# What is my IRR (rate of return)?

Computes the internal rate of return (IRR) of an investment as a yearly rate, from regular cash flows or from dated cash flows (XIRR), and the NPV at a discount rate.

- Page: https://www.acalculator.org/finance/irr-calculator
- JSON spec: https://www.acalculator.org/finance/irr-calculator.json
- Version: e1e21beb7f2f

## Default answer

Example with the default inputs (Cash flows Regular, Initial investment $10,000.00, Ending balance $15,000.00, Holding period: years 2, and months 6, Recurring amount $100.00, The recurring amount is Taken out, How often? Every month, Paid at the End of each period, Discount rate 10%): The internal rate of return is 29.77% a year: $10,000.00 put in and $18,000.00 back.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| cashFlowType | Cash flows | Regular: an investment, an optional recurring amount, and an ending balance. Dated: any amounts on any dates (XIRR). |
| investment | Initial investment | The amount paid in at the start. |
| endingBalance | Ending balance | What the investment is worth, or pays back, at the end of the holding period. |
| holdingYears | Holding period: years | The whole years from the start to the ending balance. |
| holdingMonths | and months | Extra months on top of the years. |
| recurringAmount | Recurring amount | An amount withdrawn from, or added to, the investment every period. |
| recurringType | The recurring amount is | Withdraw: you take the amount out (money back to you). Deposit: you add it (more money in). |
| recurringFrequency | How often? | How often the recurring amount is paid. |
| recurringTiming | Paid at the | Whether each recurring amount is paid at the start or at the end of its period. |
| flows | Dated cash flows | Each payment with its date: a negative amount for money you put in, a positive amount for money you get back. |
| discountRate | Discount rate | A yearly rate to discount the flows at, for the net present value. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| irr | Internal rate of return (per year) | The yearly rate, compounded once a year, at which the net present value of the cash flows is 0. |
| periodRate | Rate per period | The same return per recurring period: (1 + IRR)^(1 ÷ periods per year) − 1. |
| npv | Net present value | Every cash flow discounted to the start at the discount rate, added up. |
| moneyIn | Money put in | All payments into the investment, added up. |
| moneyBack | Money back | All payments back to you, added up. |
| profit | Profit | Money back minus money put in, before discounting. |
| warning | Note | A note when the cash flows change sign more than once, so more than one IRR can fit. |

## Method

Find the yearly rate r with Σ CFₜ ÷ (1 + r)^t = 0, where t is each cash flow’s time in years (days ÷ 365 for dated flows).

## Assumptions

- The IRR is a yearly rate compounded once a year (an effective annual rate), for regular and dated flows alike.
- Regular flows: the investment is paid at the start, the ending balance comes back at the end, and a recurring amount is paid every period at its start or end. A period that does not fit in the holding period is left out.
- Dated flows count time from the earliest date in days ÷ 365, as spreadsheet XIRR does.
- When the flows change sign more than once, several rates can fit; the one closest to 0 is shown and the note lists the others.
- Rates are searched with 1 + r from 0.000001 to 1,000,000 (−99.9999% to 99,999,900% a year); a rate outside that range is not found.
- Payments at the same time are added together before money put in and money back are counted.
- The NPV discounts every flow to the start at the discount rate, per year.

## Worked examples

1. cashFlowType = fixed, investment = $10,000.00, endingBalance = $15,000.00, holdingYears = 2, holdingMonths = 6, recurringAmount = $100.00, recurringType = withdraw, recurringFrequency = monthly, recurringTiming = end, discountRate = 10% gives irr = 29.768296%, periodRate = 2.195252%, npv = $4,478.56, moneyIn = $10,000.00, moneyBack = $18,000.00. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
2. cashFlowType = fixed, investment = $4,000.00, endingBalance = $2,000.00, holdingYears = 2, holdingMonths = 0, recurringAmount = $2,000.00, recurringType = withdraw, recurringFrequency = annually, recurringTiming = end gives irr = 28.077641%, periodRate = 28.077641%. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
3. cashFlowType = irregular, flows = {"date":"2008-01-01","amount":-10000} or {"date":"2008-03-01","amount":2750} gives irr = 37.336253%, moneyIn = $10,000.00, profit = $3,000.00. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
4. cashFlowType = fixed, investment = $10,000.00, endingBalance = $11,000.00, holdingYears = 1, holdingMonths = 0, recurringAmount = $0.00, recurringType = withdraw, recurringFrequency = monthly, recurringTiming = end gives irr = 10%. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
5. cashFlowType = fixed, investment = $10,000.00, endingBalance = $12,000.00, holdingYears = 3, holdingMonths = 0, recurringAmount = $500.00, recurringType = withdraw, recurringFrequency = annually, recurringTiming = beginning gives irr = 11.530307%. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
6. cashFlowType = fixed, investment = $1,000.00, endingBalance = $800.00, holdingYears = 0, holdingMonths = 7, recurringAmount = $10.00, recurringType = withdraw, recurringFrequency = weekly, recurringTiming = end gives irr = 20.851077%, moneyBack = $1,100.00. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
7. cashFlowType = fixed, investment = $5,000.00, endingBalance = $5,000.00, holdingYears = 2, holdingMonths = 6, recurringAmount = $200.00, recurringType = withdraw, recurringFrequency = semiannually, recurringTiming = end gives irr = 8.16%, periodRate = 4%. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.
8. cashFlowType = fixed, investment = $5,000.00, endingBalance = $7,000.00, holdingYears = 1, holdingMonths = 0, recurringAmount = $50.00, recurringType = deposit, recurringFrequency = semimonthly, recurringTiming = beginning gives irr = 14.25593%, moneyIn = $6,200.00. Source: Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d.

## FAQ

### What is a 'good' IRR?

A 'good' IRR depends on the investment's risk profile, industry, and market conditions. Venture capital typically targets 20-30%+, real estate 8-20%, and low-risk investments 5-10%.

### Can IRR be negative?

Yes, a negative IRR means the project is projected to result in a net financial loss. This occurs when total cash inflows are less than total cash outflows over the investment's life.

### What is the difference between IRR and XIRR?

Standard IRR assumes regular intervals between cash flows, while XIRR allows specific dates for each cash flow, making it more accurate for real-world investments with irregular timing. Choose Dated (XIRR) in the calculator to enter a date with each amount.

### What is the Multiple IRR Problem?

This occurs when cash flows change sign more than once, creating multiple mathematically valid IRR solutions. Our calculator detects this, lists every rate it finds, and recommends using NPV instead for more reliable analysis.

### What are IRR's main advantages?

IRR is excellent for comparing different-sized projects, expressed as an intuitive percentage, and considers the time value of money. However, it has unrealistic reinvestment assumptions and can have multiple solutions.

## Sources

- Internal rate of return and net present value: R. A. Brealey, S. C. Myers, F. Allen, Principles of Corporate Finance, chapter 5 (the −4,000, +2,000, +4,000 example, IRR = 28.08%).
- Microsoft Support, XIRR function (dated cash flows, 365-day year, example result 0.373362535). https://support.microsoft.com/en-us/office/xirr-function-de1242ec-6477-445b-b11b-a303ad9adc9d
- Multiple internal rates of return and Descartes’ rule of signs: S. A. Broverman, Mathematics of Investment and Credit, chapter 5.