Final answer:
The present value of a bond is found by discounting each of its future payments (interest and principal) by the discount rate. For an 8% coupon bond with yearly payments of $240 and a principal of $3,000, the present value is calculated for discount rates of 8% and 11%. A higher discount rate results in a lower present value for the bond.
Step-by-step explanation:
Calculating Present Value of a Bond
Calculating the present value (PV) of a bond involves discounting the future cash flows (interest payments and the principal repayment) back to their value in today's dollars. The formulas for calculating the present value of the interest payments and the principal are as follows:
PV of Interest Payments = Interest Payment × (1 - (1 + discount rate)^-number of periods) / discount rate
PV of Principal = Principal / (1 + discount rate)^number of periods
For a simple two-year bond with a face value of $3,000 and an annual 8% coupon rate, the bond will pay $240 in interest each year. Using discount rates of 8% and 11%, we will calculate the bond's present value.
Case 1: Discount Rate of 8%
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- Year 1 Interest PV = $240 / (1 + 0.08)
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- Year 2 Interest PV = $240 / (1 + 0.08)^2
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- Principal PV = $3,000 / (1 + 0.08)^2
Summing these calculations will give us the bond's present value at an 8% discount rate.
Case 2: Discount Rate of 11%
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- Year 1 Interest PV = $240 / (1 + 0.11)
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- Year 2 Interest PV = $240 / (1 + 0.11)^2
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- Principal PV = $3,000 / (1 + 0.11)^2
Again, adding these values will provide the bond's present value at an 11% discount rate.
The yield on a bond includes interest payments as well as capital gains or losses due to changes in the market interest rates.