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Miller Model Companies U and L are identical in every respect except that U is u

ID: 2709079 • Letter: M

Question

Miller Model

Companies U and L are identical in every respect except that U is unlevered while L has $17 million of 8% bonds outstanding. Both firms have an EBIT of $3 million. Assume that all of the MM assumptions are met.

Suppose that both firms are subject to a 40% 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

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

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

Now keep the other assumptions (D = $17 million, rd = 8%, EBIT = $3 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

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

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

Keep the other assumptions (D = $17 million, rd = 8%, EBIT = $3 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

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

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

Keep the other assumptions (D = $17 million, rd = 8%, EBIT = $3 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

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

Answer:

PART -1

We know that Value of unlevered firm Vu = EBIT(1-Tc)/ru

Here EBIT = $3 million , Tc = corporate tax rate = 40%, and ru = 10%

so , Vu = $3 million(1-40%) / 10% = $18 million

It is given that Td = 28%, Ts = 20% and Tc = 40%

and VL is value of levered firm = Vu + [1 - (1-Ts)(1-Tc)/(1-Td)] x B = $18 million + [1 - (1-20%)(1-40%)/(1-28%)]*17

VL = $18 million - $12.142 million = $5.857 million

and Gain on leverage is Return on asset

Therefore gain on leverage formula is:

Gain on leverage = Return on asset = EBIT / Total capital = $3 million / ($17 million + $18 million) = 8.57%

So gain on leverage is 8.57% - 8% = 0.57%

as total capital = Vu + Vd = value of equity + value of debt = $35 million.

PART-2

We know that Value of unlevered firm Vu = EBIT(1-Tc)/ru

Here EBIT = $3 million , Tc = corporate tax rate = 0%, and ru = 10%

so , Vu = $3 million(1-0%) / 10% = $30 million

It is given that Td = 0%, Ts = 0% and Tc = 40%

and VL is value of levered firm = Vu + [1 - (1-Ts)(1-Tc)/(1-Td)] x B = $18 million + [1 - (1-0%)(1-0%)/(1-0%)]*17

VL = $18 million +$0 million = $18 million

and Gain on leverage is Return on asset

Therefore gain on leverage formula is:

Gain on leverage = Return on asset = EBIT / Total capital = $3 million / ($17 million + $18 million) = 6.382%

So gain/loss on leverage is 6.382% - 8% = 1.618%

as total capital = Vu + Vd = value of equity + value of debt = $47 million.

PART-3

We know that Value of unlevered firm Vu = EBIT(1-Tc)/ru

Here EBIT = $3 million , Tc = corporate tax rate = 40%, and ru = 10%

so , Vu = $3 million(1-40%) / 10% = $18 million

It is given that Td = 0%, Ts = 0% and Tc = 40%

and VL is value of levered firm = Vu + [1 - (1-Ts)(1-Tc)/(1-Td)] x B = $18 million + [1 - (1-0%)(1-40%)/(1-0%)]*17

VL = $18 million +$6.8 million = $24.8 million

and Gain on leverage is Return on asset

Therefore gain on leverage formula is:

Gain on leverage = Return on asset = EBIT / Total capital = $3 million / ($17 million + $18 million) = 8.57%

So gain/loss on leverage is 8.57% - 8% = 0.57%

as total capital = Vu + Vd = value of equity + value of debt = $35 million.

PART-4

We know that Value of unlevered firm Vu = EBIT(1-Tc)/ru

Here EBIT = $3 million , Tc = corporate tax rate = 40%, and ru = 10%

so , Vu = $3 million(1-40%) / 10% = $18 million

It is given that Td = 28%, Ts = 28% and Tc = 40%

and VL is value of levered firm = Vu + [1 - (1-Ts)(1-Tc)/(1-Td)] x B = $18 million + [1 - (1-28%)(1-40%)/(1-28%)]*17

VL = $18 million +$6.8 million = $24.8 million

and Gain on leverage is Return on asset

Therefore gain on leverage formula is:

Gain on leverage = Return on asset = EBIT / Total capital = $3 million / ($17 million + $18million) = 8.57%

So gain/loss on leverage is 8.57% - 8% = 0.57%

as total capital = Vu + Vd = value of equity + value of debt = $35 million.