To determine which bond a prudent investor should choose between a municipal bond (MUNI) and a corporate bond, we must compare their after-tax yields. Since municipal bonds are often tax-exempt and corporate bonds are subject to taxation, we need to calculate the after-tax yield for the corporate bond to make an accurate comparison.

Step 1: Formula for after-tax yield on the corporate bond

The formula to calculate the after-tax yield of a corporate bond is:

$\text{After-tax yield} = \text{Corporate yield} \times (1 - \text{Tax rate})$

Given that:

• Corporate yield-to-maturity (YTM) = 2.2% = 0.022
• Marginal tax bracket = 35% = 0.35

$\text{After-tax yield} = 0.022 \times (1 - 0.35) = 0.022 \times 0.65 = 0.0143 = 1.43\%$

Step 2: Compare the after-tax yield to the MUNI yield

• MUNI yield-to-maturity = 1.4%
• After-tax yield on the corporate bond = 1.43%

Step 3: Conclusion

• The after-tax yield of the corporate bond is 1.43%.
• The yield-to-maturity of the MUNI bond is 1.4%.

Since the after-tax yield of the corporate bond (1.43%) is slightly higher than the MUNI bond yield (1.4%), the prudent investor should choose the corporate bond. Even after taxes, the corporate bond offers a marginally higher return.

Mathematical justification:

• Corporate bond after-tax yield = 1.43%
• MUNI bond yield = 1.4%

1.43% > 1.4%, so the corporate bond offers a higher effective return.

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Do you want more details on the calculations or any clarification?

Here are five related questions you might find interesting:

1. How do bond ratings affect the decision between municipal and corporate bonds?
2. What are the risks associated with choosing corporate bonds over municipal bonds?
3. How does a change in tax brackets influence the choice between corporate and municipal bonds?
4. What happens if the yield-to-maturity on both bonds is equal before taxes?
5. How does inflation impact bond yields and investment decisions?

Tip: Always account for tax implications when comparing investment options, as they can significantly affect the real return.