Companies U and L are identical in every respect except that U is unlevered while L has $10 million of 5.9% bonds outstanding. Assume that (1) all of the MM assumptions are met, (2) both companies are subject to a 34% federal-plus-state corporate tax, (3) EBIT is $2 million, and (4) the cost of equity to Company U is 9%. What is the value, in millions, of Company L under the MM model?
Question
Companies U and L are identical in every respect except that U is unlevered while L has 2 million, and (4) the cost of equity to Company U is 9%. What is the value, in millions, of Company L under the MM model?
Solution
To calculate the value of Company L under the Modigliani-Miller (MM) model, we need to consider the tax shield provided by the interest expense on the debt.
Step 1: Calculate the tax shield. The tax shield is the amount of tax that Company L saves because it can deduct its interest expenses from its taxable income. The formula for the tax shield is:
Tax Shield = Corporate Tax Rate * Interest Expense
The interest expense is the amount of debt * interest rate on the debt, which is 0.59 million.
So, the tax shield is 34% * 0.2006 million.
Step 2: Calculate the value of the unlevered firm (Company U). The value of an unlevered firm is the present value of its earnings before interest and taxes (EBIT), discounted at the cost of equity. The formula is:
Value of Unlevered Firm = EBIT / Cost of Equity
So, the value of Company U is 22.22 million.
Step 3: Calculate the value of the levered firm (Company L). According to the MM model, the value of a levered firm is the value of an unlevered firm plus the present value of the tax shield. The formula is:
Value of Levered Firm = Value of Unlevered Firm + Tax Shield
So, the value of Company L is 0.2006 million = $22.42 million.
Therefore, under the MM model, the value of Company L is $22.42 million.
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