Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.75. The company has a target debt–equity ratio of .4. The expected return on the market portfolio is 9 percent, and Treasury bills currently yield 5.8 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 10.6 percent. The bond currently sells for $1,260. The corporate tax rate is 40 percent. a. What is the company’s cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Cost of debt % b. What is the company’s cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Cost of equity % c. What is the company’s weighted average cost of capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) WACC %

Answer 1

Levered Beta = Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

levered beta = 1.75*(1+((1-0.4)*(0.4)))

levered beta = 2.17

D/A = D/(E+D)

D/A = 0.4/(1+0.4)

=0.2857

Weight of equity = 1-D/A

Weight of equity = 1-0.2857

W(E)=0.7143

Weight of debt = D/A

Weight of debt = 0.2857

W(D)=0.2857

Cost of equity

As per CAPM

Cost of equity = risk-free rate + beta * (expected return on the market - risk-free rate)

Cost of equity% = 5.8 + 2.17 * (9 - 5.8)

Cost of equity% = 12.74

Cost of debt

K = N

Bond Price =∑ [(Annual Coupon)/(1 + YTM)^k]     +   Par value/(1 + YTM)^N

k=1

K =20

1260 =∑ [(10.6*1000/100)/(1 + YTM/100)^k]     +   1000/(1 + YTM/100)^20

k=1

YTM = 7.9597663049

After tax cost of debt = cost of debt*(1-tax rate)

After tax cost of debt = 7.9597663049*(1-0.4)

= 4.77585978294

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=4.78*0.2857+12.74*0.7143

WACC =10.47%