Final answer:
The present value of a two-year bond paying 8% interest is calculated under two scenarios: with a discount rate of 8% and 11%. The value of the bond decreases as the discount rate increases. Treasury bonds offer lower interest rates compared to corporate bonds due to lower risk.
Step-by-step explanation:
The calculation of a bond's present value requires understanding the time value of money and how interest rates affect the value of future cash flows. When a two-year bond with a face value of $3,000 and an interest rate of 8% is considered, the bond will pay $240 in interest annually. To find the present value of this bond at an 8% discount rate, and then again at an 11% discount rate, the present value formula must be applied to the expected cash flows.
Present Value Calculation at 8% Discount Rate
Year 1: $240 / (1 + 0.08) = $222.22
Year 2: ($240 + $3,000) / (1 + 0.08)2 = $2,824.07
Total Present Value = $222.22 + $2,824.07 = $3,046.29
Present Value Calculation at 11% Discount Rate
Year 1: $240 / (1 + 0.11) = $216.22
Year 2: ($240 + $3,000) / (1 + 0.11)2 = $2,673.27
Total Present Value = $216.22 + $2,673.27 = $2,889.49
This example demonstrates how the present value of the bond decreases as the discount rate increases, reflecting higher market interest rates. Furthermore, the bond's present value can be directly compared to its face value to determine if the bond is attractive as an investment relative to current market conditions.
When discussing Treasury bonds, it's important to note that these are among the safest investment vehicles as they're backed by the full faith and credit of the U.S. government. However, they generally offer lower interest rates due to their lower risk when compared to corporate bonds, which must provide higher yields to account for their greater risk levels.