The decision rule for IRR really becomes whether it has you're making more money than the others. So I'm going to spend a little bit of time on graphics. I think graphics can help a lot, especially by something so complicated. So let me draw and I hope you follow with me zero and let me draw this NPV, and let me call this r, okay. Why am I drawing this, for two reasons I have a value of zero here. Why am I making it zero NPV? Because I know that if I'm going on the south side of this, it's not good. Why? Because I'm actually destroying value, right? So remember, value creation means positive net NPV. Why am I taking r up to zero? Because we have assumed for the purposes of our whole course that the r cannot be negative or will not be negative. I shouldn't say it cannot it can, but let's stop there for a second. So now I know what is my project? Negative 100 times zero plus 110 times 1. Got it. Okay. Now let me show you what the relationship is. Suppose I don't know the IRR of this, right? I know, because I can calculate 10%. But suppose I don't know, this is what a calculator will do. Will start off with zero. So if the IRR is zero, if the discount rate is zero, what is the NPV of the project? This is the easiest example I could ask. If time value of money is zero, what can you do? You can add, so the NPV will be 10, right? But if r, the discount rate is 10%, what do we know about the NPV of this project? It's zero, because that's the definition. If I use 10% what is the NPV? Zero, because 110 divided by 1.1 minus 100. So draw a line And this is a little bit, just pay attention a little bit to this. How difficult in this example is it to calculate the IRR of my project? Very easy in the graph, 10% is the IRR, why? Because I know at 10% the NPV is zero. What is true now, what has this told me? One simple fact that my project is going to make 10% rate of return, however, doesn't mean anything. Now I know that I have to compare it to whom, the cost of capital r, what are other people making? So look what happens, if other people are making less. Is this project valuable? Answer is yes. This is positive NPV, however, if other people are making more which direction I'm I going, my idea? Negative NPV, so the rule of Tom is very obvious here, if IRR is greater than r yes, if IRR is less than r, no. But the tragedy of this rule is what, I'm choosing this to be a yes only because in NPV is positive. Why am I saying no? Because here NPV is negative, so the tragedy of IRR is, IRR cannot work by itself, 10% by itself doesn't mean anything. And I please encourage you to internalize this, because this is so important and popular pressed, says only, reports returns. They don't mean anything in isolation. We'll see. But in order to make decisions if you calculate your IRR. What do you have to compare it to? How much other are people making? That's the benchmark okay, so if you use that benchmark, you come up with the decision rule, that you do things if you're doing them better than other people. Another example, and this will show you why we use formulas. Tell me, what is the IRR of this idea? I'm going to pass for a second and let you think about it. You see, this is going to make your mind go nuts. So tell me, let's draw the timeline. Let's draw the timeline of this, okay? So what has happened? 0, 1, 2 does it look like the same problem we had before? Yes, I've thrown to you. I've said you spend 100 today. Same as last time and let that be million dollars again. But I said your idea is such that in the first year you're more likely not to do anything, make any money. Is that possible? Of course it's possible. What do the best ideas of the world do? Not make money for a long period of time initially and then boom, right. So 110 in year 2. Do the numbers, are the numbers the same? Yep. But what have I done, I have oranges times zero apples. Time one. And now I've thrown in bananas. Time two. So by shifting time by one, what have I done? I made life a little bit miserable. And that's why you have formulas. Okay, so what is the IRR over 2 years? So if I want to say suddenly, okay, I'll solve this problem very easily. I'll just make my period 2 years. What is the IRR over 2 years? So you have negative 100. You've positive 110. 10%, right? Same answer. But is it comparable to the previous one? No, because 2 years is not the same as 1 year. I mean, you have to remember time value of money. So the question is, what the heck do I do? What is the IRR of this per year? So that's why things have to have the same periodicity to be compared. So what is the IRR per year? That's a tough one, right? Because what I have I done, I've thrown in an extra year where nothing is happening. So hopefully it will solve this problem, very easy to think about. Very tough to do, make NPV zero. What would that do? Negative 100 plus zero. How much of discounting do we do to the zero, in year 1, 1 plus IRR, plus in year 2, what do you have? 110. One plus IRR square, quick question. This is IRR, quick question. How many unknowns in this equation, zero equals 100 negative plus 0 over 1 plus IRR plus 110 over 1 plus IRR squared. How many unknowns? One. Which is IRR. What's the