Company Cosmo Cougs Inc. plans to issue 10-year bonds with a face value of $1,000 and an annual coupon rate of 8%. The market price of similar bonds is $1,054. Flotation costs are estimated to be 5.25% for each bond. If interest payments are made annually, and the company’s marginal tax rate is 34%, what is the after-tax cost of debt?

Question

BlackTom AI · Accepted Answer

We start by identifying the key data: the bond has a face value of $1,000, annual coupon rate of 8%, annual interest payments, market price of similar bonds $1,054, flotation costs 5.25%, and a marginal tax rate of 34%. We must compute the after-tax cost of debt using net proceeds from issuing the debt.

Option by option analysis:

Option A: 5.29%
This matches the standard formula for after-tax cost of debt when flotation costs are present: after-tax cost = (annual coupon × (1 − tax rate)) / net proceeds. Here, annual coupon = 0.08 × 1000 = 80. Tax shield reduces payments to 80 × (1 − 0.34) = 80 × 0.66 = 52.8. Net proceeds = market price × (1 − flotation cost) = 1054 × (1 − 0.0525) = 1054 × 0.9475 ≈ 998.665. Therefore, after-tax cost = 52.8 / 998.665 ≈ 0.0529 = 5.29%. This aligns perfectly with the calculation.

Option B: 8.02%
If one overlooked flotation costs and tax effects, one might incorrectly use the pre-tax coupon rate (8%) or miscalculate net proceeds. Using 8% directly would ignore the tax shield and flotation impact, leading to a higher, incorrect figure. Since the after-tax benefit reduces the effective cost, 8.02% is not consistent with the given data.

Option C: 4.01%
This would result from an incorrect method, such as dividing the after-tax coupon by a larger denominator or misapplying tax. For instance, if net proceeds were assumed near the full price without subtracting flotation costs, or if the tax impact were partly ignored, a value around 4% could accidentally appear, but it does not reflect the stated flotation costs and tax impact.

Option D: 7.22%
A misstep here would be to underweight the tax shield or to neglect the reduction in proceeds from flotation costs, producing a higher rate than the true after-tax cost. 7.22% is inconsistent with the correct net proceeds and after-tax coupon relationship described by the formula.

In summary, the correct approach weighs the after-tax coupon against the actual funds raised after flotation costs, yielding 5.29%. The alternative options arise from misapplying tax effects, flotation costs, or using the pre-tax coupon rate without adjustments.

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