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?

Do not include the dollar sign ($). Round your answer to 2 decimal places and respect the sign of the cash flow, e.g., 50.16 or -49.34.

To solve this, we first need to determine the price of the zero-coupon bond, calculate the income earned, and then apply the tax rate to find the after-tax cash flow.

### Step 1: Calculate the price of the bond

Since this is a zero-coupon bond, it pays no interest. The price is determined by discounting the face value using the yield to maturity (YTM). Given that the YTM is compounded semi-annually, the formula for the bond price $ P $ is:

\[
P = \frac{F}{(1 + \frac{YTM}{2})^{2}}
\]

Where:
- $ F $ is the face value = 1000
- $ YTM $ is the yield to maturity = 10.4% or 0.104
- The exponent 2 represents the two periods in one year (semi-annual).

Plugging in the values:

\[
P = \frac{1000}{(1 + \frac{0.104}{2})^2}
= \frac{1000}{(1 + 0.052)^2}
= \frac{1000}{(1.052)^2}
= \frac{1000}{1.106704}
\]

\[
P \approx 903.47
\]

So, the bond price is approximately 903.47.

### Step 2: Calculate the income earned

The income earned on the bond over one year is the difference between the face value and the price of the bond:

\[
Income = 1000 - 903.47 = 96.53
\]

### Step 3: Apply the tax rate

Since the personal income tax rate is 29%, the tax on the income is:

\[
Tax = 0.29 \times 96.53 = 27.99
\]

### Step 4: Calculate the after-tax cash flow

The after-tax cash flow is the face value minus the tax:

\[
\text{After-tax cash flow} = 1000 - 27.99 = 972.01
\]

Thus, your after-tax cash flow one year from now is **972.01**.

---

Would you like further details on any of the steps? Here are some related questions to explore this topic further:

1. What happens to the bond price if the YTM increases?
2. How would the after-tax cash flow change if the tax rate was 35% instead of 29%?
3. How does the semi-annual compounding impact the bond price calculation?
4. What is the relationship between YTM and bond price for zero-coupon bonds?
5. How can one calculate the total return on a bond investment?

**Tip**: Zero-coupon bonds offer no periodic interest payments, but they allow for significant capital gains, which are subject to tax. Always factor in your tax rate when calculating investment returns.

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?

Find out how to calculate the after-tax cash flow from a zero-coupon bond with a face value of 1000 and a YTM of 10.4% compounded semi-annually. Learn the key formulas for bond pricing, tax calculations, and investment returns, suitable for finance students and professionals.

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