problem? It's not easy to calculate why? Because of pause again. Compounding. So IRR is stuff to do mentally, because of compounding when the number of periods increase. If it's one period relatively easy, and that's why, who do we go to, to the computer and I'm going to do it in a second. Before I do it, I have two things to do. One. I'll show you the formula. Genetically, we shouldn't surprise you. How do you make NPV zero in a second? But number two, I'll go to the calculator. But before I do that, the second thing I wanted to say is, can you guess what it is? So over 2 years, if I asked you. Suddenly the world is 2 years is 1 year, one period of time. You know what the answer is 10%. What will it be per year? I think many of you will be tempted to choose 5%. But then again, you are kind of stabbing me. You're forgetting what, you're forgetting compounding. So if money earns no interest on the money, you are on the right track. But then life is very easy. We don't need to do most of this class. Turns out the IRR will be less than 5%. I can guess that simply because I know there's compounding and the actual answers probably 4.9 or something like that. It will be slightly less than 10%. So I want to do this in a calculator. But before I do that, let's just stare at the genetic formula. IRR is the return that solves the following equation. Where Io is equal to C1 plus C2. I would rewrite it if I may, in a slightly different way where NPV, which is equal to minus Io plus all this junk is equal to zero, so equating Io to the right hand side. If I take Io to the right hand side, it becomes NPV formula, and then forced it to be equal to zero. So let me ask you this, in our period how many cash flows were there? Nothing here. 110 here. Now you could have many more cash flows. The problem is from being a quadratic problem, it becomes a problem like which E equals m C squared was cool for Einstein, because he stopped at square. But when he saw N, he said, man, this is to go. This is just too much mind boggling, and it is, the power of compounding now is in reverse, it's in the denominator. We did future value and are trying to figure out present values, a tough thing to do. So what I want to do now is take that problem, simple problem and do some calculations on the calculator. So let's go on a tab and let's keep those numbers there. And actually, no, why don't we just delete that number, and what was the problem? I'm spending negative 100, right? This was what, zero, this was worth 110. Right, everybody okay. I think you're okay. Let's do it. So what is the function? IRR, open up the bracket. Parenthesis, what do you know? You want to just throw in values. Now, remember, in IRR, you have to throw in all the values. Because if you don't throw anyone IRR, they laugh at you. In fact, the excel will say, come on, get real. You're getting 110 for not doing anything. So IRR has to have a1, c1. And you don't want to look stupid even to excel, because there's no point. Now you can throw in a guess. I'm not going to, and the reason is, the answers pretty straightforward. And the reason I'm getting 5% is because the number of decimals in this is not big enough. So the answer here should be actually, if you increase the number of decimals, it should be 4.88%, okay. And the way to double check, this is what, if I use 4.88 to discount 110, what answer will I get? I'll get exactly 100 bucks. So let's do that. Let's take PV of rate of 0.0488, right. Am I okay here? Yep. Number of periods 2, pmt 0, future value 110, future value sorry 110. Exactly 100. So by this, I know that 4.88 is the answer and that the decimals are not showing up in the 5% the way it's set up right now. So what you want to do is you want to make sure always that the decimals are showing. So let me just go here and do that for you 1, 2. So now I'm showing not just zero decimals. I'm showing all, you see my answer was right because it's simple problem, that number was in my head. Now when you come back, let's take a break. When you come back, we'll do more complicated examples. We'll talk about IRR as a principal, and we'll take it to the last piece of today's session. But I think you need to understand right now how to calculate IRR and what does it mean, two things. Calculation requires making NPV of your project zero simply because it's the easiest way to figure out IRR and the multi-period context. Quadratic, higher order numbers throwing in because of compounding, the second getting 4.88 it by itself doesn't mean anything. It doesn't mean anything. 4.88, it is better than zero. Yep. But how do you judge whether this is a value creating idea? You cannot judge something just by your own cash flows. You have to go figure out what other people are making. In the banana business, this is awesome. Why am I saying that? Because if you own 5% 4.88% per year in banana business, you're in great. But if you're talking about iPads or technology, probably not such a good idea because others may be making more and money won't come to you to create a new project. So take a break. We'll come back. We'll keep plying through the stuff. This is actually both intuitive and practical. Take care. See you soon.