Final answer:
The new enterprise value of the firm after leveraging up to a debt-to-equity ratio of 4 with a tax rate of 15% is calculated as $5.6 billion, inclusive of a $600 million tax shield.
Step-by-step explanation:
The student's question pertains to the change in enterprise value of an all-equity financed firm after it adjusts its capital structure to have a debt-to-equity ratio of 4, in the context of Modigliani and Miller propositions with tax. According to MM propositions with taxes, the value of the leveraged firm is equal to the value of the unleveraged firm plus the present value of the tax shield on debt. To solve for the new enterprise value, we can apply the following formula:
VL = VU + (Debt × Tax Rate)
Where VL is the leveraged firm value, VU is the unleveraged firm value, and the tax rate is 15%.
Given that the firm's initial enterprise value is $5 billion and it wants to achieve a debt-to-equity ratio of 4, we first calculate the amount of debt it will take on. The value of equity will be one-fifth of the total leverage firm value, as it is 1 part equity to 4 parts debt.
So, Debt = 4 × Equity = 4 × ($5 billion / 5) = $4 billion
Now we can calculate the additional value due to the tax shield:
Tax Shield = Debt × Tax Rate = $4 billion × 0.15 = $600 million
So the new enterprise value would be:
VL = VU + Tax Shield = $5 billion + $600 million = $5.6 billion