Question

When personal taxes on interest income and bankruptcy costs are considered, the general expression for the value of a levered firm in a world in which the tax rate on equity distributions equals zero is:

V₁ = Vu+ [1 -(1-te)/(1-t)πt)] D - PV (Distress Costs)
where
V=The value of a levered firm.
Vo=The value of an unlevered firm.
D=The value of the firm's debt.
te=The tax rate on corporate income. for-The personal tax rate on interest income.
PV(Distress Cost) The present value of the costs of financial distress.
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 20 percent, and there are no costs of financial distress, by how much will the value of the firm change if it issues $1 million in debt and uses the proceeds to repurchase equity?

Answer 1

The value of the firm increases by $640,000 due to issuing $1 million in debt to repurchase equity, after considering the defined corporate and personal tax rates.

Step-by-step explanation:

In a world with corporate taxes and personal taxes on interest income, if the corporate tax rate is 34%, the personal tax rate on interest income is 20%, and there are no costs of financial distress, the value of the firm will change when it issues $1 million in debt to repurchase equity. The relevant formula is V1 = Vu + [1 -(1-te)/(1-t) πt)] D - PV (Distress Costs). We can insert the given values to find the change in firm value as a result of the new debt.

The value of the firm changes by $680,000 if it issues $1 million in debt to repurchase equity when considering the given tax rates and no costs of financial distress.

The detailed calculation is as follows. The corporate tax shield is (1-te) × D = (1 - 0.34) × $1,000,000 = $660,000. The personal tax on the interest income reduces the advantage of the debt by (1-t)/(1-te) × t × D = (1-0.20)/(1-0.34) × 0.20 × $1,000,000 = $20,000. The increase in the value of the firm due to the issuance of debt, after taking into account the personal tax on interest income, is therefore $660,000 - $20,000 = $640,000.