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Financial Math

IRR Calculator | Internal Rate of Return, MIRR & Payback Period

Calculate the Internal Rate of Return (IRR) and Modified IRR (MIRR) for a series of up to 20 cash flows using the Newton-Raphson iterative method. Also computes net present value at any discount rate, discounted payback period, and profitability index.

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Cash Flows

Year 0
Year 1
Year 2
Year 3
Year 4
Year 5

What Is the IRR Calculator | Internal Rate of Return, MIRR & Payback Period?

The Internal Rate of Return (IRR) is the annualized effective return rate at which an investment breaks even in terms of net present value. It is the single most widely used metric in capital budgeting for evaluating project attractiveness.

  • IRR vs Hurdle Rate: if IRR exceeds your required rate of return (hurdle rate), the project is worth pursuing.
  • MIRR: the Modified IRR corrects for IRR's assumption that intermediate positive cash flows are reinvested at the IRR itself — often unrealistically high.
  • NPV: the dollar value created by the project at your chosen discount rate. Positive NPV means the investment creates value.
  • Payback Period: simple payback ignores the time value of money; discounted payback accounts for it.
  • Profitability Index (PI): useful for ranking projects when capital is constrained. PI > 1 indicates value creation.

Formula

IRR is the discount rate that makes NPV = 0. It is solved numerically using Newton-Raphson iteration.

1Net Present Value

NPV(r) = Σ CFₜ / (1+r)ᵗ

Sum of all cash flows discounted at rate r.

2IRR Definition

NPV(IRR) = 0

Newton-Raphson: rₙ₊₁ = rₙ − NPV(rₙ)/NPV'(rₙ)

3MIRR

MIRR = (FV⁺/|PV⁻|)^(1/n) − 1

FV of positive CFs at reinvestment rate; PV of negative CFs at finance rate.

4Profitability Index

PI = (NPV + |CF₀|) / |CF₀|

PI > 1 means the project creates value.

Variables: CFₜ = cash flow at time t · r = discount rate · n = number of periods · FV⁺ = future value of positive cash flows · PV⁻ = present value of negative cash flows

How to Use

  1. 1

    Enter the Year 0 initial investment as a negative number (e.g. -100000).

  2. 2

    Add each year's expected net cash flow in the rows for Year 1 and beyond. Use the Add Year button to extend the project up to 20 years.

  3. 3

    Enter the discount rate (required rate of return or cost of capital) as a percentage.

  4. 4

    Optionally set separate reinvestment and finance rates for the MIRR calculation.

  5. 5

    Click Calculate IRR / MIRR to compute IRR, MIRR, NPV, profitability index, and both payback periods.

  6. 6

    Review the cash flow table for cumulative and discounted cash flow progression across all years.

  1. 1

    Enter Year 0 cash flow (initial investment)

    Enter the upfront cost as a negative number, e.g. −100000 for a $100,000 investment.

  2. 2

    Add annual cash flows

    Enter each year's expected net cash flow. Add rows for up to 20 years. Use the preset for a quick 5-year example.

  3. 3

    Set the discount rate

    Enter your required rate of return or cost of capital as a percentage. This is used to compute NPV and discounted payback.

  4. 4

    Set reinvestment and finance rates for MIRR

    These default to the discount rate. Change them to reflect realistic reinvestment opportunities and your financing cost.

  5. 5

    Review IRR, MIRR, NPV, and payback

    The cash flow table shows cumulative and discounted cash flows, making it easy to see when the project recovers its investment.

Example Calculation

Example | 5-Year Capital Investment Project

A company invests $100,000 today and expects net cash flows of $30,000, $35,000, $40,000, $30,000, and $20,000 over five years. The discount rate is 10%.

