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).

(b) Mr. Jackson, a shareholder of Queen Ltd, owns stocks that are worth $10,000. Calculate his annual cash flow from dividend under the current capital structure of Queen. (Show your calculations).

(c) Mr. Jackson believes that if he invests in King Ltd, it is impossible for him to have the same cash flows as he prefers from Queen Ltd. Critically evaluate whether he is true. Explain your justifications clearly with necessary calculations presented.

Answer 1

a) Calculation of cost of capital of both king and queen

Unlevered beta = Levered Beta / (1 + D/E) = 1.25 / (1 + 1/4) = 1

For Queen, Using CAPM, Cost of capital = Cost of equity = Rf + beta x (Rm - Rf) = 6% + 1 x (10% - 6%) = 10%

For King, Cost of equity = 6% + 1.25 x (10% - 6%) = 11%

Cost of debt = 6%

WACC = wd x rd + we x re = 1/5 x 6% + 4/5 x 11% = 10% is the cost of capital for King

b) Value of Queen = EBIT / r = 100,000 / 10% = $1,000,000

Mr Jackson has $10,000 worth of shares of Queen, i.e. = 10,000 / 1,000,000 = 1% of company

His dividend = 1% x EBIT = 1% x 100,000 = $1,000

c) Value of King = Value of Queen = 1,000,000

Value of King's Debt = 1/5 x 1,000,000 = 200,000

Annual Profit for King = EBIT - Interest = 100,000 - 200,000 x 6% = 88,000

Value of King's Equity = 4 / 5 x 1,000,000 = 800,000 = (or 88,000 / 11%)

With 10,000 worth of investment in King, his share = 10,000 / 800,000 = 1.25%

Dividends = 1.25% x 88,000 = 1,100

Hence, in this case he will earn higher than Queen for the same amount of investment.