Which of the following best describes a project with a NPV of zero?

Question

BlackTom AI · Accepted Answer

Net present value (NPV) of zero means the present value of a project’s expected cash inflows equals the initial investment when discounted at the required rate of return. In NPV terms: NPV = Σ [CFt / (1 + r)^t] − Initial Investment. If NPV = 0, then Σ [CFt / (1 + r)^t] = Initial Investment, so the project earns exactly the discount rate r.

1) Relevant concepts
- Time value of money: future cash flows must be discounted to present value.
- Required rate of return (discount rate or hurdle rate): used to compute NPV.
- Internal rate of return (IRR): the discount rate that makes NPV = 0.
- Interpretation: NPV > 0 adds value; NPV < 0 destroys value; NPV = 0 leaves value unchanged relative to the required return.

2) Step-by-step reasoning
Start from the NPV formula: NPV = Σ [CFt / (1 + r)^t] − I0. Set NPV = 0:
0 = Σ [CFt / (1 + r)^t] − I0 → Σ [CFt / (1 + r)^t] = I0.
This equality means the discounted cash inflows exactly cover the initial outlay at discount rate r. Thus the project’s return equals the required rate.

3) Example calculation (intermediate steps)
Invest I0 = $1,000 today; expected single cash inflow CF1 = $1,100 in one year; required r = 10% (0.10).
PV of inflow = CF1 / (1 + r) = 1,100 / 1.10 = $1,000.
NPV = PV inflows − I0 = 1,000 − 1,000 = $0. So the project returns exactly 10%, the required rate.

4) Why the correct answer is correct
Because NPV = 0 indicates the discounted inflows equal the investment when using the required rate; hence the project exactly earns that required rate — no more, no less. IRR equals the required rate in this situation.

5) Why the other options are incorrect
- “Payback period less than one year”: Payback ignores discounting and does not imply NPV = 0. A fast payback can still have positive or negative NPV.
- “The project will cause the company to lose money”: That describes a negative NPV, not zero.
- “The project is less risky than the firm's average investment”: Risk is not determined by NPV; NPV zero only addresses value at the given discount rate, not relative risk.

Conclusion: Therefore, a project with NPV = 0 exactly earns the required rate of return, which matches the provided correct answer.

Which of the following best describes a project with a NPV of zero?单项选择题

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