Jackson has the choice to invest in city of Mitchell bonds or Sundial, Incorporated corporate bonds that pay 7.2 percent interest. Jackson is a single taxpayer who earns $67,500 annually. Assume that the city of Mitchell bonds and the Sundial, Incorporated bonds have similar risk.

What interest rate would the city of Mitchell have to pay in order to make Jackson indifferent between investing in the city of Mitchell and the Sundial, Incorporated bonds for 2024? (Use tax rate schedule.)





To determine the interest rate that the City of Mitchell bonds would have to pay in order to make Jackson indifferent between investing in the City of Mitchell bonds (which are typically tax-exempt) and the Sundial, Incorporated corporate bonds (which are taxable), we need to account for the fact that the interest earned on corporate bonds is subject to federal income tax, while municipal bonds (like City of Mitchell bonds) are typically exempt from federal tax.

### Steps to Calculate the Equivalent Tax-Free Yield

1. **Identify Jackson's taxable income:**  
   Jackson earns $67,500 annually, so we need to determine his tax bracket using the 2024 IRS tax rate schedule for single filers.

2. **Determine Jackson's marginal tax rate:**  
   For 2024, the tax brackets for single filers are as follows (approximated):

   - 10% on income up to $11,000
   - 12% on income between $11,000 and $44,725
   - 22% on income between $44,725 and $95,375
   - 24% on income between $95,375 and $182,100

   Since Jackson’s income of $67,500 falls between $44,725 and $95,375, his marginal tax rate is **22%**.

3. **Calculate the after-tax yield of Sundial, Incorporated bonds:**
   The interest rate for the Sundial bonds is 7.2%. Since this interest is taxable, the after-tax yield is calculated by adjusting for the marginal tax rate.

   \[
   \text{After-tax yield} = \text{Interest rate} \times (1 - \text{Marginal tax rate})
   \]
   \[
   \text{After-tax yield} = 7.2\% \times (1 - 0.22) = 7.2\% \times 0.78 = 5.616\%
   \]

4. **Calculate the required interest rate on City of Mitchell bonds:**
   Since the City of Mitchell bonds are tax-exempt, the interest rate on these bonds would need to be **5.616%** to make Jackson indifferent between the two investment options. This is because the after-tax return on the Sundial bonds is 5.616%, and Jackson would only invest in the City of Mitchell bonds if they offer at least this return tax-free.

### Conclusion:
The City of Mitchell bonds would have to pay an interest rate of **5.616%** to make Jackson indifferent between investing in them and the Sundial, Incorporated corporate bonds.

Would you like further details on this, or do you have any questions?

---

Here are some related questions to explore:
1. How does the tax exemption on municipal bonds impact investment decisions?
2. What would happen to the required interest rate if Jackson's tax bracket changed?
3. How do tax brackets influence the after-tax yield of corporate bonds?
4. What is the general relationship between risk and return in bonds?
5. How would state taxes affect Jackson’s decision?

**Tip:** Always consider your marginal tax rate when comparing taxable vs. tax-exempt investments!

Jackson has the choice to invest in city of Mitchell bonds or Sundial, Incorporated corporate bonds that pay 7.2 percent interest. Jackson is a single taxpayer who earns $67,500 annually. Assume that the city of Mitchell bonds and the Sundial, Incorporated bonds have similar risk. What interest rate would the city of Mitchell have to pay in order to make Jackson indifferent between investing in the city of Mitchell and the Sundial, Incorporated bonds for 2024? (Use tax rate schedule.)

Explore how to calculate the tax-equivalent yield for municipal bonds compared to corporate bonds using Jackson’s scenario. Learn about marginal tax rates, after-tax yield formulas, and investment comparison methods suitable for college-level and advanced high school 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