IRR Calculator — Free Internal Rate of Return Tool

How to Use the IRR Calculator

This calculator determines the internal rate of return for investments with one or more cash flow periods. IRR is one of the most important metrics in capital budgeting and investment analysis, used by corporations, private equity firms, and individual investors to evaluate project profitability.

1. Enter the initial investment. The first cash flow represents your upfront investment and should be a negative number. For example, if you are investing $100,000 in a project, enter -100000. This negative value represents the cash leaving your pocket at the start of the project.
2. Enter expected cash flows for each period. Add the cash flows you expect to receive in each subsequent year. These are typically positive numbers representing returns, revenue, or proceeds. If a particular year has a net cash outflow (additional investment needed), enter it as a negative number.
3. Add or remove periods as needed. Click the "+ Add Cash Flow Period" button to add additional years. Use the remove button next to any row to delete it. The calculator handles any number of periods from 2 to 30 or more.
4. Review the results. The calculator displays the IRR as an annualized percentage, the total investment and total returns, the net gain or loss, and a pie chart showing the relationship between investment and returns. A positive IRR indicates a profitable investment.

The IRR is computed using the Newton-Raphson iterative method, which converges quickly for most typical investment patterns. If the cash flow pattern is unusual (such as multiple sign changes), the calculator may report that no valid IRR was found, which indicates the presence of multiple IRRs.

Understanding the IRR Formula

The internal rate of return is defined as the discount rate r that satisfies the following equation, making the net present value of all cash flows equal to zero.

The IRR Equation

Or equivalently:

Where:

• CF_t = Cash flow at time period t
• r (or IRR) = The internal rate of return we are solving for
• n = The total number of periods
• t = The time period (0, 1, 2, ... n)

Why IRR Cannot Be Solved Algebraically

Unlike simpler financial formulas, the IRR equation is a polynomial of degree n, which cannot be solved directly for n greater than 4. Instead, numerical methods like Newton-Raphson iteration are used. The algorithm starts with an initial guess and iteratively refines it until the NPV is sufficiently close to zero. This is why IRR calculators are so valuable: the computation that would take hours by hand is completed instantly.

Step-by-Step Calculation Example

Calculate the IRR for an investment of $50,000 that returns $15,000, $18,000, $20,000, and $22,000 over four years:

1. Set up the equation: 0 = -50,000 + 15,000/(1+r) + 18,000/(1+r)² + 20,000/(1+r)³ + 22,000/(1+r)⁴
2. Try r = 10%: NPV = -50,000 + 13,636 + 14,876 + 15,026 + 15,026 = $8,564 (positive, so IRR is higher than 10%)
3. Try r = 18%: NPV = -50,000 + 12,712 + 12,924 + 12,173 + 11,346 = -$845 (negative, so IRR is between 10% and 18%)
4. Iterate further: Through successive approximation, IRR converges to approximately 16.8%

This 16.8% IRR means the project generates an annualized return equivalent to investing the money at 16.8% compound interest. If the company's hurdle rate is 12%, this project exceeds the threshold and should be accepted.

The Reinvestment Rate Assumption

One critical assumption of IRR is that all interim cash flows are reinvested at the IRR itself. For a project with 20% IRR, this means assuming every dollar of interim cash flow earns 20% when reinvested. In practice, this may not be realistic, especially for very high-IRR projects. The Modified IRR (MIRR) addresses this by allowing a separate reinvestment rate assumption, typically set to the cost of capital or a market rate of return.

Practical IRR Examples

These real-world scenarios demonstrate how IRR is used across different investment types and business decisions to evaluate profitability and compare opportunities.

Capital Equipment Purchase

Marcus, a manufacturing plant manager, evaluates a $200,000 equipment upgrade that is expected to reduce operating costs by $45,000 per year for 6 years, with a $20,000 salvage value at the end. Cash flows: Year 0 = -$200,000; Years 1-5 = $45,000; Year 6 = $65,000 ($45,000 savings + $20,000 salvage). The IRR of this investment is approximately 10.4%. Since the company's weighted average cost of capital (WACC) is 9%, the project clears the hurdle rate and management approves the purchase. The positive spread of 1.4% above WACC translates to approximately $12,000 in net present value created.

Rental Property Investment

Nicole considers purchasing a rental property for $300,000 with a $60,000 down payment plus $15,000 in closing costs (total initial outlay: $75,000). After mortgage payments, taxes, and maintenance, the property generates $6,000 net annual cash flow. After 10 years, she plans to sell for $390,000, with $210,000 remaining on the mortgage, netting $180,000. Cash flows: Year 0 = -$75,000; Years 1-9 = $6,000; Year 10 = $186,000. The IRR is approximately 14.8%, significantly exceeding what Nicole could earn in a stock market index fund. However, she must consider that real estate is less liquid and requires active management.

