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, start from the given cash flows and discount them at the stated rate.
Option 1: 51,631.47 — This aligns with the standard NPV formula: NPV = -Initial Investment + PV of annuity. The PV of 40,000 received for 5 years at 10% is 40,000 × [(1 − (1+0.10)^(−5)) / 0.10] = 40,000 × 3.79078678 ≈ 151,631.47. Subtracting the upfront cost of 100,000 yields 51,631.47. This matches the calculation precisely.
Option 2: 46,937.70 — This value would arise if the PV factor were smaller, meaning either a lower discount rate, fewer years, or smaller cash flows. Given the 10% rate and five-year horizon, the correct PV is around 151,631, so subtracting 100,000 should yield about 51,631, not 46,938.
Option 3: 49,214.63 — This number is closer to a scenario where the annuity factor were around 3.4806 (40,000 × 3.4806 ≈ 139,224; 139,224 − 100,000 ≈ 39,224, not matching). The discrepancy indicates a miscalculation of the present value factor or misapplication of the discounting formula.
Option 4: 53,191.03 — This would occur if the PV of the cash flows were around 153,191, which would require a slightly different present value factor or rate detail. Since the exact annuity factor at 10% for five years is 3.79078678, this option overstates the present value by a noticeable margin.
In summary, the correct approach uses the present value of an ordinary annuity formula with r = 0.10 and n = 5, giving a PV of 151,631.47 and an NPV of 51,631.47; the other options reflect common misapplications or arithmetic slips of the discounting process.

BUSFIN 3220 AU2025 (2910) Trial Exam 2 - Requires Respondus LockDown Browser

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?

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