A company is issuing bonds that have a $1,000 face value and that pay an annual coupon of $62. The flotation cost associated with these bonds is 12.3% and they have a market value of $1,135.22. The bonds mature in 15 years. The firm’s marginal tax rate is 35%. What is the after-tax cost of debt?

Question

BlackTom AI · Accepted Answer

Question restatement: A company issues bonds with a face value of 1,000, annual coupon 62, flotation cost 12.3%, market price 1,135.22, and 15-year maturity. Tax rate is 35%. Find the after-tax cost of debt.

Step 1 — Determine net proceeds per bond after flotation costs. Flotation costs reduce the funds raised, so net proceeds = market price × (1 − flotation rate) = 1,135.22 × (1 − 0.123) = 1,135.22 × 0.877 ≈ 995.59.

Step 2 — Estimate the pre-tax cost of debt (yield to maturity) using net proceeds. The bond pays 62 annually and will repay 1,000 at maturity in 15 years. A quick approximation uses the formula: YTM ≈ [Coupon + (Face − NetProceeds)/N] / [(Face + NetProceeds)/2], where N = 15.
Plugging in: Coupon = 62, Face − NetProceeds = 1,000 − 995.59 ≈ 4.41, so (Face − NetProceeds)/N ≈ 4.41/15 ≈ 0.294. Numerator ≈ 62 + 0.294 ≈ 62.294. Denominator ≈ (1,000 + 995.59)/2 ≈ 997.79.
Thus, YTM ≈ 62.294 / 997.79 ≈ 0.0624, or about 6.24% as the pre-tax cost of debt.

Step 3 — Apply the tax shield to obtain the after-tax cost of debt. The after-tax cost is pretax cost × (1 − tax rate) = 0.0624 × (1 − 0.35) = 0.0624 × 0.65 ≈ 0.04056, or about 4.06%.

Option-by-option analysis:
- 6.25%: This represents the pre-tax yield close to the coupon rate, but the question asks for after-tax cost; applying the tax shield reduces the value to around 4.06%, not 6.25%. The correct figure should reflect tax effects, so 6.25% is not the after-tax cost.
- 4.06%: This matches our calculated after-tax cost using net proceeds and tax shield. It aligns with the estimated pre-tax yield near 6.24% multiplied by (1 − 0.35) = 0.65, yielding ~4.06%. This is the correct after-tax cost.
- 3.19%: This would imply a much larger tax adjustment or a substantially lower pre-tax yield than warranted by given coupon and net proceeds; the calculation above does not support such a low after-tax result.
- 4.91%: This would require a higher pre-tax cost or a smaller tax shield than our inputs provide. Given net proceeds and coupon, the after-tax result should be around 4.06%, not 4.91%.

Summary: Using net proceeds after flotation costs and the tax shield leads to an after-tax cost of debt of approximately 4.06%. The other options deviate from this result due to either neglecting flotation-adjusted proceeds, misapplying the tax effect, or misestimating the relation between coupon, price, and yield.

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