Final answer:
You may pay more than the face value for a bond when the market interest rate is below its coupon rate because its income stream is more valuable. The present value of such a bond's future payments, discounted at the current market rate, would exceed its face value, making it a premium bond.
Step-by-step explanation:
You might be willing to pay more than $1,000 for a coupon bond with a 10 percent coupon rate and a face value of $1,000 if the interest rate in the market is less than 10 percent. In this case, the present value of the payment flows (coupons and principal) associated with the bond would be greater than $1,000. This is because the bond's fixed coupon payments are more attractive compared to the new, lower market interest rates, and investors would be willing to pay a premium for that higher income stream.
For instance, let's consider that market interest rates have dropped to 8%. We would use the present value calculation method to determine what the bond's payments are worth today. The bond will pay $100 annually for three years (10% of $1,000 face value), plus the $1,000 face value at maturity. If these payments are discounted back to their present value at the current market rate of 8%, the total present value would exceed the bond's face value of $1,000, leading investors to be willing to pay more for this bond. The opposite situation would occur if the market interest rates were higher than 10% - the present value would be less than $1,000 and investors would not be willing to pay as much for the bond.