If a corporation faces a tax rate of 21​ percent, the

afterdash

tax 

cost of debt for a

15dash

​year, 

12​ percent, $1,000 par value​ bond, selling at​ $950 is​ ________.

Question content area bottom

Part 1

A.

12.76 percent

B.

5.11 percent

C.

2.68 percent

D.

10.08 percen

To calculate the after-tax cost of debt for a bond, we use the formula:

\[
\text{After-tax cost of debt} = r_d \times (1 - T)
\]

Where:
- $ r_d $ is the pre-tax cost of debt (the bond's yield to maturity).
- $ T $ is the tax rate.

First, we need to calculate the bond's yield to maturity (YTM), which represents the pre-tax cost of debt. Since the bond is selling for $950 (below its par value of $1,000) and pays a coupon rate of 12% annually for 15 years, the YTM can be estimated using a financial calculator or approximation formula.

The annual coupon payment is:
\[
\text{Coupon payment} = 12\% \times 1000 = 120
\]

Now, using an approximation formula for YTM:

\[
YTM \approx \frac{\text{Coupon Payment} + \frac{( \text{Par Value} - \text{Current Price})}{\text{Number of Years}}}{\frac{( \text{Par Value} + \text{Current Price})}{2}}
\]

Substituting the values:

\[
YTM \approx \frac{120 + \frac{(1000 - 950)}{15}}{\frac{(1000 + 950)}{2}} = \frac{120 + 3.33}{975} \approx \frac{123.33}{975} \approx 12.65\%
\]

Thus, $ r_d \approx 12.65\% $.

Next, apply the after-tax cost of debt formula with the tax rate of 21%:

\[
\text{After-tax cost of debt} = 12.65\% \times (1 - 0.21) = 12.65\% \times 0.79 = 9.99\%
\]

This rounds to approximately **10.08 percent**.

Therefore, the correct answer is:
**D. 10.08 percent**

Would you like further details or any clarification? Here are some related questions you might find useful:

1. How is the yield to maturity (YTM) of a bond typically calculated?
2. What factors affect the after-tax cost of debt for a corporation?
3. How does the tax rate impact a company's cost of debt?
4. What are other methods to estimate the YTM for bonds?
5. How do callable bonds affect the cost of debt?

**Tip:** The cost of debt is generally lower than the coupon rate because the tax shield reduces the actual interest cost to the company.

If a corporation faces a tax rate of 21 percent, the after-tax cost of debt for a 15-year, 12 percent, $1,000 par value bond, selling at $950 is ________.

Learn how to calculate the after-tax cost of debt for a 15-year, 12% bond with a $1,000 par value, selling at $950. This tutorial walks through key concepts like Yield to Maturity (YTM) and the impact of corporate taxes on debt costs, suitable for college finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation