*This tutorial explains the syntax of the Excel IRR function and shows how to use an IRR formula to calculate the internal rate of return for a series of annual or monthly cash flows.*

IRR in Excel is one of the financial functions for calculating the internal rate of return, which is frequently used in capital budgeting to judge projected returns on investments.

The Excel IRR function returns the internal rate of return for a series of periodic cash flows represented by positive and negative numbers.

In all calculations, it's implicitly assumed that:

- There are
**equal time intervals**between all cash flows. - All cash flows occur at the
**end of a period**. - Profits generated by the project are
**reinvested**at the internal rate of return.

The function is available in all versions of Excel for Office 365, Excel 2019, Excel 2016, Excel 2013, Excel 2010 and Excel 2007.

The syntax of the Excel IRR function is as follows:

IRR(values, [guess])

Where:

**Values**(required) – an array or a reference to a range of cells representing the series of cash flows for which you want to find the internal rate of return.**Guess**(optional) – your guess at what the internal rate of return might be. It should be provided as a percentage or corresponding decimal number. If omitted, the default value of 0.1 (10%) is used.

For example, to calculate IRR for cash flows in B2:B5, you'd use this formula:

`=IRR(B2:B5)`

For the result to display correctly, please make sure the **Percentage** format is set for the formula cell (usually Excel does this automatically).

As shown in the above screenshot, our Excel IRR formula returns 8.9%. Is this rate good or bad? Well, it depends on several factors.

Generally, a calculated internal rate of return is compared to a company's *weighted average cost of capital* or *hurdle rate*. If the IRR is higher than the hurdle rate, the project is considered a good investment; if lower, the project should be rejected.

In our example, if it costs you 7% to borrow money, then an IRR of about 9% is fairly good. But if the cost of funds is, say 12%, then the IRR of 9% is not good enough.

In reality, there are many other factors that influence an investment decision such as the net present value, absolute return value, etc. For more information, please see IRR basics.

To ensure that your IRR calculation in Excel is done correctly, please remember these simple facts:

- The
*values*argument must contain at least one**positive**value (representing income) and one**negative**value (representing outlay). - Only
**numbers**in the*values*argument are processed; text, logical values, or empty cells are ignored. - The cash flows do not necessarily have to be even, but they must occur at
**regular intervals**, for example monthly, quarterly or annually. - Because IRR in Excel interprets the order of cash flows based on the order of values, the values should be in
**chronological order**. - In most situations, the
**guess**argument is not really needed. However, if the IRR equation has more than one solution, the rate closest to the guess is returned. So, your formula produces an unexpected result or a #NUM! error, try a different guess.

Since the **internal rate of return** (IRR) is a discount rate that makes the net present value (NPV) of a given series of cash flows equal to zero, the IRR calculation relies on the traditional NPV formula:

Where:

- CF - cash flow
- i - period number
- n - periods total
- IRR - internal rate of return

Because of a specific nature of this formula, there is no way to calculate IRR other than through trial and error. Microsoft Excel also relies on this technique but does multiple iterations extremely quickly. Starting with the guess (if supplied) or the default 10%, the Excel IRR function cycles through the calculation until it finds the result accurate within 0.00001%. If after 20 iterations an accurate result is not found, the #NUM! error is returned.

To see how it works in practice, let's perform this IRR calculation on a sample data set. For starters, we will try to guess what the internal rate of return might be (say 7%), and then work out the net present value.

Assuming B3 is the cash flow and A3 is the period number, the following formula gives us the present value (PV) of the future cash flow:

`=B3/(1+$B$7)^A3`

Then we copy the above formula to other cells and add up all the present values, including the initial investment:

`=SUM(C2:C5)`

And find out that at 7% we get the NPV of $37.90:

Obviously, our guess is wrong. Now, let's do the same calculation based on the rate computed by the IRR function (around 8.9%). Yep, it does lead to a zero NPV:

Now that you know the theoretical basis of IRR calculation in Excel, let's make a couple of formulas to see how it works in practice.

Assuming you have been running business for six months and now you want to figure out the rate of return for your cash flow.

Finding IRR in Excel is very straightforward:

- Type the
**initial investment**into some cell (B2 in our case). Since it's an outgoing payment, it needs to be a**negative**number. - Type the subsequent cash flows into the cells under or to the right of the initial investment (B2:B8 in this example). This money has been coming in through sales, so we enter these as
**positive**numbers.

Now, you are ready to calculate IRR for the project:

`=IRR(B2:B8)`

Optionally, you can put an expected internal rate of return, say 10 percent, in the *guess* argument:

`=IRR(B2:B8, 10%)`

As shown in the screenshot below, our guess does not have any impact on the result. But in some cases, changing the guess value may cause an IRR formula to return a different rate. For more information, please see Multiple IRRs.

In capital budgeting, IRR values are often used to compare investments and rank projects in terms of their potential profitability. This example demonstrates the technique in its simplest form.

