IRR stands for Internal Rate of Return, and last week reader Sandeep emailed me asking about this, so I thought I’d do a post on the subject.

It’s impossible to understand IRR without understanding the concept of Net Present Value (NPV) first, so let’s begin with NPV.

You know that the cash that you receive today is more valuable than the cash you receive two years down the line or anytime in the future due to inflation. So, anytime you see cash flows going out in the future you will ask yourself how much is all this money worth today? We are all familiar with this concept because we see it every day in our life, and is relevant to a lot of things especially retirement planning, and looking at things such as how much money you will need for retirement.

So let’s say I come to you with a proposal for a project and say that you invest Rs. 1 million in the beginning and after that the project will start generating cash without any further investment, and here is how the cash flows will look like.

Time Period | Project A |

0 |
(1,000,000.00) |

1 |
450,000.00 |

2 |
400,000.00 |

3 |
350,000.00 |

4 |
300,000.00 |

5 |
250,000.00 |

Since it’s me you’d say why did I go through all this trouble of digging up the numbers; take out your check book, and write me a check – thank you!

But imagine for a moment, it was a family member – you would be on your guard then wouldn’t you?

You would obviously want to know if this is a better deal than what your bank gives you, and for that you can calculate the Net Present Value of these cash flows on the rate of interest your bank gives you which is also called the Discount Rate for this purpose. Let’s assume that the discount rate is 8% in this case.

To calculate the NPV of this project you will discount each cash flow with the discount rate keeping in mind the time lapse.

Your calculations will look something like this.

Time Period (T) | Project A | Discount Rate (DR) | DR + 1 | (DR + 1) ^ T | NPV of Cash Flow{Cash Flow / (DR +1)^T} |

0 | (1,000,000.00) | 0.08 | – | – | (1,000,000.00) |

1 | 450,000.00 | 0.08 | 1.08 | 1.08 | 416,666.67 |

2 | 400,000.00 | 0.08 | 1.08 | 1.17 | 342,935.53 |

3 | 350,000.00 | 0.08 | 1.08 | 1.26 | 277,841.28 |

4 | 300,000.00 | 0.08 | 1.08 | 1.36 | 220,508.96 |

5 | 250,000.00 | 0.08 | 1.08 | 1.47 | 170,145.80 |

NPV |
428,098.23 |

An NPV of more than 0 means that you will make more than your alternative investment (the fixed deposit) in your case, so looking at this number makes you really happy.

To sum up – NPV is the sum of all cash flows at a discount rate that represents your alternative investment potential.

## What is IRR?

Internal Rate of Return (IRR) is that rate of return at which the NPV from the above investments will become zero. It is that rate of interest that makes the sum of all cash flows zero, and is useful to compare one investment to another.

In the above example if you replace the 8% with a 25% the NPV will become zero, and that’s your IRR. Hence, the statement that IRR is the discount rate at which the NPV of a project becomes zero. How did I know that the I need to use 25%? I used the Excel formula called IRR to find that out. Manually, you will have to do a bit of a hit and trial to arrive at that, and if you have Excel handy then that’s the easiest way to calculate IRR.

Input your cash flows, select IRR from formulas, and get the result. This link explains how to calculate IRR using Excel.

Time Period | Project A | IRR | IRR + 1 | (IRR + 1) ^ T | NPV of Cash Flow |

0 | (1,000,000.00) | 0.25 | – | – | (1,000,000.00) |

1 | 450,000.00 | 0.25 | 1.25 | 1.25 | 360,000.00 |

2 | 400,000.00 | 0.25 | 1.25 | 1.56 | 256,000.00 |

3 | 350,000.00 | 0.25 | 1.25 | 1.95 | 179,200.00 |

4 | 300,000.00 | 0.25 | 1.25 | 2.44 | 122,880.00 |

5 | 250,000.00 | 0.25 | 1.25 | 3.05 | 81,920.00 |

Total of Cash Flows | 0 |

The IRR is useful if you have to compare with one project with another that has different cash flows at different times.

So, to add to our example – let’s say you are presented with the following two options to invest your money in – which project will you choose?

Time Period | Project A | Project B |

0 | (1,000,000.00) | (1,000,000.00) |

1 | 450,000.00 | 250,000.00 |

2 | 400,000.00 | 300,000.00 |

3 | 350,000.00 | 450,000.00 |

4 | 300,000.00 | 450,000.00 |

5 | 250,000.00 | 450,000.00 |

Quick mental calculation will show you that the cash flows from the second project exceed the first one, but you also notice that they do’t exceed by much and are also at later years, so it might be worth your time to calculate the IRR. In this case the IRR is 22.99% as shown by the table below because that is the discount rate at which the NPV becomes zero, or close to zero in this case due to rounding errors.

