Question

King Ltd and Queen Ltd are both listed on the New York Stock Exchange having the same business risk. The expected return on the S&P 500 Index is 10% and the risk-free rate is 6%. These two firms are identical in all aspects except for their capital structure. Queen is an all-equity firm. King has both perpetual debts and common stocks. It has a debt to equity ratio of 1:4 and an equity beta which is equal to 1.25. Assume both firms can borrow at the risk-free rate. The EBIT of Queen Ltd is expected to be $100,000 per year in perpetuity. Assume there are no taxes, and all earnings of both firms are paid out as dividends.

(a) Calculate the cost of capital of each firm. (Show your calculations).

Answer 1

Cost of capital of Queen Ltd. (Unlevered firm):

Rf = 6%

β = 1.25

Rm = 10%

CAPM = Rf + β(Rm - Rf)

= 6%+1.25*(10%-6%)

= 6%+5%

= 11%

Cost of Equity = 11%

Since Queen Ltd. is an all equity firm, therefore Cost of equity would be Cost of Capital i.e. 11%

Cost of capital of King Ltd. (Levered firm):

Firstly we have to calculate levered Beta (β) for calculating Cost of equity,

Bj = Buj[1+(D/S)(1-T)]

Bj = Levered Beta

Buj = Unlevered Beta

= 1.25*[1+(1/4)(1-0)]

= 1.25*[1+.25]

Bj = 1.5625

Cost of equity (Ke) using levered Beta (Bj) i.e. 1.5625= 6%+1.5625*(10%-6%)

= 6%+6.25%

= 12.25%

Cost of Debt (Kd) = 6% (given)

Cost of capital:

WACC = Wd*Kd+We*Ke

= 1/5*6%+4/5*12.25%

= 11%