Final answer:
To determine the yield-to-maturity (YTM) for a bond, the present value of all the future cash flows generated by the bond needs to be calculated and equated to the current market price. The YTM takes into account the coupon payments, the face value received at maturity, and the price paid for the bond. A higher YTM indicates a higher return on investment and may make the bond more attractive to investors.
Step-by-step explanation:
To determine the yield-to-maturity (YTM) for the bond, we need to calculate the present value of all the future cash flows generated by the bond and equate it to the current market price. In this case, the bond has a face value of $1,000 and a semi-annual coupon rate of 9%. It pays semi-annual coupon payments, so we will have to discount each payment using the YTM. The bond is currently trading at $1,070.41, and we will assume a 6% YTM.
1. Calculate the present value of each coupon payment by discounting it at the YTM. For example, the present value of the first coupon payment of $45 (9% of $1,000) would be $45 / (1 + 0.03) = $43.69.
2. Calculate the present value of the face value by discounting it at the YTM. In this case, the present value of the face value of $1,000 would be $1,000 / (1 + 0.03)^12 = $772.18.
3. Add up the present values of all the coupon payments and the present value of the face value to get the total present value of the bond. In this case, it would be $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $43.69 + $772.18 = $1,070.41, which is the current market price of the bond.
4. Now, to find the YTM, we need to solve for the discount rate that equates the total present value of the bond to its market price. Using iterative approximation methods or financial calculators, we find that the YTM for this bond is approximately 6.042% (annualized).
The YTM is an important metric in evaluating the investment attractiveness of the bond. It represents the annualized yield an investor can earn by holding the bond until maturity, taking into account the coupon payments, the face value received at maturity, and the price paid for the bond. A higher YTM indicates a higher return on investment and may make the bond more attractive to investors.