Calculate the Yield-to-Maturity of a Zero Coupon Bond
What is the yield-to-maturity of a zero coupon bond that is trading at $974.00, matures in exactly 5 months, and has a face value of $1,000?
The yield-to-maturity of the zero coupon bond is approximately 3.12%. This is calculated by dividing the discount by the face value and adjusting for the time to maturity.
Calculating Yield-to-Maturity of a Zero Coupon Bond
A zero coupon bond is a type of bond that does not pay periodic interest. Instead, it is issued at a discount to its face value and redeemed at face value upon maturity. The yield-to-maturity of a zero coupon bond represents the annualized rate of return an investor can expect if the bond is held until maturity.
Steps to Calculate Yield-to-Maturity:
1. Determine the discount or premium:
Calculate the difference between the bond's current price and its face value.
Discount/Premium = Face Value - Current Price
Discount/Premium = $1,000 - $974.00
Discount/Premium = $26.00 (discount)
2. Calculate the annualized yield:
Divide the discount or premium by the face value and adjust for the time to maturity.
Annualized Yield = (Discount/Premium / Face Value) * (12 / Time to Maturity in months)
Annualized Yield = ($26.00 / $1,000) * (12 / 5)
Annualized Yield = 0.0312 or 3.12%
3. Round the annualized yield to the nearest second digit after the decimal point.
Yield-to-Maturity (YTM) = 3.12% (rounded to the nearest second decimal place)
Therefore, the yield-to-maturity of the zero coupon bond is 3.12%.