Final answer:
The present value of a simple $3,000 bond with an 8% coupon rate is calculated using the discount rate. At 8% discount rate, the bond is valued at its par value of $3,000. When the discount rate is increased to 11%, the value decreases to $2,846.85, indicating an inverse relationship between bond prices and interest rates.
Step-by-step explanation:
To calculate the present value of a bond, we must discount the future cash flows (interest payments and the principal repayment) to their present value using the appropriate discount rate. In the case of a simple $3,000 two-year bond with an 8% interest rate, it will pay $240 in interest each year and return the $3,000 principal at maturity. Using the same 8% discount rate, the present value of each interest payment can be calculated, as well as the present value of the principal repayment.
If the discount rate rises to 11%, the calculation would be redone using this new rate. It's important to note that as the discount rate increases, the present value of future payments decreases, which means if interest rates rise, bonds with lower coupon rates will sell for less.
For the 8% discount rate, the calculations would be:
1st year interest: PV = $240 / (1+0.08) = $222.22
2nd year interest and principal: PV = ($240 + $3,000) / (1+0.08)^2 = $2,777.78
Total PV = $222.22 + $2,777.78 = $3,000
For the 11% discount rate, the calculations would be:
1st year interest: PV = $240 / (1+0.11) = $216.22
2nd year interest and principal: PV = ($240 + $3,000) / (1+0.11)^2 = $2,630.63
Total PV = $216.22 + $2,630.63 = $2,846.85
The bond's value would decrease from $3,000 to $2,846.85 with the increase in the discount rate, reflecting the inverse relationship between bond prices and interest rates.