Final answer:
To calculate the issue price of Air Destinations bonds, present values of semi-annual interest payments and the face value must be computed at the market rate and then summed. Since the market rate exceeds the bond’s coupon rate, the bond is issued at a discount.
Step-by-step explanation:
To calculate the issue price of the Air Destinations bonds with a face value of $500,000, due in 10 years and a stated interest rate of 11%, paid semi-annually, when the market rate is 12%, we need to find the present value of both the interest payments and the face value of the bond. To find the present value of the interest payments, which is $55,000 annually ($500,000 x 11%), we divide this by two to account for semi-annual payments, getting $27,500 every six months. We find the present value of these payments by using the present value of an ordinary annuity formula PV = Pmt x [(1 - (1 + r)^(-n))/r], where Pmt = $27,500, r = market rate per period (6%), and n = total number of periods (20). Likewise, the present value of the face value is calculated using the present value of a lump sum formula, PV = FV / (1 + r)^n, using FV = $500,000, r = 6%, and n = 20.
To determine the issue price, we simply add the present value of the interest payments and the present value of the face value. This gives us the total price that investors are willing to pay for the bond today, considering that the market interest rate is higher than the bond's coupon rate, which means that the bond will be issued at a discount.