NPV / IRR Calculator
Enter a series of cash flows to compute Net Present Value and Internal Rate of Return.
NPV (Net Present Value) discounts each future cash flow to today's dollars using a chosen rate, then sums them and subtracts the initial outlay. For cash flows CFt at period t and periodic discount rate r: NPV = Σ CFt / (1 + r)t. A positive NPV means the project earns more than the discount rate; a negative NPV means it earns less. IRR (Internal Rate of Return) is the rate r at which NPV = 0 — the project's break-even return. Example: invest 10,000 today (−10,000 at t = 0) and receive 3,000, 4,000, 5,000 over the next three years. At a 10% discount rate NPV = −210.37 and IRR = 8.90% — IRR is below 10%, so the project does not clear the hurdle. This calculator accepts any cash-flow signs, solves IRR by bisection, and shows a per-period schedule. You can also estimate IRR by linear interpolation between two trial rates.
| Period | Cash Flow | Discount Factor | Discounted Value | Cumulative CF |
|---|
Formulas:
NPV = Σ CFt / (1 + r)t— sum across all periods t.IRR: the rate r at which NPV equals zero. Computed by bisection.- Decision rule: accept the project if
NPV > 0orIRR > discount rate.
How NPV and IRR work
What NPV measures
Net Present Value is the value today of a series of future cash flows, minus the cost of the investment. If NPV is positive, the project earns more than the discount rate (i.e. it creates value). If NPV is negative, it earns less than the discount rate and should be rejected.
What IRR measures
The Internal Rate of Return is the discount rate that makes NPV exactly zero. It is the project's break-even return. Compare it to your hurdle rate (cost of capital or minimum acceptable return). IRR > hurdle rate ⇒ accept.
Sign convention
By convention, outflows are negative and inflows are positive. The initial investment is usually at t = 0 and is negative. Returns come at later periods and are positive. The calculator's default rows follow this convention; you can edit any value.
When IRR is unreliable
For non-conventional cash flows (e.g. alternating positive and negative, as in some leveraged projects), IRR can have multiple solutions or none at all. In those cases, fall back to NPV. This calculator uses bisection and reports a single rate between −99.99% and 1000%; it will show "—" if no valid IRR exists in that range.
NPV vs IRR at a glance
| NPV | IRR | |
|---|---|---|
| What it measures | Value created today, in currency | Annualized break-even return, in % |
| Decision rule | Accept if NPV > 0 |
Accept if IRR > hurdle rate |
| Formula | NPV = Σ CFt / (1 + r)t |
Solve NPV = 0 for r |
| Reinvestment assumption | Flows reinvested at the discount rate | Flows reinvested at the IRR itself |
| When they disagree | Preferred — measures absolute value created | Can mislead when projects differ in scale or timing |
How to find IRR from NPV
IRR (Internal Rate of Return) is the discount rate at which NPV equals zero — the project's break-even return. It cannot be isolated algebraically: setting NPV = 0 over multiple periods yields a polynomial in r with no general closed-form solution, so IRR is always found numerically — by trial and error, bisection, or a solver.
IRR and NPV are two readings of the same formula, NPV = Σ CFt / (1 + r)t. To calculate IRR from NPV, solve for the rate r that makes NPV exactly zero — that rate is the IRR:
- By trial and error. Pick a rate, compute NPV, adjust. In the default example (−10,000, then 3,000 / 4,000 / 5,000), a 10% rate gives NPV = −$210.37 — negative, so the IRR lies below 10%. Lower the rate and NPV rises; at 8.90% it crosses zero. That crossing point is the IRR.
- By bisection. Bracket the rate between one value where NPV is positive and another where it is negative, then halve the interval until it closes in on the zero. This is what the calculator does under the hood.
- By linear interpolation. Pick two trial discount rates r₁ and r₂ where NPV crosses from positive to negative, and connect them with a straight line to estimate the break-even return.
Linear Interpolation: Hand Calculation vs True IRR
Formula: IRR ≈ r₁ + [NPV₁ / (NPV₁ − NPV₂)] × (r₂ − r₁)
Step 2: NPV@12% = -$573.75 (NPV₂ < 0)
Step 3: Substitute into formula:
IRR ≈ 8% + [176.29 / (176.29 − (-573.75))] × (12% − 8%)
IRR ≈ 8% + [176.29 / 750.04] × 4% = 8% + 0.94% = 8.94%
Note: Linear interpolation overestimates the true IRR by about 0.04 pp due to the downward convexity of the NPV curve.
