• Skip to main content
  • Skip to footer

Fervent | Finance Courses, Investing Courses

Rigorous Courses, Backed by Research, Taught with Simplicity.

  • Home
  • Courses
  • Resource Hub
  • Articles
  • All Access Pass
How To Calculate IRR – Step-by-Step Walkthrough

How To Calculate IRR – Step-by-Step Walkthrough

April 21, 2018 By Vash Leave a Comment

Often misconstrued as a very “complicated” investment appraisal technique, the Internal Rate of Return (IRR) is actually one of the easiest and most intuitive capital budgeting tools to evaluate an investment opportunity. This post will take you from zero to pro, showing you how to calculate IRR step by step manually and on Excel® after giving you a simple explanation of what it is.

You’ll also learn what its limitations are, and what else it can be (and is) used for.

Table of Contents hide
1 What is Internal Rate of Return (IRR)?
2 How to interpret the Internal Rate of Return
3 How to use the IRR? (IRR Rules for Acceptance of Projects)
4 How to Calculate IRR?
4.1 IRR Formula
5 Like our content?
5.1 Get access to our exclusive Newsletter and learn about:
6 How to calculate IRR on Excel
6.1 How does Excel calculate IRR?
7 Limitations of the Internal Rate of Return (IRR)
7.1 Determining the number of IRRs
8 Other uses of the Internal Rate of Return

Advanced learner and just looking for the IRR formula? Here it is:

    \[IRR = \sqrt[\leftroot{-2}\uproot{2}n]{\frac{CF_n}{I}} - 1\]

Here, IRR represents the Internal Rate of Return. CF_n reflects the cash flow that occurs at time n, and I denotes the initial investment.

Note that this formula to calculate IRR only works for a single cash flow.

To calculate IRR for multiple cash flows, you’d need to use interpolation. We touch on this further down in this article.

Beginner learner? Don’t let the equation above freak you out – we’ve got your back.

Stay with us until the end of this article to learn how to calculate IRR step by step both manually and on Excel®.

Visual display of the All Access Pass to Finance and Investing Courses

What is Internal Rate of Return (IRR)?

Firstly, what is Internal Rate of Return (IRR)?

The Internal Rate of Return (IRR) is an investment appraisal tool that helps us evaluate if we should invest in a project.

Specifically, the IRR is the point at which the Net Present Value (NPV) is equal to zero.

In other words, it’s a ‘discount rate’ that gives us a 0 NPV.

RELATED: How to Calculate NPV

Here’s a video explanation to help you get your head around the concept:

Yes, we are on YouTube. No, we won’t ask you to “like”, “subscribe”, or click this button and that.

But people like you do seem to be subscribing to our channel increasingly 😉 – it’s great to have you all on board. We’re grateful.

How to interpret the Internal Rate of Return

Intuitively, there are 2 interpretations of the Internal Rate of Return.

  1. It shows us the maximum amount of cost of capital we can afford to pay, and
  2. It shows us the amount of money we’ll earn (expressed in %), given the time value of money and other risks.

Visual display of the All Access Pass to Finance and Investing Courses

Remember that the Net Present Value and the discount rate have a negative relationship, so that the NPV decreases as the discount rate increases, and increases as the discount rate decreases.

If we plotted Net Present Value and the discount rate, we’d have something like this…
How to calculate IRR - a graph showing the relationship between the discount rate and NPV, and pointing to the IRR (the point where NPV is equal to 0).

This is often called an IRR graph or an IRR chart. Let’s now take a look at how we read this chart by exploring how to use IRR.

How to use the IRR? (IRR Rules for Acceptance of Projects)

Notice the graph above… As long as the firm’s / project’s cost of capital (discount rate (“r”)) is lower than the Internal Rate of Return, it’s earning a positive NPV.

Any cost of capital that is greater than the IRR clearly results in a negative NPV.

This leads to the appraisal rule for IRR:

  • If IRR > r, accept the project.
  • If IRR < r, reject the project.
  • If IRR = r, accept* the project.

The last instance, where IRR = r means that the project will earn a 0 NPV.

In practice, it would be unwise to accept such a project.


Related: Investment Appraisal Course

This Article features a concept that is covered extensively in our Investment Appraisal Course.

If you’re interested in mastering the IRR, NPV, and other Investment Appraisal / Capital Budgeting techniques, then you should definitely check out the course.


From an academic standpoint, however, projects with IRR = r, and NPV = 0, tend to be accepted.

That’s because these projects do not lose money.

Generally speaking, the Internal Rate of Return and Net Present Value will end up giving you similar appraisal results.

Thus, IRR analysis is somewhat similar to the NPV, at least in terms of outcomes.

But the main difference between the two is that the IRR is a percentage-based result that ignores the magnitude of investment.

