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.

MSB-250-300-002 Proctored Final Exam

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?

View Explanation

Log in for full answers

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?

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?

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