Question

Problem 21-05
MM with Corporate Taxes

Companies U and L are identical in every respect except that U is unlevered while L has $16 million of 8% bonds outstanding. Assume that: (1) All of the MM assumptions are met. (2) Both firms are subject to a 35% federal-plus-state corporate tax rate. (3) EBIT is $5 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 $1.2 million should be entered as 1.2, not 1,200,000. 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 $1.2 million should be entered as 1.2, not 1,200,000. 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). Using MM with taxes, we have V_U = EBIT(1-T)/r_sU and V_L = V_U + Tax shield

where V_L = Value of the levered firm (company L)

V_U = Value of the unlevered firm (company U) and r_sU = required rate of return for an unlevered firm i.e. unlevered cost of equity

so, Value of company U = 5*(1-35%)/10% = 32.50 million

Tax shield = TD where T = tax-rate and D = debt

Tax shield = 35%*16 = 5.60 million

Value of company L = 32.50 + 5.60 = 38.10 million

b). i). rs for Firm U = unlevered cost of equity = 10% or 0.1

ii). rs for Firm L = rsU + (rsU - rd)(1-T)(D/S)

Value of the firm = Debt + Equity

Equity_L = V_L-Debt = 38.10 - 16 = 22.10 million

rs for Firm L = 10% + (10%-8%)*(1-35%)*(16/22.10) = 10.941% or 0.1

c). SL = VL - Debt = 38.10 - 16 = 22.10 million

SL + D = 38.10 million

d). WACC for Firm U = rsU = 10%

WACC for Firm L = (D/V)(1-T)(rd) + (S/V)(rsL) = (16/38.10)*(1-35%)*(8%) + (22.10/38.10)*(10.941%) = 8.53% or 0.09