Answer:
a. Firm U value = $15 million; and Firm L value = $19 million.
b. rs for Firm U = 10%; and rs for Firm L = 22%.
c. Value of levered firm = VL = SL + D => $19 million = $3 million + $16 million
d. WACC for Firm U = 10%; and WACC for Firm L = 7.89%
Explanation:
rd = cost of debt = 7%
r0 = Unlevered cost of equity = 10%
a. What value would MM now estimate for each firm?
Firm U value = Value of unlevered firm = EBIT(1 – Tax rate ) / Unlevered cost of equity = (2 * (1 – 0.25)) / 0.1 = $15 million
Firm L value = Value of levered firm = Value of unlevered firm + (Debt * Tax rate) = 15 + (16 * 25%) = $19 million
This implies that:
SL = Value of equity = Value of levered firm – Debt = $19 – 16 = $3 million
b. What is rs for Firm U? For Firm L?
rs for Firm U = r0 = Unlevered cost of equity = 10%
rs for Firm L = r0 + (r0 – rd)(D / S)(1 – Tax rate) = 10% + (10% - 7%)*(16 / 3)*(1 - 0.25) = 22%
c. Find SL, and then show that SL + D= VL results in the same value as obtained in part a.
Interest = ($16 * 7%) = $1.12 million
Earning before tax = EBIT – Interest = $2 – $1.12 = $0.88 million
Tax = 0.88 * 25% = $0.22 million
Net income = Earning before tax – Tax = $0.88 - $0.22 = $0.66 million
SL = Value of equity = Net income / rs for Firm L = 0.66 / 22% = $3 million
D = $16 million
Value of levered firm = VL = SL + D => $19 million = $3 million + $16 million
d. What is the WACC for Firm U? For Firm L?
WACC for Firm U = r0 = 10%
WACC for Firm L = rs * (SL / VL) + rd * (D / VL) * (1 – Tax rate) = (22% * (3 / 19)) + (7% * (16 / 19) * (1-0.25)) = 7.89%
