Final answer:
Calculating the present value of bonds involves discounting future interest payments and principal to their present-day values using the current discount rate. Using the present value formula, you can calculate the present value of a two-year bond with given interest and discount rates. If market interest rates rise, the bond price usually decreases to attract investors.
Step-by-step explanation:
When calculating the present value of a bond, we need to discount the future payments of interest and the principal back to the present using the current interest rate or discount rate. The present value formula is used for these calculations, which is the sum of the future cash flows divided by (1 + r)ⁿ, where r is the discount rate and n is the number of periods.
Let's consider a simple two-year bond with a face value of $3,000 and an interest rate of 8%. It pays $240 in interest annually. To find its present value at a discount rate of 8%, we calculate the present value of the interest payments and the principal. For an 8% discount rate, the present value formula gives us:
- Year 1: PV(interest) = $240 / (1 + 0.08)¹
- Year 2: PV(interest + principal) = ($240 + $3,000) / (1 + 0.08)²
Add these two values to get the total present value of the bond. If the discount rate rises to 11%, we simply replace the 8% in our calculations with 11% to get the new present value.
For a no-risk bond the present value at issuance is usually the face value. Yet, if interest rates increase, the bond's price must decrease to remain attractive to investors. For example, if rates rise to 12% when there's one year to maturity, the bond price must fall below its face value. This reflects the inverse relationship between bond prices and market interest rates.