Final answer:
When market interest rates rise, the price of a coupon bond will decrease since its fixed interest payments become less appealing compared to new bonds that are issued at higher rates. If an investor can obtain a 12% return elsewhere, they will not pay more than the discounted price that aligns with that return, which would be less than the current price of the bond.
Step-by-step explanation:
If you have purchased a coupon bond for $1040, and market interest rates rise, the price of the bond will generally decrease. This is because the bond's fixed interest payments will be less attractive compared to new bonds issued at the higher prevailing interest rates, which offer more competitive yields.
As an example, if the bond in question matures in one year and is expected to make a $1,080 payment at that time (which includes the last year's interest payment and the face value repayment), and the market interest rate rises to 12%, an investor could invest $964 in an alternative investment to receive the same $1,080 in a year. Thus, they would not be willing to pay more than $964 for the bond. This new price is calculated based on the future payment discounted by the current market interest rate, $964(1 + 0.12) = $1080.
Furthermore, the yield on the bond, or total return, considering the difference between the purchase price ($964) and the payment received ($1,080), equals 12%. This yield reflects the interest payments alongside any capital gains or losses. It's important to note that the bond's coupon rate does not change, but the bond's price adjusts to align with current market yields, which in this scenario, dictates that the bond will sell for less than its face value due to the rise in overall interest rates.