frac{\$63.18}{\$2.95}\\ =\$21.42\end{array}$

Hence, the low price to earnings ratio of Year 4 is $21.42.

Compute the average low price to earnings:

$\begin{array}{c}\text{Average low price to earnings ratio}=\frac{\text{Sum of each year's low price to earnings ratio}}{\text{Total number of years}}\\ =\frac{\$15.85+\$17.01+\$21.24+\$21.42}{4}\\ =\frac{\$75.52}{4}\\ =\$18.88\end{array}$

Hence, the average low price to earnings ratio is $18.88.

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

$\begin{array}{c}{\text{P}}_1=\text{Benchmark price to earnings ratio}\times {\text{EPS}}_1\\ =\$18.88\times \$3.22\\ =\$\text{60}\text{.79}\end{array}$

Hence, the low price of a share of stock is $60.79.