Startup Investment

A venture capital fund invests $500,000 in a technology startup. The startup generates no returns for the first 3 years while building its product. In Year 4 it returns $100,000, Year 5 returns $200,000, and in Year 6 the fund exits via acquisition for $1,200,000. Cash flows: Year 0 = -$500,000; Years 1-3 = $0; Year 4 = $100,000; Year 5 = $200,000; Year 6 = $1,200,000. The IRR is approximately 22.5%. This exceeds the fund's target of 20% IRR, validating the investment. The example illustrates how IRR handles zero-cash-flow periods and delayed returns, which are common in venture capital.

Comparing Two Business Projects

A company must choose between Project A (requires $150,000, returns $50,000/year for 4 years) and Project B (requires $150,000, returns $20,000 in Year 1, $30,000 in Year 2, $60,000 in Year 3, and $100,000 in Year 4). Project A has an IRR of 12.6%, while Project B has an IRR of 11.8%. Based purely on IRR, Project A appears superior. However, Project B's NPV at the company's 8% cost of capital is $22,400 versus $15,700 for Project A. This illustrates why IRR and NPV should be used together: different timing patterns can lead to different rankings depending on the metric used.

IRR Tips and Complete Guide

Mastering IRR analysis enables you to evaluate complex investment opportunities with confidence and make data-driven decisions about capital allocation.

Always Compare IRR to Your Hurdle Rate

Every investor and company has a hurdle rate, which is the minimum acceptable rate of return that justifies the risk of an investment. For corporations, this is typically the weighted average cost of capital (WACC). For individual investors, it might be the expected return of a passive index fund. Only invest in projects where the IRR exceeds your hurdle rate, because investing in a project with an IRR below your cost of capital actually destroys value, even if the project generates positive nominal returns.

Use IRR Alongside NPV for Better Decisions

IRR and NPV can disagree when comparing mutually exclusive projects, especially when they differ in size or timing. A small project with 30% IRR might create less total value than a large project with 15% IRR. When they conflict, NPV is generally the better decision criterion because it measures absolute value creation. However, IRR remains valuable for communicating returns to stakeholders, setting performance benchmarks, and evaluating capital efficiency.

Be Conservative with Cash Flow Projections

The quality of your IRR analysis depends entirely on the accuracy of your cash flow estimates. Build three scenarios: base case (most likely), optimistic case, and pessimistic case. Calculate the IRR for each scenario to understand the range of possible outcomes. If the pessimistic case still shows an IRR above your hurdle rate, the investment has a strong margin of safety. If the base case barely clears the hurdle rate, one small deviation could make the project unprofitable.

Account for Terminal Value in Long-Term Projects

For investments with ongoing value beyond the projection period, such as real estate or business acquisitions, include a terminal value in the final cash flow. This represents the expected sale price or ongoing value of the asset. Failing to include terminal value will significantly understate the IRR. Conversely, be careful not to overestimate terminal value, as it can dramatically inflate IRR projections for assets that may depreciate or become obsolete.

Common Mistakes to Avoid

• Forgetting to include the initial investment as negative. The first cash flow must be negative to represent the money going out. If you enter all positive numbers, the IRR calculation will not produce a meaningful result because there is no investment to generate a return on.
• Ignoring the reinvestment assumption. Traditional IRR assumes interim cash flows are reinvested at the IRR rate, which is unrealistic for high-IRR projects. A 40% IRR assumes you can reinvest every dollar at 40%, which is rarely possible. Consider using Modified IRR (MIRR) for more conservative estimates.
• Using IRR to compare projects of different scales. A $10,000 investment with 25% IRR creates $2,500 in profit, while a $500,000 investment with 12% IRR creates $60,000. IRR alone makes the small project look better, but the large project creates 24 times more value. Always consider absolute dollar returns alongside percentage returns.
• Not running sensitivity analysis. A single IRR number gives a false sense of precision. Cash flow estimates are inherently uncertain, and small changes in assumptions can significantly impact IRR. Test how the IRR changes when key assumptions vary by 10-20% to understand the robustness of the investment.
• Ignoring the time horizon. Two projects with identical IRR but different durations may tie up capital for very different periods. A 15% IRR over 2 years allows you to reinvest sooner than 15% over 10 years. Consider the opportunity cost of having capital locked in a longer-term project.