A company has 10% perpetual debt of Rs.1,00,000. The tax rate is 35%. Which one of the following is the after-tax cost of capital assuming that the debt is issued at 10% premium?

Correct option is B

The after-tax cost of debt is the cost a company incurs for borrowing funds, considering the tax deductibility of interest expenses. When debt is issued at a premium, the effective interest rate changes.

Given Information:
Face Value of Perpetual Debt (Nominal Value) = ₹1,00,000
Nominal Interest Rate = 10%
Annual Interest Payment (Coupon Payment) = 10% of ₹1,00,000 = ₹10,000
Issue Price = Face Value + Premium = ₹1,00,000 + (10% of ₹1,00,000) = ₹1,00,000 + ₹10,000 = ₹1,10,000

Tax Rate = 35%
Formula for After-Tax Cost of Perpetual Debt Issued at a Premium:
Cost of Debt (Kd) = [Interest Payment × (1 - Tax Rate)] / Net Proceeds from Issue

Calculation:
Calculate the After-Tax Interest Payment:
After-Tax Interest Payment = Annual Interest Payment × (1 - Tax Rate)
After-Tax Interest Payment = ₹10,000 × (1 - 0.35)
After-Tax Interest Payment = ₹10,000 × 0.65 = ₹6,500

Determine the Net Proceeds from Issue:
Since the debt is issued at a 10% premium, the company receives more than the face value.
Net Proceeds = Issue Price = ₹1,10,000 (Assuming no floatation costs are mentioned)

Calculate the After-Tax Cost of Capital (Kd):
Kd = After-Tax Interest Payment / Net Proceeds from Issue
Kd = ₹6,500 / ₹1,10,000
Kd ≈ 0.0590909
Convert to Percentage:
Kd ≈ 0.0590909 × 100 ≈ 5.91% ​

Conclusion:
The after-tax cost of capital for the 10% perpetual debt, issued at a 10% premium with a 35% tax rate, is approximately 5.91%.