Final answer:
Jeremy Kohn is evaluating the purchase price for a 6-year bond with a 10 percent coupon rate and semiannual payments when the market rate is 8 percent. By discounting the future cash flows of the bond at the current market rate, we determine that the maximum price that should be paid for the bond is approximately $1,117.
Step-by-step explanation:
Jeremy Kohn is interested in investing in a 6-year bond with a 10 percent coupon rate when the current market rate is 8 percent, and the bond offers semiannual payments. To calculate the maximum price that should be paid for this bond, we need to find the present value of all future cash flows from the bond, discounted at the market interest rate. The bond will pay semiannual coupons, so the annual coupon of 10 percent would be divided into two payments of 5 percent each, based on the $1,000 face value, resulting in $50 every six months.
The bond's cash flows would be as follows:
- Coupon payments: $50 semiannually for 12 periods, because there are six years and two periods per year.
- Face value repayment: $1,000 at the end of 6 years (at the twelfth semiannual period).
These cash flows need to be discounted at the semiannual market rate of 4 percent (which is the 8 percent annual market rate divided by two). The present value of the annuity (coupon payments) and the lump-sum (face value repayment) will give us the bond's price. After calculating, we find that the maximum price Jeremy should be willing to pay for this bond is closer to the provided choice $1,117.
Thus, knowing how interest rates affect bond pricing helps investors determine the value of bonds with different coupon rates in the market.