Final answer:
The bond's volatility, or modified duration, is 9.09 percent, representing the bond's price sensitivity to a change in yield. It is calculated using the bond's duration and yield to maturity. In the context of changing interest rates, the price of a bond will decrease if the market interest rates rise above the bond's coupon rate.
Step-by-step explanation:
The question is concerning the concept of bond volatility, also known as modified duration, and its calculation given the bond's yield to maturity. Modified duration is a measure that indicates the percentage change in the price of a bond for a 1% change in yield. The formula to calculate modified duration is as follows:
Modified Duration = Macaulay Duration / (1 + (Yield to Maturity / Number of Coupon Periods per Year)).
In this question, the bond has a duration of 10 years and a yield to maturity of 10 percent. Assuming the bond pays annual coupons, the modified duration would be calculated as:
Modified Duration = 10 years / (1 + (0.10 / 1)) = 10 / 1.10 = 9.09.
Therefore, the bond's volatility or modified duration is 9.09 percent. It represents how much the price of the bond would change in response to a change in interest rates. When the yield to maturity is equal to the coupon rate, the bond's price will be equal to its face value. However, if the yield to maturity differs from the coupon rate, the bond's price will either be at a premium or discount, depending on whether the yield to maturity is above or below the coupon rate.
Using the local water company example provided, when interest rates rise from the original coupon rate (6% to 9%), the existing bond's price would decrease to reflect the higher market interest rates, and thus, one would expect to pay less than the face value of $10,000 for the bond. The exact amount paid for the bond would be calculated based on the present value of future cash flows (coupons and face value) at the new required yield to maturity of 9%.