Chapter 15, Problem 11P

The Rivoli Company has no debt outstanding, and its financial position is given by the following data:

1. a. What is Rivoli’s intrinsic value of operations (i.e., its unlevered value)? What is its intrinsic stock price? Its earnings per share?
2. b. Rivoli is considering selling bonds and simultaneously repurchasing some of its stock. If it moves to a capital structure with 30% debt based on market values, its cost of equity, r_s, will increase to 12% to reflect the increased risk. Bonds can be sold at a cost, r_d, of 7%. Based on the new capital structure, what is the new weighted average cost of capital? What is the levered value of the firm? What is the amount of debt?
3. c. Based on the new capital structure, what is the new stock price? What is the remaining number of shares? What is the new earnings per share?

Summary Introduction

To determine: Company R’s intrinsic value of operations and intrinsic stock price and its earnings per share.

Explanation of Solution

Calculation of original value of operations:

Original free cash flow:

$\begin{array}{c}\text{Original free cash-flow(FCF)}=\text{NOPAT}=\text{EBIT}\left(1-\text{T}\right)\\ =\$600,000\left(1-0.25\right)\\ =\$450,000\end{array}$

Hence, original cash flow is $450,000

Original cost of capital:

$\begin{array}{c}\text{WACC}={\text{w}}_{\text{d}}{\text{r}}_{\text{d}}\left(1-\text{T}\right)+{\text{w}}_{{}_{\text{ce}}}{\text{r}}_{\text{s}}\\ =0+\left(1.0\right)\left(10\%\right)\\ =10\%\end{array}$

Hence, original cost of capital is 10%

Original value of operations:

$\begin{array}{c}{\text{V}}_{\text{op}}=\frac{\left(\text{EBIT}\right)\left(1-\text{T}\right)}{\text{WACC}}\\ =\frac{\left(\$600,000\right)\left(1-0.25\right)}{0.10}\\ =\$4,500,000\end{array}$

Hence, original value of operations is $4,500,000

Calculation of intrinsic value of stock price:

$\begin{array}{c}\text{Original}\text{intrinsic}\text{stock}\text{price}=\frac{{\text{V}}_{\text{op}}}{{\text{n}}_{\text{o}}}\\ =\frac{\$4,500,000}{200,000}\\ =\$22.50\end{array}$

Therefore, intrinsic stock price is $22.50

Calculation of original EPS:

$\begin{array}{c}\text{Original}\text{EPS}=\frac{\text{NI}}{{\text{n}}_{\text{o}}}\text{or}\frac{\left(\text{EBIT}-\text{Interest}\right)\left(1-\text{T}\right)}{{\text{n}}_{\text{o}}}\\ =\frac{\left(\$600,000-\text{\$0}\right)\left(0.75\right)}{\text{200,000}}\\ =\$2.25\end{array}$

Therefore, the original EPS is $2.25

Summary Introduction

To determine: New WACC, levered value of the firm and the amount of debt.

Explanation of Solution

Calculation of WACC:

At 30% debt,

$\begin{array}{c}\text{WACC}={\text{w}}_{\text{d}}{\text{r}}_{\text{d}}\left(1-\text{T}\right)+{\text{w}}_{{}_{\text{ce}}}{\text{r}}_{\text{s}}\\ =\left(0.3\right)\left(7\%\right)\left(1-0.25\right)+\left(0.7\right)\left(12\%\right)\\ =9.975\%\end{array}$

Hence, weighted average cost of capital of company R is 9.975%

Therefore, new beta is 11.0528%

Calculation of value of operations:

Leverage doesn’t change the cash flows, so the value of levered firm based on new WACC is as follows,

$\begin{array}{c}{\text{V}}_{\text{op}}=\frac{\left(\text{EBIT}\right)\left(1-\text{T}\right)}{\text{WACC}}\\ =\frac{\left(\$600,000\right)\left(1-0.25\right)}{0.09975}\\ =\$4,511,278.195\end{array}$

Hence, the value of operations is $4,511,278.195

Calculation of amount of debt:

$\begin{array}{c}\text{D}={\text{w}}_{\text{d}}{\text{V}}_{\text{op}}\\ =\left(0.3\right)\left(\$4,511,278.195\right)\\ =\$1,353,383.459\end{array}$

Hence, the amount of debt is $1,353,383.459

Summary Introduction

To determine: New stock price, remaining number of shares and new earnings per share based on new capital structure.

Explanation of Solution

Calculation of new stock price:

$\begin{array}{c}\text{P}=\frac{\left({\text{V}}_{\text{op}}+\text{ST}\text{investments}-\text{Debt}\right)}{{\text{n}}_{\text{prior}}}\\ =\frac{\left({\text{V}}_{\text{op}}-\text{old}\text{debt}\right)}{{\text{n}}_{\text{prior}}}\\ =\frac{\left(\$4,511,278.195-\$0\right)}{200,000}\end{array}$

     $=\$22.5564$

Therefore, the stock price after repurchase is equal to $22.5564

Calculation of total number of shares after repurchased:

$\begin{array}{c}{\text{n}}_{\text{repurchase}}=\frac{\left(\text{D}-{\text{D}}_0\right)}{{\text{P}}_{\text{post}}}\\ =\frac{\left(\$1,353,383.459\right)}{\text{\$22}\text{.5564}}\\ =60,000\end{array}$

Therefore, the number of remaining shares is 200,000-60,000 = 140,000

Calculation of earnings per share (EPS):

$\begin{array}{c}\text{EPS}=\frac{\left[\left(\$600,000-0.07\left(\$1,353,383.459\right)\right)\left(1-0.25\right)\right]}{140,000}\\ =\frac{\left[\left(\$600,000-\$94,736.8421\right)\left(0.75\right)\right]}{140,000}\\ =\$2.71\end{array}$

Therefore, the new earnings per share of company is $2.71