Final answer:
When a bond's coupon rate is lower than the market rate, the bond's price must be discounted to provide an equivalent yield to buyers. An investor would not pay more for a bond than the present value of its future payments discounted at the current market rate, resulting in a lower purchase price for the bond considered.
Step-by-step explanation:
Understanding Bond Pricing Relative to Market Interest Rates
When a bond's coupon interest rate is less than the prevailing market interest rate, it means that newer bonds are offering higher interest payments than the bond we are considering. Consequently, our bond is less attractive to buyers unless it is sold at a discount to compensate for the lower interest payments. To determine the new price of our bond, we look at the present value of the bond's future payments at the new market interest rate.
For example, if we have a bond that is expected to pay $1,080 in one year—the final interest payment plus the principal repayment—and the market interest rate is now at 12%, an investor would expect the same return ($1,080) from investing $964 at 12% instead. Therefore, the investor would not pay more than $964 for our bond which has a face value of $1,000. The bond price adjusts so the bond's yield equals the market interest rate.
In the case of the local water company bond, if the market interest rate has risen to 9%, we would expect to pay less than the original $10,000 because investors can now find bonds that pay higher interest. The actual price we would be willing to pay depends on the value of the bond's remaining payments discounted at the new market rate of 9%.