Final answer:
The present value of a two-year bond with 8% interest rate can be calculated by discounting the future cash flows at the same interest rate. If the discount rate increases to 11%, the present value of the bond decreases, illustrating the inverse relationship between discount rates and present values.
Step-by-step explanation:
Calculation of Present Value for a Two-Year Bond
To determine the present value of a two-year bond with an 8% interest rate, we need to discount the future cash flows back to their present value using the given interest rate. For the first year, the bond pays $240 in interest. The present value of the first year's interest payment is calculated as:
Present Value Year 1 = $240 / (1 + 0.08)¹ = $222.22
At the end of the second year, the bond pays an additional $240 in interest plus the $3,000 principal. The present value of these payments is calculated as:
Present Value Year 2 = ($240 + $3,000) / (1 + 0.08)² = $2,777.78
Total present value of the bond when the discount rate is 8% is the sum of the present values for each year:
Total Present Value = $222.22 + $2,777.78 = $3,000
However, if the discount rate increases to 11%, we need to recalculate the present value of these cash flows using the new rate:
Present Value Year 1 at 11% = $240 / (1 + 0.11)¹ = $216.22
Present Value Year 2 at 11% = ($240 + $3,000) / (1 + 0.11)² = $2,630.63
The total present value at an 11% discount rate is:
Total Present Value at 11% = $216.22 + $2,630.63 = $2,846.85
These calculations show that the present value of future cash flows decreases as the discount rate increases.