Chapter 8, Problem 8.1CTF

A stock is selling for $11.90 a share given a market return of 14 percent and a capital gains yield of 5 percent. What was the amount of the last annual dividend that was paid?

Summary Introduction

To determine: The amount of dividend per share paid lastly

Introduction:

Dividend is a sum of money paid to the shareholders of the company. It is distributed among the investors from the portion of a company’s earnings in the form of shares or cash.

Answer to Problem 8.1CTF

The amount of annual dividend per share paid lastly is $1.01.

Explanation of Solution

Given information:

Currently, stocks were sold at a price of $11.90 per share. The market rate of return is 14% on this stock and the capital gains yield is 5%.

The formula to calculate the amount of last annual dividend paid using required rate of return formula:

${\text{P}}_o={\text{D}}_o\times \frac{\left(1+\text{g}\right)}{\left(\text{R}-\text{g}\right)}$

Where,

P_o refers to the present price of stock

D_o refers to the recent dividend per share paid on the stock

Rrefers to the required return on the stock

g refers to the constant dividend’s growth rate

Compute the present annual dividend per share paid on the stock:

$\begin{array}{c}{\text{P}}_o={\text{D}}_o\times \frac{\left(1+\text{g}\right)}{\left(\text{R}-\text{g}\right)}\\ \$11.90={\text{D}}_{\text{o}}\times \frac{\left(1+\frac{5}{100}\right)}{\left(\frac{14}{100}-\frac{5}{100}\right)}\\ \$11.90={\text{D}}_{\text{o}}\times \frac{1+0.05}{\left(0.14-0.05\right)}\\ \$11.90={\text{D}}_{\text{o}}\times \left(\frac{1.05}{\text{0}\text{.09}}\right)\end{array}$

$\begin{array}{c}\$11.90={\text{D}}_{\text{o}}\times \text{11}\text{.667}\\ \frac{\$11.90}{\text{11}\text{.667}}={\text{D}}_{\text{o}}\\ \$\text{1}\text{.01}={\text{D}}_{\text{o}}\end{array}$

Hence, the amount of annual dividend per share paid lastly is $1.01.