Chapter 13, Problem 13.3C

Summary Introduction

To compute: The equity capital cost of the firm.

Introduction:

WACC (Weighted Average Cost of Capital) is the rate which a company is expected to pay on an average to all the security holders in order to finance its assets.

Answer to Problem 13.3C

The cost of equity capital of the firm at the debt-equity ratio of 1.2 is 18.26%.

Explanation of Solution

Given information:

The debt-equity ratio of Company C is 1.2. The cost of debt is 5%, and WACC is 11%.

Note: Using the provided information, calculate WACC to find the equity cost. The debt-equity ratio of 1.2 implies that the weight of debt is 1/2.2, and the equity weight is 1.2/2.2.

Where $\text{V}=(1+1.2)$.

Formula of WACC to calculate the cost of equity:

$\text{WACC}=\left(\frac{E}{V}\right)R_E+\left(\frac{D}{V}\right)R_D$

Calculate the cost of equity:

$\begin{array}{c}\text{WACC}=\left(\frac{E}{V}\right)R_E+\left(\frac{D}{V}\right)R_D\\ \$0.11=\left(\frac{1}{2.2}\right)R_E+\left(\frac{1.2}{2.2}\right)\left(0.05\right)\\ \$0.11=\left(\frac{1}{2.2}\right)R_E+\left(\frac{1.2}{2.2}\right)\left(0.05\right)\end{array}$

$\begin{array}{c}\$0.11=\left(\frac{1}{2.2}\right)R_E+\$0.027\\ \$0.083=\left(\frac{1}{2.2}\right)R_E\\ R_E=\$\mathrm{0.18.26}\text{ or 18}\text{.26\%}\end{array}$

Hence, the cost of equity is 18.26%.