Chapter 19, Problem 1PS

Summary Introduction

To determine: WACC (Weighted average cost of capital)

Explanation of Solution

Calculate market value of equity and debt:

$\begin{array}{c}\text{Equity}=\text{Selling price}\times \text{Number of shares}\\ =\$42\times 2.5\text{ million}\\ =\$105\text{million}\end{array}$

$\begin{array}{c}\text{Debt}=\text{Percentage of debt}\times \text{Number of book value of debt outstanding}\\ =0.90\times \$75\text{ million}\\ =\$67.5\text{million}\end{array}$

Compute percentage of debt and equity financing:

$\begin{array}{c}\frac{\text{D}}{\text{V}}=\frac{\text{Debt}}{\text{Debt}+\text{Equity}}\\ =\frac{\text{\$67}\text{.5}}{\text{\$67}\text{.5}+\text{\$105}}\\ =0.39\end{array}$

$\begin{array}{c}\frac{\text{E}}{\text{V}}=\frac{\text{Equity}}{\text{Debt}+\text{Equity}}\\ =\frac{\text{\$105}}{\text{\$67}\text{.5}+\text{\$105}}\\ =0.61\end{array}$

Compute WACC:

$\begin{array}{c}\text{WACC}=\left(\frac{\text{Market value of equity}}{\text{Total value of financing}}\times \text{Cost of equity}\right)+\left(\begin{array}{l}\frac{\text{Market value of debt}}{\text{Total value of financing}}\\ \times \text{Cost of debt}\times \left(\text{1}-\text{Tax rate}\right)\end{array}\right)\\ =\left(0.61\times 0.18\right)+0.39\times 0.09\times \left(1-0.21\right)\\ =0.1098+0.0277\\ =0.1375\text{or}\text{13}\text{.75\%}\end{array}$

Hence, WACC is 13.75%.