Final answer:
To find the present value of a two-year bond paying an annual 8% coupon at different discount rates, one must discount each payment back to its present value. The bond's present value decreases from $3,000 to $2,871.23 when the discount rate increases from 8% to 11% due to rising market interest rates.
Step-by-step explanation:
To calculate the present value of a simple two-year bond with a face value of $3,000 and an annual coupon of 8%, we need to discount the future payments by the appropriate discount rate. At a discount rate of 8%, the first year's coupon payment of $240 is discounted as follows:
PV = Payment / (1 + r)^n
For the first coupon payment: PV = $240 / (1 + 0.08)^1 = $222.22
The second year's coupon payment and the face value repayment are discounted in the same way:
For the second coupon payment and face value: PV = ($240 + $3,000) / (1 + 0.08)^2 = $2,777.78
Summing these up gives us the total present value of the bond at an 8% discount rate: $222.22 + $2,777.78 = $3,000
If the interest rates rise and the new discount rate is 11%, recalculation is needed:
For the first coupon payment: PV = $240 / (1 + 0.11)^1 = $216.22
For the second coupon payment and face value: PV = ($240 + $3,000) / (1 + 0.11)^2 = $2,655.01
Total present value at 11% discount rate: $216.22 + $2,655.01 = $2,871.23
The calculation illustrates how bond values decrease when discount rates increase due to higher prevailing market interest rates.