Time Period | Project A | IRR | IRR + 1 | (IRR + 1) ^ T | NPV of Cash Flow |

0 | -1000000 | 0.23 | – | – | (1,000,000.00) |

1 | 250000 | 0.23 | 1.2299 | 1.23 | 203,268.56 |

2 | 300000 | 0.23 | 1.2299 | 1.51 | 198,326.91 |

3 | 450000 | 0.23 | 1.2299 | 1.86 | 241,881.75 |

4 | 450000 | 0.23 | 1.2299 | 2.29 | 196,667.82 |

5 | 450000 | 0.23 | 1.2299 | 2.81 | 159,905.54 |

Total of Cash Flows | 51 |

Your new information tells you that one project has an IRR of 25% while the other has an IRR of 23% so that gives you more information to make your decision from.

So, this is the way IRR helps you in making a decision when comparing different projects, and is one of the several tools that can be used in evaluating any project that has cash flows distributed over the years.

To learn more about this concept head over to this link which does a great job of explaining IRR and getting into the details also. and leave a comment if you have any questions or clarifications, or juts see an error somewhere.

{ 64 comments… read them below or add one }

The site http://www.rupeetalk.com/calculators/pf-calculator.php gives pointers about retirement amount you need to have… found this to be another useful tool.

Thanks for the link!

Very good explanation. Thanks..

However, at times IRR can mislead and it may be better to look at MIRR. The article below puts the three in perspective.

http://finaticsonline.com/blog/2010/11/npv_vs_irr_vs_mirr/

This site is really worth visiting…..The way everything is explained is so organized and so clear.

Thnx a lot!!!! keep posting more π

Great to hear that Anamika – thanks!

haii..can u please give me some important bank interview topics…

I didnt get how to get 25% and 23% its the same problem i have in my notes, and printouts i have table of two projects but IRR is not given π

You have to enter the cash flows in an Excel or something and calculate IRR using the Excel function. You can Google up stuff on how to calculate IRR using Excel and that will help you.

You explained IRR in very clear and concise way. Can’t forget it now……thanks.

Sorry Amar this is not very clear and concise method this is very complicated method I know better from this………..

HI DEAR SOMETHING WRONG IN THE ABOVE DISOUNT RATE USED ( THAT IS 8%)

DISCOUNT RATE can NEVER BE EQUAL TO BANK FIXED DEPOSIT RATE

THE REASON BEHIND THAT IS SO SIMPLE THAT PROJECT INVOLVES RISK AND WE SHOULD ADD RISK PREMIUM TO THE NON RISKY RATE OF RETURN(fixed rate of return) THAT MEANS DISCOUNT RATE SHOULD BE RISK FREE RATE PLUS RISK PREMIUM. IN THE ABOVE EXAMPLE IT SHOULD BE 8% + LETS SAY RISK PREMIUM 6%= 14% SHOULD BE THE DISCOUNT RATE.( This is the same thing that has been conveyed in CAPM model as well and the same thing (14%) is also known as investors expected rate of return or required rate of return)

You are absolutely foolish if u use discount rate equal to 8% . if you are taking 8% discount rate it shows that you are taking risk and inspite of that you are ready to accept 8% return ! How silly and stupidity! Your risk must be compensated with higher return. otherwise you are better with 8%. Why u take more tension ( risk )? enjoy FD interest at no risk.

Naim,

the website has given a simplest explanation to a starter about the IRR, when you go in detail I am sure that there are many more details. and even if there are things to which you dont agree, we have to be polite about them and not to forget the effort the person made to explain the issue.

I would like to see you try to do better.

The author has elegantly explained the concept of IRR. You on the other hand have added nothing to the discussion. You called the author stupid, when you cannot even type out a decent sentence…

really sorry for the language , my intentions was not to pass any comment on the author , really sorry for the remark. To just give u further knowledge about IRR , it is said that IRR is using the reinvestment assumptions , this reinvestment assumptions about IRR has devided the finance community into two groups , one accepting reinvestment , other not accepting the reinvestment. There are certain problems in Capital Budgeting that can be solved only by assuming the reinvestment assumptions when there is a conflict between two projects one is good in terms of IRR and other is good in terms of NPV. in that case by assuming various reinvestment rate we decide which project is the better one. The point would be achieved when even by assuming vaious reinvestment rate we come to a rate where we are indifferent between the two project. That rate is called Fisher’s Rate . If somebody wants that research paper , i can provide that . again sorry for whatever language i have written , thanks

Yes, please share the link, that will be useful, I only knew of Fisher’s Equation about real and nominal interest rates, and this might be something useful to learn.

please follow this link and download that paper http://papers.ssrn.com/sol3/results.cfm?RequestTimeout=50000000

let me know if there is any comment about that paper

thanks

This doesn’t open up the link to the paper, just the SSRN page, what’s the name of the paper?

name of the paper is revisiting the reinvestment rate by kunal khairnar , thanks

This doesn’t seem to have anything to do with Fisher’s rate, what am I missing?

fisher rate means rate at which both the projects are indifferent as far as reinvestment rate are assumed you do not compare with the Whatever fisher rate u are talking about , this fisher rate is in terms of capital budgeting and reinvestment and conflict between IRR and NPV criteria.

