How to Calculate Internal Rate of Return (IRR)

Internal rate of return (IRR) reveals the discount rate that forces the net present value (NPV) of a project’s cash flows to zero. It is the annualised yield embedded in the timing and magnitude of the cash flows themselves. When you compare that yield to your hurdle rate or cost of capital, you decide whether the project creates value.

This walkthrough shows how to calculate IRR manually, validates the result with a full worked example, and demonstrates spreadsheet and calculator shortcuts so you can apply the concept in board decks or personal investment reviews.

Core formula and interpretation

IRR solves the discount rate r that sets the sum of discounted cash flows equal to the initial investment:

0 = Σt=0n CFt / (1 + r)t

  • CF0 is typically negative (an upfront cost). Later CF values are inflows or outflows as the project unfolds.
  • r is the IRR—the implicit annualised return baked into the timing and size of every cash flow.
  • If IRR exceeds your required return, the project adds value. If it falls short, the investment destroys value relative to the benchmark.

Because the equation is nonlinear, you usually iterate toward the solution rather than isolate r algebraically. That is where financial calculators, spreadsheets, or iterative search comes in.

Manual calculation workflow

Without software, solve for IRR by bracketing the discount rate that drives NPV to zero. Follow these steps:

  1. List every cash flow chronologically with its sign. Include upfront costs, maintenance outlays, tax effects, and terminal value.
  2. Choose a starting discount rate close to your hurdle rate or a reasonable guess (for example 8%). Compute the NPV at that rate.
  3. Adjust the rate upward or downward depending on the NPV sign. A positive NPV means the rate is too low; a negative NPV means it is too high.
  4. Repeat the process until the NPV is effectively zero. Interpolate between the last two rates to home in on the exact percentage.
  5. Document the result alongside the comparison rate (cost of capital, required return, or inflation-adjusted target).

Linear interpolation between two discount rates r1 and r2 with NPVs of opposite sign gives a quick estimate:

IRR ≈ r1 + [NPVr1 / (NPVr1 − NPVr2)] × (r2 − r1)

Use the interpolation as a cross-check even if you rely on a calculator. It catches data-entry errors and confirms the intuition behind the computed IRR.

Worked example

Imagine a project that requires an initial investment of $120,000 and delivers cash flows of $45,000, $55,000, $40,000, and $30,000 over the next four years. Follow the workflow above:

  1. Compute NPV at 10%: NPV10% = −120,000 + 45,000/1.10 + 55,000/1.10² + 40,000/1.10³ + 30,000/1.10⁴ = $7,311 (positive).
  2. Compute NPV at 12%: NPV12% = −120,000 + 45,000/1.12 + 55,000/1.12² + 40,000/1.12³ + 30,000/1.12⁴ = −$2,487 (negative).
  3. Interpolate between 10% and 12% using the formula above. The estimate lands at roughly 11.2%.
  4. Verify by plugging 11.2% into the NPV equation or by using a spreadsheet IRR function. The rounded result should be 11.19%.

Because 11.2% exceeds an 8% cost of capital, the project creates value. If your hurdle rate were 12%, the same analysis would flag the investment as insufficient.

Spreadsheet and calculator shortcuts

Modern tools remove the manual iteration but still benefit from clean cash-flow inputs and sanity checks:

  • Excel or Google Sheets: Use =IRR(range) for evenly spaced periods or =XIRR(cashflows, dates) when timing is irregular. Provide a reasonable guess (for example 0.1) if the function struggles to converge.
  • Financial calculators: Store each cash flow in the cash-flow register, enter the frequency of repeats where applicable, and press the IRR key to compute the yield automatically.
  • CalcSimpler tools: Pair this article with the Net Present Value calculators below to confirm the discount-rate logic before pitching stakeholders.

No matter the tool, cross-verify the output by ensuring the NPV at the reported IRR is effectively zero—small rounding residuals are normal.

Interpreting IRR in decision frameworks

  • Compare to hurdle rates: Accept projects with IRR above the minimum attractive rate of return (MARR) or weighted average cost of capital (WACC). Document the spread to demonstrate value creation.
  • Rank competing projects: When capital is scarce, rank opportunities by IRR only after confirming they are comparable in scale and duration. Combine the metric with NPV to see total value added.
  • Blend with payback or MIRR: Use payback for liquidity insight and modified IRR (MIRR) when reinvestment assumptions need to reflect reality. IRR alone may overstate returns if intermediate cash flows cannot be reinvested at the same rate.
  • Communicate assumptions: Share the cash-flow schedule, discount rates tested, and any adjustments (inflation, taxes, working capital) so stakeholders can replicate the analysis.

Troubleshooting and edge cases

  • Multiple sign changes: Non-conventional cash flows (negative to positive and back to negative) can generate multiple IRRs. Verify with an NPV curve or switch to MIRR to avoid ambiguous results.
  • No IRR exists: If the NPV never crosses zero, the project may always destroy or always create value. In those cases, rely on NPV and profitability index instead of forcing an IRR.
  • Uneven timing: Annual IRR assumes equal spacing between cash flows. Use XIRR or discount exact dates when months or quarters vary.
  • Rounding drift: Very large or very small projects can produce rounding errors. Normalise cash flows in thousands or millions and confirm the IRR with at least two tools.

Document any adjustments you make—such as grouping monthly cash flows into annual totals—so future reviews understand how the IRR was produced.

Related resources on CalcSimpler

Expand your analysis with these companion guides and category overviews.

  • Finance & Business Calculators

    Browse calculators that benchmark profitability, ROI, and growth so you can compare IRR insights against other metrics.

    Read more

  • Personal Finance & Loans Hub

    Track household investments, debt payoff, and savings scenarios alongside time-value-of-money concepts like IRR.

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  • Calculation Standards & Notation

    Refresh the math typography conventions that keep discounted cash-flow equations readable and auditable.

    Read more

Calculators that support IRR analysis

Launch these tools to validate discount rates, compare projects, and translate your IRR findings into actionable numbers.

  • Net Present Value Calculator

    Quickly discount equal cash flows to cross-check whether the IRR you derived aligns with a zero NPV.

    Launch

  • Annuity Net Present Value Calculator

    Model recurring inflows or savings plans and see how changing the discount rate affects IRR comparisons.

    Launch

  • Total Investment Return Rate Calculator

    Summarise simple returns before layering on time-value-of-money calculations like IRR or MIRR.

    Launch