Calculate the​ after-tax return of​ a(n) 5.69 ​percent, 20-year,​ A-rated corporate bond for an investor in the 10 percent marginal tax bracket. Compare this yield to​ a(n) 4.82 ​percent, 20-year,​ A-rated, tax-exempt municipal​ bond, and explain which alternative is better. Repeat the calculations and comparison for an investor in the 35 percent marginal tax bracket.
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Part 1
The​ after-tax return of the 5.69​%, ​20-year, A-rated corporate bond for an investor in the 10​% marginal tax bracket is

5.12​%. ​ (Round to two decimal​ places.)
Part 2
Compare this yield to the 4.82​%, ​20-year, A-rated,​ tax-exempt municipal bond and explain which alternative is better.  ​(Select the best answer​ below.)
A.
The after dash tax yield of 5.12 % for the corporate bond is a better alternative than the 4.82 % tax dash free municipal bond at the 10​% tax rate.
B.
The 4.82 % tax dash free municipal bond is a better alternative than the after dash tax yield of 5.12 % for the corporate bond at the 10​% tax rate.

To solve this problem, we need to calculate the after-tax yield for both a 10% and a 35% marginal tax bracket and compare them to the 4.82% yield on the tax-exempt municipal bond.

### Part 1: After-Tax Return Calculation (10% Marginal Tax Bracket)

The after-tax return for a corporate bond is calculated using the formula:

\[
\text{After-Tax Return} = \text{Yield} \times (1 - \text{Tax Rate})
\]

Given:
- Corporate bond yield = 5.69%
- Tax rate = 10%

\[
\text{After-Tax Return} = 5.69\% \times (1 - 0.10) = 5.69\% \times 0.90 = 5.121\%
\]

So, the after-tax return for the corporate bond is approximately **5.12%**.

### Comparison at 10% Tax Rate

- After-tax return of the corporate bond = 5.12%
- Municipal bond yield (tax-exempt) = 4.82%

Since **5.12%** (corporate bond) is greater than **4.82%** (municipal bond), the **corporate bond is a better alternative** at the 10% tax rate.

The correct answer is:
**A. The after-tax yield of 5.12% for the corporate bond is a better alternative than the 4.82% tax-free municipal bond at the 10% tax rate.**

---

### Part 2: After-Tax Return Calculation (35% Marginal Tax Bracket)

We will now repeat the calculation for an investor in the 35% tax bracket.

\[
\text{After-Tax Return} = 5.69\% \times (1 - 0.35) = 5.69\% \times 0.65 = 3.6985\%
\]

So, the after-tax return for the corporate bond is approximately **3.70%**.

### Comparison at 35% Tax Rate

- After-tax return of the corporate bond = 3.70%
- Municipal bond yield (tax-exempt) = 4.82%

At this tax rate, **4.82%** (municipal bond) is greater than **3.70%** (corporate bond), so the **municipal bond is a better alternative** at the 35% tax rate.

---

### Conclusion:

1. For an investor in the 10% tax bracket, the corporate bond is better.
2. For an investor in the 35% tax bracket, the municipal bond is better.

Would you like more details or have any questions about the process?

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Here are 5 related questions for further exploration:
1. How would changes in interest rates affect the comparison between these two bonds?
2. What are the risks associated with corporate bonds versus municipal bonds?
3. How does the tax-exempt status of municipal bonds vary across different states?
4. Can municipal bond yields be higher than corporate bond yields in any scenario?
5. What is the impact of inflation on long-term bond investments?

**Tip:** Always consider the tax implications when comparing investments to ensure you're comparing after-tax returns for an accurate picture.

Calculate the after-tax return of a 5.69 percent, 20-year, A-rated corporate bond for an investor in the 10 percent marginal tax bracket. Compare this yield to a 4.82 percent, 20-year, A-rated, tax-exempt municipal bond, and explain which alternative is better. Repeat the calculations and comparison for an investor in the 35 percent marginal tax bracket.

Learn how to calculate the after-tax return of a 5.69% A-rated corporate bond for investors in the 10% and 35% marginal tax brackets, and compare it to a 4.82% tax-exempt municipal bond. Explore which bond is the better investment based on the tax bracket and the formulas involved.

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