Final answer:
To calculate the present value of the bond, interest payments and the principal were discounted at both 8% and 11%. The bond's value is $3,000 when discounted at 8%, but falls to $2,847.30 at an 11% discount rate.
Step-by-step explanation:
The question is asking to calculate the present value of a bond with a face value of $3,000, an annual interest rate of 8%, and a term of two years using two different discount rates—8% and 11%. First, let's find out the present value of the bond using the 8% discount rate.
The bond pays $240 in interest each year (which is $3,000 × 8%), and it will pay this amount at the end of the first and second years, plus the $3,000 principal at the end of the second year. The formula for present value (PV) is PV = C/(1+r)^n, where 'C' is the cash flow, 'r' is the discount rate, and 'n' is the number of periods.
So, for the first year:
$240/(1+0.08)1 = $222.20
And for the second year (including the principal):
$3,240/(1+0.08)2 = $2,777.80
The total present value at an 8% discount rate is thus the sum of these two amounts:
$222.20 + $2,777.80 = $3,000.
Now, let's recalculate the present value of the bond using an 11% discount rate.
So, for the first year:
$240/(1+0.11)1 = $216.22
And for the second year:
$3,240/(1+0.11)2 = $2,631.08
The total present value at an 11% discount rate is thus the sum of these two amounts:
$216.22 + $2,631.08 = $2,847.30.
When the discount rate increases from 8% to 11%, the present value of the bond decreases, suggesting that the bond's value diminishes as interest rates rise. This aligns with the concept that when interest rates go up, the price of existing bonds generally falls to yield a return that is competitive with the current interest rate.