Final answer:
The present value of a bond is calculated using the present value formula, taking into account the stream of future payments discounted back at a specified rate. The calculations change as the discount rate changes, demonstrating the relationship between the discount rate and the present value of a bond.
Step-by-step explanation:
The question deals with the calculation of the present value of a simple two-year bond, first using a discount rate of 8%, which matches the bond's coupon rate, and then using a higher discount rate of 11%. Present value is the current worth of a future sum of money or stream of cash flows given a specified rate of return, also known as the discount rate. The stream of payments that the bond will pay out consists of two annual interest payments of $240 each and a principal amount (face value) of $3,000 at the end of the second year.
Using the present value formula, we can calculate the bond's present value with both discount rates. The formula for present value is PV = C / (1+r)^t where C is the cash flow, r is the discount rate, and t is the period.
When the discount rate is 8%, the present value of the first year's interest is $240 / (1 + 0.08) = $222.22 and the second year's interest and principal is ($240 + $3,000) / (1 + 0.08)² = $2,671.30. The sum of these amounts gives us the total present value of the bond at an 8% discount rate.
If the discount rate rises to 11%, the present value is recalculated using this new rate, resulting in a lower present value given the inverse relationship between discount rate and present value.