Final answer:
The bond's value is calculated using the present value formula and is influenced by the discount rate, which if higher, results in a lower value. Bonds sell at a discount or premium depending on whether they offer a rate above or below the market interest rate. Rising market rates cause existing bonds with lower rates to be devalued due to interest rate risk.
Step-by-step explanation:
To calculate a bond's present value with a discount rate of 8%, we consider the bond's future cash flows: $240 interest at the end of the first year and $240 interest plus the $3,000 principal at the end of the second year. Using the present value formula, these cash flows are discounted back to their present value.
If the market interest rates rise to 11%, the same bond's value needs to be recalculated using the higher discount rate, which will yield a lower present value for the bond.
The price of a bond also changes in relation to the market interest rate. If a bond's interest payment is less than the market interest rate, the bond will sell at a discount. For example, if a bond's last payment is expected to be $1,080 in a year, and the market interest rate is 12%, the bond's present value would be calculated so that $964 invested at 12% would grow to $1,080 in one year.
Bonds are subject to interest rate risk. If the market interest rates rise above the bond's coupon rate, like going from 8% to 12%, the bond's price would fall because it pays less interest compared to new bonds issued at the higher rate. This interest rate risk reflects the opportunity cost of having funds tied up in a lower-paying bond when more attractive rates are available.