Final answer:
The present value of a bond is determined by discounting the future cash flows, consisting of interest payments and return of principal, using the market interest rate. Increases in market interest rates will lower the present value of a bond. For example, a two-year bond issued at 8% will have its value decrease if market rates rise to 11% and inversely, a bond will need to be sold at a lower price if its interest payments are below current market rates.
Step-by-step explanation:
Present Value Calculation of Bonds
When analyzing the value of a bond, we often determine its present value based on the future cash flows it provides. These cash flows include interest payments and the return of principal at maturity. The present value is calculated by discounting these future cash flows at a rate reflecting the risk and opportunity cost of capital, which is typically the market interest rate.
A simple two-year bond with a principal amount of $3,000 and an annual interest rate of 8% pays $240 in interest each year. To calculate the present value of this bond with a discount rate of 8%, the same as the bond's interest rate, we would not expect to see much difference between the present value and the face value. However, if interest rates rise to 11%, increasing the discount rate, the present value of the bond will decrease since the future cash flows will be discounted at a higher rate.
In a scenario with Ford Motor Company issuing a bond, the coupon payment relative to the face value provides the interest rate Ford is paying. If the interest rate increases after issuance, the value of the bond will decrease because new bonds yield more, making the existing ones less attractive unless they are sold at a lower price. Lastly, with the hypothetical local water company bond, if the market interest rate rises above the bond's coupon rate, one would expect to pay less than the face value for the bond to achieve a yield comparable to the new market rate.