Chapter 7, Problem 7.1C

Section 7.1    What is the total return for a stock that currently sells for $50, just paid a $1.75 dividend, and has a constant growth rate of 8 percent?

Summary Introduction

To determine: The total return for a stock.

Introduction:

Return is the minimum percentage an investor earns from the investment of stock in the market.

Stock is a type of security in a company which denotes ownership. On issuing stocks, the company can raise capital.

Answer to Problem 7.1C

The total return for a stock is 11.78%.

Explanation of Solution

Given information:

The current stock price is $50 and the currently paid dividends are $1.75. The constant growth rate is 8%.

The formula to calculate the dividend of next year (D₁):

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

Where,

D₁ refers to the dividend per share of next period,

D_orefers to the dividend just paid,

g refers to the constant growth of dividends.

The formula to calculate the required return:

$\text{R}=\left(\frac{{\text{D}}_1}{{\text{P}}_o}\right)+\text{g}$

Where,

R refers to the required return,

D₁ refers to the dividend per share of next period,

P_o refers to the present value of a share of stock,

g refers to the constant growth of dividends.

Compute the dividend of next year (D₁):

$\begin{array}{c}{\text{D}}_1={\text{D}}_o\times \left(1+\text{g}\right)\\ =\$1.75\times \left(1+\frac{8}{100}\right)\\ =\$1.75\times \left(1+0.08\right)\\ =\$1.75\times 1.08\\ =\$1.89\end{array}$

Hence, the dividend of next year is $1.89.

Compute the required return:

$\begin{array}{c}\text{R}=\left(\frac{{\text{D}}_1}{{\text{P}}_o}\right)+\text{g}\\ =\left(\frac{\$1.89}{\$50}\right)+\frac{8}{100}\\ =0.0378+0.08\\ =0.1178\end{array}$

Hence, the required return is 0.1178 or 11.78%.