NPV and IRR calculator for investment and capital-project feasibility analysis. Includes payback period and project comparison.
Four tabs: NPV (dynamic cash flows + go/no-go decision), IRR (Newton-Raphson method), payback period (simple and discounted), and side-by-side comparison of two projects.
Disclaimer: Estimates only. Investment decisions should also weigh risk and market conditions.
Calculator information
📋 How to use this calculator
- Select the type of analysis: NPV (Net Present Value), IRR (Internal Rate of Return), payback period, or a comparison of two projects.
- Enter the initial investment (year 0) as a negative or positive number per your convention, in US dollars.
- Add cash flows for each year of the project; values can differ year over year.
- Enter the discount rate matching the firm's cost of capital, typically 8-12% for US corporate projects.
- Click compute to view NPV (acceptable if >0), IRR (acceptable if > discount rate), and payback period (faster is better).
- Tip: compare IRR with the firm's WACC (Weighted Average Cost of Capital) or an industry benchmark return. For mutually exclusive projects, choose the highest NPV (not the highest IRR).
🧮 NPV, IRR, and Payback Period
NPV = sum(CF_t / (1+r)^t) - Initial_investment | IRR: the value of r that makes NPV = 0, solved iteratively (Newton-Raphson) | Simple_payback = year_when_cumulative_CF_equals_investment | Discounted_payback = year when cumulative NPV = 0 | PI (Profitability Index) = PV_Cash_Inflows / Investment
- CF_t = Cash Flow at year t
- r = discount rate (cost of capital, decimal percent)
- t = year period (0, 1, 2, ..., n)
- Initial_investment = capital outlay at year 0
- IRR = internal rate of return that makes NPV = 0
- PI > 1 means the project is acceptable (equivalent to NPV > 0)
Investment decision: NPV > 0 and IRR > cost of capital means the project is acceptable. For mutually exclusive projects, use NPV because IRR can mislead when projects differ in scale. IRR can also have multiple solutions when cash flows change sign more than once.
💡 Worked example: $100,000 investment, 5-year returns, 12% discount rate
Given:- Initial investment: $100,000 (year 0)
- Cash flows years 1-5: 25, 30, 35, 40, 30 (in thousands of dollars)
- Discount rate: 12%
Steps:- Compute PV of each cash flow: PV1 = 25/(1.12)^1 = 22.32, PV2 = 30/(1.12)^2 = 23.92, PV3 = 35/(1.12)^3 = 24.91, PV4 = 40/(1.12)^4 = 25.42, PV5 = 30/(1.12)^5 = 17.02
- Total PV Cash Inflows: 22.32 + 23.92 + 24.91 + 25.42 + 17.02 = $113,590
- NPV = 113.59 - 100 = $13,590 (POSITIVE, acceptable)
- IRR: by iteration, NPV = 0 at r = 16.5% (higher than 12%, acceptable)
- Simple payback: year 1 ($25k), year 2 ($55k cumulative), year 3 ($90k), year 4 ($130k), reached at year 3.25
- Profitability Index: 113.59 / 100 = 1.136 (>1, acceptable)
Result: NPV $13,590 (acceptable), IRR 16.5% (>12% acceptable), payback 3.25 years, PI 1.136. The project is recommended for approval.
❓ Frequently asked questions
What is the difference between NPV and IRR?
NPV (Net Present Value) computes the present value of all future cash flows minus the initial investment, expressed in dollars. IRR (Internal Rate of Return) is the discount rate that makes NPV = 0, expressed as a percentage. NPV shows the absolute dollar value created; IRR shows the effective return. For comparing projects of different scales, NPV is more reliable because IRR can mislead: a small project may show a high IRR but a small NPV.
What is the right discount rate for investment analysis?
The discount rate should reflect the cost of capital and project risk. For a corporation, use WACC (Weighted Average Cost of Capital), which blends debt and equity costs. Common US benchmarks: 7-9% for low-risk projects, 10-12% for medium risk, 15-20%+ for high risk (startups, R&D). Risk-free rate + risk premium of 5-10% is a practical approach. The risk-free rate typically uses the 10-year Treasury yield.
What is payback period and what are its weaknesses?
Payback period is the time required to recover the initial investment from project cash flows. Simple payback uses nominal cash flows, while discounted payback accounts for the time value of money. Weaknesses: it ignores cash flows after payback (projects with large late-year cash flows look less attractive), it does not measure total profitability, and there is no objective standard threshold. Best used alongside NPV/IRR.
When is NPV positive but IRR has no solution?
IRR can be undefined or have multiple values when cash flows change sign more than once (non-conventional cash flows), for example a mining project with initial investment, positive cash flows, then end-of-life remediation costs. In such cases, use MIRR (Modified IRR) or rely on NPV as the primary decision. Some projects also show unrealistic IRRs (>100%) with small NPVs because of small scale.
How do I calculate IRR by hand?
IRR is solved iteratively because there is no closed-form formula. Trial and error: guess r (say 10%), compute NPV; if positive try a higher r (15%); if negative try a lower r; then linearly interpolate between two r values that produce positive and negative NPVs. Interpolation formula: IRR = r1 + (NPV1 / (NPV1 - NPV2)) x (r2 - r1). Calculators use Newton-Raphson, which converges faster. In Excel, use IRR() or XIRR() for irregular cash flow dates.
📚 Sources & references
Last updated: May 11, 2026