Assume the marginal corporate tax rate is 30 percent.The firm has no debt in its capital structure.It is valued at $100 million.What would be the value of the firm if it issued $50 million in perpetual debt and repurchased the same amount of equity?

Question

Quizplus · Accepted Answer

The value of the firm with debt can be calculated using the following formula: 
Value of firm with debt = Value of firm without debt + Tax shield on debt

Tax shield on debt = Annual interest payment on debt x Marginal tax rate

Since the debt is perpetual, the annual interest payment is the interest rate on the debt multiplied by the amount of debt issued. Let's assume an interest rate of 5% on the debt.

Value of firm without debt = $100 million

Tax shield on debt = 5% x $50 million x 30% = $7.5 million

Value of firm with debt = $100 million + $7.5 million = $107.5 million

When the firm repurchases $50 million in equity, the total value of the firm remains the same. Therefore, the new value of equity can be calculated as follows:

Value of equity = Value of firm with debt - Value of debt

Value of debt = $50 million (perpetual)

Value of equity = $107.5 million - $50 million = $57.5 million

Therefore, the new value of the firm would be $50 million (debt) + $57.5 million (equity) = $107.5 million, which is option B.

Assume the Marginal Corporate Tax Rate Is 30 Percent