Whereas the NPV is a “dollar-based tool”, which factors in the magnitude of an investment opportunity.

How to Calculate IRR?

The IRR calculation is typically done with some algebraic manipulations by hand, or by using something like Excel® or Google Sheets.

Let’s take a look at the algebraic/manual method first.

Consider this example.

UE Inc. expects to earn $5,800 next year if it invests $5,000 today.

What is the IRR of this investment?

Visual display of the All Access Pass to Finance and Investing Courses

We start with the fundamentals, beginning with the equation for the Net Present Value:

    \[NPV = PV - I\]

Where PV refers to the Present Value of future cash flows. And I reflects the initial investment.

    \[NPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - I\]

In UE Inc’s case, there’s only one cash flow (CF); strictly, there’s only one cash inflow. So t = n = 1. The equation then becomes:

    \[NPV = \frac{CF_1}{(1+r)^1} - I\]

Since IRR is the point at which NPV = 0, it is the point at which PV = I. Because when PV = I, NPV must be equal to zero!

Using this logic, and the numbers from the question including an initial investment of $5,000, we have:

    \[PV = I\]

    \[\frac{CF_1}{(1+IRR)^1} = I\]

    \[\frac{\$5,800}{(1+IRR)^1} = \$5,000\]

Multiply both sides by (1+IRR) and divide both sides by $5,000 to get the final answer.

    \[1+IRR = \frac{\$5,800}{\$5,000}\]

    \[1+IRR = 1.16\]

    \[IRR = 0.16 \equiv 16\%\]

So there you have it! It really is that simple.

IRR Formula

Now, this IRR example above didn’t use an IRR formula explicitly by any means. Rather, we just solved for the IRR using a little bit of algebra.

But of course, we could use this approach to formalize an IRR formula as:

    \[IRR = \sqrt[\leftroot{-2}\uproot{2}n]{\frac{CF_n}{I}} - 1\]

This formula will hold for single cash flows.

Visual display of the All Access Pass to Finance and Investing Courses

A common misconception people have is that it is impossible to calculate IRR for multiple cash flows manually.

This is simply not true.

If you’re looking to calculate IRR for multiple cash flows, you can use interpolation as follows:

    \[IRR = \frac{NPV_1}{NPV_1 - NPV_2} (r_2 - r_1)\]

Here, IRR denotes the Internal Rate of Return as before.

NPV_1 reflects a positive Net Present Value that is obtained by using a rate r_1

NPV_2 on the other hand reflects a negative Net Present Value that is obtained by using a different discount rate r_2

We explain this particular approach in significantly more detail in our investment appraisal course, so do check that out if you’re interested in learning more.

For now, let’s move on to exploring how to calculate IRR on Excel quickly and easily.


Like our content?

Get access to our exclusive Newsletter and learn about:

  • Latest Articles by Fervent
  • Finance and Investing Courses
  • Investing Resources and Tips

How to calculate IRR on Excel

Excel® makes life a lot easier. There are two functions you can use to calculate IRR on Excel®, creating your very own IRR calculator:

  1. The “IRR” function, or
  2. The “RATE” function.

Visual display of the All Access Pass to Finance and Investing Courses

The Excel IRR function takes a bit more work in that you need to layout the stream of cash outflow and cash inflow first, and only then apply the formula. Like this…

Image showing How to Calculate IRR on Excel (using the Excel IRR Function)

Notice that we’ve laid out -5,000 in one cell, and then 5,800 right beside it.

You could of course place them one below the other, but the important thing is that the two are right next to each other, failing which the Excel IRR function won’t work!

In this particular example (UE Inc.), using the IRR function / RATE function requires about the same amount of time and effort.

But when you’ve got larger future cash flow streams (e.g. 5, 10, 20, 100 years) then you’ll want to use the RATE function, like so:

Image showing How to Calculate IRR on Excel (using the Excel RATE Function)

Notice that we just left the “pmt” option blank, hence the double commas.

You’ll want to use the “pmt” option when you’ve got an annuity stream of cash flows.

How does Excel calculate IRR?

Okay, so now you know how to calculate IRR on Excel. But how exactly does Excel calculate IRR itself?

Excel calculates the IRR using interpolation when it’s working with multiple cash flows.

It’s always useful – often crucial – to know how and why any software computes things.

This is why we teach you how to calcuate IRR using interpolation extensively in our course on Investment Appraisal so do take a look there.

And while we’re on the subject of courses, know that you can get unlimited access to all our finance and investing courses via the Super Learner All Access Pass.

Okay, coming back to the IRR…

Now that you know how to calculate IRR step by step by hand (manually) and on Excel, let’s think about its limitations.

