# Net Present Value: Turning Project Cash Flows Into Today's Value

NPV discounts incremental project cash flows to today and subtracts required investment; the result depends on cash-flow scope, timing, risk, taxes, and discount-rate consistency.

Canonical: https://wiki.fcontext.com/stocks/net-present-value/
Fact checked: 2026-07-21

> For educational purposes only; not investment advice.

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## Direct answer

Net present value, or NPV, is the present value of all incremental cash flows from a project, including the initial investment. Under a specified forecast and risk-adjusted discount rate, positive NPV means expected cash inflows exceed the opportunity cost of capital; negative NPV means they do not.

NPV is conditional, not a guarantee. A precise positive number can still rest on weak assumptions about sales, costs, timing, taxes, working capital, terminal value, or risk.

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## Formula and cash-flow rules

`NPV = CF0 + CF1 / (1 + r)^1 + ... + CFn / (1 + r)^n`

`CF0` is commonly a negative initial outlay. Include only cash flows that change because the project is accepted: capital spending, operating cash flows, taxes, working-capital investment and release, opportunity costs, cannibalization, and after-tax disposal value. Exclude sunk costs that cannot be changed by the decision.

Cash flow and discount rate must describe the same claim. Enterprise free cash flow is commonly discounted with a project-appropriate WACC without separately deducting interest. Equity cash flow uses a cost of equity and reflects debt financing. Nominal cash flows require a nominal rate; real cash flows require a real rate.

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## Worked example

A project costs `$1,000,000` today, produces `$300,000` at each of the next four year-ends, and adds `$100,000` of after-tax disposal proceeds in year four. At a `10%` discount rate:

`NPV = -$1,000,000 + $300,000/1.10 + $300,000/1.10^2 + $300,000/1.10^3 + $400,000/1.10^4`

`NPV ≈ $19,200`

The base case is only slightly positive. If annual cash flow falls to `$250,000`, NPV becomes about `-$139,200`. The approximate annual cash flow required for NPV to equal zero is `$293,900`, after accounting for the disposal proceeds.

That break-even figure is often more actionable than a single base-case NPV because actual performance can be monitored against it.

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## Decision risks

- Forecast errors compound across price, volume, margin, tax, capital expenditure, and working capital.
- A company-wide discount rate can accept risky projects and reject safer ones if project risk differs.
- Financing costs can be double-counted by subtracting interest from enterprise cash flow and also using WACC.
- Terminal value can dominate long-lived projects and conceal weak near-term economics.
- Mutually exclusive projects should be compared by value created, not only IRR or percentage return.
- Static NPV can omit managerial options to delay, expand, contract, or abandon.
- Model governance matters: assumption changes, versions, owners, and actual-versus-plan results should remain traceable.

Use sensitivity, scenario, and break-even analysis. A result that reverses under a small plausible input change has little margin of safety.

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## Common misconceptions

- “Positive NPV guarantees success.” It means positive value only under the stated assumptions.
- “Accounting profit is cash flow.” Depreciation, capital spending, taxes, and working capital make them different.
- “Owned resources are free.” Forgone rent or sale proceeds are opportunity costs.
- “One WACC fits every project.” The rate should reflect project risk and cash-flow type.
- “The highest IRR creates the most value.” Scale and timing can make a lower-IRR project produce more NPV.
- “NPV is a stock-price target.” Project appraisal and equity valuation are related but not interchangeable.

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## Related topics

- [Discounted Cash Flow](/stocks/discounted-cash-flow/)
- [Internal Rate of Return](/stocks/internal-rate-of-return/)
- [Discount Rate](/stocks/discount-rate/)

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## Authoritative sources

- SEC, financial-statement and cash-flow reading guidance.
- Federal Reserve, H.15 interest-rate reference data.
- NYU Stern, Investment Valuation materials.
- Modigliani and Miller, capital-cost and investment theory.