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    Net Present Value (NPV)

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    Finance · Capital budgeting

    Net Present Value (NPV): Formula, Calculation, and Worked Example

    Net present value measures the estimated value an investment adds after allowing for the timing of its cash flows and the required return. It answers a dollar question: how much more are the expected benefits worth today than the investment requires? ← Finance hub · IRR · Payback Period
    Quick definition: NPV is the sum of project cash flows discounted to the valuation date. A positive NPV indicates estimated value creation at the selected required return, subject to the cash-flow, risk, and timing assumptions.

    The NPV formula

    NPV = CF0 + CF1/(1+r) + CF2/(1+r)2 + … + CFn/(1+r)n.
    • CF0: cash flow today, normally negative for the initial investment.
    • CFt: incremental net cash flow in period t, including terminal items where applicable.
    • r: required return per period, consistent with the cash-flow basis and risk.
    • n: number of forecast periods.
    The exponent reflects timing. A dollar received later has a lower present value at a positive discount rate. Cash paid today is already at time zero and is not discounted by another period.

    Build the cash flows before calculating

    Compare the project with the realistic alternative of not doing it. Include incremental equipment, installation, operating effects, working-capital commitments, terminal proceeds, and relevant cash tax effects. Exclude costs already incurred that the decision cannot change. Include opportunity costs when the project consumes a resource that could otherwise create value. Profit is not cash flow. Depreciation is noncash, although it can affect cash taxes. A working-capital increase consumes cash even when it is not an expense; its eventual recovery must be supported rather than assumed automatically. Keep financing and discounting consistent. For an unlevered project cash-flow analysis using an appropriate project cost of capital, do not also subtract financing interest and principal from the same cash flows as if they were operating costs. An equity cash-flow analysis requires a different, consistent approach.

    Worked investment example

    Original hypothetical equipment project: equipment and installation cost $100,000 today, plus $10,000 of incremental working capital. The project lasts four years. The table’s operating figures are assumed incremental cash flows after operating cash costs and project cash taxes, before financing flows. Year 4 includes $5,000 of after-tax disposal proceeds and full recovery of the $10,000 working-capital investment. The required return is an illustrative 10% annually. All future cash flows are assumed to arrive at year-end, with no additional capital spending or other cash flows. The same timeline is used in the companion IRR and Payback guides.
    Time Incremental operating cash flow Investment / terminal items Total project cash flow
    0: today — Equipment and installation −$100,000; working capital −$10,000 −$110,000
    End of Year 1 $30,000 — $30,000
    End of Year 2 $35,000 — $35,000
    End of Year 3 $40,000 — $40,000
    End of Year 4 $40,000 After-tax disposal proceeds $5,000; working-capital recovery $10,000 $55,000

    Calculate the present value of each cash flow

    Time Cash flow Calculation at 10% Present value
    0 −$110,000 No discounting at time zero. −$110,000.00
    1 $30,000 $30,000 ÷ 1.10 $27,272.73
    2 $35,000 $35,000 ÷ 1.10² $28,925.62
    3 $40,000 $40,000 ÷ 1.10³ $30,052.59
    4 $55,000 $55,000 ÷ 1.10⁴ $37,565.74
    NPV Sum of all present values. $13,816.68
    The future benefits have a present value of $123,816.68. Subtracting the $110,000 initial outlay leaves $13,816.68 of estimated value at a 10% required return. This is not the cash balance, annual profit, or a guaranteed gain. Use unrounded values in the underlying calculation and round only the reported result.

    How to interpret positive, zero, and negative NPV

    • Positive: the modeled benefits exceed the required investment after discounting at the required return.
    • Zero: the project is modeled to earn exactly that required return; it does not mean the undiscounted cash profit is zero.
    • Negative: the modeled project does not meet the selected required return.
    For an independent project with credible assumptions and no other constraints, positive NPV supports acceptance on value grounds. Real decisions must also address feasibility, liquidity, risk, resource limits, and competing uses of capital. For mutually exclusive choices, compare incremental value under consistent assumptions. Differences in scale, timing, useful lives, or replacement options may require additional analysis. A higher percentage return does not necessarily mean more value in dollars.

    How sensitive is the result to the required return?

    Annual required return Project NPV
    8% $19,964.57
    10% $13,816.68
    12% $8,112.20
    15% $299.06
    20% −$11,022.38
    For this conventional cash-flow pattern, increasing the rate reduces NPV. Its break-even discount rate is approximately 15.12%, the project’s internal rate of return. The 10% rate here is an assumption, not a recommended rate for every project.

    Test operating assumptions as well as the discount rate

    At 10%, a downside case with future cash flows of $24,000, $28,000, $32,000, and $47,000 has NPV of −$8,897.62, using the same −$110,000 initial outlay. In that downside case, Year 4 comprises $32,000 operating cash plus the same $15,000 terminal items. This shows why the positive base result needs evidence. Review demand, savings, execution costs, operating capacity, terminal proceeds, and working-capital recovery. A sensitivity changes one input; a scenario changes a coherent set of assumptions. Do not label either one a probability distribution without further support.

    Calculate NPV in Excel

    Place period numbers 0–4 in cells A2:A6 and the corresponding total cash flows −110000, 30000, 35000, 40000, and 55000 in B2:B6. Put the annual 10% discount rate in E2.
    Excel formula for this timing: =NPV(E2,B3:B6)+B2 Excel’s NPV function treats its listed cash flows as end-of-period amounts beginning one period from today. Add the time-zero cash flow separately.
    Including B2 inside the NPV range would move the initial investment to the end of the first period and shift every other flow too. For actual irregular dates, use a date-based method such as XNPV with supported cash-flow dates. Its day-count timing can produce a different result from a simple equal-period model.

    NPV compared with IRR and payback

    Method Question Shared example result
    NPV What value is added at the required return? $13,816.68 at 10%.
    IRR Which discount rate makes NPV zero? Approximately 15.12% annually.
    Payback When is the initial cash outlay recovered? At the end of Year 4 under the stated year-end timing.
    Use Payback Period to examine recovery timing. Recovery speed is useful context, but it is not a substitute for evaluating the whole project’s value.

    Common NPV mistakes

    • Discounting accounting earnings instead of incremental cash flows.
    • Omitting working capital, installation, later investment, or terminal cash costs.
    • Counting a working-capital recovery twice or assuming full recovery without support.
    • Mixing monthly cash flows with an annual rate without conversion.
    • Using nominal cash flows with a real rate, or otherwise mixing inflation conventions.
    • Subtracting financing costs while also charging for them through an inconsistent discount rate.
    • Treating a detailed spreadsheet as evidence that its commercial assumptions are reliable.

    Frequently asked questions

    Is NPV the same as profit?

    No. NPV discounts a sequence of incremental cash flows. Accounting profit recognizes revenue and expense according to the relevant accounting basis.

    Does positive NPV mean the project is affordable?

    No. Funding and cash timing still matter. A valuable project can create a near-term liquidity shortfall.

    What discount rate should I use?

    Use a supported rate consistent with the cash-flow definition, risk, currency, inflation basis, and period. Do not use this example’s 10% by default.

    Continue learning

    Review Time Value of Money for discounting, WACC for cost-of-capital assumptions, and Sensitivity and Scenario Analysis to test the investment case.

    Compare IRR and Payback, then use Rolling Forecasts to update operating assumptions. Return to Finance.

    Sources and example notes

    The project, calculations, downside case, and decision commentary are original educational illustrations. All assumptions require validation for an actual investment.