Final answer:
The yield to maturity (YTM) for a bond that has a coupon rate of 6.25%, a face value of $1,000, selling at $932.24, and with 3 years to maturity can be calculated using the present value formula for both coupon payments and face value. The YTM is the rate that equates these present values to the bond's current price. It is found through an iterative process, with the YTM being higher than the coupon rate to compensate for the bond's lower price.
Step-by-step explanation:
The yield to maturity (YTM) of a bond is the internal rate of return that equates the present value of all future cash flows (coupon payments and principal repayment) to the current bond price. To calculate the YTM, we can use a financial calculator or a numerical method such as trial and error, since the relationship between the price and the yield of the bond is not linear and requires iterative calculation.
For the given bond with a coupon of 6.25%, face value of $1,000, selling at $932.24, and maturity of 3 years, YTM would be the rate 'r' that satisfies the following equation:
Present Value of Coupons + Present Value of Face Value = Current Bond Price
PV(Coupons) = (62.5 / (1+r)) + (62.5 / (1+r)^2) + (62.5 / (1+r)^3), PV(Face Value) = 1000 / (1+r)^3, and Current Bond Price = 932.24.
Solving this equation for 'r' will give us the YTM. The bond's YTM is higher than the coupon rate because the bond is selling for less than its face value, which indicates that the yield has increased since the bond was issued to compensate for the lower price.