Chapter 7, Problem 7.1STP

a.

Summary Introduction

To determine: The value of the common stock if the growth rate is 0.00% to infinity.

Answer to Problem 7.1STP

The value of the common stock if the growth rate is 0.00% to infinity is $15.00.

Explanation of Solution

Given information:

Required rate: 12.00%

Annual dividend: $1.80

Formula used to calculate the stock price if the growth rate is 0.00% to infinity.

$\text{Stock}\text{price}\text{=}\frac{\text{Annual}\text{dividend}}{\text{Required}\text{rate}}$

Calculation of the stock price:

$\begin{array}{c}\text{Stock}\text{price}\text{=}\frac{\text{Annual}\text{dividend}}{\text{Required}\text{rate}}\\ =\frac{\$1.80}{12.00\%}\\ =\$15.00\end{array}$

Therefore, the stock price is $15.00.

b.

Summary Introduction

To determine: The value of the common stock if the growth rate is 5.00% to infinity.

Answer to Problem 7.1STP

The value of the common stock if the growth rate is 5.00% to infinity is $27.00.

Explanation of Solution

Given information:

Required rate: 12.00%

Annual dividend: $1.80

Growth rate: 5.00%

Formula used to calculate the stock price

$\text{Stock}\text{price}\left(P_0\right)=\frac{\text{Annual year-end dividend}\times \left(\text{1}+\text{Growth}\right)}{\text{Required}\text{rate}-\text{Growth}}$

Calculation of the stock price if the growth rate is 5.00% to infinity:

$\begin{array}{c}\text{Stock}\text{price}\left(P_0\right)=\frac{\text{Annual year-end dividend}\times \left(\text{1}+\text{Growth}\right)}{\text{Required}\text{rate}-\text{Growth}}\\ =\frac{\$1.80\left(1+5.00\%\right)}{12.00\%-5.00\%}\\ =\frac{\$1.89}{7.00\%}\\ =\$27.00\end{array}$

Therefore, stock price is $27.00.

b.

Summary Introduction

To determine: The stock price if expected to grow at an annual rate of 5% for each of the next 3 years, followed by a constant annual growth rate of 4% in year 4 to infinity.

Answer to Problem 7.1STP

The stock price if expected to grow at an annual rate of 5% for each of the next 3 years, followed by a constant annual growth rate of 4% in year 4 to infinity is $24.03.

Explanation of Solution

Calculation of the stock price:

Excel working:

Therefore, stock price is $24.03.