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Formula & Calculator

Net Present Value

The present value of future cash flows minus the initial investment.

Written by the Vorzep Team

Economics & FinanceCorporate FinanceValuation

Net Present Value Calculator NPV = Σ Cₜ/(1+r)ᵗ − C₀

NPV = Σ Ct / (1+r)t − C0
NPV = net present value  ·  Ct = cash flow at time t  ·  r = discount rate  ·  C0 = initial investment
⟹ Solve ⟷ NPV, C0, r, Ct
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Cash Flows (C₁ .. C₅)
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Please fix the errors above.
Solve for:
Presets:
Net Present Value (NPV) —
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NPV: — C₀: — r: — Σ PV of CFs: —
✓ Copied!
NPV Magnitude —
Negative Near Zero Positive
NPV = Σ Cₜ/(1+r)ᵗ − C₀  ·  Positive NPV indicates a profitable investment.
NPV = Σ Cₜ/(1+r)ᵗ − C₀
Net Present Value

Variables

SymbolQuantityUnit
NPVNet present value
CₜCash flow at time t
rDiscount rate
C₀Initial investment

What it means

Net Present Value (NPV) is a capital budgeting tool that calculates the present value of a project’s expected future cash flows, discounted at the project’s cost of capital (r), minus the initial investment (C₀). A positive NPV means the project is expected to generate more value than its cost, adding to shareholder wealth. NPV is widely used in corporate finance to rank investment projects, in real estate for property valuation, and in public sector for cost‑benefit analysis. It accounts for the time value of money and is considered the most reliable investment criterion. Understanding NPV is essential for financial managers to make informed capital allocation decisions and to maximize firm value.

Worked example

Net Present Value – Two Detailed Examples

Real‑World
Scenario: A manufacturing firm is considering a new machine that costs $10,000 today. The machine is expected to generate a single cash inflow of $13,000 after 3 years. The company's required rate of return is 8%. The CFO wants to know whether this project will add value to the firm, so they compute the NPV to make an informed capital budgeting decision.
ParameterValue
C₀10000
Cₜ13000
r0.08
t3
1PV = 13000 / (1.08)^3 = 13000 / 1.2597 = 10,319.2
2NPV = 10,319.2 − 10,000 = $319.2
Result $319.20 ✓ Positive NPV → accept the project
Scenario: A real estate developer is evaluating a land investment that requires $8,000 upfront. The property is expected to be sold for $12,000 after 6 years. The developer uses a discount rate of 7% to account for the risk. They compute the NPV to determine if the project will meet their minimum profitability threshold and whether they should proceed with the purchase.
ParameterValue
C₀8000
Cₜ12000
r0.07
t6
1PV = 12000 / (1.07)^6 = 12000 / 1.5007 = 7,996.3
2NPV = 7,996.3 − 8000 = -$3.7
Result -$3.70 ✓ Slightly negative NPV → reject or reevaluate
Insight: A positive NPV indicates that the project is expected to generate value above the cost of capital. Negative NPV suggests the project may destroy value.

Common mistakes

  • Discount rate r: The required rate of return – in decimal form.
  • Time period t: The number of periods (years) – ensure consistency with rate.
  • Initial investment C₀: Usually a negative cash flow (outflow) – do not omit it.
  • Cash flows Cₜ: May be positive or negative – ensure correct signs.
  • Interpretation: NPV > 0 means the project is worth investing in – compare to zero.

Applications

Net Present Value (NPV) is the sum of the present values of all future cash flows (positive and negative) minus the initial investment, discounted at a required rate of return. It is the most widely used criterion for investment appraisal in corporate finance. A positive NPV indicates that the investment is expected to add value to the firm. Engineers and project managers use NPV to evaluate capital projects, to choose among alternatives, and to justify budgets. In infrastructure and energy projects, NPV helps compare long‑term costs and benefits, including environmental and social factors. By applying NPV, decision‑makers can ensure that resources are allocated to the most profitable ventures, aligning with shareholder wealth maximisation. Understanding NPV is crucial for financial planning and investment analysis.

  • Capital budgeting for plant expansion, equipment purchase, and R&D
  • Project selection in engineering and construction
  • Energy project feasibility (solar, wind, oil & gas)
  • Mergers and acquisitions valuation
  • Government infrastructure project assessment