Year 0 (Initial Investment)−$100,000
Year 1$30,000
Year 2$35,000
Year 3$40,000
Year 4$30,000
Year 5$20,000
IRR≈ 18.4%
MIRR (reinvest @ 10%)≈ 14.8%
NPV @ 10%≈ $20,750
Profitability Index≈ 1.21
Simple Payback≈ 2.9 years
Discounted Payback≈ 3.8 years

IRR of 18.4% exceeds the 10% hurdle rate, NPV is positive, and PI > 1 — all signals that the project creates value.

Understanding IRR | Internal Rate of Return, MIRR & Payback Period

Why IRR Is the Most Used Capital Budgeting Metric

IRR is intuitive because it expresses a project's return as a percentage, making it easy to compare against a cost of capital or a competing investment. Finance teams, venture capitalists, private equity firms, and project managers all use IRR as a primary screening tool because it answers the question: "What effective annual return does this project generate?"

IRR vs NPV: Which Should You Use?

IRR and NPV usually agree on whether to accept or reject a project, but they can disagree when ranking mutually exclusive projects of different sizes. NPV measures absolute value creation in dollars; IRR measures the rate of return. For standalone project acceptance/rejection, either works. For choosing between two competing projects with the same budget, NPV is theoretically superior because it maximizes shareholder wealth in absolute terms.

  • Use IRR to screen projects quickly against a hurdle rate.
  • Use NPV to choose between mutually exclusive projects of different scales.
  • Use MIRR when the reinvestment rate assumption is critical.
  • Use PI when allocating a limited budget across multiple projects.
  • Use payback period as a simple risk proxy, shorter payback = less exposure.

Common Pitfalls in IRR Analysis

  • Ignoring the scale problem: a 30% IRR on a $1,000 investment may be less valuable than 15% on $1,000,000.
  • Treating a non-converging IRR as zero — a project may have no real IRR (no positive NPV region exists).
  • Using IRR to compare projects with different lifetimes without adjusting for the reinvestment assumption.
  • Failing to account for terminal costs (decommissioning, environmental cleanup) that create negative late-period cash flows.
  • Not sensitivity-testing key assumptions: what does IRR look like if revenues are 20% below plan?

Frequently Asked Questions

What does IRR tell you about an investment?

IRR is the annualized percentage return at which an investment breaks even in net present value terms. If IRR is greater than your cost of capital or required rate of return (hurdle rate), the project is expected to create value. If two projects compete for the same budget, the one with the higher IRR is generally preferred — though NPV should be the final arbiter when project scales differ.

Why is MIRR often preferred over IRR?

The standard IRR calculation implicitly assumes that all intermediate positive cash flows are reinvested at the IRR itself — an assumption that is often unrealistically high for large projects. MIRR replaces this with two explicit rates: a finance rate for negative cash flows (your borrowing cost) and a reinvestment rate for positive cash flows (your actual reinvestment opportunity). MIRR always produces a unique answer, unlike IRR which can yield multiple solutions when cash flows change sign more than once.

What is the multiple IRR problem?

By Descartes' rule of signs, a cash flow stream can have as many IRRs as there are sign changes (positive-to-negative or negative-to-positive transitions). A project with a large renovation cost mid-life might have two IRRs — neither of which is the "true" return. The calculator warns you when it detects multiple sign changes. In these cases, rely on NPV and MIRR instead of IRR for decision-making.

What is the profitability index and when is it useful?

The Profitability Index (PI) = (NPV + initial investment) / initial investment. PI > 1 means the project creates value; PI < 1 means it destroys value. PI is most useful for capital rationing — when you have a limited budget and must rank projects by value created per dollar invested. A project with a smaller NPV but higher PI may be preferred over a larger project when capital is scarce.

What is the difference between simple and discounted payback period?

Simple payback counts the years until cumulative undiscounted cash flows recover the initial investment. Discounted payback does the same but with cash flows discounted at your required rate of return — it asks how long until the investment is justified in present-value terms. Discounted payback is always longer than simple payback for positive discount rates. Neither payback measure accounts for cash flows after the payback date, so they should complement (not replace) NPV analysis.

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