What is IRR and how is it calculated?

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.