What is the present value of the tax shield to a firm that has total assets of $80 million and a net worth of $55 million, if the average interest rate on perpetual debt is 8.5%, the average return on equity is 14%, and the marginal tax rate is 35%?
A) $8.75 million
B) $12.25 million
C) $0.85 million
D) $0.744 million

Question

Quizplus · Accepted Answer

The present value of the tax shield can be calculated using the formula: PV of tax shield = Debt * Tax Rate * Interest Rate on Debt. The firm's debt is $80 million (total assets) - $55 million (net worth) = $25 million. Therefore, the PV of the tax shield = $25 million * 35% * 8.5% = $0.7375 million, which rounds up to $0.744 million. However, the correct interpretation involves recognizing that the tax shield should be considered on a perpetual basis, not just for one year. The correct formula for the perpetual tax shield is Debt * Tax Rate = $25 million * 35% = $8.75 million, which matches choice A. The initial calculation was incorrect because it mistakenly applied the interest rate to the tax shield calculation for a perpetual scenario.

What Is the Present Value of the Tax Shield to a Firm