Final answer:
The price of a bond will be less than its face value when the market interest rate exceeds the bond's coupon rate. In the example, a bond expected to make a $1,080 payment in one year would not be priced higher than $964 if the current market rate is 12%. Calculations of bond prices adjust for market changes reflecting the present value of future payments.
Step-by-step explanation:
The question relates to the calculation of a bond's price when its coupon interest rate is less than the market interest rate, also known as the yield to maturity (YTM). When the market interest rate increases above the bond's coupon rate, the price of the bond must decrease to make it an attractive investment relative to new bonds with the higher rates. Conversely, if market rates fall below the coupon rate, the bond's price increases.
Using the provided scenario, the bond will make a payment of $1,080 one year from now. With current market interest rates at 12%, an alternative investment of $964 growing at this rate will also yield $1,080 in a year. Therefore, in a competitive market, the bond's price wouldn't exceed $964.
As for the example calculations:
- For a $10,000 bond with a 6% coupon when market rates are at 9%, you would expect to pay less than the $10,000 face value.
- The present value of a $3,000 bond at an 8% discount rate would factor in both the interest payments and the principal sum to calculate the current worth of future payments. Rerunning the calculation at an 11% discount due to an interest rate rise will reduce the present value of the bond.