When should we use IRR (Internal Rate of Return)? The Case of Delayed Investments

Although the internal rate of return is a very valuable tool in terms of evaluating whether or not to take on a project, in some cases for example: When you have a delayed investment IRR will break down and fail and you're better off using net present value to make your decision. So just a quick review the IRR decision rule is that we're only going to accept a project if the internal rate of return is greater than the cost of capital and by cost of capital I'm talking about the opportunity cost of capital what you could have done with that money.

So we think about this only is the IRR guaranteed to work (by guaranteed I mean in every situation could you count on it) if all of the negative cash flows are going to come before the positive cash flows. So when you have in a situation like that you've got the negative cash flow coming first and then all the positive cash flows when that happens then you can trust IRR always.

However, if that is not the case for example A delayed investment IRR might break down.

So let's say that,

You started your own construction company and you receive 10 million dollars up front to do your very first project. So you've got the 10 million dollars in the bank but you still have to go and build this building or whatever your project is and that's gonna cost you 4 million dollars a year for the next 4 years in order to complete that project.

So if we were going to think about mapping out your cash flows it would look like this.

So you're gonna have a positive 10million and then you're gonna have a cash flow of negative 4million. So you're receiving 10million dollars upfront, we're gonna call that year zero, which is just the beginning and then at the end of the year when you payout four million in terms of costs on this project and so forth, at the end of year two, at the end of year three and the end of the year four, that's how the cash flows are gonna look for this project. So we're gonna call that a delayed investment because you're actually investing the cash later. Upfront you're getting the money and then you're investing the cash. so let's take a look at what the IRR would be. (I actually used Microsoft Excel and I just used the following formula)

Which is Equals and then Rate and then I have here the 4 for the four periods and then I have here the negative 4million and then I have here the 10million you receive upfront and then the zero at the end. 

So you don't have to use this you could use the IRR function. You could solve it by hand we've got another article on that. Right now let's just focus on what the IRR is. It's 21.86%, if you use that formula that's what you get. So that's the IRR and now let's think about this. Our cost of capital is 12% so normally if we go back to to our IRR decision rule, we're gonna accept if the IRR is greater than that opportunity cost of capital,

So is the IRR greater than 12%? Of course, it is. So according to the IRR decision rule we should accept this project. However if we were to calculate out the net present value we would actually see that the net present value.

I've just calculated it for you to save time, so the net present value is actually negative. What does that mean? That means that you reject this project and we've talked about it in another article and I'll just remind you here that if there's ever a debate between the net present value or a difference between the net present value and the IRR there's some kind of conflict go within that present value the net present value decision rule will always give you the optimal decision whether or not to do the project or not. 

So it's clear here you're going to reject this. So then you might think hey what is going on here? The IRR is 21.86% and yet you know that's higher than the cost of capital so why is the IRR (higher in this case) is it telling me to accept, when the NPV is saying to reject

Well, the way that cash flows are set up it's almost like you're borrowing money. If you look at it you're getting 10million in the beginning and then you're paying out these negative cash flows over the life of the project. Isn't that like as if you were to borrow the 10million and then you pay it back over time? Now I know that's not what's happening here but it structured the same way. So basically this rate it's almost like an interest rate it's almost like this is the rate you're paying. 

So this 21.86% is almost like the rate you're paying instead of what you're earning. I know that it's not the case of reality but that's the way it's kind of set up and so, in that case, you would only accept the project if the IRR which is 21.86% here was actually less than your cost of capital.

So just in this kind of weird situation where you have this delayed investment in this particular situation, it would actually be reversed. So since 21.86% is higher than the cost of capital (which is 12%) this is like the rate you're paying on the investment is higher than your cost again then you wouldn't want to do it. In this situation, IRR is only guaranteed to work if all the negative cash flows come first and we have a positive cash flow right off the back but still, it is useful to know the IRR even in this situation because then you can look at its sensitivity analysis and say for example you would have underestimated your cost of capital here by 9.86%.

So this means you would have had to underestimate this by 9.86% before the NPV would actually become positive. So it can give you a little idea of sensitivity. So even if you have the cost of capital is actually 14% or something like that you still should be rejecting the project so it is useful with sensitivity analysis but bear in mind the NPV is what's going to tell you here correctly that you need to reject this.

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