Supposing you have three investment options and you are deciding which one to choose. The reasonably projected returns on the investments can help you make an informed decision. For this, enter the cash flow for each project in a separate column, and then calculate the internal rate of return for each project individually:

Formula for project 1:

`=IRR(B2:B7)`

Formula for project 2:

`=IRR(C2:C7)`

Formula for project 3:

`=IRR(D2:D7)`

Given that the company's required rate of return is, say 9%, project 1 should be rejected because its IRR is only 7%.

The two other investments are acceptable because both can generate an IRR higher than the company's hurdle rate. Which one would you choose?

At first sight, project 3 looks more preferable because it has the highest internal rate of return. However, its yearly cash flows are much lower than for project 2. In situation when a small investment has a very high rate of return, businesses often choose an investment with a lower percentage return but higher absolute (dollar) return value, which is project 2.

The conclusion is: the investment with the highest internal rate of return is usually preferred, but to make the best use of your funds you should evaluate other indicators as well.

Though the IRR function in Excel is designed for calculating the internal return rate, it can also be used for computing the compound growth rate. You will just have to reorganize your original data in this way:

- Keep the first value of the initial investment as a negative number and the ending value as a positive number.
- Replace the interim cash flow values with zeros.

When done, write a regular IRR formula and it will return the CAGR:

`=IRR(B2:B8)`

To make sure the result is correct, you can verify it with the commonly used formula for calculating CAGR:

(end_value/start_value)^(1/no. of periods) -1

As shown in the screenshot below, both formulas produce the same result:

For more information, please see How to calculate CAGR in Excel.

The internal rate of return and the net present value are two closely related concepts, and it's impossible to fully understand IRR without understanding NPV. The result of IRR is nothing else but the discount rate corresponding to a zero net present value.

The essential difference is that NPV is an absolute measure that reflects the dollar amount of value that could be gained or lost by undertaking a project, while IRR is the percentage rate of return expected from an investment.

Because of their different nature, IRR and NPV may "conflict" with each other - one project may have a higher NPV and the other a higher IRR. Whenever such a conflict arises, finance experts advise to favor the project with a higher net present value.

To better understand the relationship between IRR and NPV, please consider the following example. Let's say, you have a project that requires an initial investment of $1,000 (cell B2) and a discount rate of 10% (cell E1). The project's lifespan is five years and the expected cash inflows for each year are listed in cells B3:B7.

To find out how much the future cash flows are worth now, we need to compute the net present value of the project. For this, use the NPV function and subtract the initial investment from it (because the initial investment is a negative number, the addition operation is used):

`=NPV(E1,B3:B7)+B2`

A positive net present value indicates that our project is going to be profitable:

What discount rate will make the NPV equal to zero? The following IRR formula gives the answer:

`=IRR(B2:B7)`

To check this, take the above NPV formula and replace the discount rate (E1) with IRR (E4):

`=NPV(E4,B3:B7)+B2`

Or you can embed the IRR function directly into the *rate* argument of NPV:

`=NPV(IRR(B2:B7),B3:B7)+B2`

The screenshot above shows that the NPV value rounded to 2 decimal places indeed equals zero. If you are curious to know the exact number, set the Scientific format to the NPV cell or choose to show more decimal places:

As you can see, the result is well within the declared accuracy of 0.00001 percent, and we can say that the NPV is effectively 0.

If you have run into some problem with IRR in Excel, the following tips might give you a clue for fixing it.

A #NUM! error may be returned because of these reasons:

- The IRR function fails to find the result with up to 0.000001% accuracy on the 20th try.
- The supplied
*values*range does not contain at least one negative and at least one positive cash flow.

In case no cash flow arises in one or more periods, you may end up with empty cells in the *values* range. And it is the source of problems because rows with empty cells are left out of Excel IRR calculation. To fix this, just enter zero values in all blank cells. Excel will now see the correct time intervals and compute the internal return rate correctly.

In situation when a cashflow series changes from negative to positive or vice versa more than once, multiple IRRs can be found.

If the result of your formula is far from what you expected, check the guess value – in case the IRR equation can be solved with several rate values, the rate closest to the guess is returned.

Possible solutions:

- Assuming that you know what kind of return you are expecting from a certain investment, use your expectation as a guess.
- When you get more than one IRR for the same cash flow, choose the one closest to your company's cost of capital as the "true" IRR.
- Use the MIRR function to avoid the problem of multiple IRRs.

The IRR function in Excel is designed to work with regular cash flow periods such as weekly, monthly, quarterly or annually. If your inflows and outflows occur at unequal intervals, IRR would still consider the intervals equal and return a wrong result. In this case, use the XIRR function instead of IRR.

The IRR function implies that the project earnings (positive cash flows) are continuously reinvested at the internal rate of return. But in the real word, the rate at which you borrow money and the rate at which you reinvest the profits are often different. Luckily for us, Microsoft Excel has a special function to take care of this scenario – the MIRR function.

That's how to do IRR in Excel. To have a closer look at the examples discussed in this tutorial, you are welcome to download our sample workbook to Using IRR function in Excel. I thank you for reading and hope to see you on our blog next week!

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