Final answer:
The present value of a bond is calculated by discounting its future cash flows back to the present using the specified discount rate. For an 8% discount rate, the same as the bond's interest rate, its present value equals its face value. When the discount rate increases to 11%, the present value will decrease below the bond's face value.
Step-by-step explanation:
To calculate the current or present value of a bond with an 8% discount rate, you first need to determine the cash flows it will provide. In the case of a simple two-year bond with a $3,000 principal and an 8% interest rate, the bond will pay $240 in interest each year. At the end of the second year, it will also repay the $3,000 principal.
The present value of the bond, when discounted back at the same rate of interest (8%), would be calculated as follows:
- The present value of the first interest payment after one year: $240 / (1 + 0.08) = $222.20
- The present value of the second interest payment and the principal after two years: ($240 + $3,000) / (1 + 0.08)² = $2,777.80
The total present value of the bond is the sum of these amounts: $222.20 (first year) + $2,777.80 (second year) = $3,000, which is equal to the bond's face value, as expected since the discount rate matches the bond's interest rate.
However, if the discount rate increases to 11%, the present value of the cash flows would be:
- The present value of the first interest payment after one year: $240 / (1 + 0.11) (calculate for exact value)
- The present value of the second interest payment and the principal after two years: ($240 + $3,000) / (1 + 0.11)² (calculate for exact value)
The total present value at a discount rate of 11% would then be the sum of the calculated values for the first and second years, which will be less than the face value due to the higher discount rate.