The NPV formula adds the present values of all project cash flows, including the initial investment. Discount each future cash flow by its timing; a positive net present value means the project adds value relative to the required return used in the calculation.
NPV = Σ[t=0 to n] CF_t ÷ (1 + r)^t
— Net cash flow at time t; the initial outlay at t = 0 is usually negative
— Discount rate per period as a decimal
— Number of periods from the valuation date to the cash flow
— Final period in the forecast
Cash flows on different dates are not directly comparable. The NPV calculation moves every forecast cash flow to t = 0, the valuation date, and then adds them. The initial investment is already at t = 0, so its denominator is one.
The discount rate represents the return required for the cash flow’s risk and timing. In a company analysis it may be a project hurdle rate or weighted average cost of capital, provided that the rate matches the cash flows being discounted. A higher rate reduces the present value of future inflows and therefore reduces NPV.
Use net cash flows, not accounting profit. Include project-related cash receipts and payments at the dates they occur. Depending on the assignment, this can include the initial asset cost, working-capital investment, after-tax operating cash flows, terminal working-capital recovery, and disposal proceeds. Depreciation is not itself a cash outflow, though its tax effect may change cash flow.
Start with a timeline. Put the initial outlay at year 0 and each later net cash flow at its year-end. Compute a discount factor for every future year, multiply or divide to obtain each present value, and add the signed results. Keeping negative signs on outflows makes the final sum easier to audit.
A packaging company is considering a sorting machine that costs $128,400 today. Forecast net cash inflows are $38,600 in year 1, $44,900 in year 2, $51,300 in year 3, and $57,800 in year 4. The required return is 9% annually, and all forecast inflows occur at year-end.
| Time | Cash flow | Present-value calculation | Present value |
|---|---|---|---|
| Year 0 | −$128,400 | −$128,400 ÷ 1.09^0 | −$128,400.00 |
| Year 1 | $38,600 | $38,600 ÷ 1.09^1 | $35,412.84 |
| Year 2 | $44,900 | $44,900 ÷ 1.09^2 | $37,791.43 |
| Year 3 | $51,300 | $51,300 ÷ 1.09^3 | $39,613.01 |
| Year 4 | $57,800 | $57,800 ÷ 1.09^4 | $40,946.98 |
| NPV | Sum of present values | $25,364.26 |
The project’s NPV is approximately $25,364.27 using unrounded calculations. At a 9% required return, the present value of the future inflows is about $153,764.27, which exceeds the $128,400 cost by that amount. Under the standard decision rule, accept an independent project when NPV is positive, reject it when NPV is negative, and remain indifferent on value grounds when NPV is zero.
That rule is conditional on the forecasts and discount rate. A positive output does not make uncertain cash flows certain. Test assumptions such as sales volume, operating costs, project life, and terminal value rather than treating one NPV as a guarantee.
Spreadsheet NPV functions usually treat the first value in their range as arriving one period after the valuation date. That means the time-zero investment should normally be added separately.
Spreadsheet NPV = NPV(rate, Year 1 : Year n cash flows) + Year 0 cash flow
— Discount rate for each equal spreadsheet period
— Future cash flows occurring at equal period-end intervals
— Initial outlay entered separately, usually as a negative number
For the example, enter the four future inflows in the function and then add −128400. Including the initial cost inside the function discounts it for one year, which is a timing error. For irregular calendar dates, use a date-aware function such as XNPV with actual dates rather than pretending every interval is equal.
Using profit instead of cash flow. NPV values cash movements. Convert accounting forecasts to incremental after-tax cash flows as the problem requires.
Forgetting the initial outlay’s sign. If later benefits are positive, the project cost is normally negative. Adding a positive cost overstates value.
Discounting year 0. A cash flow paid today has no waiting period. Its present value equals the cash flow itself.
Mismatching nominal and real values. Nominal cash flows that include inflation need a nominal discount rate. Real cash flows stated in constant purchasing power need a real rate.
Comparing mutually exclusive projects by IRR alone. NPV measures dollar value added and handles differences in project scale more directly. When projects conflict, use the decision framework specified by the course or firm, with NPV usually the primary value criterion.
Hiding terminal assumptions. A large final-year recovery or resale value can drive the answer. Show it as a separate cash-flow line so the reader can see its effect.
The example assumes every inflow arrives at year-end. If the $38,600 year-1 inflow arrived today instead, it would not be discounted and the NPV would rise. If it arrived at the end of year 2, it would be discounted for an extra period and NPV would fall. The amount did not change; only its location on the timeline changed.
This is why a forecast table needs explicit dates or period labels. A list of cash flows without timing is not enough to reproduce an NPV. When cash flows occur throughout a year, an analyst may use a midyear convention, but that convention must be stated and applied consistently.
A project NPV should include cash flows that occur because the project is accepted. Sunk costs already paid do not change between the accept and reject choices and are excluded. Opportunity costs do matter: using a warehouse for the project can sacrifice rent that the company would otherwise earn. Side effects on existing products can matter as well.
Working capital is another frequent omission. Extra inventory or receivables often require a cash investment near the project’s start. If that working capital is released when the project ends, show the release as a later inflow. The initial investment and final recovery occur at different dates, so they do not cancel in present-value terms.
The $25,364.27 result is an estimate built from forecasts, not an observed profit. Recalculate NPV under plausible lower inflows, higher costs, shorter useful life, and a different discount rate. A project whose NPV stays positive across reasonable cases is more resilient than one that turns negative after a small assumption change.
For mutually exclusive projects, compare NPVs at the same valuation date using consistent assumptions. A longer project may require an equivalent-annual-value adjustment if projects can be repeated and lives differ. The essential discipline remains the same: compare incremental cash flows after moving them to a common date.
Put every signed cash flow on a timeline, discount each future amount to time zero, and add the initial outlay without discounting it.
NPV is the sum of each cash flow divided by one plus the discount rate raised to that cash flow’s period. Include the time-zero investment as a signed cash flow.
It means the project’s forecast inflows are worth more today than its forecast outflows at the chosen required return. The project is expected to add the reported dollar value under those assumptions.
It occurs at time zero, so the discount exponent is zero and the denominator equals one. Spreadsheet NPV functions often require that amount to be added separately.
Use a rate appropriate for the cash flow’s risk, timing, currency, and inflation convention. In corporate finance this may be a project hurdle rate or WACC when those assumptions match.
NPV reports value added in currency. IRR reports the discount rate that makes NPV equal zero. NPV is generally clearer when mutually exclusive projects differ in size or timing.
Discount each cash flow using its actual time from the valuation date or use a date-aware spreadsheet function such as XNPV. The standard NPV function assumes equally spaced periods.
By the FinanceBrain Team · Last verified July 12, 2026 · How we produce and verify articles