An unlevered firm has a value of $30 million. An identical firm has debt of $2 million with a 7 percent annual coupon. The tax rate is 40 percent. What is the value of the levered firm?Multiple choice question.$30 million$30.8 million$32 million$29.2 million
Question
An unlevered firm has a value of 2 million with a 7 percent annual coupon. The tax rate is 40 percent. What is the value of the levered firm?Multiple choice question.30.8 million29.2 million
Solution
The value of the levered firm can be calculated using the Modigliani-Miller theorem, which states that the value of a levered firm equals the value of an unlevered firm plus the present value of the tax shield.
The tax shield is the amount of money a company saves in income taxes by deducting the interest paid on its debt. The present value of the tax shield can be calculated as the debt amount times the tax rate.
Here are the steps to calculate the value of the levered firm:
- Calculate the annual interest expense: 0.14 million
- Calculate the tax shield: 0.056 million
- Calculate the present value of the tax shield: 0.8 million
- Add the value of the unlevered firm and the present value of the tax shield to get the value of the levered firm: 0.8 million = $30.8 million
So, the value of the levered firm is $30.8 million.
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