Final answer:
The issue price of the $25,000, 10%, 5-year bond that pays interest semi-annually, with the market rate at 12%, is calculated by summing the present value of the semi-annual interest payments and the principal repayment, discounted at the semi-annual market interest rate of 6%.
Step-by-step explanation:
The question involves calculating the issue price of a bond. A bond's issue price can vary depending on the market interest rate relative to the bond's coupon rate. In this case, we need to calculate the issue price of a $25,000, 10%, 5-year bond that pays interest semi-annually, with the market interest rate at 12%.
To determine the issue price, we must calculate the present value of all future cash flows (interest payments and the principal repayment) by discounting them at the market rate. Since the bond pays interest semi-annually, we'll have 10 interest payments of $1,250 each ($25,000 * 10% / 2), and a final payment of $25,000 at maturity.
Let's look at the example of a simpler bond to understand the concept. A two-year bond with a principal of $3,000 and an 8% interest rate will have annual interest payments of $240. At an 8% discount rate, each payment's present value is calculated and then summed to determine the bond's present value. This happens similarly for the $25,000 bond, but using the semi-annual periods and a 12% annual market interest rate.
For the $25,000 bond, we discount the semi-annual interest payments and the final principal repayment at a semi-annual rate of 6% (half of the 12% market rate). The present value of each payment is found, and then all are summed up to get the bond's issue price.