NPV Profile Curve
The NPV Profile graphs Net Present Value across discount rates from 0% to 30%. The curve intersects the zero line at the exact IRR (8.90%).
NPV and IRR on a TI-84 calculator
The TI-83 / TI-84 graphing calculator has both functions built into its Finance app, using the same NPV and IRR formula as this page:
- Key sequence:
APPS → 1:Finance… → 7:npv(or8:irr((APPS → Finance → npv / irr). - NPV:
npv(rate, CF0, CFList)— the rate is a percent:npv(10, -10000, {3000, 4000, 5000})returns −210.37. - IRR:
irr(CF0, CFList)— no rate argument:irr(-10000, {3000, 4000, 5000})returns 8.90 (percent, 8.90%). - Excel:
=NPV(10%, B2:B4) + B1returns −210.37 — Excel's NPV starts discounting at period 1, so add CF0 (B1) separately;=IRR(B1:B4)returns 8.90%. For irregular dates, useXNPV/XIRR.
Type the braces and commas exactly as shown: CF0 is the period-zero flow and CFList holds everything after it. The numbers are this page's worked example, so you can cross-check your handheld against this web calculator in seconds.
Worked examples
Example 1: A simple project
Invest $10,000 today (t = 0: −10,000) and receive $3,000 / $4,000 / $5,000 over the next three years. With a 10% discount rate, the default rows show NPV = −$210.37 and IRR = 8.90%. Since IRR < 10%, the project does not clear the hurdle.
Example 2: Adding periods
Click "+ Add period" to insert another row. The new row defaults to t = max(existing) + 1 and amount = 0. Edit it. The schedule, totals, and IRR all recompute on the fly.
Example 3: Removing a row
Click the × on any row to remove it. The schedule and IRR update. Note: if you remove all positive or all negative cash flows, IRR becomes undefined (there is no rate that returns zero) and the result shows "—".
Related tools
NPV and IRR are the right tools whenever you have a stream of cash flows at different points in time and need to decide whether the stream is worth more or less than a single upfront amount. Three situations where this calculator earns its keep:
- Capital budgeting. A factory costs $500,000 today and produces $120,000/year for six years. Discount rate 8%. Plug in and read NPV directly: if NPV is positive, the project clears the hurdle.
- Comparing investments with different timelines. NPV flattens everything to a single present-day number, so projects of different lengths become comparable.
- Real-estate rental analysis. Down payment as t=0 outflow, monthly rent as inflows, sale price as a final inflow. See whether the numbers work.
For a single future lump sum (no stream), use the Present Value Calculator. For a fixed monthly payment with no flexibility, use the Loan Calculator. For a steady savings rate, use the Compound Interest Calculator.
Frequently asked questions
Why does IRR show "—"?
Either there are no positive cash flows to discount against the negatives (or vice versa), or the rate that zeros out the NPV lies outside the search range (−99.99% to 1000%). Try adjusting the cash flows or check that your signs are right (outflows negative, inflows positive).
Should I trust NPV or IRR more?
For most project decisions they give the same answer, and NPV is generally preferred in finance because it directly measures the dollar value created. Use IRR when comparing to a hurdle rate or when communicating to non-finance stakeholders ("we earn 18% on this").
What discount rate should I use?
The cost of capital for a project of similar risk. For a corporate project, the weighted average cost of capital (WACC). For a personal investment, the return you could earn on a comparable-risk alternative. The same rate is used to compare projects of the same risk class.
How do I find IRR from NPV?
IRR is the discount rate at which NPV equals zero. There is no closed-form solution, so solve numerically: try rates until NPV crosses zero, or use bisection. This calculator shows the IRR automatically — no rate input needed. See How to find IRR from NPV, or the TI-84 section for handheld keystrokes.
How to calculate IRR from NPV using linear interpolation?
Linear interpolation estimates the IRR by finding two discount rates r₁ and r₂ where NPV changes sign, then connecting them with a straight line: IRR ≈ r₁ + [NPV₁ / (NPV₁ − NPV₂)] × (r₂ − r₁). For example, at r₁ = 8%, NPV₁ = $176.29; at r₂ = 12%, NPV₂ = -$573.75. The formula estimates IRR ≈ 8.94%, within 0.04 pp of the true 8.90% value.
What does IRR mean?
IRR is the discount rate that makes the NPV of the cash flows exactly zero. It is the project's break-even return. Compare it to your hurdle rate: if IRR is higher, the project is worth doing.