Question

2. Consider Table 1 Table 1 Levered Firm L Liabilities and Shareholders' Equit Assets 100 200 Equi Assets 100 Debt Total 200 200 Total Additional Financial Information for Levered Firm L 80 Earnings Before Interest and Tax Cost of debt capital 8% 12% 255% Cost of unlevered equi Corporate tax rate 15% 30% Personal tax rate on debt income Personal tax rate on equity income Consider Table 1. Calculate the interest expense, earnings before taxes, the tax liability, and the total cashflow to shareholders and bondholders for the levered firm L (b) Consider Table 1. Calculate the present value of the interest tax shield and the value of the levered (a) firm (c) Consider Table 1. Calculate the after-tax WACC and the required return on equity capital for the levered firm Consider Table 1. Calculate the gain to leverage and the value of the levered firm given corporation and personal taxes (d)

Answer 1

Part (a)

Interest expense, I = Interest rate x Debt = 8% x 100 = 8

EBIT = 80

Earnings before taxes, EBT = EBIT - I = 80 - 8 = 72

Corporate tax rate, T = 20%

Tax liability, TL = T x EBT = 20% x 72 = 14.40

Total cash flow to shareholders = Net income = NI = EBT - TL = 72 - 14.40 = 57.60

Total cash flow to bond holders = Interest = I = 8

Part (b)

Present value of interest tax shield = PV (ITS) = T x Debt = 20% x 100 = 20

Value of unlevered firm, V_U = EBIT x (1 - T) / Unlevered cost of equity

Hence, V_U = 80 x (1 - 20%) / 12% = 533.33

Value of levered firm = V_L = V_U + PV (ITS) = 533.33 + 20 = 553.33

Part (c)

Return on unlevered equity, Keu = We x Ke + Wd x Kd

Hence, 12% = 0.5 x Ke + 0.5 x 8%

Hence, required return on levered equity = Ke = (12% - 0.5 x 8%) / 0.5 = 16%

Post tax WACC = Wd x Kd x (1 - T) + We x Ke = 0.5 x 8% x (1 - 20%) + 0.5 x 16% = 11.20%

Part (d)

As we can see the value of the levered firm, V_L > Value of unlevered firm V_U by an amount = PV (ITS) = 20.

Thus leverage has created additional value for the firm.