Final answer:
The price of a bond issued by Caspian Sta with an 8.1316% coupon rate depends on the present value of its future cash flows, discounted by the yield to maturity. To calculate the bond's price at different YTMs, one would use the present value formula over the bond's cash flows including annual coupons and par value.
Step-by-step explanation:
To calculate the price of the bond when Caspian Sta plans to issue it with an 8.1316% coupon rate, we need to understand that the price of a bond is the present value of its future cash flows, which include the annual coupon payments and the par value of the bond at maturity. These cash flows need to be discounted back to their present value using the yield to maturity (YTM). When the YTM is 7.91%, and again when the YTM is 8.42%, the present value of these cash flows will give us the bond's price. To find the present value, we use the present value formula, discounting each coupon payment and the final par value by the YTM. In this case, with a par value of $1,000 and an annual coupon payment (which is par value times the coupon rate), we can calculate the price by summing the present value of all these payments. As it requires several calculations based on the given YTM, a financial calculator or spreadsheet software would typically be used to compute the exact bond price.