1. What is a Zero Coupon Bond?

A zero coupon bond is a debt security that doesn't pay periodic interest but is issued at a discount to its face value. The bond's return comes from the difference between its purchase price and its face value at maturity.

2. How Does the Calculator Work?

The calculator uses the zero coupon bond pricing formula:

Where:

• \( FV \) — Face value of the bond ($)
• \( ytm \) — Yield to maturity (as decimal)
• \( m \) — Compounding frequency per year
• \( n \) — Years to maturity

Explanation: The formula discounts the bond's face value back to present value using the yield to maturity and compounding frequency.

3. Importance of YTM in Bond Pricing

Details: Yield to maturity (YTM) is the total return anticipated on a bond if held until maturity. It's a crucial metric for comparing bonds with different maturities and coupon rates.

4. Using the Calculator

Tips: Enter face value in dollars, YTM as percentage (e.g., 5 for 5%), compounding frequency (typically 1 for annual, 2 for semiannual), and years to maturity. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why does compounding frequency matter?
A: More frequent compounding increases the effective yield, resulting in a lower present value for the bond.

Q2: How does YTM affect bond price?
A: Higher YTM leads to lower bond prices, and vice versa. There's an inverse relationship between yield and price.

Q3: What's the difference between YTM and coupon rate?
A: Coupon rate is fixed and determines periodic interest payments (not applicable to zero coupon bonds), while YTM reflects total return including price appreciation.

Q4: Are zero coupon bonds riskier?
A: They have higher interest rate risk (duration risk) than coupon bonds of similar maturity since all cash flow occurs at maturity.

Q5: How are zero coupon bonds taxed?
A: In many jurisdictions, the imputed interest is taxable annually as it accrues, even though no cash payment is received.