Companies U and L are identical in every respect except that U is unlevered whil
ID: 2710987 • Letter: C
Question
Companies U and L are identical in every respect except that U is unlevered while L has $8 million of 5% bonds outstanding. Both firms have an EBIT of $2 million. Assume that all of the MM assumptions are met.
1. Suppose that both firms are subject to a 35% federal-plus-state corporate tax rate, investors in both firms face a tax rate of Td = 28% on debt income and Ts = 20% (on average) on stock income, and the appropriate required pre-personal-tax rate rsU is 10%.What is the value of the unlevered firm, VU? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
2. What is the value of the levered firm, VL? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
3. What is the gain from leverage? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
4. Now keep the other assumptions (D = $8 million, rd = 5%, EBIT = $2 million, and rsU = 10%) but set Tc = Ts = Td = 0. What is the value of the unlevered firm, VU? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
5. What is the value of the levered firm, VL? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
6. What is the gain from leverage? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
7. Keep the other assumptions (D = $8 million, rd = 5%, EBIT = $2 million, and rsU = 10%) but now suppose Td = Ts = 0 and Tc = 40%. What is the value of the unlevered firm, VU? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
8. What is the value of the levered firm, VL? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
9. What is the gain from leverage? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
10. Keep the other assumptions (D = $8 million, rd = 5%, EBIT = $2 million, and rsU = 10%) but now suppose that Td = 28%, Ts = 28%, and Tc = 40%. Now what is the value of the levered firm? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
11. What is the gain from leverage? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$ million
Explanation / Answer
Let us say the market value of unlevered firm is $ 10 Million
Then U = $ 10 Million of Equity
And L = $ 2 Million of Equity + 8 Million of Debt with 5% bonds outstanding
EBIT = $ 2 Million
Answer (1)
Tax rate on U & L = 35%
Personal Tax rate of Investors Td = 28% and Ts = 20%
Required rate of return rsU = 10%
For Firm U
EBIT = $ 2 Million
Interest = 0 (all equity firm)
EBT = $ 2 Million
EAT = $ 2 Million * (1-0.35) = $ 1.3 Million
After tax rate of return to investors = 0.10 * (1-0.20) = 0.08 or 8%
Value of the Firm = $ 1.3/1.08 = $1 2037 Million or $ 1.20 Million (rounded off)
This is because the amount available to investor from the firm is after corporate tax. So while valuing the firm the same should be taken at after tax value.
Value of Firm U = $ 1.20 Million
Answer (2)
For Firm L
EBIT = $ 2 Million
Interest = $ 0.4 Million
EBT =$ 2 Million - $ 0.4 Million = $ 1.6 Million
EAT = $ 1.6 Million * (1-0.35) = $ 1.04 Million
After tax required rate of return on debt = 0.10 * (1-0.28) = 0.072 or 7.2%
After-tax required return on equity = 0.10 * (1-0.20) = 0.08 or 8%
Value of the Firm L = $ 40 Million / 1.072 + $ 1.6 Million /1.08
= $ 0.3731 Million + 1.4815 Million = 1.8546 Million or 1.85 Million
Value of the Firm L = $ 1.85 Million
Answer (3)
Value of Firm U = $ 1.20 Million
Value of Firm L = $ 1.85 Million
Gain from Leverage = $ 1.85 Million - $ 1.20 Million = $ 0.65 Million
Answer (4)
If Tc =Ts = Td = 0
For Firm U
EBIT = EBT = EAT = $ 2 Million
Value of the Firm U = $ 2 Million / 1.10 = $ 1.818 Million or $1.82 Million (rounded off)
Value of Firm U = $ 1.82 Million
Answer (5)
EBIT = $ 2 Million
Interest = $ 8 Million * 5% = $ 0.40 Million
EBT = $ 2 Million - $ 0.4 Million = $ 1.6 Million
EAT = $ 1.6 Million as Tc =0
Value of the Firm L = $ 0.40 Million / 1.10 + $ 1.6 Million / 1.10
= $ 0.3636 Million + $ 1.4545 Million
= $ 1.8181 Million or $ 1.82 Million (rounde off)
Value of Firm L = $ 1.82 Million
Answer (6)
Gain on Leverage = Value of Firm L - Value of Firm U = $ 1.82 - $ 1.82 = 0
Answer (7)
If Ts = Td = 0 But Tc = 40%
For Firm U
EBIT = EBT = $ 2 Million
EAT = $ 2 Million* (1-0.4) = $ 1.2 Million
Value of the Firm U = $ 1.20 Million / 1.10 = $ 1.09 Million
Answer (8)
Ts = Td =0 But Tc = 40%
EBIT = $ 2 Milllion
Interest = $ 0.40 Million
EBT = $ 1.60 Million
EAT = $ 1.6 Million * (1-0.40) = $ 0.96 Million
Value of Firm L = $ 0.40 Million / 1.10 + $ 0.96 Million /1.10
= $ 0.3636 Million + $ 0.8727 Million
= $ 1.2363 Million or $ 1.24 Million (rounded off)
Value of Firm L = $ 1.24 Million
Answer (9)
Gain from Leverage = $ 1.24 Million - $ 1.09 Million = $ 0.15 Million
Answer (10)
Td = 28%, Ts = 28% Tc = 40%
After tax required rate of return on debt = after tax required rate of return on equity
= 10% * (1-0.28) =7.2%
For Firm U
EBIT = EBT = $ 2 Million
EAT = $ 2 Million * (1-0.4) = $ 1.2 Million
Value of Firm U = $ 1.2 Million / 1.072 = $ 1.119 Million or $ 1.12 Million (rounded off)
Value of Firm U = $ 1.12 Million
For Firm L
EBIT = $ 2 Million
Interest = $ 0.40 Million
EBT = $ 1.6 Million
EAT = $ 1.6 Million * (1-0.4) = $ 0.96 Million
Value of Firm = $ 0.40 Million / 1.072 + $ 0.96 Million / 1.072 = 0.37331 Million + 0.8955 Million
= $ 1.2686 Million or $ 1.27 Million (rounded off)
Answer (11)
Gain from Leverage = $ 1.27 Million - $ 1.12 Million = $ 0.15 Million
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