Hi, welcome back to finance for Non-Finance Professionals. In this video, I'd like to talk about a couple of wrinkles with the internal rate of return. In our last video, we introduced internal rate of return as one of our capital budgeting tools for how to spend money within the firm. There's a couple of things that we need to be careful about with the internal rate of return, we liked it. We said, it was a lot like net present value, which was our gold standard capital budgeting tool. And since IRR was a lot like MPV, we talked about a lot of the benefits of using IRR, but there's a couple of complications in practice that I want to at least talk through with you. But first is loan kinds of flows when the cash flows get reversed, when they come in and go out, come in and go out. IRR can get a little bit funky for some math reasons that I'll talk about at a high-level. The other is the scale problems. We can sometimes make bad capital budgeting decisions based only on IRR, because we got rid of the scale. In other words, we rather have more money than less, but IRR has gotten rid of how much money were making overall. It's put in percentage terms, we need to be careful about that. The other is a timing problem and the other is some mathematical complications with IRR that I'll talk about at sort of, again, at sort of a high-level. Let's talk about loan flows. When the cash flows are reversed, an IRR can sometimes give me a misleading picture about whether or not the project is adding value to the firm. Money comes in and then money goes out, the sign can actually flip. Anytime the sign flips, I need to be careful about using IRR. In other words, if I spend money on a machine and then the machine generates revenue and then I have to retool the machine in year three and I spent more cash and that money comes back in again, that's two sign changes. Money out, money in. Money out, money in. Anytime that flips a couple of times, you have to hesitate say, hang on and be careful about using IRR. So, let's talk about that a little bit. Consider these two projects, X and Y. In the first, I'm going to spend 500. So this is our normal capital budgeting, I'm going to spend $400 in order to generate $500 a year from now. If I work out the NPV, it comes out to 54.54. If I compute the IRR, it comes out to 25%. In the second project though, I've got $400 coming in and then I spend $500 in year one. That's like a loan. I'm getting money in, paying it back later. What happens here, the net present value is minus 54.54, the whole thing flipped. I'm not making $54, I'm losing $54. I compute the IRR, it's the same, it's 25%. What happened? Did something get screwed up? Not really, the math is clean, the solution too. What rate sets that NPV equals 0 is 25%? It's just the NPV flips sign. So, we have to be careful anytime there's a flip in the sign of the cash flows. If I think about it from the graph perspective that we talked about when we talked about IRR in the first project, the NPV kind of looks like this and that's the IRR. But in the second project, the returns, the NPV looks like that. They have the same IRR. But for a low discount rate, this one's going to give me a negative NPV, whereas the other one was going to give me a positive NPV. Something to be careful about, loan-type flows. Any time the cash flows switch sign, again, what's the solution? Just put it next to an NPV. If you compute an IRR, put it next to a net present value that always serves as a check on whether you're getting the right capital budgeting decision. The other thing that we need to talk about is comparing scale with the IRR. It's hard to compare to what we called mutually exclusive projects. In other words, if I have an apple or an orange and I can only choose one piece of fruit, I have to choose either the apple or the orange. I can't have both. So in choosing those, we call those mutually exclusive choice. In choosing the apple, I have to forego the orange. In choosing the orange, I have to forego the apple. So, let's think about how we would compare mutually exclusive projects with the IRR. The higher the IRR, it's hard to determine whether or not that's going to imply a higher NPV. Let's look through a simple example. In Project X, in my first project, I'm just going to spend $1. Maybe I've got a rig and all I'm going to do is leave the rig where it is to keep drilling the end of a well. That's going to generate $2 in period one. Well, hey, that's a great project, because I'm only spending $1 in order to make 2, that's a 100% IRR. Doesn't that look like a great project. Here's the problem, I could move that same well to a new hole. That would cost $100, but would generate 120. Now, that's only a 20% IRR. It looks like project X is bigger than project Y in terms of adding value, because it's got such a bigger IRR. But if I compute the net present value, this generates $0.82 per dollar. This generates $9.10. Much bigger net present value, I should move to rig. Project Y is much better from a net present value standpoint, because it is generating a lot more value for the firm. It's just that project X is generating a relatively higher number, that's what the IRR is telling me. But in getting rid of the scale, we got rid of the scale. Again, how do we solve the problem or how do we make sure we made the right decision? We take that IRR, put it next to a net present value and that checks with the IRR is large enough or whether the scale is giving us the right decision with IRR. Again, we could see this graphically as one project might have an IRR here, but a similar project might have the same IRR, but a much higher net present value. Obviously, this project is preferable to this project. Because for all discount rates less than the IRR, it's going to generate more NPV. We just have to be careful of the scale. Always put that IRR next to present value. It could be that there's no rate. There's no solution to that polynomial. You've put in Excel and it gives you that dreaded not applicable or gives you dollar signs or gives you some kind of weird symbol in Excel that says and you keep banging on it, it won't give you an answer. It could be that there's multiple IRRs or no IRRs. If we consider, this example on this slide, I've got two projects for you. In both cases, we spend $100 in order to make 235 and 136 or in the next project to make 120 and 50, minus 50. In the first project, there are actually two IRRs not one. In the second project, there is no IRR. Well, how could that be? If I put it in Excel and I hit return, it might be that there's actually no way to solve that problem and Excel kind of chokes on it. Well, let's think about why that might be the case. Remember, the IRR is just a solution to a math equation. It could well be that the project looks something like that. The NPV gets bigger for a while, then starts to go down. This project would have two IRRs, like we have in that example. It could bee the project such a total loser that it never gets up to a positive NPV. That also would have no IRR, because it never crosses. Again, how do we solve the problem? It's easy, just put that IRR next to a net present value and you can always check whether or not the IRR is giving you the right capital budgeting decision. So IRR is a good capital budgeting tool, but we need to be careful. If there are changes in mutually exclusive projects, the scale problem, timing or whether or not there's an answer or solution, always check next to present value. As long as you put IRR next to NPV, it's a perfectly legitimate. In fact, it's a nice way to get a scaled down or a smashed down version of what the return on the project is relative to the discount rate.