You just bought a zero-coupon bond that matures one year from now. Its YTM is 10.4% (assuming semi-annual frequency) and its face value is $1,000. Assuming that you personal income tax rate is 29%, what is your after-tax cash flow one year from now?

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:

---

### 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. 

---

### 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**.

---

### Step 3: Calculate the interest earned (imputed income).
The **interest earned** is the difference between the **face value** and the **purchase price**:

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

---

### Step 4: Calculate the tax owed on the interest.
Since your **income tax rate** is 29%, the tax on the interest earned is:

\[
\text{Tax} = 96.55 \times 0.29 = 28.00
\]

---

### 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:

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

---

### Final Answer:
Your **after-tax cash flow one year from now** will be:

\[
\boxed{972.00}
\]

---

Do you want further details or have any questions?  

---

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.

You just bought a zero-coupon bond that matures one year from now. Its YTM is 10.4% (assuming semi-annual frequency) and its face value is $1,000. Assuming that your personal income tax rate is 29%, what is your after-tax cash flow one year from now?

Learn how to calculate the after-tax cash flow from a zero-coupon bond with a 10.4% yield to maturity (YTM), a face value of $1,000, and a 29% tax rate. This problem involves bond valuation, semi-annual compounding, and tax calculations on investment income.

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