A company has outstanding long-term debt with a yield to maturity of 7.5% and a marginal income tax rate of 30%. Given this information, what is the after-tax cost of debt for this company?

Question

BlackTom AI · Accepted Answer

To assess the after-tax cost of debt, we apply the formula: after-tax cost = pre-tax yield × (1 − tax rate).
Option 1: 6.25% — If we plug in tax effects briefly, 7.5% × (1 − 0.30) would not yield 6.25%; this value corresponds to a smaller deduction and is not consistent with the tax shield concept.
Option 2: 5.25% — This matches the standard approach: 7.5% × 0.70 = 5.25%. The tax shield reduces the effective cost, since interest expense is deductible, lowering the after-tax cost.
Option 3: 6.75% — This would imply a smaller tax shield than the correct calculation or perhaps applying tax non-deductibility in a way that increases the cost; it does not reflect the full deduction available from the tax rate.
Option 4: 5.75% — This is slightly higher than the correct calculation and could arise if the tax rate or yield were misapplied, but it does not align with the straightforward 7.5% × (1 − 0.30) computation.
In summary, the after-tax cost of debt accounts for the tax-deductible nature of interest, scaling the pre-tax yield by (1 − tax rate). Among the options, 5.25% precisely equals 7.5% × 0.70, which embodies the tax shield concept and yields the correct after-tax cost.

FA25-BL-BUS-F307-1134 Practice Question Set: Final Exam- Requires Respondus LockDown Browser

A company has outstanding long-term debt with a yield to maturity of 7.5% and a marginal income tax rate of 30%. Given this information, what is the after-tax cost of debt for this company?

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