Chapter 13, Problem 9QP

Calculating the WACC In the previous problem, suppose the company’s stock has a beta of 1.15. The risk-free rate is 3.7 percent, and the market risk premium is 7 percent. Assume that the overall cost of debt is the weighted average implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35 percent. What is the company’s WACC?

Summary Introduction

To determine: The WACC of the Company.

Introduction:   The WACC (Weighted Average Cost of Capital) is the total rate of return for a company which anticipates reimbursing all their investors. It is considered as a financing resource in the target capital structure of a company and it measured in terms of weights of fractions.

Answer to Problem 9QP

The WACC of the Company is 9.87%

Explanation of Solution

Determine the Cost of Equity using CAPM

$\begin{array}{c}CostofEquity\left(R_e\right)=\left[\begin{array}{l}RiskfreeRate\left(R_f\right)+Beta\left(\beta \right)\times \\ MarketRisk\mathrm{Pr}emium\left(R_m\right)\end{array}\right]\\ =\left[3.7\%+1.15\times 7\%\right]\\ =\left[0.037+\text{0}\text{.0805}\right]\\ =\text{0}\text{.1175}or11.75\%\end{array}$

Therefore the Cost of Equity is 11.75%

Determine the Yield to Maturity for First Bond Issue

Using excel function =rate we calculate the yield to maturity as,

Excel Spreadsheet:

Therefore the Yield to Maturity for First Bond Issue is 5.69%

Determine the Yield to Maturity for Second Bond Issue

Using excel function =rate we calculate the yield to maturity as,

Excel Spreadsheet:

Therefore the Yield to Maturity for Second Bond Issue is 6.78%

Determine the Total Market Value of Debt

$\begin{array}{c}MarketValueofDebt=\left[\begin{array}{l}\left(FaceValue\times BondQuot{e}_{Issue1}\right)+\\ \left(FaceValue\times BondQuot{e}_{Issue2}\right)\end{array}\right]\\ =\left[\left(\$70,000,000\times 108.3\%\right)+\left(\$60,000,000\times 108.9\%\right)\right]\\ =\left[\$75,810,000+\$65,340,000\right]\\ =\$141,150,000\end{array}$

Therefore the Total Market Value of Debt is $141,150,000

Determine the Market Value of Equity

$\begin{array}{c}MarketValueofEquity=\left[Share\mathrm{Pr}ice\times CommonStockOuts\tan ding\right]\\ =\left[\$53\times 8,300,000\right]\\ =\$439,900,000\end{array}$

Therefore the Total Market Value of Equity is $439,900,000

Determine the Total Market Value of Company

$\begin{array}{c}TotalMarketValue=\left[MarketValueofDebt+MarketValueofEquity\right]\\ =\left[\$141,150,000+\$439,900,000\right]\\ =\$581,050,000\end{array}$

Therefore the Total Market Value of Company is $581,050,000

Determine the Market Value Weights of Debt

$\begin{array}{c}WeightofDebt=\left[\frac{MarketValueofEquity}{TotalMarketValue}\right]\\ =\left[\frac{\$439,900,000}{\$581,050,000}\right]\\ =0.757078or75.71\%\end{array}$

Therefore the Market Value Weights of Debt is 75.71%

Determine the Market Value Weights of Equity

$\begin{array}{c}WeightofEquity=\left[1-WeightofDebt\right]\\ =\left[1-0.757078\right]\\ =0.242922or24.29\%\end{array}$

Therefore the Market Value Weights of Equity is 24.29%

Determine the Weight of First Bond Issue

$\begin{array}{c}Weigh{t}_{Issue1}=\left[\frac{\left(FaceValue\times BondQuot{e}_{Issue1}\right)}{MarketValueofDebt}\right]\\ =\left[\frac{\left(\$70,000,000\times 108.3\%\right)}{\$141,150,000}\right]\\ =\left[\frac{\$75,810,000}{\$141,150,000}\right]\\ =0.53708or53.71\%\end{array}$

Therefore the Weight of First Bond Issue is 53.71%

Determine the Weight of Second Bond Issue

$\begin{array}{c}Weigh{t}_{Issue2}=\left[\frac{\left(FaceValue\times BondQuot{e}_{Issue2}\right)}{MarketValueofDebt}\right]\\ =\left[\frac{\left(\$60,000,000\times 108.9\%\right)}{\$141,150,000}\right]\\ =\left[\frac{\$65,340,000}{\$141,150,000}\right]\\ =0.46291or46.29\%\end{array}$

Therefore the Weight of Second Bond Issue is 46.29%

Determine the Weighted Average After-tax for both the bond issues

$\begin{array}{c}WAC{C}_{Bonds1\&2}=\left[\begin{array}{l}\left(\left(Weigh{t}_{Issue1}\times YT{M}_{Issue1}\right)+\left(Weigh{t}_{Issue2}\times YT{M}_{Issue2}\right)\right)\times \\ \left(1-TaxRate\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\left(53.71\%\times 5.69\%\right)+\left(46.29\%\times 6.78\%\right)\right)\times \\ \left(1-35\%\right)\end{array}\right]\\ =\left[\left(0.03056+0.031385\right)\times 0.65\right]\\ =\left[0.061946\times 0.65\right]\\ =0.040265or4.03\%\end{array}$

Therefore the Weighted Average After-tax for both the bond issues is 4.03%

Determine the WACC of the Company

$\begin{array}{c}WACC=\left[\left(Weigh{t}_{Equity}\times Rat{e}_{Equity}\right)+\left(Weigh{t}_{Debt}\times Rat{e}_{Debt}\right)\right]\\ =\left[\left(75.71\%\times 11.75\%\right)+\left(24.29\%\times 4.03\%\right)\right]\\ =\left[0.088957+0.00979\right]\\ =0.09874or9.87\%\end{array}$

Therefore the WACC of the Company is 9.87%.