The yield to maturity (YTM) of a bond is the total return anticipated on a bond if the bond is held until it matures. It is expressed as an annual rate. To calculate the YTM for a $1000 7% semi-annual coupon bond that matures in 2 years and currently sells for $997.07, we need to follow these steps:
- Determine the coupon payment: The bond has a 7% annual coupon rate, which means it pays 7% of the face value annually. Since the bond pays semi-annually, each coupon payment is:
Coupon Payment = (7% / 2) * $1000 = $35 - Determine the number of periods: The bond matures in 2 years with semi-annual payments, so there are:
Number of Periods = 2 years * 2 = 4 periods - Determine the present value of the bond: The bond currently sells for $997.07, which is the present value of all future cash flows (coupon payments and the face value at maturity).
- Calculate the YTM: The YTM is the discount rate that equates the present value of the bond’s cash flows to its current price. This requires solving the following equation for YTM:
$997.07 = ($35 / (1 + YTM/2)^1) + ($35 / (1 + YTM/2)^2) + ($35 / (1 + YTM/2)^3) + ($35 / (1 + YTM/2)^4) + ($1000 / (1 + YTM/2)^4)This equation is typically solved using a financial calculator or spreadsheet software.
After performing the calculations, you will find that the YTM for this bond is approximately 3.56% per semi-annual period, or 7.12% annually.