Limitations of the Internal Rate of Return (IRR)

While a very useful technique, the IRR is not without limitations.

For instance, the IRR cannot handle “unconventional” (read, real-life) cash flows / uneven cash flow.

Consider the textbook / “conventional” cash flow stream…

Year 0Year 1Year 2Year 3Year 4Year 5
-$100,000$35,000$42,000$27,000$62,000$71,000

By conventional, we mean a stream that has one initial outflow (the initial investment), followed by a stream of inflows (the cash inflows from Year 1 – Year 5).

The IRR for this is 32.24%. See if you can calculate it!

Now consider a more real-world, “unconventional” cash flow stream…

Year 0Year 1Year 2Year 3Year 4Year 5
-$100,000$52,000-$60,000$39,000$84,000$91,000

By unconventional, we mean a stream that has more than 1 negative cash flow.

Or in simple English, it means that an investment is made on more than one occasion.

In the example above, $100,000 is invested today (Year 0), and a further $60,000 is invested 2 years later.

In an unconventional or uneven cash flow setting, multiple IRRs can exist, and this is perhaps the greatest limitation of the Internal Rate of Return.

Here, you’ll have up to 3 IRRs! And there’s no way of really knowing which one is the “true” IRR.

So even though the Excel IRR calculation returns an IRR = 20.43% for this stream, one has to take it with a pinch of salt.

And this goes to show why it’s important to understand things, rather than just blindly inputting numbers/functions in software.

Determining the number of IRRs

How do we know we’ll have up to 3 IRRs?

Easy – just count the number of times the ‘sign’ changed.

From Year 0 to Year 1, the sign changed once (negative cash flow of -$100,000 to a positive cash flow of $52,000.

Then there was another change from Year 1 to Year 2 (positive cash flow to a negative one).

And finally, another change from Year 2 to Year 3 (negative cash flow to a positive one).

The cash flows from Year 3 to Year 5 are all positive, meaning the number of ‘sign changes’ is zero.

Other uses of the Internal Rate of Return

Apart from investment appraisal, the Internal Rate of Return is also useful for valuing bonds!

In fact, a bond’s discount rate (aka Yield to Maturity, or more simply, Yield) is its Internal Rate of Return!

So if you know how to calculate the IRR, then you’re pretty much 60% on your way to knowing how to value bonds.

On another note, fun fact, Vanguard uses the IRR to display investment performance for its investors!

Okay, but hopefully, you now know how to calculate IRR and you understand the process and intuition behind the Internal Rate of Return.

If you’d like to learn more about other investment appraisal techniques like the Net Present Value or Profitability Index, feel free to check out our other articles.

Alternatively, do check out the course below to gain a solid command of Investment Appraisal / Capital Budgeting.


Related Course: Investment Appraisal Mastery

Do you want to become a PRO at Investment Appraisal / Capital Budgeting?

Explore the Course

Filed Under: Capital Budgeting, Finance

Reader Interactions

Leave a Reply Cancel reply

You must be logged in to post a comment.

Footer CTA

Do You Want To Crack The Code of Successful Investing?

Yes! Tell Me More

  • About Us
  • Write For Us
  • Contact Us

Copyright © 2025, Fervent · Privacy Policy · Terms and Conditions


Logos of institutions used are owned by those respective institutions. Neither Fervent nor the institutions endorse each other's products / services.

We ethically use cookies on our website to give you the best possible user experience. By clicking “Accept All”, you consent to the use of ALL the cookies. However, you may visit "Cookie Settings" to provide a controlled consent.
Cookie SettingsAccept All
Manage consent

Privacy Overview

This website uses cookies to improve your experience while you navigate through the website. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. We also use third-party cookies that help us analyze and understand how you use this website. These cookies will be stored in your browser only with your consent. You also have the option to opt-out of these cookies. But opting out of some of these cookies may affect your browsing experience.
Necessary
Always Enabled
Necessary cookies are absolutely essential for the website to function properly. These cookies ensure basic functionalities and security features of the website, anonymously.
CookieDurationDescription
cookielawinfo-checkbox-analytics11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Analytics".
cookielawinfo-checkbox-functional11 monthsThe cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional".
cookielawinfo-checkbox-necessary11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary".
cookielawinfo-checkbox-others11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Other.
cookielawinfo-checkbox-performance11 monthsThis cookie is set by GDPR Cookie Consent plugin. The cookie is used to store the user consent for the cookies in the category "Performance".
viewed_cookie_policy11 monthsThe cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. It does not store any personal data.
Functional
Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features.
Performance
Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors.
Analytics
Analytical cookies are used to understand how visitors interact with the website. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc.
Advertisement
Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. These cookies track visitors across websites and collect information to provide customized ads.
Others
Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet.
SAVE & ACCEPT