Chapter 15, Problem 8P

a)

Summary Introduction

To determine: The effects on using leverage on the firm’s value

Explanation of Solution

Compute the Original value of the firm:

$\begin{array}{c}\text{V}=\text{D}+\text{S}\\ =0+\left(\$15\right)\left(200,000\right)\\ =\$3,000,000\end{array}$

$\begin{array}{c}\text{V}=\text{D}+\text{S}\\ =0+\left(\$15\right)\times \left(200,000\right)\\ =\$3,000,000\end{array}$

Compute the original cost of capital:

$\begin{array}{c}\text{WACC}=w_d{r}_d\left(1-T\right)+w_{ce}{r}_s\\ =0+\left(1.0\right)\left(10\%\right)\\ =10\%\end{array}$

With financial leverage (w_d=30%):

$\begin{array}{c}\text{WACC}=w_d{r}_d\left(1-T\right)+w_{ce}{r}_s\\ =\left(0.3\right)\left(7\%\right)\left(1-0.40\right)+\left(0.7\right)\left(11\%\right)\\ =8.96\%\end{array}$

$\begin{array}{c}{\text{V}}_{\text{op}}=\frac{\text{FCF}}{\text{WACC}}\\ =\frac{\left(\text{EBIT}\right)\left(\text{1}-\text{T}\right)}{\text{WACC}}\\ =\frac{(\$500,000)(1-0.40)}{0.0896}\\ =\$3,348,\mathrm{214.286.}\end{array}$

Increasing the financial leverage by adding debt of $900,000 results in an growth in the  value of the firm’s from $3,000,000 to $3,348,214.286.

b)

Summary Introduction

To determine: The price of Company R’s stock.

Explanation of Solution

Compute price of stock:

$\begin{array}{c}\text{D}={\text{w}}_{\text{d}}\text{V}\\ =0.30\times \left(\$3,348,214.286\right)\\ =\$1,004,464.286\end{array}$

Value of equity:

$\begin{array}{c}\text{S}=\text{V}–\text{D}\\ =\$2,343,750\end{array}$

Price of stock:

$\begin{array}{c}\text{P}=\frac{\left[\text{S + }\left({\text{D – D}}_{\text{0}}\right)\right]}{{\text{n}}_{\text{0}}}\\ =\left[\frac{\text{\$2,343,750}+\left(\text{\$1,004,464}\text{.286–0}\right)}{\text{200,000}}\right]\\ =\$16.741\end{array}$

Hence, price of the stock is $16.741.

c)

Summary Introduction

To determine: The effects EPS of the firm after recapitalization.

Explanation of Solution

Compute number of shares:

$\begin{array}{c}\text{X}=\frac{\left({\text{D – D}}_{\text{0}}\right)}{\text{P}}\\ =\frac{\text{\$1,004,464}\text{.286}}{\text{\$16}\text{.741}}\\ =\text{60,000}\text{.256}\\ \text{Number of shares}=200,000-60,000\\ =140,000\end{array}$

Initial position:

$\begin{array}{c}\text{EPS}=\frac{\text{NI}}{n_0}\\ =\frac{\left[\left(EBIT–\text{Interest}\right)\left(1-\text{T}\right)\right]}{n_0}\\ =\frac{\left[\left(\$500,000-0\right)\left(1-0.40\right)\right]}{200,000}\\ =\$1.50\end{array}$

Financial leverage:

$\begin{array}{c}\text{EPS}=\frac{\left[\left(\$500,000-0.07\right)\times \$1,004,464.286\times \left(1-0.40\right)\right]}{140,000}\\ =\$1.842\end{array}$

EPS:

$\begin{array}{c}\text{EPS}=\$1.842-\$1.50\\ =\$0.342\end{array}$

Hence, change in EPS is $0.342.

d)

Summary Introduction

To determine: The times-interest-earned ratio and the probability of not covering the interest payment at 30% debt level.

Explanation of Solution

Compute price of stock:

$\begin{array}{c}\text{TIE}=\frac{\text{EBIT}}{\text{I}}\\ =\frac{\text{EBIT}}{\text{\$70,312}\text{.5}}\end{array}$

Excel workings:

Excel spread sheet:

• The interest payment is not covered if TIE < 1.0. 
• The probability of this occurring is 10%.