Chapter 21, Problem 7P

a)

Summary Introduction

To determine: Horizon value at year 3.

Explanation of Solution

Compute the value:

$\text{Horizon Value at Year }3=\frac{\text{FCFF3}\times \left(1+\text{G}\right)}{\text{Rsu}-\text{G}}$

$\begin{array}{c}{\text{HV}}_{\text{U,3}}=\frac{\$40\left(1.07\right)}{\left(0.13-0.07\right)}\\ =\$713.33\end{array}$

Hence, the value is $713.33.

b)

Summary Introduction

To determine: Current unlevered value of operations

Explanation of Solution

Formula to calculate unlevered value of operations:

$\begin{array}{c}\text{Unlevered Value}=\left(\begin{array}{l}\text{Present Value of FCFF}1+\text{Present Value of FCFF}2\\ +\text{Present Value of FCFF}3+\text{ Horizon Value at Year }3\end{array}\right)\\ =\left(\begin{array}{c}\left(\text{FCFF}1\times \left(\text{PVF, }13\%\text{, Year }1\right)\right)+\left(\text{FCFF}2\times \left(\text{PVF, }13\%\text{, Year }2\right)\right)\\ +\left(\text{FCFF}3\times \left(\text{PVF, }13\%\text{, Year }3\right)\right)\\ +\left(\text{Horizon Value Year}3\times \left(\text{PVF, }13\%\text{, Year }3\right)\right)\end{array}\right)\end{array}$

Calculation of unlevered value:

$\begin{array}{c}\text{Unlevered Value}=\left(\begin{array}{l}\left(\$20\text{ million}\times \text{0}\text{.885}\right)+\left(\$30\text{ million}\times \text{0}\text{.7831}\right)\\ +\left(\$40\text{ million}\times \text{0}\text{.6931}\right)+\left(\$713.33\text{ million}\times \text{0}\text{.6931}\right)\end{array}\right)\\ =\$17.70\text{ million}+\$23.49\text{ million}+\$27.72\text{ million}+\$494.37\text{ million}\\ \text{=}\$563.29\text{ million}\end{array}$

Therefore, unlevered value of operations is $563.29 million.

c.

Summary Introduction

To calculate: Horizon value of tax shield at year 3

Explanation of Solution

Formula to calculate horizon value of tax shield at year 3:

$\text{Horizon Value}=\frac{\text{Tax Shield}\times \left(1+\text{G}\right)}{\text{Rsu}-\text{G}}$

Calculation of horizon value:

$\begin{array}{c}\text{Horizon Value}=\frac{\$4\text{ million1}\times \left(1+7\%\right)}{13\%-7\%}\\ =\$71.33\text{ million}\end{array}$

Therefore, horizon value of tax shield is $71.33 million.

Working Notes:

Calculate tax shield (TS) of expense:

$\begin{array}{c}\text{Tax Shield for Year 1}=\text{Tax Rate}\times \text{Interest Expense}\\ =40\%\times \$8\text{ million}\\ =\$3.2\text{ million1}\end{array}$

$\begin{array}{c}\text{Tax Shield for Year 2}=\text{Tax Rate}\times \text{Interest Expense}\\ =40\%\times \$9\text{ million}\\ =\$3.6\text{million}\end{array}$

$\begin{array}{c}\text{Tax Shield for Year 3}=\text{Tax Rate}\times \text{Interest Expense}\\ =40\%\times \$10\text{million}\\ =\$4\text{ million}\end{array}$

d.

Summary Introduction

To calculate: Current value of tax shield

Explanation of Solution

Formula to calculate current value of tax shield:

$\begin{array}{c}\text{Current Value}=\left(\begin{array}{l}\text{Present Value of TS}1+\text{Present Value of TS}2\\ +\text{Present Value of TS}3\\ +\text{ Horizon Value of Tax Shield at Year }3\end{array}\right)\\ =\left(\begin{array}{c}\left(\text{TS}1\times \left(\text{PVF, }13\%\text{, Year }1\right)\right)+\left(\text{TS}2\times \left(\text{PVF, }13\%\text{, Year }2\right)\right)\\ +\left(\text{TS}3\times \left(\text{PVF, }13\%\text{, Year }3\right)\right)\\ +\left(\text{Horizon Value of Tax Shield at Year}3\times \left(\text{PVF, }13\%\text{, Year }3\right)\right)\end{array}\right)\end{array}$

Calculation of current value:

$\begin{array}{c}\text{Current Value}=\left(\begin{array}{l}\left(\$3.21\text{ million}\times \text{0}\text{.885}\right)+\left(\$3.62\text{ million}\times \text{0}\text{.7831}\right)\\ +\left(\$43\text{ million}\times \text{0}\text{.6931}\right)+\left(\$71.33\text{ million}\times \text{0}\text{.6931}\right)\end{array}\right)\\ =\$2.83\text{ million}+\$2.82\text{ million}+\$2.77\text{ million}+\$49.44\text{ million}\\ \text{=}\$57.86\text{ million}\end{array}$

Therefore, unlevered value of tax shield is $57.86 million.

e.

Summary Introduction

To calculate: Current total value

Explanation of Solution

Formula to calculate current total value:

$\text{Current Total Value}=\left(\begin{array}{l}\text{Current Value of Operations}\\ +\text{Current Value of Tax Shield}\end{array}\right)$

Calculation of current total value:

$\begin{array}{c}\text{Current Total Value}=\text{\$563}\text{.29 million}+\$57.86\text{ million}\\ =\$621.15\text{ million}\end{array}$

Therefore, current value is $621.15 million.