# Calculate the after-tax cost of debt under each of the following conditions: a. A tax rate of...

## Question:

Calculate the after-tax cost of debt under each of the following conditions:

a. A tax rate of 37%, and a yield to maturity of 7.9%

b. A tax rate of 25%, and a pre-tax cost of debt of 10.2%

c. A tax rate of 0%, and a yield to maturity of 7.9%

## Debt Cost:

This question requires knowledge of monetary debt, which is an obligation due from a borrower to an investor. From the perspective of a corporate borrower, or issuer, the cost of debt is an important consideration in structuring an optimal capital structure.

This problem is fairly straightforward. The key is in understanding the following terms are synonymous: yield to maturity and pre-tax cost of debt. They both refer to the cost of servicing a debt, before consideration for taxes. Since interest expense is tax deductible, the after-tax cost of debt is the most relevant measure. It's computed as follows:

After-tax Cost of Debt = Effective Annual Interest Rate * (1 - Tax Rate)

The computations for the three scenarios are illustrated below.

a. After-tax Cost of Debt = .079 (1 - .37) = .049 or 4.9%

b. After-tax Cost of Debt = .102 (1 - .25) = .076 or 7.6%

c. After-tax Cost of Debt = .079 (1 - .00) = .079 or 7.9% 