Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.10. The company has a target debt-equity ratio of .75. The expected return on the market portfolio is 11 percent and Treasury bills currently yield 3.6 percent. The company has one bond issue outstanding that matures in 29 years, a par value of $2,000, and a coupon rate of 6.3 percent. The bond currently sells for $2,100. The corporate tax rate is 22 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.)

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.)

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.)

Answer 1

Answer a.

Face Value = $2,000
Current Price = $2,100

Annual Coupon Rate = 6.30%
Annual Coupon = 6.30% * $2,000
Annual Coupon = $126

Time to Maturity = 29 years

Let Annual YTM be i%

$2,100 = $126 * PVIFA(i%, 29) + $2,000 * PVIF(i%, 29)

Using financial calculator:
N = 29
PV = -2100
PMT = 126
FV = 2000

I = 5.935%

Annual YTM = 5.935%

Before-tax Cost of Debt = 5.94%

Answer b.

Levered Beta = Unlevered Beta * [1 + (1 - tax) * Debt-Equity Ratio]
Levered Beta = 1.10 * [1 + (1 - 0.22) * 0.75]
Levered Beta = 1.10 * 1.585
Levered Beta = 1.7435

Cost of Equity = Risk-free Rate + Beta * (Expected Return on Market - Risk-free Rate)
Cost of Equity = 3.60% + 1.7435 * (11.00% - 3.60%)
Cost of Equity = 16.50%

Answer c.

Debt-Equity Ratio = 0.75

Weight of Debt = 0.75 / 1.75
Weight of Debt = 0.4286

Weight of Equity = 1.00 / 1.75
Weight of Equity = 0.5714

WACC = Weight of Debt * Cost of Debt * (1 - tax) + Weight of Equity *Cost of Equity
WACC = 0.4286 * 5.94% * (1 - 0.22) + 0.5714 * 16.50%
WACC = 11.41%