Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.4. The company has a target debt–equity ratio of .3. The expected return on the market portfolio is 12 percent, and Treasury bills currently yield 5.1 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 9.2 percent. The bond currently sells for $1,190. 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

(a)-After-Tax Cost of Debt

· The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value

· The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

· The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 9.20%]	PMT	92
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [20 Years]	N	20
Bond Price/Current Market Price of the Bond [-$1,190]	PV	-1,190

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the annual yield to maturity on the bond (1/Y) = 7.36%.

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

The After-tax cost of debt = Annual Yield to maturity on the bond x (1 – Tax Rate)

= 7.36% x (1 – 0.40)

= 7.36% x 0.60

= 4.42%

(b)-The Cost of Equity

As per Capital Asset Pricing Model [CAPM], the cost of equity is calculated by using the following equation

Cost of equity = Risk-free Rate + Beta[Market rate of return - Risk-free Rate]

= Rf + B[Rm – Rf]

= 5.10% + 1.40[12.00% - 5.10%]

= 5.10% + [1.40 x 6.90%

= 5.10% + 9.66%

= 14.76%

(c)-The company’s weighted average cost of capital (WACC)

Weighted Average Cost of Capital (WACC) = [After Tax Cost of Debt x Weight of Debt] + [Cost of equity x Weight of Equity]

= [(4.42% x (0.30/1.30)] + [14.76% x (1.00 / 1.30)]

= [4.42% x .23077] + [14.76% x 0.76923]

= 1.02% + 11.35%

= 12.37%

“Hence, the company’s weighted average cost of capital (WACC) will be 12.37%”

NOTE

Weight of Debt = Debt-to-equity ratio / (1 + Debt-to-equity ratio)

Weight of Equity = 1 / (1 + Debt-to-equity ratio)