To find your after-tax cash flow from the zero-coupon bond, we need to determine the bond's maturity value (face value), and then calculate the tax implications based on the income generated. Let’s walk through the steps systematically:

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Step 1: Understanding the zero-coupon bond.

• Face Value (FV): $1,000
• Maturity: 1 year
• YTM (yield to maturity): 10.4% annualized, with semi-annual compounding
• Personal income tax rate: 29%

Since this is a zero-coupon bond, it pays no interest during the year, but you earn interest as the difference between the price you pay and the bond’s face value upon maturity.

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Step 2: Calculate the purchase price of the bond.

A zero-coupon bond’s price is given by the formula:

$\text{Price} = \frac{\text{Face Value}}{(1 + r)^n}$

where:

• $r$ = semi-annual yield = $\frac{10.4\%}{2} = 5.2\%$ or 0.052
• $n$ = 2 (since there are 2 semi-annual periods in one year)

$\text{Price} = \frac{1,000}{(1 + 0.052)^2}$

$\text{Price} = \frac{1,000}{1.052^2} = \frac{1,000}{1.107} \approx 903.45$

So, you buy the bond for approximately $903.45.

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Step 3: Calculate the interest earned (imputed income).

The interest earned is the difference between the face value and the purchase price:

$\text{Interest earned} = 1,000 - 903.45 = 96.55$

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Step 4: Calculate the tax owed on the interest.

Since your income tax rate is 29%, the tax on the interest earned is:

$\text{Tax} = 96.55 \times 0.29 = 28.00$

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Step 5: Calculate your after-tax cash flow.

At maturity, the bond pays the full face value of $1,000. After accounting for taxes, your after-tax cash flow becomes:

$\text{After-tax cash flow} = 1,000 - 28.00 = 972.00$

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Final Answer:

Your after-tax cash flow one year from now will be:

$\boxed{972.00}$

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Do you want further details or have any questions?

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Here are 5 related questions:

1. How would the after-tax cash flow change if the tax rate was 20% instead?
2. What is the effective annual yield (EAY) for this bond given the semi-annual compounding?
3. How does the price of a zero-coupon bond change with different interest rates?
4. What if the bond had a maturity period of 5 years—how would that change the purchase price?
5. How do different types of bonds (e.g., coupon bonds) affect taxable income?

Tip: The earlier you buy a zero-coupon bond (with longer maturity), the lower the purchase price, but the more sensitive it becomes to interest rate changes.