Final answer:
To find the NPV for the project, calculate the present value of all cash flows and subtract the initial investments. The NPV is approximately $2,666.67 with the closest option being $2,668 when using a 2.5% discount rate. The correct answer is option 1.
Step-by-step explanation:
You’re asking about calculating the Net Present Value (NPV) for a project with two cash investments of $5,000 and a future cash flow of $15,000, with a discount rate of 2.5%. To determine the NPV, you need to discount all future cash flows back to their present value and sum these up, subtracting the initial investments.
Let's start by finding the present value (PV) of the $5,000 investment made today, which is simply $5,000 as it's already in present terms. Now, we calculate the PV of the second $5,000 investment made in 3 years. This is done using the formula PV = FV / (1 + r)^n. Here, FV is the future value which is $5,000, r is the discount rate (2.5% or 0.025), and n is the number of years until the payment, which is 3.
PV of the second investment after 3 years = $5,000 / (1 + 0.025)^3 = $5,000 / (1.077625) = $4,639.20 approximately.
Next, we find the PV of the $15,000 that will be received in 8 years using the same formula:
PV of the $15,000 after 8 years = $15,000 / (1 + 0.025)^8 = $15,000 / (1.218402) = $12,305.87 approximately.
Now, we subtract the PV of both investments from the PV of the future cash flow:
NPV = $12,305.87 (PV of future cash flows) - $5,000 (PV of first investment) - $4,639.20 (PV of second investment) = $2,666.67 approximately.
So, the closest NPV for this project, from the given options, is $2,668.