Question

MM with Corporate Taxes

Companies U and L are identical in every respect except that U is unlevered while L has $12 million of 6% bonds outstanding. Assume that: (1) All of the MM assumptions are met. (2) Both firms are subject to a 40% federal-plus-state corporate tax rate. (3) EBIT is $3 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

a). Value of the unlevered firm Vu = EBIT*(1-tax)/cost of unlevered equity

= 3,000,000*(1-40%)/10% = 18,000,000 or 18.00 million

Value of the levered firm VL = Vu + Tax shield

= 18 + (40%*12) = 22.80 million

b). rs for firm U = cost of unlevered equity =10.0%

rs for firm L = cost of levered equity:

rsL = rsU + (rsU - rd)*(D/E)*(1-Tax)

E = 22.80 - 12 = 10.8 million

= 10% + (10% - 6%)*(12/10.8)*(1-40%)

= 12.7%

c). SL = value of stock for the levered firm = VL - D = 22.8 - 12 = 10.80 million

SL + D = 10.80 + 12.00 = 22.80 million

d). WACC for firm U = cost of unlevered equity = 10.00%

WACC for firm L = wd*rd*(1-Tax) + ws*rsL

= (12/22.8)*6%*(1-40%) + (10.8/22.8)*12.7%

= 7.89%