economics · cashflow
Net Present Value (Variable Cash Flow)
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Inputs
$
Paste one row per line — separate columns with a comma or tab: Net Cash Flow ($/yr)
⚠ Needs at least 2 valid rows to calculate — 0 so far.
fraction
Description
Computes the net present value of an arbitrary year-by-year sequence of annual cash flows, discounted at a constant annual rate, net of the up-front investment — the array-input counterpart of npv_cashflow, for a genuinely variable or declining production-revenue stream instead of a single level amount. Reopens the level-annuity scoping limitation npv_cashflow disclosed from the start, now that the array-input schema exists.
Variables
| Symbol | Unit | Description |
|---|---|---|
| NPV | $ | Net Present Value |
| C0 | $ | Up-front capital cost (drilling, completion, facilities) incurred at time zero, before any cash flow begins. |
| CFₜ | — | One row per year, in order starting at year 1 (the end of the first year after the investment): that year's own net cash flow, revenue minus operating cost, pre-tax. Unlike npv_cashflow's single level CF, each row can be any value — rising, falling, or irregular — so a genuinely declining production-revenue stream can be entered directly instead of approximated as a level annuity. Paste at least 2 years. |
| r | fraction | Annual discount rate (company hurdle rate or weighted average cost of capital), applied once per year (discrete, not continuous, compounding). |
Assumptions
- Each row's cash flow is received at the end of that year (discrete/annual discounting), matching npv_cashflow's timing convention exactly.
- Cash flow and discount rate are both in nominal (current, non-escalated) dollars — no inflation or price-escalation adjustment is applied.
- Cash flow is pre-tax.
- A single constant discount rate applies to every period — the rate itself is not allowed to vary year to year.
- For a type-curve well, the cash-flow array's revenue rows are typically built outside this calculator from a decline-curve rate forecast (decline_hyperbolic/decline_harmonic) converted to volume × price, less operating cost; use economic_limit_rate to decide the last year worth including.
Limitations
- No income, severance, or ad valorem tax deduction is applied; post-tax NPV will be lower and is jurisdiction-dependent — do not treat this as an after-tax value.
- A single constant discount rate is used for every period; risked or time-varying discount rates are not supported.
- For a level (uniform) annual cash flow, npv_cashflow is simpler to use and produces an identical result — this tool's value is specifically for a genuinely variable or declining year-by-year stream.
Use Cases
- → Declining-production project screening: Value a well or project whose annual net cash flow genuinely declines with production, instead of approximating it as a level annuity.
- → Irregular cash-flow projects: Handle a cash flow stream with a ramp-up period, a mid-life workover cost, or any other year-to-year irregularity that a single level CF can't represent.
- → Type curve economics: Evaluate NPV for a decline-curve-forecast well: use decline_hyperbolic/decline_harmonic (Reservoir) to project annual production, price and cost each year's volume by hand into a cash-flow array, then discount it here.
Related Calculations
Region Notes
General
Discount/hurdle rates used in practice vary widely by operator, project risk, and commodity-price environment — often quoted in the 10-15% nominal range for conventional development and higher (15-25%+) for higher-risk unconventional or exploration projects. This tool does not select a rate for you.
References
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