Final answer:
The present value of a bond is calculated based on the bond's future cash flows and the discount rate applied to these cash flows, reflecting the current market interest rate. A simple two-year bond paying an 8% interest rate and a principal of $3,000 will have its present value affected when the discount rate changes to 8% or 11%. Moreover, when the market interest rate increases to 12%, the bond's price would adjust so that it does not exceed the equivalent value of an alternative investment adjusted for the current interest rate.
Step-by-step explanation:
The valuation of a bond in the present is dependent on the expected future cash flows and the discount rate applied to those cash flows. When dealing with a bond that has an annual interest rate of 8% and a principal amount of $3,000, the bond would pay $240 each year for two years, and the full principal of $3,000 at the end of the second year. To calculate the present value of these cash flows with an 8% discount rate, you would use the present value formula. The same applies when recalculating the bond's present value with an increased discount rate of 11% due to rising interest rates.
If the market interest rate increases to 12%, the price of a bond with this interest rate would be less than the bond's face value. Using the concept of present discounted value, the bond's price when its interest rate is less than the market interest rate would be calculated based on the principle that you should not pay more for the bond than you could earn from an alternative investment with the current market interest rate. For example, with a market interest rate of 12%, a payment of $1,080 expected one year from now would mean the bond can be priced at $964, as $964 invested at 12% would yield the same $1,080 in a year's time.