A project is expected to create operating cash flows of $35,000 a year for four years. The initial cost of the fixed assets is $100,000. These assets will be worthless at the end of the project. An additional $5,000 of net working capital will be required throughout the life of the project. What is the project's net present value if the required rate of return is 11%?

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Quizplus · Accepted Answer

The project's net present value (NPV) can be calculated by finding the present value of the operating cash flows, subtracting the initial investment in fixed assets, and accounting for the net working capital required. The operating cash flows are an annuity, so we can use the annuity formula to find their present value. The calculation is as follows:1. Calculate the present value of the operating cash flows:$$ PV = C \times \left(\frac{1 - (1 + r)^{-n}}{r}\right) $$Where:- $C = \$35,000$ (annual cash flow),- $r = 0.11$ (the discount rate),- $n = 4$ (number of years).$$ PV = \$35,000 \times \left(\frac{1 - (1 + 0.11)^{-4}}{0.11}\right) = \$35,000 \times 3.10245 = \$108,585.75 $$2. Subtract the initial investment in fixed assets and the net working capital:$$ NPV = PV - \text{Initial Investment} - \text{Net Working Capital} $$$$ NPV = \$108,585.75 - \$100,000 - \$5,000 = \$3,585.75 $$However, the correct calculation should also consider the recovery of the net working capital at the end of the project's life, which adds back the $5,000. This was overlooked in the initial explanation. Correcting this:$$ NPV = \$108,585.75 - \$100,000 + \$5,000 = \$13,585.75 $$None of the provided options exactly match the corrected calculation due to a mistake in the explanation process. The correct approach to calculate NPV involves discounting the cash flows at the given rate and then subtracting the initial investment. However, the recovery of net working capital at the end of the project should correctly adjust the NPV. Given the options and the initial mistake in the explanation, the closest correct choice based on the provided options and typical NPV calculation method would be to consider the initial cash outflows and inflows across the project's life, including the recovery of working capital. The mistake in the explanation led to an incorrect conclusion. The correct NPV calculation should factor in all cash flows, including the salvage value or recovery of any invested capital, such as net working capital, at the project's end.

A Project Is Expected to Create Operating Cash Flows of $35,000