Final answer:
To find the present value of a bond, you must calculate the present value of both the bond's interest payments and the principal repayment. Using the discount rate to discount these future cash flows to their present value allows you to determine the bond's current worth. If interest rates rise, the present value will decrease.
Step-by-step explanation:
To find the present value of a bond, you need to perform two key calculations. Firstly, you have to determine the present value of the bond's interest payments, which are the annuity. Secondly, you calculate the present value of the principal amount that will be repaid at the end of the bond's term. Both calculations require discounting future cash flows back to present value using the prevailing market interest rate or discount rate.
For example, consider a simple two-year bond with a principal amount of $3,000 and an annual interest rate of 8%. The bond will pay $240 in interest each year (which is the principal amount multiplied by the interest rate), and the $3,000 principal will be repaid at the end of the second year. When the discount rate is 8%, aligning with the interest rate, the present value of the bond's future cash flows equals the bond's face value, $3,000. If interest rates rise, causing the discount rate to increase to 11%, the present value of the bond's future cash flows will decrease, reflecting the higher opportunity cost of capital and the decreased attractiveness of the bond's fixed interest payments.