The Internal Rate of Return

The Internal Rate of return is a very important finance tool to evaluate long term projects. In simple terms, it can be understood as the benchmark rate or the break even rate at which:

The Present Value of the inflows equals the present value of the outflows.

In our example, we have an investment of Rs.1 lakh made in the project which gives us a return of Rs.60,000 each in the first and the second year.

Now we want to find out what is the inherent rate for the project. For example, say you are investing Rs.10,000 in a bank. The bank pays a 10% return.

So, our investment becomes Rs.11,000 at the end of the first year which comprises of Rs.10,000 which is the principal and the interest of Rs.1,000 at 10%. 

So, the initial investment here is Rs.10,000. The inflow is Rs.11,000. Now, what is the internal rate of return of this bank deposit?

Well, Rs.1 invested today at 10% will become Rs.1.1 at the end of the first year. So, what amount invested at 10% will become Rs. 1?

Interest Rate 10%
Year 0Year 1

Well, the answer is 1/1.1 which is Rs.0.9091. This is commonly called the present value factor for the first year at 10%. Using the same technique, we can easily calculate the present value factor for every year at a given rate. So, the internal rate of return of the bank deposit is 10%. If you discount Rs.11,000 which is the inflow in the bank deposit for 1 year at 10%, you get Rs.11,000 multiplied by 0.9091 which is Rs. 10,000. This is exactly equal to the present value of cash outflows which is our initial deposit of Rs.10,000

To find the internal rate of return though, we don’t have the interest rate because that is the internal rate which we have to find out. So, how do we do it?

Let’s first have a look at the numbers we have in hand. We have the cash inflows in each year which is Rs.60,000 in each of the years 1 and 2.

We have the present value of cash outflow which is Rs.1 lakh. We also have the duration which happens to be 2 years.

So, how do we find the internal rate? Very simple!

We know that at the internal rate of return, the present value of cash inflows equals to the present value of cash outflows. So, logically we have to guess a few rates and by trial and error find out what is the internal rate of return.

But then, guessing the rate cannot go on endlessly since there are millions of interest rates which can be 1%, 2%, 14.23%, 9.7% and so on.

So, we use the technique of interpolate where we guess the answer using 2 rates and then interpolate the numbers to arrive at the actual internal rate of return.

How to do this?

Let’s first use the guess rates 10% and 12% and find out what present value we are arriving at in each of these two cases.

So, we see that neither rates give us our exact initial outflow of Rs.1 lakh. In simple terms, if we had invested Rs.1,04,132 today at 10% for 2 year, we would have got Rs.60,000 each in the years 1 and 2. Likewise, if we had invested Rs.1,01,403, we would have got Rs.60,000 in years 1 and 2 at 12%.

But if you see, we have invested just Rs.1 lakh and got the same inflows in years one and two.

So, it follows that our internal rate of return from the project is higher than both 10% and 12%. So, how do we find this? For this, we need to adopt the process of interpolation.

This is what we call as IRR. It is something similar to a return on capital employed but is more scientifically calculated. It is a very important tool in project evaluation. If the IRR is greater than the cost of capital, the project is a good project and can be selected. If the IRR is lower than the cost of capital, then the project is not a viable project.