Question

Companies U and L are identical in every respect except that U is unlevered while L has $8 million of 5% 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 $2 million. (4) The unlevered cost of equity is 12%.

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

Debt Value(D)	8 million		rD is the interest rate (cost of debt)
EBIT	2 million		rS is the return on equity (cost of equity)
Corp. taxes(Tc)	25%		rE is the return on unlevered equity (cost of capital)
Rate of debt(rD)	5%		D is the value of debt
Rate of equity(rE)	12%

a.

Value of Unelevered firm(vU)
Formula:	[EBIT * (1-Tc)]/rE
Firm Value (vU)	12.5 million

Value of Levered firm(vL)
Formula:	vL = vU + TcD
Firm Value(vL)	14.5 million

b. Using the below formula:

rS = rE + (D/VL)×(1-Tc)×(rE - rD)

The rS for an unlevered firm will be same as rE. As the there is no debt in an unlevered firm.

rS = 12% + (8/14.5)(75%)(7%)

The rS for a levered firm will be ~ 14.9%

c. sL = EBIT/rS

sL = 6.5 million

sL + D = vL

6.5 + 8 = 14.5 million

d. WACC (weighted avg cost of capital) = [E/(E+D)]rE + (1-Tc)[D/(E+D)]rD

The WACC for Unlevered firm is same as rE

WACC for levered firm can be found using above formula which will be ~ 8.7%