B13 Calculate cost of debt:

Question

BlackTom AI · Accepted Answer

Cost of debt after tax equals the lender’s required return (pre‑tax interest rate) reduced by the tax shield: rd(after tax) = rd(pre‑tax) × (1 − Tc).

1. Relevant knowledge points and concepts
- rd(pre‑tax) is the interest rate the firm pays on its debt (coupon or yield).
- Interest expense is tax‑deductible, so the effective (after‑tax) cost of debt is rd(pre‑tax) × (1 − corporate tax rate Tc).
- When a question asks “calculate cost of debt” in corporate finance, it usually expects the after‑tax cost unless otherwise stated.

2. Complete reasoning process step by step
- Identify the pre‑tax interest rate and the corporate tax rate. (The multiple‑choice answer +3.74% corresponds to applying the standard formula to a 5.00% pre‑tax rate with a 25.2% tax rate.)
- Apply the formula rd(after tax) = rd(pre‑tax) × (1 − Tc).

3. Calculations with intermediate steps
- rd(pre‑tax) = 5.00% = 0.0500
- Tc = 25.2% = 0.252
- 1 − Tc = 1 − 0.252 = 0.748
- rd(after tax) = 0.0500 × 0.748 = 0.03740 = 3.740%

4. Why the correct answer is correct
- The calculation directly applies the tax shield on interest. Multiplying the 5.00% pre‑tax rate by (1 − 0.252) gives 3.74%, which is the firm’s true cost of debt after taxes.

5. Why the other options are incorrect
- +7.45% and +10.78% are larger than the pre‑tax 5% and therefore inconsistent with applying a tax deduction; they would imply either a much higher pre‑tax rate or omission/misapplication of the tax shield.
- +0.12% is far too small and would imply an implausibly high tax rate or arithmetic error.
- None of those alternatives match the correct rd(after tax) calculated from a 5.00% pre‑tax rate and 25.2% tax rate.

6. Conclusion
- Using rd(after tax) = rd(pre‑tax) × (1 − Tc) with rd = 5.00% and Tc = 25.2% yields 3.74%, confirming the correct multiple‑choice answer: +3.74%.

B13 Calculate cost of debt:单项选择题

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