When to Use IRR (Internal Rate of Return)? The Case of Multiple IRRs for the Same Project

The internal rate of return is a really useful tool in deciding whether or not to accept a project for a firm but in some cases, you actually end up where you have multiple IRRs. So you might have an IRR of 10% and 21% and then maybe one of -7% all for the same project and in such cases you really can't do anything with the IRR it's really kind of useless and you're better off just using net present value.


So I'm going to go through an example in which you'd have multiple IRRs but first let me just give you a quick review of the decision rule with IRR is that you're only going to accept the project if the IRR exceeds the cost of capital and by the cost of capital I'm talking about the opportunity cost of capital.

So IRR is only guaranteed to work right if all of the negative cash flows come before the positive cash flows. So if you have you have negative 10million and then you have positive 3million and then positive 5million then positive 8million etc you have some set of cash flows that look like this


then you can use IRR. So let's take an example:

let's say that. 
You start a construction company and you're accepting your very first project and for this project you're going to receive $500,000 upfront so we'll call that year zero, so right upfront you're going to get five hundred grand and then at the end of year 5 you will get your second and final payment of 10million. Now throughout the life of the project you're going to spend 4million dollars a year building any building or whatever for the next 4years to complete the project so at the end of year 5 you don't have a payment and your cost of capital is 10%.  

So we've got Year Zero, One, Two, Three, Four and Five and then the cash flows upfront you're getting positive 500k and then in year one negative 4million and four negative 4million and then year five you're going to have positive 10million and you don't have to worry about that 4million expenditure that's not coming, So you've got a positive cash flow upfront and then at the end, negative cash flows in the middle, that's the way that this is laid out.

So let's calculate our internal rate of return. Now you could do it by hand we have an article on that if that's what you prefer, I use the Microsoft Excel 

So you just put an equal sign and then the IRR function and then in parenthesis you've got the cash flows. So you start with and 500k here then you would have the negative 4million and then so you just list all the cash flows there in order of time and then at the end you don't have to put this but sit when there are multiple IRRs (it's a guess) you're guessing at what the internal rate of return might be so in this case I'm using (.4).

So I got the answer of negative 17.24% and 799.61%. That's a pretty big difference there right? So if you just looked here and said oh wow we actually got a negative internal rate of return but then you look at the 2nd one and it's a ridiculously high number so the reality is that you should be ignoring both of these. Just ignores the IRR altogether and what you really want to be doing is you want to look at your net present value and so I've just kind of put here

If you were going to calculate the net present value you've got, I'm not going to go through those all the calculations for you, but does this give you the end result so you'd have a negative -5,9702,49 and I just got that number from this NPV equation. The net present value of this project is negative so you're going to reject this project. So again don't get into if you got more than one IRR regardless of what they are just ignore them, and just go and calculate the net present value and it's important.

If you're wondering why we even have this situation where we have multiple IRS well if you remember we said that IRR is only guaranteed to work when all the negative cash flows happen first they have to come before the positive cash flows, if we look here we got the negative cash flows here but what happens before that we actually have a positive cash flow right off the back so that's why this is kind of messed up you're getting more than one internal rate of return so in a situation like this just calculate the NPV and go with that.


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