Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.7. The company has a target debt–equity ratio of .6. The expected return on the market portfolio is 10 percent, and Treasury bills currently yield 5.7 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 10.4 percent. The bond currently sells for $1,250. The corporate tax rate is 34 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

Answer a.

Face Value = $1,000
Current Price = $1,250

Annual Coupon Rate = 10.40%
Semiannual Coupon Rate = 5.20%
Semiannual Coupon = 5.20% * $1,000
Semiannual Coupon = $52

Time to Maturity = 20 years
Semiannual Period = 40

Let Semiannual YTM be i%

$1,250 = $52 * PVIFA(i%, 40) + $1,000 * PVIF(i%, 40)

Using financial calculator:
N = 40
PV = -1250
PMT = 52
FV = 1000

I = 3.947%

Semiannual YTM = 3.947%
Annual YTM = 2 * 3.947%
Annual YTM = 7.894% or 7.89%

Cost of Debt = 7.89%

Answer b.

Unlevered Beta = 1.70
Risk-free Rate = 5.70%
Market Return = 10.00%

Unlevered Cost of Equity = Risk-free Rate + Unlevered Beta * (Market Return - Risk-free Rate)
Unlevered Cost of Equity = 5.70% + 1.70 * (10.00% - 5.70%)
Unlevered Cost of Equity = 13.01%

Levered Cost of Equity = Unlevered Cost of Equity + (Unlevered Cost of Equity - Cost of Debt) * (Debt-Equity Ratio) * (1 - tax)
Levered Cost of Equity = 13.01% + (13.01% - 7.89%) * 0.60 * (1 - 0.34)
Levered Cost of Equity = 15.04%

Answer c.

WACC = Weight of Debt * Cost of Debt * (1 - tax) + Weight of Equity * Levered Cost of Equity
WACC = (0.60/1.60) * 7.89% * (1 - 0.34) + (1.00/1.60) * 15.04%
WACC = 11.35%