Final answer:
To determine the bond's price, one must calculate the present value of the bond's semiannual interest payments and the face value at maturity using the discount rate of 13%. The bond will sell for less than face value because the discount rate is higher than the coupon rate.
Step-by-step explanation:
To calculate the price of a semiannual coupon bond with a face value of $1,000, a coupon rate of 8%, maturing in 17 years, and a market discount rate of 13%, we need to find the present value of the bond's cash flows. The bond pays semiannual interest; therefore, it provides $40 (which is $1,000 × 4%) every six months. Over 17 years, there will be 34 payments. The present value of these interest payments can be calculated using the present value of an annuity formula. Additionally, the present value of the $1,000 face value, which will be received at the end of 17 years, is also calculated at the 13% market discount rate, but semiannually (6.5% per period). The sum of the present value of the interest payments and the present value of the face value gives us the bond's current price.
Without the cash flows and formula calculations provided, we cannot give an exact price, but the method would involve discounting each payment by the market rate. Since the market rate of 13% is higher than the bond's coupon rate of 8%, the bond will sell for less than its face value. To discount a cash flow, the formula is Cash Flow / (1+r)^n where r is the market discount rate per period and n is the number of periods until the payment is received