Final answer:
The value of a bond changes when market interest rates change. If rates rise above the bond's coupon rate, the bond's price will fall below its face value. To find the price for a bond, you calculate the present value of the remaining cash flows at the new market interest rate.
Step-by-step explanation:
The valuation of a bond is based on calculating the present value of its future cash flows, including the payment of interest and the repayment of principal at maturity.
When the market interest rates change, the value a buyer would be willing to pay for an existing bond changes as well since buyers will demand a yield that matches the current market rates.
For instance, consider a 10-year bond with a face value of $10,000 and a coupon rate of 6%. If there's only one year left until maturity and the current market interest rate has risen to 9%, an investor would expect to pay less than the face value for the bond since the coupon payments are less than the current market rate.
The discount would reflect that the bond's return is below the market rate.
To determine the price to pay for this bond, we calculate the present value of the remaining cash flows (one year of interest plus the principal) discounted at the new market rate of 9%. Using the present value formula:
- The present value of the interest payment (PVinterest) is $600 ($10,000 * 6%) discounted at 9% for one year.
- The present value of the principal (PVprincipal) is the $10,000 discounted at 9% for one year.
The sum of these two present values will give us the price we would be willing to pay for the bond.