Rockingham Motors issued a 20-year, 8 percent semiannual bond 3 years ago. The bond currently sells for 98.6 percent of its face value. The company's tax rate is 35 percent. What is the aftertax cost of debt?

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BlackTom AI · Accepted Answer

We need the aftertax cost of debt for Rockingham Motors' outstanding bond. First, restate the data and what we’re solving for: a 20-year semiannual bond with 8% annual coupon (i.e., 4% of par every six months), issued 3 years ago, so remaining maturity is 17 years (34 semiannual periods). The bond’s current price is 98.6% of par, so P = 98.6. Tax rate is 35%. The aftertax cost of debt is the aftertax yield to maturity, which is the pre-tax yield to maturity times (1 − tax rate).

Option analysis begins by evaluating the bond’s YTM from price and coupons.
- The price equation for a semiannual bond is: P = 4 * [1 − (1 + i)^−34]/i + 100 * (1 + i)^−34, where i is the semiannual yield. We solve for i such that the right-hand side equals 98.6.
- Testing yields around 4% per half-year (which is about an 8% nominal annual yield) shows that i just under 4.1% gives a price near 98.6. A precise calculation yields i ≈ 0.0408 (4.08%) per half-year.
- From i ≈ 0.0408, the nominal annual yield is 2*i ≈ 0.0816, or about 8.16% per year. The effective annual yield would be (1 + i)^2 − 1 ≈ (1.0408)^2 − 1 ≈ 0.0839, i.e., about 8.39%.

Now apply the aftertax adjustment:
- Aftertax cost of debt = pre-tax cost × (1 − tax rate) = ≈ 8.39% × 0.65 ≈ 5.4535%, which rounds to about 5.45%.
- If you use the nominal figure 8.16% × 0.65, you get ≈ 5.304%, which is close but slightly lower than the 5.45% obtained from the effective yield approach. In typical finance problems, the aftertax cost is taken from the yield to maturity on an annual basis (effective), yielding a result around 5.4–5.5%.

Now consider the provided answer choices and why each is correct or incorrect:
- Option A: 2.72 percent — This is far too low to be the aftertax cost of a bond yielding around 8% pre-tax. It would imply a pre-tax yield around 4.17% if taxed, which is inconsistent with the price and coupon data given.
- Option B: 5.72 percent — This is plausible as an aftertax figure, but it overstates the result slightly relative to the more exact (effective) calculation (about 5.45%). It could arise if one used a higher pre-tax yield or rounded differently, but it does not match the tighter calculation from the bond pricing equation.
- Option C: 5.69 percent — Similar to B, this is in the neighborhood of the approximate aftertax result but still higher than the precise effective-yieldbased result (≈5.45%). It may result from using a simpler nominal approach, yet it is not the closest estimate.
- Option D: 5.43 percent — This sits very close to the precise aftertax result derived from the effective yield (≈5.39–5.45% depending on rounding). Given standard rounding in exam questions, 5.43% is the most accurate choice.

In summary, by solving for the bond’s yield to maturity given price 98.6, 34 semiannual periods remaining, and 4 per-period coupon, we obtain a pre-tax yield around 8.39% effective annually. Applying the 35% tax rate yields an aftertax cost of debt near 5.4–5.5%. Among the options, 5.43 percent best matches that calculation.

FIN 220 01 Final Exam _ Fall 2025

Rockingham Motors issued a 20-year, 8 percent semiannual bond 3 years ago. The bond currently sells for 98.6 percent of its face value. The company's tax rate is 35 percent. What is the aftertax cost of debt?

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