Question

Given: Base amount = $500, gradient = -$100, i = 10%, n = 3. For the given values, determine the present worth of the cash flow series in year 0.

a.$1,147.12
b.$1,010.52
c.$1,259.20
d.$1,098.15

Answer 1

To determine the present worth of the cash flow series in year 0, calculate the present value of each cash flow and sum them up.

Step-by-step explanation:

To determine the present worth of the cash flow series in year 0, we need to calculate the present value of each cash flow and then sum them up.

Given:

• Base amount = $500
• Gradient = -$100
• Interest rate (i) = 10%
• Number of periods (n) = 3

To calculate the present value, we can use the formula:

Present Value (PV) = Cash Flow / (1 + i)^n

Applying the formula to each cash flow, we get:

• Present Value of Base Amount: $500 / (1 + 0.10)^0 = $500
• Present Value of Gradient (Year 1): -$100 / (1 + 0.10)^1 = -$90.91
• Present Value of Gradient (Year 2): -$100 / (1 + 0.10)^2 = -$82.64
• Present Value of Gradient (Year 3): -$100 / (1 + 0.10)^3 = -$75.13

Adding up the present values, we get:

Present Worth = $500 + (-$90.91) + (-$82.64) + (-$75.13) = -$97.68

Therefore, the present worth of the cash flow series in year 0 is -$97.68.