Chapter 11, Problem 17P

Compute $K_e\text{ and }{K}_n$ under the following circumstances:

$\begin{array}{l}\text{a}\text{. }{D}_{1 }=\$5.00, P_0 =\$70, g =8\%, F =\$\mathrm{7.00.}\hfill \\ \text{b}\text{. }{D}_{1 }=\$0.22, P_0 =\$28, g =7\%, F =\$\mathrm{2.50.}\hfill \\ \begin{array}{l}\text{c}\text{. }{E}_1\left(\text{earnings at the end of period one}\right)=\$7,\text{ payout ratio equals 40 percent},\\ P_0 =\$30, g = 6.0\%, F =\$\mathrm{2.20.}\end{array}\hfill \\ \text{d}\text{. }{D}_0\left(\text{dividend at the beginning of the first period}\right)=\$6,\text{ growth rate for dividends and earnings }\left(g\right) =7\%, P_0 =\$60, F =\$3.\hfill \end{array}$

Summary Introduction

To calculate: The costs of retained earnings and new common stock according to the given circumstances.

Introduction:

Retained Earnings (Ke):

They are considered the profits of the company not distributed as dividend to shareholders. They are reserved for the purpose of reinvesting into the business, that is, for the expansion of the business.

New common stock (Kn):

Also termed as ordinary shares, it is a type of security that represents corporate equity ownership. It is the best means to earn a real rate of return ahead of inflation in the long run.

Answer to Problem 17P

The costs of retained earnings and new common stock are 15.14% and 15.94%, respectively.

Explanation of Solution

Calculation of the cost of retained earnings (Ke):

$\begin{array}{c}{\text{K}}_{\text{e}}=\frac{\text{Dividend }}{\text{Current Price}}+\text{Growth Rate}\\ =\frac{\$5}{\$70}+8\%\\ =7.14\%+8\%\\ =15.14\%\end{array}$

Calculation of the cost of common stock (Kn):

$\begin{array}{c}{\text{K}}_{\text{n}}=\frac{\text{Dividend }}{\text{Current Price}-\text{Flotation Cost}}+\text{Growth Rate}\\ =\frac{\$5}{\$70-\$7}+8\%\\ =\frac{\$5}{\$63}+8\%\\ =15.94\%\end{array}$

Summary Introduction

To calculate: The costs of retained earnings and new common stock according to the given circumstances.

Introduction:

Retained Earnings (Ke):

They are considered the profits of the company not distributed as dividend to shareholders. They are reserved for the purpose of reinvesting into the business, that is, for the expansion of the business.

New common stock (Kn):

Also termed as ordinary shares, it is a type of security that represents corporate equity ownership. It is the best means to earn a real rate of return ahead of inflation in the long run.

Answer to Problem 17P

The costs of retained earnings and new common stock are 7.79% and 7.86%, respectively.

Explanation of Solution

Calculation of the cost of retained earnings (Ke):

$\begin{array}{c}{\text{K}}_{\text{e}}=\frac{\text{Dividend }}{\text{Current Price}}+\text{Growth Rate}\\ =\frac{\$0.22}{\$28}+7\%\\ =0.79\%+7\%\\ =7.79\%\end{array}$

Calculation of the cost of common stock (Kn):

$\begin{array}{c}{\text{K}}_{\text{n}}=\frac{\text{Dividend }}{\text{Current Price}-\text{Flotation Cost}}+\text{Growth Rate}\\ =\frac{\$0.22}{\$28-\$2.50}+7\%\\ =\frac{\$0.22}{\$25.50}+7\%\\ =7.86\%\end{array}$

Summary Introduction

To calculate: The costs of retained earnings and new common stock according to the given circumstances.

Introduction:

Retained Earnings (Ke):

They are considered the profits of the company not distributed as dividend to shareholders. They are reserved for the purpose of reinvesting into the business, that is, for the expansion of the business.

New common stock (Kn):

Also termed as ordinary shares, it is a type of security that represents corporate equity ownership. It is the best means to earn a real rate of return ahead of inflation in the long run.

Answer to Problem 17P

The costs of retained earnings and new common stock are 15.33% and 16.07%, respectively.

Explanation of Solution

Calculation of the cost of retained earnings (Ke):

$\begin{array}{c}{\text{K}}_{\text{e}}=\frac{\text{Dividend }}{\text{Current Price}}+\text{Growth Rate}\\ =\frac{\$2.80}{\$30}+6\%\\ =9.33\%+6\%\\ =15.33\%\end{array}$

Calculation of the cost of common stock (Kn):

$\begin{array}{c}{\text{K}}_{\text{n}}=\frac{\text{Dividend }}{\text{Current Price}-\text{Flotation Cost}}+\text{Growth Rate}\\ =\frac{\$2.80}{\$30-\$2.20}+6\%\\ =\frac{\$2.80}{\$27.80}+6\%\\ =16.07\%\end{array}$

Working Note:

Calculation of dividend:

$\begin{array}{c}\text{Dividend}=\text{Payout ratio}\times \text{Earnings at the end of period }\left({\text{E}}_{\text{1}}\right)\\ =40\%\times \$7\\ =\$2.80\end{array}$

Summary Introduction

To calculate: The costs of retained earnings and new common stock according to the given circumstances.

Introduction:

Retained Earnings (Ke):

They are considered the profits of the company not distributed as dividend to shareholders. They are reserved for the purpose of reinvesting into the business, that is, for the expansion of the business.

New common stock (Kn):

Also termed as ordinary shares, it is a type of security that represents corporate equity ownership. It is the best means to earn a real rate of return ahead of inflation in the long run.

Answer to Problem 17P

The costs of retained earnings and new common stock are 17.7% and 18.26%, respectively.

Explanation of Solution

Calculation of the cost of retained earnings (Ke):

$\begin{array}{c}{\text{K}}_{\text{e}}=\frac{\text{Dividend }}{\text{Current Price}}+\text{Growth Rate}\\ =\frac{\$6.42}{\$60}+7\%\\ =10.7\%+7\%\\ =17.7\%\end{array}$

Calculation of the cost of common stock (Kn):

$\begin{array}{c}{\text{K}}_{\text{n}}=\frac{\text{Dividend }}{\text{Current Price}-\text{Flotation Cost}}+\text{Growth Rate}\\ =\frac{\$6.42}{\$60-\$3}+7\%\\ =\frac{\$6.42}{\$57}+7\%\\ =18.26\%\end{array}$

Working Note:

Calculation of dividend:

$\begin{array}{c}\text{Dividend}=\text{Dividend at the beginning of the period}\times \left(\text{1}+\text{Growth Rate}\right)\\ =\$6\times \left(1+0.07\right)\\ =\$6\times \left(1.07\right)\\ =\$6.42\end{array}$