Final answer:
The price of a $1.8 million bond issue, when the market interest rate is 12%, would be $1,735,200. This is calculated by scaling down the price of an individual $1,000 bond, which would sell for $964 under these market conditions, to the total bond issue size.
Step-by-step explanation:
To determine the price of a $1.8 million bond issue when the interest rate of the bond is less than the market interest rate, let's use the provided example of a $1,000 bond as reference. If the market interest rate rises to 12%, and we expect a payment of $1,080 from the bond in one year (which includes the final interest payment and the principal repayment), the price of the bond must be discounted to match the yield of a new 12% investment. Thus, you could invest $964 in an alternative 12% investment to receive $1,080 in a year; the calculation for this would be $964(1 + 0.12) = $1,080. Accordingly, an investor will not pay more than $964 for our original $1,000 bond. To scale this to a $1.8 million bond issue, we assume each $1,000 bond will sell for $964. Hence, the price of the $1.8 million bond issue = ($1,800,000 / $1,000) * $964, which equals $1,735,200