Final answer:
The bond's price would be $964 when the interest rate is less than the market interest rate of 12%. An investor would not pay more than this because they could otherwise invest in an alternative at the market rate. To induce investors, the seller must discount the bond to make the yield comparable to the current market rate.
Step-by-step explanation:
Bond Pricing
To calculate a bond's price when its interest rate is lower than the market interest rate, we must consider the expected future cash flows of the bond and discount them to present value at the new market interest rate. In the given scenario, the bond is expected to pay $1,080 in one year, which includes the final interest payment plus the principal amount of $1,000. If the market interest rate is now 12%, an investment of $964 today would grow to $1,080 in one year ($964(1 + 0.12) = $1,080). Thus, an investor would not be willing to pay more than $964 for this bond, as they could otherwise invest the same amount in an alternative at the market rate and receive the same future value. Considering the changed market conditions and the rise in interest rates to 12%, the bond's price would need to be adjusted downwards from its face value of $1,000 to remain an attractive investment compared to alternative opportunities.
To further induce an investor to buy an 8% bond that carries no risk in a market where new bonds offer 12%, its price must be discounted enough to equate the bond's yield to the market rate. Since the bond is unattractive at its face value due to the higher market rates, the seller would lower the price to a level where an investor would be indifferent between holding the 8% bond or investing in a new bond at the prevailing 12% rate.