Final answer:
Bond valuation is crucially dependent on the chosen discount rate. A $3,000 bond paying 8% annual interest has a present value of $2,777.80 using an 8% discount rate. However, if the discount rate increases to 11%, the bond's present value drops as higher market interest rates make other investments more attractive.
Step-by-step explanation:
Understanding Bond Valuation with Different Discount Rates
When examining how much a bond is worth, the present value is important. With a simple two-year bond issued for $3,000 at an 8% interest rate, it pays $240 each year in interest. The present value of these payments must be calculated using the discount rate. At an 8% discount rate, the present value of the interest payments and principal repayment is $2,777.80. This represents the total discounted value of receiving $240 in the first year and $3,240 ($240 in interest plus the $3,000 principal) in the second year.
If market interest rates rise, causing the discount rate to increase to 11%, the bond's present value will drop as the payments from the bond would be less attractive compared to the new higher-yielding investments available. Therefore, the current price someone would be willing to pay for the bond lowers.
For example, if the bond's expected payments a year from now are $1,080 (final interest plus the principal repayment), and the market rate is 12%, one could invest $964 at this market rate to end up with $1,080 after a year. Consequently, for the bond to be attractive, it should be priced at no more than $964 in this scenario, underlining how the bond price is negatively correlated with the discount rate or the prevailing market interest rates.