What is my IRR (rate of return)?

How the IRR is worked out

The internal rate of return is the yearly rate r at which the net present value (NPV) of all the cash flows is 0:

NPV(r) = Σ CFₜ ÷ (1 + r)^t = 0

Each cash flow CFₜ is negative for money you put in and positive for money you get back, and t is its time in years from the start. There is no formula for r, so the calculator finds it numerically, for rates with 1 + r from 0.000001 to 1,000,000: from −99.9999% to 99,999,900% a year. A rate outside that range is not found, and the calculator says that no rate in the range fits.

To find every rate, it writes the NPV as a sum of powers of x = 1 ÷ (1 + r). By Descartes' rule of signs, which also holds for powers that are not whole numbers, there are at most as many rates as sign changes in the cash flows in time order. With one sign change there is at most one rate. With more, the range is split at the points where the NPV has a peak or a dip (found the same way, one level down); between two such points the NPV only rises or only falls, so each piece holds at most one rate. Each rate is then narrowed down to full precision. Rates close together, such as 2% and 3%, are both found.

The IRR is an effective yearly rate: money grows by (1 + r) in one year, compounded once a year.

Regular cash flows

• The initial investment is paid at time 0.
• The ending balance comes back at the end of the holding period: years + months ÷ 12.
• A recurring amount is paid every period of the chosen frequency (1, 2, 4, 12, 24, 26, or 52 times a year). "Taken out" is money back to you (positive). "Added" is more money in (negative).
• At the end of each period: payments at 1, 2, 3, … periods, up to the end of the holding period. At the start of each period: payments at 0, 1, 2, … periods, for every period that starts before the end.
• The rate per period is (1 + r)^(1/periods per year) − 1. For monthly flows, this is the monthly rate whose 12th power is the yearly rate. It is shown only when there is a recurring amount above 0.

Dated cash flows (XIRR)

Each amount has a date. Time is counted from the earliest date: t = days ÷ 365, as in spreadsheet XIRR. Payments on the same day are added together.

Money put in and money back

Payments at the same time are added together first, for regular and dated flows alike. Money put in adds the negative totals and money back the positive totals. For example, $10,000 invested with $500 taken out at the start of each of 3 years and $12,000 back makes −9,500 at time 0, so money put in is $9,500 and money back is 500 + 500 + 12,000 = $13,000. When there is no money put in or no money back after this, no rate fits.

When there is more than one IRR

If the cash flows change sign more than once, several rates can make the NPV 0. The calculator shows the rate closest to 0 and a note that lists every rate it found. The NPV at your discount rate is then the better guide. If the flows never change sign, no rate works and the calculator says so.

Net present value

NPV = Σ CFₜ ÷ (1 + d)^t at your yearly discount rate d. It is positive when d is below the IRR of a normal investment (money in first, money back later).

Worked examples by hand

The default: $10,000 in, $100 taken out every month for 2 years 6 months, $15,000 at the end. There are 30 monthly withdrawals. The monthly rate m solves −10,000 + 100 × (1 − (1 + m)^−30) ÷ m + 15,000 ÷ (1 + m)^30 = 0, which gives m = 2.1953%. The yearly IRR is 1.021953^12 − 1 = 29.77%. (The old page showed 0.54%, see the parity notes.) At a 10% discount rate, the NPV is $4,478.56.

The textbook example: −4,000 now, +2,000 in a year, +4,000 in two years. With v = 1 ÷ (1 + r): 4,000v² + 2,000v − 4,000 = 0, so v = (−2,000 + √(2,000² + 4 × 4,000 × 4,000)) ÷ 8,000 = 0.780776, and r = 1 ÷ 0.780776 − 1 = 28.08%.

Dated flows: −10,000 on January 1, 2008; +2,750 on March 1, 2008; +4,250 on October 30, 2008; +3,250 on February 15, 2009; +2,750 on April 1, 2009. The times are 0, 60, 303, 411, and 456 days ÷ 365. The rate that makes the NPV 0 is 37.34%, the same as the XIRR example from Microsoft.

$10,000 grows to $11,000 in one year. 11,000 ÷ 1.1 = 10,000, so the IRR is 10%.

$10 taken out every week for 7 months, $800 at the end, from $1,000. 7 months is 7/12 × 52 = 30.33 weeks, so 30 withdrawals fit, at 1/52, 2/52, … 30/52 of a year; the $800 comes at 7/12 of a year. The rate that makes the NPV 0 is 20.85%.

$200 taken out every half year for 2 years 6 months, $5,000 back from $5,000. The money earns 200 ÷ 5,000 = 4% each half year, so the rate per period is 4% and the yearly IRR is 1.04² − 1 = 8.16%.

$50 added at the start of every half month for a year, $7,000 back from $5,000. The first $50 is paid at time 0 with the $5,000, then 23 more at 1/24, 2/24, … 23/24 of a year. Money put in: 5,000 + 24 × 50 = $6,200. The IRR is 14.26%.

$500 taken out at the start of each of 3 years, $12,000 at the end. The flows are −9,500 at 0, +500 at years 1 and 2, and +12,000 at year 3. The IRR is 11.53%.

Understanding Internal Rate of Return (IRR)

Master the art of investment analysis with our comprehensive guide to IRR calculation and interpretation

What is Internal Rate of Return (IRR)?

Internal Rate of Return (IRR) is a financial metric used to estimate the profitability of an investment. In simple terms, you can think of it as the annualized rate of growth that an investment is expected to generate.

