Value a signed cash-flow schedule at an explicit rate and date. Inspect operating cash, terminal value, recovery timing and comparable projects.
Project parameters
Optional WACC helper
Enter your own costs and weights. The helper does not estimate project risk.
Signed operating cash flows
Positive amounts are receipts; negative amounts are payments. Every row occurs at its stated endpoint. No within-period interpolation.
Terminal value
Terminal value = reference × (1 + growth) ÷ (discount − growth). Growth and reference use the same rate period as the discount rate. For dated cash they are annual. The model assumes the next receipt one such period after the terminal boundary. Discount must exceed growth.
Terminal cash is a discrete receipt or cost. Its date cannot precede the last operating cash flow. Changing operating timing does not silently move the terminal endpoint.
Modified return and root-search assumptions
Finance and reinvestment rates are explicit assumptions, applied per selected period (annual with Actual/365 dates). Root search is bounded numerical analysis; close roots may remain unresolved.
Net present value
PV receipts
PV payments
Terminal PV / share
NPV at entered rate
Returns and recovery
PV receipts ÷ PV payments
Finite-ledger IRR / XIRR
Modified return
Simple recovery
Discounted recovery
PI uses every gross receipt and payment, including separately entered terminal cash. Recovery is reported only for a conventional net investment pattern, after all cash at the same time. It may be unavailable for mixed or financing cash flows.
Numerical root receipt
Candidate rate
Scaled residual
Condition
Cash-flow evidence
Discounted cash-flow ledger
Amounts show currency cents; factors and exports retain calculation precision. Separate same-time operating and terminal rows preserve gross flows. The last cumulative PV equals NPV.
Cash flows at the selected rate and valuation date
Source
Date / period
Signed amount
Discount factor
Present value
Cumulative PV
Scenario analysis
Scale all signed operating amounts. Time-zero cash and a flat terminal amount stay fixed. Growing terminal value follows the scaled reference. These are input sensitivities, not probabilities or forecasts.
Project comparison
Project B uses A's valuation date, timing, frequency and row dates. Its discount rate must match A before comparing NPV. Enter B's separate terminal amount at A's terminal endpoint. IRR is not the ranking rule.
Private financial inputs
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3 min read4 steps6 terms2 examples6 FAQsNPV = Σᵢ CFᵢ / (1+r)^tᵢ; tᵢ = period endpoint or (dᵢ−d₀)/365
Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365.
2
Signed operating cash flows
Positive amounts are receipts; negative amounts are payments. Every row occurs at its stated endpoint. No within-period interpolation.
3
Terminal value
Terminal cash is a discrete receipt or cost. Its date cannot precede the last operating cash flow. Changing operating timing does not silently move the terminal endpoint.
4
Returns and recovery
Educational valuation under entered assumptions. Positive NPV is not a guarantee or a personal investment recommendation.
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Reference
Formula & Methodology
3 formulas▸
Net present value
NPV = Σᵢ CFᵢ / (1+r)^tᵢ; tᵢ = period endpoint or (dᵢ−d₀)/365
Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365.
Gross PV receipts / gross PV payments
PI = PV(CF⁺) / |PV(CF⁻)|
PI divides PV of all gross positive cash flows by PV of all gross negative cash flows. Separate terminal cash remains separate; PI is undefined without payments.
Modified return
MIRR = (FV(receipts) / |PV(payments)|)^(1/T) − 1
MIRR uses per-period finance and reinvestment assumptions and the last cash-flow endpoint as its horizon. Annual equivalent is a conversion, not a forecast. Dated modified return uses annual finance and reinvestment assumptions and the Actual/365 terminal horizon. It is a dated extension, not Excel periodic MIRR.
Reviewer: Calculover Editorial Review - Source and limitation review
Last reviewed: 2026-08-10
Last verified: 2026-08-10
Data effective: 2026-08-10
Methodology
Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365.
Assumption: Use a discount rate consistent with the cash-flow period, currency, inflation treatment and risk assumptions. There is no universal suitable rate.
Assumption: Separate discrete terminal amount
Assumption: MIRR uses per-period finance and reinvestment assumptions and the last cash-flow endpoint as its horizon. Annual equivalent is a conversion, not a forecast.
