Question

Accelerated issued 50000 at 8% debentures at a discount of 5% the tax rate is 50% the cost of debt capital is________.

a. 0.05
b. 0.04
c. 4.2%.
d. 0.046

Answer 1

The cost of debt capital for Accelerated's issued debentures is calculated as an after-tax cost of debt. When considering the 50% tax rate and the 5% discount on issuance, the correct cost is 4.21%, which corresponds to option c in the given choices.

Step-by-step explanation:

The cost of debt capital when Accelerated issues 50,000 at 8% debentures at a discount of 5% with a tax rate of 50% can be calculated using the formula for after-tax cost of debt. The formula takes into account the interest rate, the discount on debentures, the face value, and the tax rate.

First, we calculate the net proceeds from the issue of debentures. Since the debentures are issued at a discount of 5%, the net proceeds will be 95% of the face value. Then, the annual interest payment is calculated based on the 8% interest rate applied to the face value of the debentures. The cost of debt before tax is the annual interest divided by the net proceeds. Since interest on debentures is tax-deductible, the after-tax cost of debt is adjusted by the tax rate.

Here is the step-by-step calculation:

1. Net proceeds = Face value - Discount = 50,000 x (1 - 0.05) = 50,000 x 0.95 = $47,500.
2. Annual interest payment = Face value x Interest rate = 50,000 x 0.08 = $4,000.
3. Cost of debt before tax = Annual interest / Net proceeds = 4,000 / 47,500 = 0.0842 or 8.42%.
4. After-tax cost of debt = Cost of debt before tax x (1 - Tax rate) = 0.0842 x (1 - 0.50) = 0.0842 x 0.50 = 0.0421 or 4.21%.

Thus, the correct after-tax cost of debt is 4.21%, which is option c.