Final answer:
To determine the present value of a two-year bond with a discount rate of 8% and then 11%, we discount each future cash flow back to its present value. This assessment of present discounted value is crucial to understand the impact of changing market interest rates on the bond's valuation, reflecting the bond's investment risk.
Step-by-step explanation:
To calculate the present value of a two-year bond with an initial value of $3,000 and an interest rate of 8%, we would assess the bond's cash flow, which includes interest payments of $240 at the end of each year, along with the $3,000 principal repayment at the end of the second year. Using a discount rate equal to the interest rate of 8%, the present value (PV) of each payment would be discounted back to its present discounted value. If we then increase the discount rate to 11% to simulate a rise in market interest rates, these future cash flows would be worth less in today's dollars, reducing the bond's attractiveness and posing a potential investment risk if selling the bond is necessary.
To illustrate this with numbers: Year 1 interest PV at 8%: $240/(1 + 0.08), Year 2 interest PV at 8%: $240/(1 + 0.08)^2, Year 2 principal PV at 8%: $3,000/(1 + 0.08)^2, Total PV at 8%: Sum of the above three amounts, And with a discount rate of 11%, calculations would be: Year 1 interest PV at 11%: $240/(1 + 0.11), Year 2 interest PV at 11%: $240/(1 + 0.11)^2, Year 2 principal PV at 11%: $3,000/(1 + 0.11)^2. Total PV at 11%: Sum of the above three amounts