# IRR Calculator to CalculateAPY of Regular, Unequal Cash Flows

The IRR Calculator on this page will instantly calculate the internal rate of return for up to 20 cash flows having regular intervals.

This calculator will help you to determine the average annual rate of return on an investment having unequal cash flows that occur on a regular basis.

You can choose from Annual, Semi-Annual, Quarterly, or Monthly cash flow intervals, as well as set the date of the beginning time period.

Plus, once you choose the cash flow frequency and set the starting time period, the calculator will automatically fill in all subsequent time periods for you. Cool!

Finally, once you have entered all cash flows and clicked the "Calculator IRR" button, the calculator will even generate a printable report showing the future value of each entered cash flow. In other words, unlike other online IRR calculators, this calculator won't leave you guessing as to the validity of the internal rate of return result.

Note that if you want to calculate the internal rate of return for an investment having non-periodic cash flows, please use the XIRR Calculator instead.

### What is IRR?

IRR stands for Internal Rate of Return and is used to describe the average annual return on investments where deposits and payments vary in amounts.

And since the cash flows vary in amounts, standard time value of money formulas cannot be used to solve for the rate of return (they only work for equal cash flow amounts).

To calculate the internal rate of return of a series of unequal cash flows (deposits and income), those familiar with spreadsheet software (Excel™, OpenOffice Calc, etc.) can simply use the IRR function to solve for the average annual return of unequal cash flows.

However, if you are not familiar with how to set up a spreadsheet to solve for the internal rate of return of a series of unequal cash flows, you can now find a solution using the calculator on this page -- which has it's own built-in IRR function.

### What is IRR Function and How Does It Work?

The IRR function is an iterative process (algorithm) of trial and error used to find a rate of return that would solve for a schedule of unequal cash flows.

Specifically, the IRR function starts with a guess (usually 10%) and calculates the future values of all cash flows based on that guess. If the result is less than the actual combined future values, the function increments the guess by a small fraction of a percentage. And conversely, if the result is greater than the actual future values, the function decrements the guess by a small fraction.

Next, in either case, the function recalculates using the new guess. It then repeats the process of adjusting the guess and recalculating until either a result is found, or the preset maximum number of tries (iterations) has been reached.

### Preset Limitations To Be Aware Of

Since the number of iterations required to solve extreme sets of unequal cash flows can be astronomical, I've taken the following steps to limit the amount of time it takes for this online IRR calculator to complete its calculations.

1. Preliminary iteration starts with a guess of -100% and adds 1 percent to the guess until the result is greater than the actual combined future values.
2. Secondary iteration starts with the guess arrived at by the primary iteration and then subtracts .0001 percent from the guess until the result is within \$0.05 of the actual combined future values.
3. Maximum number of both the primary and secondary tries (iterations) is set to 100,000.

If you would like to see the above limitations relaxed to give a more accurate result, please let me know.

With that, let's use the IRR Calculator to calculate the average annual rate of return for cash flows occurring at regular intervals.

IRR Calculator

Instructions: Select the applicable cash flow interval and select/enter the corresponding time period of the initial investment.

Next, for each applicable time period, enter either an additional investment amount or a withdrawal amount. Note that the beginning value and at least one withdrawal or ending value must exist before the calculator will begin the IRR calculation.

Once you have all of the periodic cash flows entered, click the "Calculate IRR" button. If the Number of iterations result is equal to 100,000, this means the iteration limit was reached before the calculator found a solution within +/- \$0.05 of the ending value. The Calculated balance result will indicate how close the calculations got to zero before reaching the limit.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the IRR Calculator.

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Cash flow interval:
Month and year of initial investment:

Year

Investments

Withdrawals
& End Value
<< Begin Value
Profit (-Loss):
Number of regular time periods:
Calculated balance:
Number of iterations:
Internal Rate of Return:
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### IRR Calculator Glossary of Terms

Cash flow interval: Select whether the cash flow frequency is Annual, Semi-Annual, Quarterly, or Monthly.

Month and year of initial investment: Indicate the beginning time period of the initial investment by selecting the applicable month and entering the 4-digit year. Changing the initial time period will automatically populate the Date Column with the proper series of time periods.

Date column: This column will be automatically populated with the time periods based on the selections/entries in the first two lines of the IRR calculator.

Investments column: Enter the starting investment amount on the first line and then on any subsequent lines where additional amounts were invested (enter as positive values). Note that numbers entered in this column are usually entered as negative values when using an IRR spreadsheet function, however this IRR Calculator converts the values to negative for you.

Withdrawals & End Value column: For time periods where withdrawals occurred, enter the amounts in this column. If no cash flow occurred in an interim time period you can either enter a zero or leave the field blank. You must have at least one value in this column for the IRR calculation to begin.

Profit (-Loss): This is the sum of all withdrawals and the ending value minus the sum of all invested amounts.

Number of regular time periods: This is the total number of time periods that were included in the calculations.

Calculated balance: The closer this result is to zero, the more accurate the Internal Rate of Return result.

Number of iterations: This is the number of secondary iterations (tries) it took to find a rate of return that would support the entered schedule of investments and withdrawals. If this result is equal to 100,000 it means the IRR Calculator reached its limit of tries before finding a solution within +/- \$0.05 of a zero balance.

Internal Rate of Return: This is the estimated average annual rate of return of the entered cash flows having regular intervals.

IRR Calculator

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