Question

Ajax has a tax rate of 30% and an EBIT of $50 million. The unlevered cost of capital is 14%.

a) What is the value of the unlevered firm? What is the cost of equity for the unlevered firm? What is the WACC of the unlevered firm?

b) Now suppose that Ajax issues $90 million in debt to buy back stock. The cost of debt is 8%. For the levered firm, find the value of the levered firm, the cost of equity, and the WACC.

c) A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that leads to the highest expected return for the stock. How would you respond to this argument?

Answer 1

a) Value of Unlevered Firm = EBIT*(1-tax Rate)/Unlevered cost of capital = 50*(1-30%)/14% = 250
Cost of equity = 14%
WACC is also same as cost of capital at 14%

b) Total value of firm = Value of Unleverd Firm + debt * tax Rate = 250 + 90*30% = 277
Value of equity = 277 - 90 = 187
Debt =90
Cost of equity = Cost of Unleverd equity + D/E* (Cost of Equity - Cost of Debt) *(1-Tax rate ) = 14%+90/187*(14%-8%)*(1-30%) = 16.02%
Cost of capital = EBIT*(1-Tax rate)/Total Value = 50*(1-30%)/277 = 12.64%

c) The argument is wrong. The portfolio should be chosen to give maximum returns but at optimum risk or volatility. This can be obtained by choosing portfolio with negative correlation which maximise diversification and minimises risk.