Final answer:
To find the issue price of the bond, calculate the present value of semiannual interest payments and the face amount using the market rate of 7%. The steps involve finding present value factors for an annuity and a single sum, and then applying them to the cash flows of the bond. The closest issue price from the given options must be determined using these calculations. Therefore, the correct option is C.
Step-by-step explanation:
To calculate the issue price of the bond when the market interest rate is higher than the bond's stated interest rate, we need to discount the bond's cash flows at the market rate. The cash flows from the bond include semiannual interest payments and the repayment of the face amount at maturity. For the Air Destinations bond with a face value of $500,000 and a stated interest rate of 6%, the semiannual interest payment is $500,000 * 6% / 2 = $15,000. Since the market rate is 7%, we must calculate the present value (PV) of these payments using the 7% semiannual market rate.
The bond pays $15,000 every six months for 20 periods (10 years semiannually) and repays $500,000 at the end of the 10 years. To find the bond's price, we'll calculate the present value of an annuity (PVA) for the interest payments and add the present value (PV) of the $500,000 face amount.
To do this using present value factors:
- Find or calculate the PVA factor for $1 at 3.5% (7% annual market rate divided by 2 for semiannual periods) for 20 periods.
- Find or calculate the PV factor for $1 at 3.5% for 20 periods.
- Multiply the PVA factor by the semiannual interest payment of $15,000.
- Multiply the PV factor by the face amount of $500,000.
- Add the results of steps 3 and 4 to get the total present value, which is the issue price of the bond.