I am going to move on to the third criteria, that criterion we are talking about today which to me is extremely, extremely important for two reasons. One, it's used [SOUND] even more now. I mean, almost as much now as it was 40 years ago. And it competes with NPV in the proportion of people, even in the developed capital markets, we use it. It's called the Internal Rate of Return. I want to spend a lot of time on it and emphasize it similarly as I did with NPV. I kind of went quickly over payback, but I'll recommend very strongly don't use it, okay? However, I think IRR is used almost as much, or in fact, slightly more than NPV. And I want you to understand it fully, so that's why at the beginning of this class, I decided that I'm not going to just teach you what is maybe the better thing to do. You need to also recognize what's done in the real world, and recognize its strengths and weaknesses. And IRR is very subtle. IRR is a seductive, it's subtle, it's intuitive, yet it has problems. It's not blatantly got issues like payback does, right? So let's start. And I want you to recognize, that ironically, even though it's used a lot and we all get a feeling like we know it, we don't. So therefore I have to do a lot of effort here on what the heck is it. So let me ask you this. As always, what is the IRR of this simple example? So what is happening? At time zero you're spending $100 million, and let's make it for convenience. So that you're not, let's make everything in millions. So that we are not worried about, for $10, why should I even do this problem, right? [LAUGH] You want some excitement in life. So let's make it exciting. You have an idea, or somebody has an idea, which involves $100 million of outflow. Setting up the factory, getting the right thing and it lasts for one year. Again for simplicity, we go longer. How much does it get to you in one year? 110, can you tell me the rate of return on this? Hit a pause for a second becaise I think if you have a little bit of math ability in your mind, you should tell me the answer. The return, everybody intuitively understands. It's how many did you make on the investment you put in? So look what you'll tell me. I think almost all of you will tell me the answer is 10%. And the reason you're going to tell me that is how much have I made over one year? Yes? I spent 100 subtracted out from the 110. But remember the units. It's on how much did I make 10 bucks. 100. So it's 10%, right. So I gave you a very simple example. So what is the IRR of this problem? 10%, okay, let me see what we have done. This is what you've calculated, I'm just reflecting what you did in your mind. And I think this is an excellent way of teaching IRR that I found over the years, rather than just throwing a formula at you. I think I cannot say it often enough how just a little bit of insight on how to teach or how to understand something yourself, how it goes a long way, and I follow a simple principle which I hope I'm reflecting in everything I'm doing. I just try to think, what the heck am I doing before I use a formula. So think about r, it's very intuitive. FV is the future value, PV is the present value. You subtract the present value from the future value and what's the present value. It's a negative number because I made an investment of 100 and then you divide by your investment which was the present value. And this is what you came up with. Two things to remember about this. One, it's a percentage and it's per period, in this case, year. So its a number that is calculated over time and its a percentage. Because its calculated over time it applies to a period of time. So if your time is one year, its 10%, if time in one month probably a smaller number. How would you say it in English? You'll say what is my final sum, and what is the initial sum? Which is what I put in, and the difference between the top and bottom many times called the money you made or the profit divided by your investment which is 10 bucks divided by investment of 100 bucks. Right? Pretty obvious, right? So now, I'm going to mess with you, meaning I'm going to try to figure out whether you really know rate of return and what does it mean. Okay, what is the intuition? What does the NPV of the idea if you use the IRR to calculate it? What am I saying here? What is my cash flow, right? What is the NPV of the idea if I do do it. So let me just quickly, before I go to the next bullet point, let me just quickly write something here. The NPV of the idea would be -100 + 110 / 1 + R. Right? Why am I dividing by 1 + R? Because I want to bring the 110 back. The question I'm asking you is, you calculated your IRR and you put it in here, 10%, what do you get? Zero. And don't, this is very important, because i'm going to use this formula later. So see what IRR is doing. If I use my IRR to calculate my NPV the answer should always be 