Question

Big Door Company has 8.4 million shares outstanding, which are currently trading for about $18 per share and have an equity beta of 1.4. Big Door has 20,200 outstanding bonds, with a 7% coupon rate, payable semi-annually and due in 10 years. The bonds are rated BBB. Currently the credit spread for BBB is 171 basis points over equivalent-maturity Government of Canada debt. The current yield on 10-year Canada bonds is 3%, compounded semi-annually. The risk-free interest rate is 2.7%, and the market risk premium is 6.9%. The company has a 35% tax rate. (Do not round intermediate calculations.)

   

a.	Calculate Big Door's WACC. (Round your answer to 2 decimal places.)
	WACC _____%
b.	Calculate Big Door's unlevered beta, using the following formula:
	βU=βlevered+βdebt × (1−Tc )×D/E1+(1−Tc )×D/EβU=βlevered+βdebt⁢ × (1−Tc⁢ )×D/E1+(1−Tc⁢ )×D/E
	(Round your answer to 2 decimal places.)
	Unlevered beta _____
c.	If Big Door was 50% debt-financed, what would be its WACC? Assume that the beta of its debt is unchanged by the capital structure change. (Round your answer to 2 decimal places.)
	WACC _____%

Answer 1

(a) Cost of Debt: Number of Bonds Outstanding = D = 20200, Coupon Rate = 7%, Tenure = 10 years or (10 x 2) = 20 half-years, Par Value = $ 1000, Current Yield of Government of Canada = Y(c) = 3%, Spread of BBB Bond = 171 basis point, Applicable Yield = Y(c) + Spread = 3 + 1.71 = 4.71 %

Cost of Debt = Applicable Yield = kd = 4.71 %

Semi-Annual Coupon = 0.07 x 0.5 x 1000 = $ 35

Bond Price = P = Total Present Value of All Semi-Annual Dividends + Par Value = 35 x (1/0.02355) x [1-{1/(1.02355)^(20)}] + 1000 / (1.02355)^(20) = $ 1180.97

Total Debt Value = D x P = 20200 x 1180.97 = $ 23855498.74

Cost of Equity: Number of Shares Outstanding = N = 8.4 million, Price per Share = $ 18, Equity Beta = 1.4, Risk-Free Rate = Rf = 2.7% and Market Risk Premium = MRP = 6.9 %

Cost of Equity = ke = Rf + MRP x Beta = 2.7 + 1.4 x 6.9 = 12.36 %

Total Equity Value = 8400000 x 18 = $ 151200000

Total Firm Value = 151200000 + 23855498.74 = $ 175055498.74

Equity Proportion = E = 151200000 / 175055498.74 = 0.8637 and Debt Proportion = D = (23855498.74/175055498.74) = 0.1363

Firm's Tax Rate = t = 35 %

WACC = E x ke + (1-t) x D x kd = 0.8637 x 12.36 + (1-0.35) x 0.1363 x 4.71 = 11.093 % ~ 11.09 %

(b) Equity Beta = 1.4, Asset Beta (Unlevered Beta) = 1.4 / [1+(1-0.35) x (D/E)] = 1.4 /[1+(1-0.35) x (0.1363/0.8637)] = 1.27

(c) New Debt Ratio = 50%

Asset Beta = 1.27 , New Equity Beta = 1.27 x [1+(1-0.35) x (1)] = 2.095

New Cost of Equity = Rf + 2.095 x MRP = 2.7 + 2.095 x 6.9 = 17.16%

Cost of Debt = 4.71 %

Therefore, New WACC = 0.5 x (1-0.35) x 4.71 + 0.5 x 17.16 = 10.109 % ~ 10.11 %