Question

MM with Corporate Taxes

Companies U and L are identical in every respect except that U is unlevered while L has $16 million of 6% bonds outstanding. Assume: (1) All of the MM assumptions are met. (2) Both firms are subject to a 25% federal-plus-state corporate tax rate. (3) EBIT is $4 million. (4) The unlevered cost of equity is 10%.

1. What value would MM now estimate for each firm? (Hint: Use Proposition I.) Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Round your answers to two decimal places.

   Company U: $   million
   Company L: $   million

2. What is r_s for Firm U? Round your answer to one decimal place.

   %

   What is r_s for Firm L? Do not round intermediate calculations. Round your answer to one decimal place.

   %

3. Find S_L, and then show that S_L + D = V_L results in the same value as obtained in Part a. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answers to two decimal places.

   S_L = $   million

   S_L + D = $   million

4. What is the WACC for Firm U? Do not round intermediate calculations. Round your answer to two decimal places.

   %

   What is the WACC for Firm L? Do not round intermediate calculations. Round your answer to two decimal places.

   %

Answer 1

Part (a)

Value of the unlevered firm U = V_u = EBIT x (1 - Tax rate) / Unlevered cost of equity = 4 x (1 - 25%) / 10% = $ 30.00 million

Value of the levered firm L, V_l = V_u + Tax rate x Debt = 30.00 + 25% x 16 = $ 34.00 million

Part (b)

r_s for Firm U = unlevered cost of equity = 10.0%

r_s for Firm L = levered cost of equity = r_sl = r_su + (r_su - r_d) x (1 - Tax rate) x (Debt / Equity) = 10% + (10% - 6%) x (1 - 25%) x x 16 / (34 - 16) = 12.7%

Part (c)

SL = PAT / Levered cost of equity = (EBIT - Interest rate x Debt) x (1 - Tax rate) / r_sl = (4 - 6% x 16) x (1 - 25%) / 12.7% = $ 18.00 million

SL + D = 18 + 16 = $ 34.00 million = VL derived in part (a)

Part (d)

WACC for firm U = r_su = 10.00%

WACC for firm L = Wd x r_d x (1 - Tax rate) + We x r_sl

where Wd = proportion of debt in capital structure = D / V_l = 16 / 34 = 0.4706; We = proportion of equity = 1 - Wd = 1 - 0.4706 = 0.5294

Hence, WACC for firm L = Wd x r_d x (1 - Tax rate) + We x r_sl = 0.4706 x 6% x (1 - 25%) + 0.5294 x 12.7% = 8.82%