[MUSIC] We just learned that IRR and NPV can be equivalent, right? You make the same decision using either IRR or NPV, okay? But before we start moving too fast and say yeah, we don't need NPV we can just compute IRR, we have to talk about a few problems with IRR, okay? There are some issues that you have to know about that actually limit your ability to use IRR to evaluate projects, okay? The first notion is that there are some investments that are not going to have a well-defined rate of return, okay? Sounds a bit strange but consider this example. Suppose we have this timeline and we already learned about timelines, okay? So we have an investment that gives you $20 million today, right? So this is like the accounts receivable problem. You get $20 million today, and then you have to pay $22 million tomorrow. Okay, so you lose $2 million, right? Using the same intuition that we used when we first talked about IRR, it sounds like the rate of return on this project should be minus 10%, right? You're losing 10%, okay? But try to use Excel, write down this problem in Excel, I mean it, it'll really do it. If you have Excel, try this, okay. Write down the timeline in Excel, okay. And then write down 20 minus 22, and ask Excel to give you the IRR. Excel will tell you the IRR is 10%, okay. And now this is not a Microsoft problem, [LAUGH] okay? This really is a mathematical problem. What Excel is doing is, Excel is doing those two steps that I told you about. Compute the NPV, and then set the NPV to zero by trial and error. Computers can do trial and error algorithms very quickly, right? So I have Excel just trying a bunch of possible discount rates, and it turns out that if you discount minus 22 by 10%, you're gonna get minus 20. So 20 minus 20 is zero the NDT is zero. Okay, the IRR is 10%. Excel gets a solution. The problem though is we know the solution is wrong, this is the, you know, this investment is a, this is an investment that is losing money, right? You're not making 10%, you are losing 10%. Something is wrong. Okay, right? And here you might think okay, I'm clever, I can figure this out. If I have an investment like that, all I need to do is reverse the sign. I do this in Excel instead of getting positive ten I take minus ten. That's the rate of return, okay? That could be, the problem is that it gets more complicated. Suppose you have this case, again another timeline. Minus 4, 25, minus 25, okay. So, you invest minus four today then you get the payoff of 25, let's say million dollars, tomorrow or in a year. But then you have to pay again. You have to pay minus 25 million in two periods, okay? Let's try to use Excel. So write down the cash flows, use the IRR function, okay. Excel will tell you that the IRR is 25%, okay. I write the answer here. Is that reasonable? I mean, who know I mean now it doesn't sound crazy that you have a 25% rate of return here, right? The 25 minimum payoff comes before the -25, maybe, okay? But this is the problem, write down this equation, okay. If you have the time, the patience to do that, just write it down in a calculator or in pen, you know just do this calculation. Minus 4 + 25/(1+400%)- 25/ (1+400%) ^2, so, what does this, let me actually write this down here for you. This is the NPV of the investment. This is the NPV of this cashflow. Of these cash flows, okay. The NPV is equal to zero, okay. If the discount rate is 400%, right? What does this mean? Is 400% also an IRR? Okay, so do we have two possible IRR that doesn't make any sense right? An investment should have one rate of return, not two rates of return. So there's something wrong with this problem as well. The other thing you can do, by the way, just do it in Excel, is you don't wanna do this equation. Write down the NPV in Excel to convince yourself that if the discount rate is 400%, you should also get the zero NPV, okay? There is a problem. Think about the following thing. What is the common feature of these two examples, okay? The common feature is that you have a negative cash flow that is coming after a positive one, okay? You have positive and then negative, so 20 minus 22, 25 minus 25. Here's my advise, okay. If you see this pattern, positive, negative, do not use IRR, okay. It is tricky, it is complicated. And it might lead you to make the wrong decision, okay. So if there's positive and then negative, unfortunately, you should not use IRR, okay. That is the lesson, and there is really no reliable mathematical way to solve this problem, okay? The second problem that you have to know is an issue of magnitude, okay? So the NPV as we talked about is in the same unit as cash flows. So if the cash flow is in dollars, the NPV will be in dollars. The cash flows is in pounds, the NPV is going to be in pounds, okay? The higher the NPV the greater the impact of a project on value that concept we learned when we're talking about NPV, okay? The IRR in other hand is a percentage return. If you recall our lesson, that is the reason why we're using IRR is because we want to measure investments and percentage but this can create problems. Okay, think about the following. Suppose we have two investments. We have an investment that requires one cent today and pays off two cents next year, okay? So you make one cent in a year, he's asking one cent today. And then you have an investment that requires one hundred dollars today and pays off two hundred dollars next year, okay? If you compute the rates of return of these two investments you're gonna find what? You're gonna find 100% for both, okay. The first investment, you invest one, get two, right? The second one you invest 100, you get 200. It's in a different unit, right? The first one you're investing cents, the other one you're investing dollars, so invest two requires a bigger investment. It gives you a bigger payoff. Both have the same rate of return, okay. But try to answer the following question. Now comes the question for you based on this simple example. Suppose the discount rate is 10% which investments would you take, okay? And then think about which one is the better investment and which investment has the greater NPV. So you can either calculate NPV, but I think it will actually be obvious which investment has the greater NPV, okay? But you can do the calculation if you want. So lets do the answer here, okay. Which investments would you take? Remember the rule, we take all investments that create shareholder value, right? So we would actually take both okay. Investment one, you know, it's something, you know, one cent we don't care about, right? But it is a good investment, it is creating value. So you would actually take both, right? That's what we should do. But, obviously, Investment 2 is the better one, right? You are making a hundred dollars instead of one cent, right? So it is obviously the better investment to take, okay. Which investment has the better NPV? Investment 2, right? You can do the calculation if you want but it's obvious that investment 2 is going to have the higher NPV, okay. So think about tha the IRR is telling you correctly that both investments are good, but the IRR cannot tell you which investment is better, okay. The IRR will tell you that both investments have the same rate of return, right? Whereas, if we use NPV, we'll be able to figure out that Investment 2 is going to create more shareholder value, okay. So this is the other problem, and there are really only three rules to remember. The bottom line of all of this discussion we are having about IRR and NPVs that there are three rules that you have to remember, okay. The first one is that IRR and NPV are going to lead to identical decisions in most cases. So if the IRR is bigger than the discount rate, the NPV is going to be positive, okay. That is a really important idea and you should remember that, okay. However, there are the qualifications, right? There are cases where you should not try to compute an IRR, okay. If you see a negative cash flow coming up after a positive one, don't compute IRR. For example, recall that we worked on our accounts receivable problem, but I never computed an IRR in that problem. We solved that problem only by using NPV, okay, right? Why? Because that was a case where the positive cash flow came first and then the negative cash flows came later. Okay, so don't compute INR in that case. And third rule which is simple beware of magnitudes. Okay, so you cannot reliably use IRR to compare investments of different sizes. So our cents versus dollars example showed that very clearly. So if you want to compare investments, the safest way to do it, is to use net present line.