Question

Companies U and L are identical in every respect except that U is unlevered while L has $12 million of 8% 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 $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	B	C	D	E	F	G	H	I
2
3		Debt for L	$12,000,000
4		Cost of debt	8%
5		Tax rate	40%
6		EBIT	$3,000,000
7		Unlevered cost of equity	10%
8		a)
9
10		Calculation of unlevered i.e. all equity value of the firm:
11
12		EBIT	$3,000,000
13		Unlevered Cost of equity	10%
14		Tax Rate	40%
15		Free cash flow can be calculated as follows:
16		Free cash flow	=EBIT*(1-Tax Rate) + Depreciation - CAPEX - Change in working capital
17			=$3,000,000*(1-40%)+0-0-0
18			$1,800,000.00	=D12*(1-D14)
19
20		Since EBIT of the firm is constant forever, therefore,
21
22		Unlevered value of the firm, VU	=Free Cash Flow / unlevered cost of Equity
23			=$1,800,000 / 10%
24			$18,000,000.00	=D18/D13
25
26		Hence Unlevered value of the firm, VU	$18,000,000.00
27
28		As per MM proposition I, the value of the firm is independent of its capital structure, therefore
29
30		Value of the levered firm, VL	=Value of the unlevered firm
31			$18,000,000.00
32
33		Hence Value of the levered firm, VL	$18,000,000.00
34
35		b)
36
37		rs for firm U	=unlevered cost of Equity
38			10%
39
40		Unlevered cost of equity is also the cost of asset, ra
41		therefore the levered cost of equity (rL) can be calculated as follows:
42		rL = rU+(D/E)*(rU-rD)*(1-Tax rate)
43		Where rU is the unlvered cost of equity and rD is the cost of debt.
44
45		Given the following data:
46		Value of the firm	$18,000,000
47		Value of the Debt	$12,000,000
48		Value of Equity	$6,000,000	=D46-D47
49
50		D/E	2
51		rU	10%
52		rD	8%
53		Tax rate	40%
54
55		rL	= rU+(D/E)*(rU-rD)*(1-Tax rate)
56			=10%+2*(10%-8%)*(1-Tax rate)
57			12.40%	=D51+D50*(D51-D52)*(1-D53)
58
59		Hence levered cost of equity, rLis	12.40%
60