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.
Thanks Manshu, for your informative post, can you help me out regarding the following:
How we calculate / estimate the cash flow for calculating IRR
Cash flow is not expected to consider the inflation, does that meen cash flow series in normal cases will remain constant for all future years (no cost escalation, no price escalation, and assuming constant rate of production)
Does it include interest rate on which one had taken loan
Does it consider depreciation and the scrap value at the end of the project.
Thanks in Advance.
Sonal
Hi Sonal,
You have to make a series of assumptions about cash flows and then estimate it. You can have it increase at a rate of say 10% for the next 5 years and then a terminal rate of 2% or some other thing. This varies hugely from one person to another and is dependent on what set of assumptions you make.
Very interesting. can you make it little simpler for the benefit of all. http://ddramanathan.blogspot.in/
Many thanks for making it so very clear to me in such a short time. I have tried so very hard to understand and resorted to lot of approaches. But indeed it is explained in a lucid language.
Appreciate your effort.
Regards.
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 .
Dear pratik ,
we are in a process of finding out present value of the future cash flow. you know the equation that FV= PV(1+r)^n , now if we want to find the present value then we need to divide the future value by (1+r)^n and not multiply.
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.. 🙂
Thank you so much. i fully understood it.. You explained so nice and in simple words.. thank you..
Very good explanation.
Thanks!
nice explanation….bt hav doubt with discount rate n calculations
What is the doubt?
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.
so i got it now, my quest for everything i always wanted to know about finance and economics ends here………..!!!!!!!!!!
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.
Hi dat explanation is d boomb. Pls can u send me concrete examples on,these; Cost benefit analysis,NPV,& IRR. Thanx
The last IRR of 23% is NOT the “IRR”!
Because your NPV is not zero. Higher the IRR, better the return on investment.
I still don’t get it how to calculate IRR other than excell
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
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
thanks Manshu. You have done a good job.
GOD’s blessings. Pls explain WACC AND CAPM TOO.
My Name Asir Mohamed Ahmed
From Sudan woking in UAE from 1997 Till now
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.