a.     Given the following information, which bond should a prudent investor choose? Justify your answer with mathematical proof.

MUNI yield-to-maturity = 1.4%    Corporate yield-to-maturity = 2.2%   

Marginal tax bracket = 35%                   

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.

Given the following information, which bond should a prudent investor choose? Justify your answer with mathematical proof.

MUNI yield-to-maturity = 1.4%
Corporate yield-to-maturity = 2.2%
Marginal tax bracket = 35%

Compare municipal and corporate bonds by calculating after-tax yields. In this detailed solution, we use a marginal tax rate of 35% to determine which bond offers a higher effective return. Learn how the after-tax yield of a corporate bond surpasses a MUNI bond's yield with mathematical proof.

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