Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of .90. The company has a target debt-equity ratio of .45. The expected return on the market portfolio is 11 percent and Treasury bills currently yield 2.9 percent. The company has one bond issue outstanding that matures in 20 years, a par value of $1,000, and a coupon rate of 5.9 percent. The bond currently sells for $1,045. 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

a). Par Value = $1000

Annual coupon rate = 5.9%

Annual Coupon payment = $1000*5.9% = $59

Price = $1,045

Calculating YTM using IRR technique:-

First, we will take YTM = 6%

Price = $ 676.72 + $311.80

Price = $ 988.52

Taking YTM as 5%

Price = $ 735.27 + $376.89

Price = $ 1,112

Now, calculating YTM:-

YTM = 5.52%

a). Company's Cost of Debt = 5.52%(1-0.22)

= 4.31%

b).Stock's all equity Beta = 0.90

Calculating the unlevered beta of stock;-

Levered Beta = Unlevered Beta*[1+(1-Tax rate)*D/E]

= 0.90*[1+(1-0.22)*0.45]

= 1.2159

So, levered Beat = 1.2159

As per CAPM,

Rf = Risk free Return = 2.9%

Rm = Market return = 11%

Expected Return = 2.9% + 1.2159(11% - 2.9%)

= 12.75%

So, Company's cost of equity = 12.75%

c). Debt-Equity = 0.45

Debt value in Debt-equity = 0.45

Equity value in Debt-equity = 1

Calculating WACC:-

WACC= (Weight of Debt)(Cost of Debt) + (Weight of Equity)(Cost of Equity)

WACC = [0.45/(0.45+1)](4.31%) + [1/(0.45+1)](12.75%)

WACC = 1.3376% + 8.7931%

WACC = 10.13%

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Price =- Coupon Payment Coupon Payment (1 + YTM) (1 + YTM)2 FaceValue (1 + YTM) Coupon Payment (1 + YTM)"

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Price =- Coupon Payment Coupon Payment (1 + YTM) (1 + YTM)2 FaceValue (1 + YTM) Coupon Payment (1 + YTM)"

Price = 7 59 59 (1 +0.05)1*(1 + 0.05) 2 59 (1 + 0.05)20 1000 (1 +0,05)20 T

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1112.16 - 1045 YTM=5+ 1112.16 - 988 50 *(6-5)

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