Question

3. A firm is initially unlevered and the market value of its equity is $800 million. The firm is planning to issue $250 million of perpetual debt and repurchase equity of an equal amount. The corporate tax rate is 20%. Assume that there are no costs of financial distress and that the discount rate for the interest tax shields is equal to the cost of debt. Remarks: i. Assume the EBIT each year will be high enough so the 30 percent limit on the interest deduction will not be reached. (Therefore the entire interest expense is tax deductible.) ii. The cost of debt rD is not given. This is not a mistake, you can answer this question without knowing rD. (Hint: with perpetual debt, you pay the same amount of interest each year, so the interest tax shield is a perpetuity.)

a. What will be the increase in the value of the firm after this transaction?

b. What is the market value of the equity after the transaction?

c. What is the wealth of the shareholders before and after the change in capital structure?

Answer 1

a]	Value of the unlevered firm Vu [given]	$           800.00	million
	Value of the levered firm [Vl] = Vu+B*t, where
	B = Borrowings and t = tax rate.
	= 800+250*20% =	$           850.00	million
	Increase in value of the firm after the transaction = 850+800 =	$             50.00	million
	Also equal to B*t = 250*20% = $50 million
b]	MV of equity = Vl-B = 850-250 =	$           600.00	million
c]	Wealth of the shareholders' before change in capital structure = Value of equity before change in capital structure =	$           800.00	million
	Wealth of the shareholders' after change in capital structure = Value of equity after change in capital structure+Cash received on repurchase by the firm = 600+250 =	$           850.00	million