Final answer:
To calculate a bond's present value, you discount its future payments by the prevailing market interest rate. If the discount rate is equal to the bond's interest rate, the bond sells at face value. When market interest rates are higher, the bond's price decreases to align its yield with the market rate.
Step-by-step explanation:
To calculate the present value of a simple two-year bond with a principal of $3,000 and an annual interest rate of 8%, we can apply the present value formula. For the first year, the bond pays interest of $240 (8% of $3,000). In the second year, it pays another $240 in interest plus the $3,000 principal. When the discount rate matches the interest rate of the bond (8%), the present value of the bond's expected payments would be $240/(1.08)^1 + ($3,240)/(1.08)^2. This represents the value of the first year's interest payment and the second-year's interest and principal payment, both discounted at 8%.
If the discount rate rises to 11%, the present value calculations would be adjusted accordingly to $240/(1.11)^1 + ($3,240)/(1.11)^2. This reflects the decreased present value of the expected payments as the discount rate exceeds the bond's interest rate. In this case, the bond would sell for less than its face value due to the higher market interest rate.
Furthermore, when the bond's interest rate is less than the market interest rate (for instance, 12%), the price of the bond will decrease. Using a market interest rate of 12%, the expected payments of $1,080 from the bond one year from now can be discounted at the higher rate to calculate the current price, resulting in a bond value of less than the face value, specifically $964. This is because $964 invested at 12% for one year equals the payment expected from the bond. Consequently, the bond's yield would be equal to the market interest rate of 12%, accounting for both the interest payments and the capital gain (or loss).