Chapter 16, Problem 11QP

a)

Summary Introduction

To determine: Stock’s beta after refinancing.

Explanation of Solution

Given information:

Beta of firm entirely by equity and debt is 1, so beta of equity is 0.5 and beta of debt is 0.5.

The formula used is,

${\text{β}}_{\text{assets}}=\left({\text{β}}_{\text{debt}}\times \frac{\text{D}}{\text{V}}\right)+\left({\text{β}}_{\text{equity}}\times \frac{\text{E}}{\text{V}}\right)$

Calculation of beta after refinancing:

$\begin{array}{l}\text{1}=\left({\text{β}}_{\text{debt}}\times 0.5\right)+\left({\text{β}}_{\text{equity}}\times 0.5\right)\\ 1=0+\left({\text{β}}_{\text{equity}}\times 0.5\right)\\ {\text{β}}_{\text{equity}}=\frac{1}{0.5}=2\end{array}$

Hence, value of beta after refinancing is 2.

b)

Summary Introduction

To determine: Required return and risk premium before refinancing.

Explanation of Solution

Given information:

The return on stock is 10%, and return on assets also be 10%,

The risk free rate of return is 5%,

Calculation of risk premium:

$\begin{array}{c}\text{Risk}\text{premium}={\text{r}}_{\text{equity}}-{\text{r}}_{\text{debt}}\\ =10\%-5\%\\ =5\%\end{array}$

Hence, return on stock is 10% and risk premium is 5%.

c)

Summary Introduction

To determine: Required return and risk premium after refinancing.

Explanation of Solution

Given information:

Debt value ratio is 0.5

Calculation of return on equity:

$\begin{array}{l}{\text{r}}_{\text{assets}}={\text{r}}_{\text{assets}}+\left(\frac{\text{D}}{\text{E}}\times \left({\text{r}}_{\text{assets}}-{\text{r}}_{\text{debt}}\right)\right)\\ {\text{r}}_{\text{equity}}=0.1+\left(\text{1}\times \left(0.1-0.05\right)\right)\\ {\text{r}}_{\text{equity}}=15\%\end{array}$

Hence, return on equity is 15%

Calculation of risk premium:

$\begin{array}{c}\text{Risk}\text{premium}={\text{r}}_{\text{equity}}-{\text{r}}_{\text{debt}}\\ =15\%-5\%\\ =10\%\end{array}$

Hence, risk premium is 10%.

d)

Summary Introduction

To determine: Required return on debt.

Explanation of Solution

The required return on debt is here, is as same as risk free rate of 5%

e)

Summary Introduction

To determine: Required return on asset after refinancing.

Explanation of Solution

Given information:

The return on stock is 15%, and return on debt is 5%

Calculation of return on asset:

$\begin{array}{c}{\text{r}}_{\text{assets}}=\left({\text{r}}_{\text{debt}}\times \frac{\text{D}}{\text{V}}\right)+\left({\text{r}}_{\text{equity}}\times \frac{\text{E}}{\text{V}}\right)\\ =\left(5\%\times 0.5\right)+\left(15\%\times 0.5\right)\\ =10\%\end{array}$

Hence, return on asset is 10%

f)

Summary Introduction

To determine: Percentage increase in EPS after refinancing.

Explanation of Solution

Given information:

Total equity before financing is $10,000

Expected earnings would be $1,000 ($10,000 x 10%)

Calculation of interest:

$\begin{array}{c}\text{Interest}=\text{Debt}\times \text{Interest}\text{rate}\\ =\$5,000\times 5\%\\ =\$250\end{array}$

Calculation of equity earnings:

$\begin{array}{c}\text{Equity earnings}=\text{Operating}\text{income }-\text{Interest}\\ =\$1,000-\$250\\ =\$750\end{array}$

Calculation of earnings per share before refinancing:

$\begin{array}{c}\text{Earnings per share}\text{before}\text{ refinancing}=\frac{\text{Equity}\text{earnings}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$1,000}{1,000}\\ =\$1\end{array}$

Calculation of earnings per share after refinancing:

$\begin{array}{c}\text{Earnings per share}\text{after}\text{ refinancing}=\frac{\text{Equity}\text{earnings}}{\text{Number}\text{of}\text{shares}\text{outstanding}}\\ =\frac{\$750}{500}\\ =1.5\end{array}$

Calculation of increase in EPS:

$\begin{array}{c}\text{Increase in EPS}=\left(\frac{\text{EPS}\text{After}\text{refinancing}-\text{EPS}\text{before}\text{refinancing}}{\text{EPS}\text{before}\text{refinancing}}\right)\\ =\left(\frac{1.5-1}{1}\right)\times 100\\ =50\%\end{array}$

Hence, increase in EPS is 50%.

g)

Summary Introduction

To determine: New price multiple.

Explanation of Solution

Calculation of new price multiple:

$\begin{array}{c}\text{New price multiple}=\frac{10}{1.5}\\ =6.67\end{array}$

Hence, new price multiple is 6.67