Hey Manshu , you got the point or not please do reply

Hey sunil look I have added the most controversial topic in IRR : that is reinvestment assumption , I have also mentioned the name of the paper below . I am sorry about my language ,but your argument is wrong , as I have added very good topic of IRR that is its reinvestment assumption , please go through that research paper.thanks

Please appreciate the patience and time which Manshu has taken to do this post.Look at the target readers.It is not for an IIT MBA Finance reader.You talk of risk factor. I have many other more significant factors.I immensely like One Mint because of its simplicity and the reactions from the readers which are always polite.Calling some one who is doing an excellent job as stupid is certainly not in my opinion, a sign of politeness.I have always wondered what Manshu gets out of this.

Very informative! really appreciate your website π

Altough, I calculated IRR of the LIC Moneyback Policy I have with me. It is giving me a return of 5% only. Before visiting this page I was under impression that the policy was best choice with their periodic returns.

Thanks a lot!

I’m sure a lot of people share that misconception Rajeev – I’m glad you found this page and were able to clear it. Perhaps you could help out a few friends by talking to them about this as well. Thanks for your comment!

hi, when calculating project irr, is the cash flow before or after interest? how would this differ from equity irr?

XL is returning an error while calculating for IRR with 37 rows. however when I reduce the rws to a maximum of 20, i am getting an IRR output. Any idea why this is happening?

Thanks,

naresh

It’s nothing to do with the rows I’m sure, but rather I think there is something between your 21st and 37th row that’s causing the formula to not work. Double check to see if it’s all numbers only, and also to see if the numbers are such that there is no IRR to show, i.e. they are only negative numbers. Look for anything odd.

I’ve never looked at this product and am not knowledgeable about ULIPs in general so I won’t be able to comment about this. Sorry.

This video will show you in 3 minutes what IRR is and how to use it in Excel.

http://www.youtube.com/watch?v=UJXrCeCOtNc

Hi Manshu

Thanks just saw your post on IRR..its very nicely presented. Its an invaluable tool for financial planners also, to calculate the returns from insurance policies and mutual fund SIP investments.

Thanks Abhinav, a lot of people have in fact started realizing that this is how you calculate returns from SIP or insurance policies and I have separate posts on that topic in here somewhere too.

After reading the explanation of the IRR it kind of made sense but still am a little confused as to where to begin assuming the rate to get to zero?

Can anyone help me further??

Any help would be greatly appreciated.

thanks

I’m not sure what you mean, the rate will remain constant, the rate won’t change or get to zero….the NPV of cash flows will become zero.

You can assume any rate to begin with and see what happens to your numbers, and adjust accordingly. The starting point will just be a guess.

Ok great thank you for your response Manshu π

In the THREE tables, the % sign within the rows in the THIRD COLUMN might mislead the readers. You’ve already converted the percentages to decimals, so you might want to delete the % sign from the columns; that is if I am not wrong on this.

Thanks for pointing that out – I’ve made the edits.

Hey,

Im still struggling with the IRR! I cant get me head around it.

I have three different cash flows all of which increase from year one two and three. Im not sure

what im meant to do exactly. When i try to figure out what the IRR is are the cash flows meant to decrease or increase to get the total to 0 and how do i get to that and am i subtracting this from my NPV???

Can someone help? im finding this quite confusing… π

Hi Manshu,

Thanks for coming up with this article on IRR and for explain in great detail. I’m sure readers will find it valuable and interesting too.

I’ve a few suggestions (pls. dont take it as a critic view).

1. I think you could drop the explanation about IRR being the rate at which NPV is zero. Instead of the detailed calculations you could have directly computed IRR using the IRR function in one shot and display it below the cash flows. The detailed calculation in my view is not required. However, I’d be wrong too because it also educates or helps people learn how IRR works. But today given the availability of spreadsheet the calculation part is important but not that critical.

2. I feel explaining the decision making part is important too, though it may sound theoretical it has a lot of practical relevance. What Im trying to say is

– When you look at a project’s viability using NPV method using your required discount rate then it has to be positive for a project to be selected. I think this has to be mentioned though obvious for you and me. For this you could have taken another project showing negative NPV to illustrate it.

