Chapter 17, Problem 8P

a)

Summary Introduction

To determine: The value of levered firm VL and VUL.

Explanation of Solution

Computation of value of levered firm VL and unlevered firm:

$\begin{array}{c}{\text{V}}_{\text{U}}=\frac{\text{EBIT}\left(1-{\text{T}}_c\right)\left(1-{\text{T}}_{\text{s}}\right)}{{\text{r}}_s\text{U}\left(1-{\text{T}}_s\right)}\\ =\frac{\$2\left(1-0.4\right)\left(1-0\right)}{0.10\left(1-0\right)}\\ =\$12\text{ million}\end{array}$

$\begin{array}{c}{\text{V}}_{\text{L}}={\text{V}}_{\text{U}}+\left[1-\frac{\left(1-{\text{T}}_{\text{C}}\right)\left(1-{\text{T}}_s\right)}{\left(1-{\text{T}}_d\right)}\right]\text{D}\\ =\text{\$12+}\left[1-\frac{\left(1-0.4\right)\left(1-0.2\right)}{1-0.28}\right]\$10\\ =\$15.33\text{ million}\end{array}$

$\begin{array}{c}\text{Gain}={\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}\\ =\$15.33-\$12\\ =\$3.33\text{ million}\end{array}$

b)

Summary Introduction

To determine: The value of levered firm VL and VUL.

Explanation of Solution

Computation of value of levered firm VL and unlevered firm:

$\begin{array}{c}{\text{V}}_{\text{U}}=\frac{\text{EBIT}\left(1-{\text{T}}_c\right)\left(1-{\text{T}}_{\text{s}}\right)}{{\text{r}}_s\text{U}\left(1-{\text{T}}_s\right)}\\ =\frac{\$2\left(1-0\right)\left(1-0\right)}{0.10\left(1-0\right)}\\ =\$20\text{ million}\end{array}$

$\begin{array}{c}{\text{V}}_{\text{L}}={\text{V}}_{\text{U}}+\left[1-\frac{\left(1-{\text{T}}_{\text{C}}\right)\left(1-{\text{T}}_s\right)}{\left(1-{\text{T}}_d\right)}\right]\text{D}\\ =\text{\$20+}\left[1-\frac{\left(1-0\right)\left(1-0\right)}{1-0}\right]\$10\\ =\$20\text{ million}\end{array}$

$\begin{array}{c}\text{Gain}={\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}\\ =\$20-\$20\\ =0\end{array}$

c)

Summary Introduction

To determine: The value of levered firm VL and VUL.

Explanation of Solution

Computation of value of levered firm VL and unlevered firm:

$\begin{array}{c}{\text{V}}_{\text{U}}=\frac{\text{EBIT}\left(1-{\text{T}}_c\right)\left(1-{\text{T}}_{\text{s}}\right)}{{\text{r}}_s\text{U}\left(1-{\text{T}}_s\right)}\\ =\frac{\$2\left(1-0.4\right)\left(1-0\right)}{0.10\left(1-0\right)}\\ =\$12\text{ million}\end{array}$

$\begin{array}{c}{\text{V}}_{\text{L}}={\text{V}}_{\text{U}}+\left[1-\frac{\left(1-{\text{T}}_{\text{C}}\right)\left(1-{\text{T}}_s\right)}{\left(1-{\text{T}}_d\right)}\right]\text{D}\\ =\text{\$20+}\left[1-\frac{\left(1-0.4\right)\left(1-0\right)}{1-0}\right]\$10\\ =\$16\text{ million}\end{array}$

$\begin{array}{c}\text{Gain}={\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}\\ =\$16-\$12\\ =\$4\end{array}$

d)

Summary Introduction

To determine: The value of levered firm VL and VUL.

Explanation of Solution

Computation of value of levered firm VL and unlevered firm:

$\begin{array}{c}{\text{V}}_{\text{U}}=\frac{\text{EBIT}\left(1-{\text{T}}_c\right)\left(1-{\text{T}}_{\text{s}}\right)}{{\text{r}}_s\text{U}\left(1-{\text{T}}_s\right)}\\ =\frac{\$2\left(1-0.4\right)\left(1-0.28\right)}{0.10\left(1-0.28\right)}\\ =\$12\text{ million}\end{array}$

$\begin{array}{c}{\text{V}}_{\text{L}}={\text{V}}_{\text{U}}+\left[1-\frac{\left(1-{\text{T}}_{\text{C}}\right)\left(1-{\text{T}}_s\right)}{\left(1-{\text{T}}_d\right)}\right]\text{D}\\ =\text{\$20+}\left[1-\frac{\left(1-0.4\right)\left(1-0.28\right)}{1-0.28}\right]\$10\\ =\$16\text{ million}\end{array}$

$\begin{array}{c}\text{Gain}={\text{V}}_{\text{L}}-{\text{V}}_{\text{U}}\\ =\$16-\$12\\ =\$4\end{array}$