Final answer:
To determine the NPV for the project, we discount the cash flows at 4.94% and subtract the initial investment. We calculate the present value for each cash flow for six years and sum them up. A positive NPV suggests the project is financially viable.
Step-by-step explanation:
To calculate the net present value (NPV) of the project, we need to discount each of the project's after-tax cash flows back to its present value at the discount rate of 4.94%. First, we calculate the present value (PV) of the initial cash flow which is a cost and hence will be taken as negative. Then, we calculate the PV of the cash flows received at the end of the next three years ($144 each year), and subsequently, the PV of the cash flows received for the following three years ($1,984 each year).
The formula for Present Value is PV = FV / (1 + r)^n where FV is the future cash flow, r is the discount rate, and n is the number of periods until the payment.
For the $144 cash flows, the formula is applied for each of the first three years. For the $1,984 cash flows, the formula is applied for the fourth, fifth, and sixth years.
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- Year 1: $144 / (1 + 0.0494)^1
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- Year 2: $144 / (1 + 0.0494)^2
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- Year 3: $144 / (1 + 0.0494)^3
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- Year 4: $1,984 / (1 + 0.0494)^4
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- Year 5: $1,984 / (1 + 0.0494)^5
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- Year 6: $1,984 / (1 + 0.0494)^6
The sum of these present values minus the initial investment is the NPV of the project. The NPV is the sum of these values, so we calculate each one, sum them up, and subtract the initial cost of $5,000.
After completing these calculations, we compare the NPV to zero. A positive NPV indicates that the project adds value at the given discount rate, and a negative NPV suggests it does not.