The total amount raised by the company through the issue of debentures is:
8000 debentures x $100 per debenture = $800,000
The discount on the issue of debentures is 5%, which means that the debentures were issued at 95% of their face value. The amount of discount is:
5% x $100 per debenture x 8000 debentures = $40,000
Therefore, the net amount raised by the company after deducting the discount is:
$800,000 - $40,000 = $760,000
The commission payable to underwriters and brokers is $40,000. This is an additional cost to the company.
The after-tax cost of debt is calculated as follows:
Interest expense = Face value of debentures x Interest rate
= $800,000 x 8% = $64,000
Tax shield = Interest expense x Tax rate
= $64,000 x 60% = $38,400
After-tax cost of debt = (Interest expense - Tax shield) / (Net amount raised - Commission)
= ($64,000 - $38,400) / ($760,000 - $40,000)
= $25,600 / $720,000
= 0.0356 or 3.56%
Therefore, the after-tax cost of debt is 3.56%.
Premium is the amount paid by the investors over and above the face value of the debentures. Since the debentures were issued at a discount, there is no premium involved in this case.