Question

consider an all-equity firm that is certain to be able to use interest deductions to reduce its corporate tax bill. if the corporate tax rate is 34 percent, the personal tax rate on interest income is 30 percent, and there are no costs of financial distress, by how much will the value of the firm change if it issues $2.5 million in debt and uses the proceeds to repurchase equity?

Answer 1

The value of the firm changes by the net tax shield benefit of issuing $2.5 million in debt. With corporate taxes saving $850,000 and personal taxes on interest at $67,500, the annual benefit is $782,500. Without costs of financial distress, this is the change in firm value.

Step-by-step explanation:

To calculate the change in the firm's value when it issues $2.5 million in debt to repurchase equity, we need to consider the corporate and personal tax savings due to the interest deductions. For the firm, the corporate tax shield on the debt is the tax rate times the amount of debt: 0.34 × $2.5 million = $850,000.

However, the personal taxes on the interest income reduce the benefit. At a personal tax rate of 30%, the personal tax paid on the interest is 0.30 × (interest on the debt). If we assume that the interest rate on the debt is the cost of capital (which could be 9% as per the additional information provided), the interest paid annually is 0.09 × $2.5 million = $225,000. Therefore, personal tax on this interest would be 0.30 × $225,000 = $67,500.

So, the net tax benefit each year would be $850,000 - $67,500 = $782,500. Assuming a perpetual benefit of this tax shield (no growth or change in rates), the change in value of the firm is simply the tax shield benefit, as there are no costs of financial distress.