IRR standardizes the returns of different types of investments—whether real estate, stocks, or a new business project—into a single percentage, allowing for an apples-to-apples evaluation of where to allocate capital.

IRR and Net Present Value

Technically, the IRR is the specific discount rate that makes the Net Present Value (NPV) of all of an investment's cash flows equal to zero. This relationship is the foundation of modern investment analysis.

Time Value of Money

A dollar received today is worth more than a dollar promised in the future because today's dollar can be invested and earn a return. IRR accounts for this fundamental principle.

The IRR Formula

0 = Σ(CFₜ / (1 + IRR)ᵗ) - C₀

Where C₀ is the initial investment, CFₜ is the cash flow for period t, and IRR is the internal rate of return.

Note: This formula cannot be solved directly for IRR. It requires iterative calculation, which is why financial software like this calculator is essential for accurate results.

Why We Use XIRR (Extended IRR)

The Problem with Standard IRR

Standard IRR assumes all cash flows occur at perfectly regular intervals (e.g., exactly one year apart). This is rarely true in real-world investments.

Example: An investment made on March 15, 2023, and sold on September 30, 2028, doesn't fit the standard IRR model and will produce inaccurate results.

The XIRR Solution

XIRR pairs each cash flow amount with a specific date, allowing for precise calculation of returns over irregular time periods.

Benefit: More accurate and flexible tool for virtually all investment scenarios, from real estate to private equity. Choose "Dated (XIRR)" in the calculator to use it.

The Multiple IRR Problem

When an investment's cash flow stream changes sign more than once (e.g., an initial outflow, followed by inflows, followed by a final outflow for decommissioning costs), multiple mathematically valid IRR solutions can exist.

Our Solution

• Automatic detection of unconventional cash flow patterns
• A note under the result that lists every rate found when multiple IRRs are possible
• Recommendation to use Net Present Value (NPV) for more reliable analysis, with an NPV at your discount rate and a chart of NPV against the rate

Best Practices for IRR Analysis

1. Use Consistent Time Periods

Ensure all cash flows are measured over the same time periods for accurate comparison.

2. Consider Risk Profile

Higher IRR targets are appropriate for higher-risk investments. Adjust expectations accordingly.

3. Compare with Alternatives

Always compare IRR against other investment opportunities and market benchmarks.

Frequently Asked Questions

Get answers to common questions about IRR calculation and interpretation

1. What is a 'good' IRR?

A "good" IRR is not a single number but is highly dependent on the investment's risk profile, the industry, and prevailing market conditions. Here are some benchmarks:

Venture Capital

• High-risk, seed-stage: 30%+ target
• Less risky, later-stage: 20%+ target

Real Estate

• Stable, low-risk: 8-12%
• Value-add projects: 15-20%
• Ground-up development: 20%+

Low-Risk Investments

For investments perceived as very low-risk, an IRR in the 5% to 10% range can be considered attractive.

2. Can IRR be negative? What does it mean?

Yes, an investment's IRR can be negative. A negative IRR signifies that the project is projected to result in a net financial loss.

In simpler terms, the total sum of all cash inflows is less than the total sum of all cash outflows over the life of the investment.

Example: If you invest $1,000 in a project (a −$1,000 cash flow) and the project only returns a total of $900 in cash over its lifetime, the IRR will be negative.

Note: In rare cases, a project with a negative IRR might be accepted for strategic reasons, such as a mandatory environmental or regulatory compliance project that doesn't have a direct financial payoff.

3. What is the difference between IRR and XIRR?

The primary difference lies in how they treat the timing of cash flows:

Standard IRR

Assumes all cash flows occur at regular, evenly spaced intervals (e.g., at the end of each year).

XIRR (Extended IRR)

Allows you to assign a specific date to each cash flow. More accurate and flexible for real-world investments.

Because real-world investments rarely follow perfect schedules, XIRR provides a more precise calculation of an investment's true return.

4. What is the 'Multiple IRR Problem' and why did the calculator warn me about it?

The Multiple IRR Problem occurs when an investment's cash flow stream changes sign more than once (e.g., an initial outflow, followed by inflows, followed by a final outflow for decommissioning costs).

Why This Happens

When cash flows change from negative to positive and back to negative (or vice versa), the IRR equation can have multiple mathematically valid solutions, making the result ambiguous.

Our Solution

The calculator detects this pattern and recommends using Net Present Value (NPV) instead, which provides a clear dollar value and avoids the multiple-solution ambiguity entirely.

5. What is Modified IRR (MIRR) and how is it different?

Modified IRR (MIRR) is an alternative to IRR that attempts to solve some of IRR's flaws, particularly the unrealistic assumption that cash flows are reinvested at the IRR itself.

IRR Assumption

Assumes all positive cash flows are reinvested at the IRR rate, which is often unrealistic.

MIRR Solution

Uses a separate, more realistic reinvestment rate (often the cost of capital or market rate).

MIRR provides a more conservative and realistic estimate of an investment's return by using more reasonable assumptions about reinvestment rates.

6. What are the main advantages and disadvantages of using IRR?

Advantages

• Excellent for comparing percentage returns of different-sized projects
• Expressed as an intuitive percentage
• Considers the time value of money

Disadvantages

• Unrealistic reinvestment rate assumption
• Multiple IRR problem with unconventional cash flows
• Doesn't account for project scale

7. How does IRR compare to other investment metrics?

Here's how IRR compares to other key financial metrics: