Final answer:
The value of a leveraged firm includes the tax shield from its debt. For a firm with $2 million in debt at a 7% coupon and a 40% tax rate, the tax shield would be $56,000, which is added to the unlevered firm's value.
Step-by-step explanation:
When considering the value of a leveraged firm, one must take into account the tax shield provided by the debt. The tax shield is simply the amount of tax saved by the firm due to the tax-deductible nature of interest payments. In this case, the firm has debt of $2 million with a 7 percent annual coupon. This means that the firm pays $140,000 in interest payments annually ($2,000,000 × 7%). With a tax rate of 40 percent, the tax shield is equal to the interest payment multiplied by the tax rate, which would be $56,000 ($140,000 × 40%). The value of the tax shield is therefore the present value of these annual tax savings, which, in a perpetual context, can be taken as the nominal amount itself since it is a perpetuity.
To find the value of the leveraged firm (VL), we add the tax shield to the value of the unlevered firm (VU).
- VL = VU + Tax Shield
- VL = $30,000,000 + $56,000
- VL = $30,056,000
However, this is not one of the options provided in the multiple-choice question. The closest answer to the calculated value is option D, $30 million, but this is not correct as it does not consider the tax shield.
It's possible that there's an error in the provided choices or in the assumptions made for the calculation, such as perpetuity of tax shield or other factors not outlined in the question.