Final answer:
The net present value of the project is 2. -$74,102, rounded to the nearest dollar. This is closest to option (2) -$74,477. It is calculated by discounting the future cash flows at the required rate of return of 8% and subtracting the initial investment.
Step-by-step explanation:
To calculate the net present value (NPV) of this project, we need to discount the expected cash flows back to their present value using the required rate of return of 8%. The formula for the present value of future cash flows is:
Present Value = Future Cash Flow / (1 + r)^n
Where r is the rate of return, and n is the number of years.
Now let's calculate:
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- Year 1: $350,000 / (1 + 0.08)^1 = $324,074
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- Year 2: $350,000 / (1 + 0.08)^2 = $300,069
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- Year 3: $150,000 / (1 + 0.08)^3 = $119,377
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- Year 4: $180,000 / (1 + 0.08)^4 = $132,378
The total present value of the future cash flows is:
$324,074 + $300,069 + $119,377 + $132,378 = $875,898
The cost of the new system is $950,000, so the NPV of the project is:
NPV = Total Present Value - Initial Investment
NPV = $875,898 - $950,000
NPV = -$74,102 (rounded to the nearest dollar)
The closest answer provided in the multiple-choice options is (2) -$74,477. However, note that some small discrepancies could occur due to different rounding methods at each step.