Final answer:
Given a market interest rate of 9%, one would expect to pay less than the $10,000 face value for a bond with a coupon rate of 6%. The present value calculations show that the bond's value would be approximately $9,724.77, taking into account the single remaining interest payment and the principal repayment.
Step-by-step explanation:
When considering purchasing a bond one year before maturity, we must examine the difference between the bond's coupon rate and the current market interest rate to determine its value. The local water company issued a $10,000 bond at an interest rate of 6%, which pays $600 annually. As the market interest rate is now 9%, the bond's yield must be adjusted to match this new rate if one were to buy it now.
In scenario a), given the increase in market interest rates to 9%, one should expect to pay less than the bond's face value of $10,000 since its coupon rate is less attractive than the current market rate.
For scenario b), to calculate the price we would be willing to pay for the bond, we must calculate the present value of the bond's remaining payments (one year of interest plus the principal repayment). Using the formula for present value (PV = C / (1 + r)^n), where C is the cash flow, r is the discount rate, and n is the number of periods, we find:
Interest payment (C): $600
Principal repayment (C): $10,000
Discount rate (r): 9% or 0.09
Number of periods (n): 1
The present value of the interest payment is $600 / (1 + 0.09)^1 = $550.46
The present value of the principal payment is $10,000 / (1 + 0.09)^1 = $9,174.31
Adding these two amounts gives us the total present value of the bond's remaining cash flows: $550.46 + $9,174.31 = $9,724.77
Therefore, we would be willing to pay $9,724.77 for the bond, which is less than its face value due to the higher market interest rate.