Final answer:
The cash received for a $500,000 bond issue at 10% that sold at 102 is $510,000. If market interest rates increase, the price of a bond decreases, which means a bond issued at a lower interest rate would be sold for less than its face value.
Step-by-step explanation:
How Much Cash Was Received for a $500,000 Bond Issue?
To calculate the cash received from a bond issue, we multiply the face value of the bonds by the percentage at which they were sold. In this case, a $500,000 bond with a contract rate of 10% sold at 102 (102% of the face value). Therefore, the cash received from the bond sale is calculated as follows:
$500,000 (face value) × 1.02 (102%) = $510,000
This means the issuer received $510,000 from the sale of the bond.
Regarding the example of a local water company's $10,000 bond at an interest rate of 6%, if interest rates rise to 9%, the market value of the bond would decrease. This happens because newer bonds likely provide the higher current interest rate, making the older bonds with lower interest less desirable. Therefore, you would expect to pay less than $10,000 for this bond.
Applying this to the $500,000 bond issuance question, if the market interest rates were higher than the bond's contract rate, the bond would also sell for less than its face value. However, in our scenario, the bond sold for more than its face value because it presumably offered an attractive rate compared to the market.