Final answer:
The present value of future cash flows from an annuity of a bond decreases as the discount rate increases, illustrating the inverse relationship between discount rates and present value. A two-year bond with an 8% interest rate has its present value equal to its face value when the discount rate is also 8%. With a discount rate of 11%, the present value of the bond decreases.
Step-by-step explanation:
When calculating the present value of a bond or annuity, we apply the present value formula that discounts future cash flows to their present worth. In the primer provided in the question, we see a simple two-year bond issued at $3,000 with an 8% interest rate, which provides a $240 payment at the end of the first year and $3,240 ($240 interest + $3,000 principal) at the end of the second year. When the discount rate is equal to the coupon rate (8%), the bond's present value equals its face value. However, if the discount rate rises to 11%, the present value decreases; this illustrates the inverse relationship between discount rates and the present value of future cash flows.
The present value calculations use the formula PV = C / (1 + r)^n, where C represents the cash flow, r is the discount rate, and n is the time period. In the case of our 8% bond, the first year cash flow discounted back at 8% is $240 / (1 + 0.08)^1 = $222.22, and the second year cash flow discounted back is $3,240 / (1 + 0.08)^2 = $2,777.78. Summing these gives the bond's present value. If we change the discount rate to 11%, the first year cash flow discounted back is $240 / (1 + 0.11)^1 = $216.22, and the second year is $3,240 / (1 + 0.11)^2 = $2,624.17.