Answer:
Option "b-2" has a higher present value, making it the preferred option.
Explanation:
To calculate the present value of the cash flows, we can use the formula for the present value of an annuity:
PV = C * (1 - (1 + r)^(-n)) / r
Where:
PV is the present value
C is the annual payment
r is the interest rate per period
n is the number of periods
Let's calculate the present value for each option:
a-1. Annual payment of $775 for 10 years at 4% interest:
C = $775, r = 4%, n = 10
Using the formula, the present value is:
PV = 775 * (1 - (1 + 0.04)^(-10)) / 0.04 ≈ $6,668.71
a-2. Annual payment of $575 for 15 years at 4% interest:
C = $575, r = 4%, n = 15
Using the formula, the present value is:
PV = 575 * (1 - (1 + 0.04)^(-15)) / 0.04 ≈ $7,610.58
a-3. To determine which option is preferred, we compare the present values. In this case, option "a-2" has a higher present value, which means it is the preferred option.
b-1. Annual payment of $775 for 10 years at 16% interest:
C = $775, r = 16%, n = 10
Using the formula, the present value is:
PV = 775 * (1 - (1 + 0.16)^(-10)) / 0.16 ≈ $3,051.84
b-2. Annual payment of $575 for 15 years at 16% interest:
C = $575, r = 16%, n = 15
Using the formula, the present value is:
PV = 575 * (1 - (1 + 0.16)^(-15)) / 0.16 ≈ $4,699.35
b-3. Similarly, we compare the present values to determine the preferred option. In this case, option "b-2" has a higher present value, making it the preferred option.
To summarize:
Option "a-2" is preferred over option "a-1" at 4% interest.
Option "b-2" is preferred over option "b-1" at 16% interest.
Thus,
Option "b-2" has a higher present value, making it the preferred option.