– When you talked about IRR for decision making you could have explained a little more that IRR of 25% for project. I think the last table should be titled “Project B” – please verify. You could have concluded that Project A, which provides superior returns of 25% is better than Project B. Ofcourse this is based on one criteria….and discussion other factors is beyond the scope.

– Lastly, though its obvious I request you to also say in simple layman’s language that IRR is the annual rate of return expected from the project. This makes their understanding easier. If FD provides 8% and investment in this project provides 25% then the project is more attractive than the FD though the project may carry higher risk. And if project A provides 25% and project B provides 20% return then assuming all other factors are constant project A is better.

In simple terms IRR and NPV can be seen as two different measures.

NPV just tells you if the project (s) at its present value generates more money than your original investment.

IRR indicates the compounding rate of return for 1 year or one period for the project.

NPV tells you if its viable or not, while IRR tells you the quantum of return (or how good the return is in terms of a %age).

Sorry for the lengthy comment. Just wanted to share my gyan, which I hope makes sense.

Unfortunately, the indexes mentioned above, i.e. IRR1=25% and IRR2=23% does not give you any idea to make a decision. Such comparison may be done for NPV1 and NPV2.

The problem is that, the projects which are being offered may be negative (Benefit-Cost<0), but they are "required" to be positive in the other periods, year2, year3, … IN AGAINST CASE IRR BECOMES STUPID/FOOLISH METHOD TO MAKE ANY DECISION!!!!

Therefore, NPV is most convenient method to make decisions, but also this method has a lot of negative points (e.g. the factors are "assumed" for several years, based on experience, trends, data forecasts… )

Thanks .this page is so helpful

Your explanation of the IRR is very good makes even those of us who are not financially inclined understand. By far the best explanation I’ve come across. Excellent!!

Thanks a lot manshu for your highly informative article. It was explained clearly and it helped me a lot into understanding what IRR is and also Sekar comment was also incisive. Thanks Manshu and Sekar.

My Name Asir Mohamed Ahmed

From Sudan woking in UAE from 1997 Till now

thanks Manshu. You have done a good job.

GOD’s blessings. Pls explain WACC AND CAPM TOO.

Can you do this calculation in exell in spreadsheet format, where you insert the values and get the answer?

I am an mechanic so for me to do this calculations is out. I need someone to do this for me!!!!

I did like the reading by the way and it helped me understand what IRR means, thanks

We make investments to earn returns. Investment return is the change in value of an investment over a given period of time. For example

Mr Sharma invested Rs 10,000 in a mutual fund and 2 years of holding it became Rs 20,000

Mr. Patil invested Rs 50,000 in Gold for 7 years and it became Rs 4,00,000

Who earned more? How to calculate returns so that we do not end up comparing apple to oranges! There are many different measures such as, absolute return, simple annualised return, compounded annual growth, among others. Our article Understanding Returns: Absolute return, CAGR, IRR etc covers different ways to compare returns.

Hope it helps your readers

I still don’t get it how to calculate IRR other than excell

The last IRR of 23% is NOT the “IRR”!

Because your NPV is not zero. Higher the IRR, better the return on investment.

Hi dat explanation is d boomb. Pls can u send me concrete examples on,these; Cost benefit analysis,NPV,& IRR. Thanx

Hey thank you for the explanation. I have one doubt. In the 2nd table where you have explained how to calculate the NPV, Can u please tell me in the end how did you get the figure of 428,098.23?

That is the total of all the values above it.

so i got it now, my quest for everything i always wanted to know about finance and economics ends here………..!!!!!!!!!!

The explanation is very strategic and helpful. Suggest you may add how the IRR is interpreted in various industrial segment. Certainly this will be a value addition

It is used the same manner everywhere which is to see how the returns from one fund compares with another.

nice explanation….bt hav doubt with discount rate n calculations

What is the doubt?

Very good explanation.

Thanks!

Thank you so much. i fully understood it.. You explained so nice and in simple words.. thank you..

Thanks for the useful explanation…

Your explanation is initiated interest for me to study the topic of project Evaluation techniques in BE. CSE..

Thanks a lot.. π

i would like to know that while calculating the irr or npv why do we

IRR

1 250000 0.23 1.2299 1.23 203,268.56

2 300000 0.23 1.2299 1.51

form were did i got 1.23 and 1.51 why there is a difference

NPV

1 450,000.00 0.08 1.08 1.08 416,666.67

2 400,000.00 0.08 1.08 1.17

from were did we got 1.08 and 1.17

can u pls explain me in detail from were did we got this amt and also why we have to divide the this (1.08 or 1.17) with the number called outflow why i cant multiply why we have to divide pls pls pls it is a request to explain me this myth.

thanks in advance

god bless u .

I am sorry I didn’t follow it.

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