Final answer:
The present value of a bond is determined by discounting future cash flows (interest payments and face value) at the prevalent discount rate. A bond's worth decreases with an increase in the discount rate, demonstrating the inverse relationship between discount rates and bond prices. The yield on the bond represents interest payments plus capital gains or losses due to price fluctuations.
Step-by-step explanation:
Calculating Present Value and Bond Pricing
To find the present value of a bond, we must discount the future interest payments and the face value repayment at the prevailing discount rate. For a simple two-year bond with a face value of $3,000 and an interest rate of 8%, the bond will pay $240 in interest each year. To calculate the present value with a discount rate of 8%, we would use the present value formula for each cash flow:
- Present Value of first year's interest = $240 / (1 + 0.08)^1
- Present Value of second year's interest = $240 / (1 + 0.08)^2
- Present Value of face value repayment = $3,000 / (1 + 0.08)^2
Adding these three present values together gives us the present value of the bond at the 8% discount rate.
If the interest rates rise and the new discount rate is 11%, we must recalculate the present value using the new rate:
- Present Value of first year's interest = $240 / (1 + 0.11)^1
- Present Value of second year's interest = $240 / (1 + 0.11)^2
- Present Value of face value repayment = $3,000 / (1 + 0.11)^2
Again, by adding these values, we find the present value of the bond at an 11% discount rate. This exercise shows that as the discount rate increases, the present value of future payments decreases, leading to a lower bond price.
In the context of yields, the yield on the bond would be the interest payments plus the capital gains or loss on the bond, which results from the price difference between the purchase price and the face value. Notably, even if the coupon rate of 8% does not change, the market price of the bond can fluctuate based on prevailing interest rates.