Chapter 26, Problem 2P

a)

Summary Introduction

To determine: The company V’s pre-acquisition levered cost of equity and unlevered cost of equity.

Explanation of Solution

The computation of company V’s pre-acquisition levered cost of equity and unlevered cost of equity is as follows:

Current b = 1.4; r_RF = 5%; RP_M = 6%; current w_d = 30%; T = 40%; r_d = 8%,

$\begin{array}{c}{\text{r}}_{\text{sL}} ={\text{ r}}_{\text{RF}}+{\text{ RP}}_{\text{M}}\left(\text{b}\right)\\ =5\%+6\%\left(1.4\right) \\ =13.4\%\end{array}$

$\begin{array}{c}{\text{r}}_{\text{sU }}={\text{w}}_{\text{d}}{\text{r}}_{\text{d}}+{\text{ w}}_{\text{s}}{\text{r}}_{\text{sL}}\\ \text{=}0.30\left(8\%\right)+0.70\left(13.4\%\right)\\ =11.78\%\end{array}$

Hence, the levered cost of equity and unlevered cost of equity is 13.4% and 11.78% respectively.

b)

Summary Introduction

To determine: The unlevered value of operations.

Explanation of Solution

The computation of unlevered value of operation is as follows:

$\begin{array}{c}\text{Unlevered horizon value}=\frac{{\text{FCF}}_{\text{4}}\left(\text{1}+\text{g}\right)}{\left({\text{r}}_{\text{sU}}-{\text{g}}_{\text{L}}\right)}\\ =\frac{3.57\left(1.05\right)}{\left(0.1178-0.05\right)}\\ =55.29\end{array}$

$\begin{array}{c}\text{Unlevered value of operations} =\frac{2.5}{1.1178}+\frac{2.9}{{(1.1178)}^2}+\frac{3.4}{{(1.1178)}^3}+\frac{3.57+55.29}{{(1.1178)}^4}\\ =\$44.69\end{array}$

Hence, the unlevered value of operation is $44.69.

c)

Summary Introduction

To determine: The value of tax shield.

Explanation of Solution

The computation of value of tax shield is as follows:

$\begin{array}{c}\text{Tax shield horizon value }=\frac{{\text{TS}}_{\text{4}}\left(\text{1}+\text{g}\right)}{\left({\text{r}}_{\text{sU}}\text{-g}\right)}\\ =\frac{0.5888\left(1.05\right)}{\left(0.1178-0.05\right)}\\ =9.12\end{array}$

$\begin{array}{c}\text{Value of tax shields}=\frac{0.600}{1.1178}+\frac{0.600}{{(1.1178)}^2}+\frac{0.600}{{(1.1178)}^3}+\frac{0.5888+9.12}{{(1.1178)}^4}\\ =\$7.67\text{million}\text{.}\end{array}$

Hence the value of tax shield is $7.67million.

d)

Summary Introduction

To determine: The total intrinsic value of operations, intrinsic value of company V’s equity to company H and company V’s intrinsic stock price per share.

Explanation of Solution

The computation of total value of operation is as follows:

$\begin{array}{l}\text{Value of operations = Unlevered Vops + Value of tax shields}\hfill \\ =\$44.69+\$7.67\hfill \\ =\$52.36{\text{ million}}_{}\hfill \end{array}$

Hence the total value of operation is $52.36 million.

The computation of equity value to acquirer is as follows:

$\begin{array}{c}\text{Equity value to acquirer}={\text{V}}_{\text{ops}}\text{– Assumed debt}\\ \text{=}\$52.36\text{ million }-\$10.82\text{ million}\\ \text{=}\$41.54\text{ million}\end{array}$

Hence, the equity value of company V to company H is $41.54million.

The computation of intrinsic stock price per share is as follows:

$\begin{array}{c}\text{Intrinsic value per share}=\frac{\left(\text{Equity value to acquirer}\right)}{\left(\text{Number of shares}\right)}\\ =\frac{\left(\text{\$41}\text{.54 million}\right)}{\left(\text{1 million shares}\right)}\\ =\$41.54\text{ Per share}\text{.}\end{array}$

Hence, the intrinsic stock price per share is $41.54per share.