Final answer:
The YTM of a bond is calculated by equating the present value of the bond's future cash flows to its market price. Semiannual coupon payments and the total number of semiannual periods are accounted for in the calculation, which is typically done using financial calculators or spreadsheets due to its iterative nature.
Step-by-step explanation:
The student has asked how to calculate the yield to maturity (YTM) for a bond issued by Crossfade Corporation, which has a par value of $2,000, sells for $1,971.44, has a coupon rate of 6.57%, makes semiannual coupon payments, and matures in 15 years.
How to Calculate Yield to Maturity (YTM)
To calculate YTM, which is the total expected return on a bond if held to maturity, you need to equate the present value of the bond's future cash flows to its current market price. Since the bond pays semiannual coupons, you need to divide the annual coupon rate by two to find the semiannual coupon payment and also adjust the number of periods to reflect semiannual periods over the bond's life.
The formula for calculating the YTM for a semiannual coupon bond is as follows:
- Current Bond Price = C * (1 - (1 + YTM)^(-n)) / YTM + Par Value / (1 + YTM)^(n)
Where:
- C is the semiannual coupon payment
- YTM is the yield to maturity
- n is the number of semiannual periods to maturity
- Par Value is the face value of the bond
Yield to maturity is calculated iteratively, usually using a financial calculator or spreadsheet software, because it involves solving for YTM in the bond-pricing equation, which does not allow for algebraic manipulation to isolate YTM. You can approximate the YTM by comparing the bond's current price to its face value, noting whether it is a discount or premium, calculating the current annual interest income based on the coupon rate, and adjusting for the investment horizon and the reinvestment risk.