Chapter 26, Problem 5P

a)

Summary Introduction

To determine: The value of unlevered operations and tax shield.

Explanation of Solution

The computation of unlevered cost of equity is as follows:

$\begin{array}{c}{\text{r}}_{\text{sU}} ={\text{ w}}_{\text{d}}{\text{r}}_{\text{d}}{\text{+ w}}_{\text{s}}{\text{r}}_{\text{sL}}\\ \text{=}0.25\left(9\%\right)+0.75\left(11.85\%\right)\\ =11.14\%\end{array}$

Hence, the value of unlevered operation is 11.14%.

The computation of tax rate is as follows:

$\begin{array}{c}\text{Interest}={\text{Debt}}_{\text{4}}\times \left(9.5\%\right)\\ =\$22.27\times \left(9.5\%\right)\\ =2.116\end{array}$

$\begin{array}{c}{\text{TS}}_5={\text{ Interest}}_{\text{5}}\times \left(\text{Tax rate}\right)\\ =2.116\times \left(0.35\%\right) \\ =0.7405\end{array}$

In the other years, the tax shield is equivalent to the interest cost multiplied by the rate of tax:

TS₁ = 1.2(0.35) = 0.42, TS₂ = 0.595, TS₃ = 0.98, TS₄ = 0.735

$\begin{array}{c}{\text{HVTS}}_{\text{5}}=\frac{{\text{TS}}_{\text{6}}}{\left({\text{r}}_{\text{sU}}\text{– g}\right)}\\ =\frac{{\text{TS}}_{\text{5}}\left(\text{1 + g}\right)}{\left({\text{r}}_{\text{sU}}\text{– g}\right)}\\ =\frac{0.7405\times \left(1.06\right)}{\left(0.1114–0.06\right)}\\ =\$15.28\text{Million}\text{.}\end{array}$

$\begin{array}{c}\text{Value of the tax shields}=\left(\begin{array}{l}\frac{0.42}{1.1114}+\frac{0.595}{{(1.1114)}^2}+\frac{0.980}{{(1.1114)}^3}+\\ \frac{0.735}{{(1.1114)}^4}+\frac{0.741+15.28}{{(1.1114)}^5}\end{array}\right)\\ =\$11.50\text{Million}\text{.}\end{array}$

Hence, the value of tax shield is $11.50million.

The computation of unlevered horizon value is as follows:

$\begin{array}{c}{\text{HVUL}}_{\text{5}}=\frac{{\text{FCF}}_5\left(1+g\right)}{\left({\text{r}}_{\text{sU}}\text{– g}\right)}\\ =\frac{2.12\times \left(1.06\right)}{0.1115-0.06}\\ =\$43.74\text{million}\text{.}\end{array}$

Hence, the unlevered horizon value is $43.7million.

The computation of unlevered value of operation is as follows:

$\begin{array}{c}\text{Unlevered value of operations}=\left(\begin{array}{l}\frac{1.3}{1.1114}+\frac{1.5}{{(1.1114)}^2}+\frac{1.75}{{(1.1114)}^3}\\ +\frac{2.0}{{(1.1114)}^4}+\frac{2.12+43.74}{{(1.1114)}^5}\end{array}\right)\\ =\$32.02\text{million}\text{.}\end{array}$

Hence, the unlevered value of operation is $32.02million.

b)

Summary Introduction

To determine: The dollar value of company C’s operations and how much the company M ready to pay for company C.

Explanation of Solution

The computation of dollar value of operation is as follows:

$\begin{array}{c}\text{Value of operation}=\text{Interest tax shield }+\text{Unlevered value}\\ \text{=11}\text{.50+32}\text{.02}\\ \text{=\$43}\text{.52million}\end{array}$

Hence, the dollar value of operation is $43.52million.

The computation of amount ready to pay for company C is as follows:

$\begin{array}{c}\text{Equity}=43.52-10.00\\ =33.52\text{million}\end{array}$

Hence, the amount pay for company C is 33.52million.

Although not requisite for the value computation, the WACC at the new capital structure can be computed.  At the new capital structure of 40 percent debt with a rate of 9.5 percent, the new levered cost of equity and WACC will be:

$\begin{array}{c}{\text{r}}_{\text{sL}} ={\text{ r}}_{\text{sU}}+\left({\text{r}}_{\text{sU}}{\text{–r}}_{\text{d}}\right)\left(\frac{\text{D}}{\text{S}}\right)\\ =11.14\%+\left(11.14\%-9.5\%\right)\left(\frac{0.40}{0.60}\right)\\ =12.23\%\\ {\text{WACC = w}}_{\text{d}}{\text{r}}_{\text{d}}\left(\text{1}-\text{T}\right){\text{ + w}}_{\text{s}}{\text{r}}_{\text{s}}\\ =0.40\times \left(9.5\%\right)\times \left(1-0.35\right)+0.60\times \left(12.23\%\right)\\ =9.81\%\end{array}$

Hence the WACC is 9.81%.