Limitations & guidance
Finite amounts are limited to 1 trillion per gross row, 126 operating rows and 200 years. Overflow is unavailable. Equality uses 64 machine epsilons times gross PV; tiny differences inside numerical uncertainty are break-even.
IRR candidates make a fixed signed ledger approximately zero within the searched rate domain. Multiple, absent or sensitive roots prevent a single-rate decision.
Educational valuation under entered assumptions. Positive NPV is not a guarantee or a personal investment recommendation.
Professional guidance: NPV Calculator is for investment math education only and is not investment, tax, legal, or financial advice. Consider risk, fees, taxes, and suitability before acting.
Discount Rate ↗Use a discount rate consistent with the cash-flow period, currency, inflation treatment and risk assumptions. There is no universal suitable rate.
Net Present Value (NPV) ↗Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365.
Initial Investment ↗The upfront capital outlay required to start the project, treated as a Year 0 cash outflow in the NPV calculation.
Internal Rate of Return (IRR) ↗IRR candidates make a fixed signed ledger approximately zero within the searched rate domain. Multiple, absent or sensitive roots prevent a single-rate decision.
Profitability Index (PI) ↗PI divides PV of all gross positive cash flows by PV of all gross negative cash flows. Separate terminal cash remains separate; PI is undefined without payments.
Cash Flow ↗Actual cash received or paid in each period of the project, as opposed to accounting profit which includes non-cash items like depreciation.
NPV at 8% = US$5,897.94 and PI = 1.118. The five US$14,000 year-end receipts exceed the US$50,000 initial outlay in present value under these assumptions.
NPV = US$38,683.95 at 10% and US$28,985.86 at 12%. Both are positive for the entered six-year cash-flow schedule; this does not guarantee actual returns.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Educational valuation under entered assumptions. Positive NPV is not a guarantee or a personal investment recommendation.
Signed operating cash flows
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Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365. Use a discount rate consistent with the cash-flow period, currency, inflation treatment and risk assumptions. There is no universal suitable rate.
Terminal value
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Terminal value = reference × (1 + growth) ÷ (discount − growth). Growth and reference use the same rate period as the discount rate. For dated cash they are annual. The model assumes the next receipt one such period after the terminal boundary. Discount must exceed growth. Growing terminal value can dominate NPV. The growth and discount spread is an assumption, not a verified long-term outcome.
Returns and recovery
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PI divides PV of all gross positive cash flows by PV of all gross negative cash flows. Separate terminal cash remains separate; PI is undefined without payments. IRR candidates make a fixed signed ledger approximately zero within the searched rate domain. Multiple, absent or sensitive roots prevent a single-rate decision. PI uses every gross receipt and payment, including separately entered terminal cash. Recovery is reported only for a conventional net investment pattern, after all cash at the same time. It may be unavailable for mixed or financing cash flows.
Project Comparison
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Project B uses A's valuation date, timing, frequency and row dates. Its discount rate must match A before comparing NPV. Enter B's separate terminal amount at A's terminal endpoint. IRR is not the ranking rule. Finite amounts are limited to 1 trillion per gross row, 126 operating rows and 200 years. Overflow is unavailable. Equality uses 64 machine epsilons times gross PV; tiny differences inside numerical uncertainty are break-even.
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Questions
Frequently Asked Questions
6 questions▸
How do signs and dates work?+
Sum each signed amount multiplied by its discount factor at the selected valuation date. Regular schedules use period endpoints; dated schedules use actual calendar days divided by 365.
How is terminal cash counted?+
Terminal cash is a discrete receipt or cost. Its date cannot precede the last operating cash flow. Changing operating timing does not silently move the terminal endpoint.
Which discount rate should I enter?+
Use a discount rate consistent with the cash-flow period, currency, inflation treatment and risk assumptions. There is no universal suitable rate.
Why can PI differ from an initial-cost ratio?+
PI divides PV of all gross positive cash flows by PV of all gross negative cash flows. Separate terminal cash remains separate; PI is undefined without payments.
Does one displayed return prove a unique solution?+
IRR candidates make a fixed signed ledger approximately zero within the searched rate domain. Multiple, absent or sensitive roots prevent a single-rate decision.
How should projects be compared?+
Comparison paused: both projects need the same discount rate and valuation convention. Common rate and valuation convention verified. Different project horizons remain an economic assumption.
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