0. And the reason is very simple. The internal rate of return is called internal rate of return because it only needs one thing to calculate it. Remember to calculate NPV, you need two things. You need 100, negative, 110. But for IRR to calculate it, look at this. All I needed was the 110 and the 100 which is the cash flows. So that's why it's called internal. It's internal to the idea. So when I calculate a 10% rate of return and use that same IRR which is based on the cash flows to then calculate the NPV of the idea what am I using? I'm using the idea's own return to calculate the NPV. Is that right? The answer is obviously not. Why? Because if I use my own rate of return to calculate my own value I'll come up with where I began. Zero, right? So, remember, this equation is not what you should do to figure out NPV, this equation just tells you what the text book tells you. Suppose you want to calculate the IRR of the following problem. Negative 100, 110, what is the rule you'll use to calculate it? Well, you use the rule of figuring out that number which makes your NPV Zero. And the intuition here is to remember you're using your cash flows to figure out your rate of return. That's all you're doing, and its a mechanical process of calculating. So let's use this a little bit, what does this tell us? -100 = -110 / 1 + R, so both sides are become negative. I've taken to this to the other side, which implies R is equal to 10%, so this is a rule of thumb we use in calculating R. In this example, it's very straightforward. So let me ask you. Let's do a simple exercise. In this example, suppose I don't know my IRR. The first number to start is what? Zero. Why zero? What will you get? -100 + 110 / 1 + 0 is ten bucks and it's not equal to zero, right? Then try a higher number, it's called trial and error which the laptop or the computer will do to figure out your rate of return. But it's such a simple problem, you don't need an Excel to do it. Okay? So I'm going to now ask you, is this idea a good idea? Sorry, there's a little bit of overlap in my writing, but we'll manage. Is this idea a good idea? Which idea? An idea where I spend 100 bucks and get 110. What do you think? I hope you say you don't know. Because lot of people will turn on and say very cool idea. 10% rate of return but the tragedy of IRR is that it has no benchmark built in. There's nothing that tells me whether the 10% is good or bad so let me bring in that thing that I asked you to put away at the back of your head. Risk. Right now we're ignoring risk so it's becoming difficult to internalize this. But suppose the risk of this business is such that even 20% rate of return is too low. Is this a good idea? Maybe not. Right? On the other hand, if the risk is so low that you're a genius, you're able to create 10% rate of return, it's a good idea. So here's the question. What if others in this type of business are making 8%? Tell me what is this 8% now? What do I mean by, others in this type of business making 8%? This is called r, remember? If I want to calculate the NPV of this idea, it is what others are doing who are my competitors in a similar business that is to be used as my discount rate. Now tell me what will you do? Is this idea good or bad? It's a great idea. Why? Because I'm making 10%and everybody else is making, less. What should happen? Money should flow to me, not just mine, other people's. Is that clear? Why, and please do this. What is the NPV of this added percent? And you'll find it's greater than zero. I'm not even going to do it, you can do it visually. -100 + 110 / 1.08 has to be a number greater than 0 because at 1.1 it's exactly equal to 0. Now let me throw in a little curve ball there, suppose instead you made a mistake, you're analysis wasn't right. You go and try and figure out did I get other people in this business right? Then measure their return right? And there are ways of doing that, we will get to later in the class. And you'll find out, boy, no, I was wrong. Other people actually making 12% on ideas like this. Should I do this or not? No, because others are doing better than I am. So, R In this case, is greater than IRR. Don't do it. And you'll find that NPV is less than 0. So the important element in all of this is to remember that if you calculate an IER of 10%,it doesn't mean anything in isolation. So the first thing to remember is doing an IRR calculation just requires you to know your business well. It's internal to your business. All it needs is your business's initial investments and future profits. However, it's not telling you anything because there's no benchmark. So if the benchmark is 8% and you're making it 10%, good news. But if your benchmark is 12%, that's what other people are making. Somebody would be really silly, including yourself, to put your investment in your project rather than other people's projects.