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?

Question

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.

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? Single choice

Similar Questions

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?

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?

A firm's aftertax cost of debt will increase if there is a(n):

TB MC Qu. 60 USA Manufacturing issued... USA Manufacturing issued 30-year, 7.2 percent semiannual bonds 6 years ago. The bonds currently sell at 101 percent of face value. What is the firm's aftertax cost of debt if the tax rate is 21 percent?

Which of the following statements regarding the aftertax cost of debt is accurate?

Galvatron Metals has a bond outstanding with a coupon rate of 6.1 percent and semiannual payments. The bond currently sells for $1,933 and matures in 19 years. The par value is $2,000 and the company's tax rate is 22 percent. What is the company's aftertax cost of debt?

Venus Limited has market value of debt of $80 million, market value of equity of $140 million, and cash of $20 million. The pre-tax cost of debt is 10%, the cost of equity is 14%, and the tax rate is 30%. The after-tax cost of debt is …………

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler