Final answer:
The present value of a $10,000 5-year bond would be less than $10,000 if the bond's contractual interest rate is less than the current market rate, as it would then have to be sold at a discount to attract investors.
Step-by-step explanation:
The present value of a $10,000 5-year bond would be less than $10,000 if the contractual rate of interest is less than the market rate of interest. This is because investors would demand a discount on the bond's price to compensate for the lower interest income compared to market alternatives. For example, if a bond's contractual interest rate is lower than the current market interest rate, like in the scenario where a bond paying 6% is competing with new bonds offering 9%, the bond must be sold at a discount to make it an equally attractive investment. This results in a present value that is less than the bond's face value.
Using the provided example of a bond's last year payment of $1,080 and a market interest rate of 12%, you could invest $964 in an alternative investment and receive $1,080 in a year. So, you would not be willing to pay more than $964 for the bond, which is less than $1,000.