Net Present Value (NPV) Calculator
Discount each period's cash flow to compute the Net Present Value (NPV) of an investment project.
Input Data
Results
At a glance:Net Present Value (NPV) discounts each year's net cash flow back to today at the discount rate and subtracts the initial investment: NPV = −C₀ + Σ Cᵢ ÷ (1 + r)^i, where C₀ is the initial outlay, Cᵢ is the Year-i net cash flow and r is the discount rate. A positive NPV means the project still yields a net surplus after the time value of money is deducted and is, in theory, worth pursuing; a negative NPV means the discounted inflows fall short and the project should be reconsidered or rejected.
Formula
NPV = −C₀ + Σ Cᵢ ÷ (1 + r)^i, i from 1 to n.
C₀ = initial investment; Cᵢ = Year-i net cash flow; r = discount rate.
PV of inflows = sum of each year's cash flow discounted (excl. initial outlay).
$$NPV = -C_0 + \sum_{i=1}^{n} \dfrac{C_i}{(1+r)^i}$$How to Use
- Set the discount rate (cost of capital or required return).
- Enter the initial investment and the Year 1–9 net cash flows (outflows as negatives).
- Leave years with no cash flow as 0; the NPV shows instantly.
FAQ
What does a positive NPV mean?
A positive NPV means the project still produces a net surplus after the time value of money is deducted, and is in theory worth pursuing; a negative NPV means the discounted inflows fall short, so the project should be reconsidered or rejected.
How should I set the discount rate?
The discount rate usually reflects your cost of capital or required minimum return — for example the borrowing rate, the weighted average cost of capital (WACC), or a prudent investment return. The higher the discount rate, the lower the present value of future cash flows and the more conservative the NPV. In Hong Kong, if you use it as a required project return, you might reference the HKMA's best lending rate (P) plus a risk premium, or use your own expected return on equity as the threshold.
Which is more reliable, NPV or the internal rate of return (IRR)?
The two are complementary. NPV tells you directly in dollars how much present value the project earns net, and its conclusion is stable even when cash flows change sign several times; IRR expresses the result as a percentage and is intuitive, but when cash flows alternate positive and negative it may yield multiple or no solutions. Academically and in practice NPV is generally the primary decision rule, with IRR as a supplementary reference. If the two conflict (common with mutually exclusive projects), follow NPV.
Does NPV account for inflation?
It depends on how you enter the cash flows and the discount rate. If cash flows are nominal amounts (including inflation), the discount rate must also be nominal; if cash flows are real amounts (inflation stripped out), the discount rate must be real. The two must be consistent, otherwise the result is biased. Hong Kong's long-run inflation is roughly 2%–3%, which matters especially for long-term projects.
Why does the NPV change so much when I change the discount rate?
Because discounting's effect grows exponentially with time. A given set of cash flows may show an NPV of about HK$39,242 at a 3% discount rate but only about HK$13,328 at 12%. The longer the horizon and the higher the discount rate, the more future cash flows are compressed. For high-risk or long-payback projects, NPV is extremely sensitive to the discount-rate assumption, so it is wise to run a conservative and an optimistic rate and see whether the conclusion holds.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.