Chapter 22, Problem 5P

a.

Summary Introduction

To determine: The levered and unlevered cost of equity.

Introduction: Cost of equity is the return paid to equity investors for investing in the company. It is financial compensation made to investor to bear risk of investment.

Explanation of Solution

Formula to calculate cost of equity:

${\text{r}}_{\text{sL}}={\text{r}}_{\text{RF}}+\text{b}\left({\text{RP}}_{\text{M}}\right)$

r_sL is levered cost of equity

r_RF is risk free rate

b is beta

RP_M is market risk premium

Substitute 5% for risk-free rate r, 6% for risk premium RP, 1.4 for beta to calculate the  levered cost of equity:

$\begin{array}{c}{r}_{sL} =r_{RF}+R{P}_M\times \text{beta} \\ =5\%+6\%\left(1.4\right) \\ =13.4\%\end{array}$

Substitute 8% for debt rate , 30% for debt percentage, 70% percent for equity and 13.4% for cost of equity to calculate the  unlevered cost of equity:

$\begin{array}{l}{r}_{sU}=w_d{r}_d+w_s{r}_{sL}\hfill \\ =0.30\left(8\%\right)+0.70\left(13.4\%\right)\hfill \\ =11.78\%\hfill \end{array}$

b.

Summary Introduction

To determine: the intrinsic unlevered value of operations.

Explanation of Solution

$\begin{array}{l}\text{Unlevered horizon value}={\text{FCF}}_{\text{4}}\left(\text{1+g}\right)\text{/}\left({\text{r}}_{\text{sU}}{\text{-g}}_{\text{L}}\right)\hfill \\ =\text{3}\text{.57}\left(\text{1}\text{.05}\right)\text{/}\left(\text{0}\text{.1178-0}\text{.05}\right)\hfill \\ =\text{55}\text{.288}\hfill \end{array}$

$\begin{array}{c}{V}_{unlevered}=\frac{2.5}{1.1178}+\frac{2.9}{{(1.1178)}^2}+\frac{3.4}{{(1.1178)}^3}+\frac{3.57+55.288}{{(1.1178)}^4}\\ \\ =\$44.69\end{array}$

c.

Summary Introduction

To determine: The value of tax shield.

Explanation of Solution

The tax shield is calculated by multiplying tax rate with the interest. Tax shield for the first three years is same which is $\$1.5\left(0.25\right)=\$0.375$ and for the fourth year it is $\$1.472\left(0.25\right)=\$\mathrm{0.368.}$

Substitute $0.368 for tax shield, 5% for growth, 11.78% for unlevered cost of equity to calculate the tax shield horizn value:

$\begin{array}{l}Taxshieldhorizonvalue=Tax\text{ shield for fourth year}\left(1+g\right)/\left(r_{sU}-g\right)\hfill \\ =\$0.368\left(1.05\right)/\left(0.1178-0.05\right)\hfill \\ =\$5.699\hfill \end{array}$

$\begin{array}{c}Val\text{ue of t}ax\text{ shield}=\frac{\$0.375}{1.1178}+\frac{\$0.375}{{(1.1178)}^2}+\frac{\$0.375}{{(1.1178)}^3}+\frac{\$5.699+\$1.472}{{(1.1178)}^4}\\ \\ =4.790million\end{array}$

d.

Summary Introduction

To determine: The total intrinsic value, maximum price per share, value of equity.

Explanation of Solution

Substitute $44.692 for unlevered value of operations, $4.790 for value of tax shield to calculate the total intrinsic value:

$\begin{array}{l}Totalintrinsicvalue=unleveredVops+valueoftaxshields\hfill \\ =\$44.692+\$4.790\hfill \\ =\$49.482millio{n}_{}\hfill \end{array}$

$\begin{array}{l}Equityvalueto\text{ V}=\text{Total intrinsic value}-Assumeddebt\hfill \\ =\$49.482million-\$10.19million\hfill \\ =\$39.292million\hfill \end{array}$

$\begin{array}{l}Intrinsicvaluepershareofexistingsharesto\text{ V}:\hfill \\ =\frac{\left(Equityvaluetoacquirer\right)}{\left(numberofshares\right)}\hfill \\ =\frac{\left(\$39.29million\right)}{\left(1.5millionshares\right)}\hfill \\ =\$26.1947pershare\hfill \end{array}$

Note: Due to constant value of capital structure, the value of FCF is used to calculate VOPS at horizon.