Firm P borrows at 12% p.a. and pays tax at 30%. Firm Q borrows at 10% p.a. and pays tax at 10%. For both firms, interest is a deductible expense.
Which statement about their after-tax cost of debt is correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Firm P has the lower after-tax cost of debt: 8.4% against 9% for Firm Q.
Given:
Firm P: interest rate = 12%; tax rate = 30%
Firm Q: interest rate = 10%; tax rate = 10%
After-tax cost of debt = Interest rate × (1 − Tax rate)
Firm P = 12% × (1 − 0.30)
Firm P = 12% × 0.70 = 8.4%
Firm Q = 10% × (1 − 0.10)
Firm Q = 10% × 0.90 = 9%
8.4% is lower than 9%, so Firm P has the lower after-tax cost of debt.
Option (1) Firm Q has the lower after-tax cost of debt, as it borrows at the lower rate. — Incorrect. This compares only the rates before tax. Firm P saves more tax, so its real cost falls below Firm Q’s.
Option (2) Firm Q has the lower after-tax cost of debt: 1% against 3.6% for Firm P. — Incorrect. These figures are the tax saved (10% × 10% = 1%; 12% × 30% = 3.6%).
Option (3) Firm P has the lower after-tax cost of debt: 8.4% against 10% for Firm Q. — Incorrect. Firm P is right, but 10% leaves out Firm Q’s own tax saving. Its cost is 9%.
Interest is a deductible expense, so a higher tax rate makes debt cheaper.
NCERT (2026-27 Edition): “6. Tax Rate: Since interest is a deductible expense, cost of debt is affected by the tax rate. The firms in our examples are borrowing @ 10%. Since the tax rate is 30%, the after tax cost of debt is only 7%. A higher tax rate, thus, makes debt relatively cheaper and increases its attraction vis-à-vis equity.” |