A project has an upfront cost of $100,000 and annual cash flows of $40,000 for five years. The discount rate is 10%. What is the NPV?

Question

BlackTom AI · Accepted Answer

To evaluate the NPV, first identify the cash flows: an upfront cost of 100,000 at t = 0 and annual cash inflows of 40,000 for years 1 through 5, with a discount rate of 10%. The NPV formula is NPV = -Initial Investment + Sum of PV of each cash flow.

Option A: $51,631.47
- This aligns with the correct calculation of the present value of the annuity at 10% for 5 years minus the initial cost. Using the annuity factor for 5 years at 10%: (1 - (1.1)^-5) / 0.1 ≈ 3.79079. Multiply by 40,000 gives ≈ 151,631.5. Subtract the initial 100,000 yields ≈ 51,631.5. This approximates the provided figure.

Option B: $46,937.70
- This value would occur if the present value of the 40,000 cash flows were around 146,937.70, implying a smaller annuity factor or a larger initial deduction. Since the annuity factor at 10% for 5 years is about 3.7908, the PV of inflows is around 151,631.9, not 146,937.7. Therefore this option underestimates the PV of inflows.

Option C: $49.214.63
- This looks like a formatting with a misplaced decimal point, suggesting a mis-typo or misplacement of tens and thousands. The calculation steps do not plausibly lead to 49,214.63 given 40,000 per year for 5 years at 10% unless the cash flows or discounting are drastically altered. It does not follow from standard NPV mechanics here.

Option D: $53,191.03
- This would imply a higher present value of inflows than the correct 151,631.5, or an initial investment lower than 100,000, or a different discounting approach. Since the PV of inflows is fixed by the schedule and rate, this option overstates the NPV relative to the accurate calculation.

In summary, the core idea is to take the 40,000 annual inflows, discount them 10% per year for 5 years, sum the present values, and subtract the initial 100,000. The correct present value of the inflows is about 151,631.5, and subtracting 100,000 yields approximately 51,631.5, matching Option A. The other choices arise from arithmetic missteps, formatting errors, or incorrect assumptions about the cash-flow timing or the discounting process.

A project has an upfront cost of $100,000 and annual cash flows of $40,000 for five years. The discount rate is 10%. What is the NPV?单项选择题

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Question at position 1 (3 marks, difficulty level: Easy) What is the NPV of this project? Assume the cost of capital is 9%. [table] Year | Project A 0 | -300,000 1 | 250,000 2 | 90,000 3 | 90,000 4 | 100,000 5 | 110,000 [/table]$216,940.48$234,156.78$205,873.92$228,454.01

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