Internal Rate of Return (IRR) Calculator
IRR based on fixed cash flow
This calculator computes the IRR based on a fixed recurring cash flow or no cash flow.
IRR based on irregular cash flow
This calculator computes the IRR based on the initial investment and subsequent annual cash flows. If you want to calculate the IRR for cash flows that are not annual, please use our Average Return Calculator.
In investments and finance, decision-makers and analysts often face the challenge of comparing multiple project proposals or investment opportunities. Each project typically comes with a forecasted series of future cash flows, an upfront cost (or costs), and a certain degree of risk. To accurately judge the potential profitability of these endeavors, financial analysts employ various metrics. One popular and powerful metric for project evaluation is the Internal Rate of Return (IRR). Understanding IRR can be immensely helpful for anyone involved in capital budgeting, corporate finance, personal investing, or any scenario that requires evaluating the viability of cash-flow-generating projects.
What is the internal rate of return?
At its core, the internal rate of return is a discount rate at which the net present value (NPV) of a project's cash flows equals zero. When investors or businesses undertake a project, they typically pay an initial cost (the investment) and may make additional investments as well as receive a series of returns (cash inflows) over time. Because money today is worth more than the same amount of money in the future, future cash flows need to be adjusted (or "discounted") back to their present value. The internal rate of return is the specific discount rate that makes the project's net present value exactly zero.
In other words, IRR is the "break-even" rate of return for an investment when considering the time value of money. If the IRR of a project is higher than the company's required rate of return or the cost of capital, the project is generally considered worthwhile because it implies that the project will generate a return higher than its cost. Conversely, if the IRR is below the required rate of return, the project may not be viable, as it may not generate sufficient returns to justify the investment.
How is IRR calculated?
The formula for the internal rate of return is essentially the same as the net present value formula except that instead of calculating NPV for a given discount rate, we solve for the discount rate that sets NPV to zero. The net present value (NPV) equation for a series of cash flows can be written as,
where:
- CFt is the cash flow over period t. (Note that CF0 is typically negative if it represents the initial investment).
- r is the discount rate, or in this context, the IRR.
- t is the time period (from 0 to n).
To find the IRR, we adjust r until the sum of the present values of all cash inflows and outflows equals zero. In practice, this cannot be solved by simple algebraic manipulation for most real-world projects. Instead, analysts typically use financial calculators (such as the one provided above), spreadsheet software, or specialized financial tools that iteratively find the rate at which NPV equals zero.
What is the use of IRR?
Ultimately, IRR helps translate complicated patterns of cash inflows and outflows into a single number that can be compared directly to alternatives or required benchmarks. Whether you are deciding whether to purchase new equipment, evaluating real estate deals, or considering a long-term business expansion, IRR can help bring clarity and structure to the evaluation process, enabling you to make more data-driven decisions. The following are some of the specific applications of IRR in finance and business.
1. Investment decision making
Businesses and investors use IRR to evaluate different investment opportunities. If an investment's IRR exceeds the company's required rate of return (hurdle rate), it is considered a good opportunity.
2. Capital budgeting
Companies use IRR to compare different projects and determine which ones will generate the highest returns. Projects with higher IRRs are often prioritized.
3. Loan and lease analysis
Lenders and financial analysts use IRR to assess the cost of financing options and lease agreements to ensure profitability.
4. Private equity and venture capital
IRR is commonly used in venture capital and private equity to measure return on investment over time. Higher IRR indicates better-performing investments.
5. Real estate investment analysis
Real estate investors use IRR to assess the profitability of properties by factoring in purchase price, rental income, maintenance costs, and potential sale price.
Example 1: A simple investment project
Let's say a small manufacturing firm is evaluating the purchase of a machine that costs $40,000 upfront. The machine is expected to generate the following cash inflows:
- End of Year 1: $10,000
- End of Year 2: $20,000
- End of Year 3: $30,000
To find the IRR using the "IRR based on irregular cash flow" calculator above enter $40,000 as the initial investment and $10,000, $20,000, and $30,000 in the year 1, 2, 3 fields, respectively, then click the "Calculate" button. The calculator should return an IRR of 19.438%. This indicates that the machine's purchase and the subsequent cash inflows yield an annualized return of 19.438% once we factor in the time value of money.
Now, if the firm's cost of capital is 12%, then a 19.438% IRR is comfortably above the hurdle rate, which suggests that the project is financially appealing. Conversely, if the firm's cost of capital were 20%, then the 19.438% IRR does not meet the required rate of return.
Example 2: Multiple projects
Imagine you have two potential real estate investments. Both require an initial outlay of $100,000. Over a five-year period, each will generate different cash inflows:
Investment A:
- End of Year 1: $5,000
- End of Year 2: $20,000
- End of Year 3: $25,000
- End of Year 4: $40,000
- End of Year 5: $60,000
Investment B:
- End of Year 1: $0
- End of Year 2: $10,000
- End of Year 3: $30,000
- End of Year 4: $30,000
- End of Year 5: $80,000
If you were to just sum the total cash flows, you might notice that each investment pays out a total of $150,000. Considering only simple ROI yields:
| ROI = | Total Cash Inflow - Initial OutlayInitial Outlay |
| = | $150,000 - $100,000$100,000 = 50% |
Thus, both investments have a 50% ROI, but they do not pay out evenly over the years. This difference in timing is crucial. When you factor in the time value of money using IRR, the one that pays earlier might actually have a higher IRR because receiving cash sooner allows for reinvestment or reduces the duration of investment risk. Plugging these individual yearly inflows into the "IRR based on irregular cash flow" calculator yields:
- IRR of Investment A: 11.290%
- IRR of Investment B: 10.259%
Despite both generating the same total returns over five years, Investment A appears more attractive on an annualized basis (11.290% vs. 10.259%). This is a classic example of why IRR provides more nuanced insight than basic ROI in many capital budgeting scenarios.
Limitations of IRR
While IRR is a powerful financial metric for evaluating investments and making business decisions, it isn't without its drawbacks:
- Scale of projects: IRR does not account for the overall scale of the project. A project with a smaller investment and a high IRR might generate a smaller total profit than a larger project with a slightly lower IRR.
- Risk of projects: IRR does not explicitly factor in the risk or uncertainty of the cash flows being analyzed. Instead, IRR focuses purely on the timing and magnitude of projected cash flows and assumes they will occur as forecasted. Often, a project with a lower IRR but relatively low uncertainty may be preferred over a project with a higher IRR with significant risk.
- Assumption of reinvestment rate: The IRR calculation implicitly assumes that interim cash flows are reinvested at the IRR itself. This assumption may not always be realistic.
- Multiple IRRs: In some cases (especially projects that have alternating signs of cash flows—e.g., negative, then positive, then negative again), the mathematical formula can yield more than one IRR. This can be confusing and reduces the straightforward interpretability of IRR in certain real-world situations.
That being said, IRR is not a one-size-fits-all metric. Other metrics like NPV, modified internal rate of return (MIRR), or payback period can provide supplemental perspectives. In practice, decision-makers and financial analysts typically look at multiple measures, including IRR, to arrive at the most informed decision.