Let's get started. Suppose you have mutually exclusive projects. Till now, the examples we did with IRR were, you have one project to look at but really many times what you do have is several projects and for whatever reason, you want to see which one to move at first or at least rank them in some way. This happens all the time. Turns out, if you fall back on NPV and think about it, which project would you take? Then the answer was pretty obvious, the one with the highest value because NPV is creating value and measuring value directly. Dollars or Yen and so on is our fundamental way of measuring value. Again, it could be [inaudible] but as long as we all agree what it is, it could be a currency in your local economy, it doesn't matter. What matters is the more acceptable the measurement unit and if that's the stuff that you use for your decision criteria, it's good. First of all, remember IRR is in percentage terms which should already make you feel a little wary. Suppose you have two projects and you are more, which one would you choose? A natural instinct of most people is to go with the high IRR, makes sense. Rank based on returns. If the highest project is 15 percent and the next is 10, which one most people would, say, choose? 15. I'm going to show you that this unfortunately is not right. There is systematic biases in IRR. I'm going to not spend the entire time talking about IRR. I'll give you two examples which are obviously a little bit constructed for the purposes of conveying the idea to you, but the same pattern is there in life. I would look at patterns, not necessarily the example. Let me show you some couple of examples which show you biases of IRR. The first bias is IRRs like short-term projects. Now, you see very clearly what the problem with that is. It remind you of another criterion actually, and it should, which is payback. But remember, payback is a little bit blatant about its bias. How soon am I getting my money back? IRR is much more seductive in devious in some senses. If IRR was a person who is purposely trying to deceive us, it'll be very tough to figure out what's going on. I'm going to spend some time. Now, look at projects A and B, they're right in front. I'll let you just reflect on them. I would recommend very strongly that even if I don't take a specific pause or the clip is not broken up video for certain examples, this example, take a break after this, think about it. Next example, take a break after that and think about it. Here are IRR cash flows. Project A, 0, 1, 2 minus 2,000, 400, 2,400. Remember, the timing of it is very simple. At time zero, spend some money, end of period 1, you get some money 400 and 2,400. Similarly for project B. Now, what I'm going to do is I'm going to calculate the IRR using Excel with you. However, remember what is the IRR? IRR is that rate of return which makes the NPV of this project zero. For example, if there was only one period, you know what you would do. But here there are two periods, so it's compounding, makes your life a little bit difficult. We'll go to a calculator. Are you ready? We're going to calculate it using Excel. You can use calculators too. Let's go to Excel. If you notice, I have already put in the numbers for cash flows. If you go up to row number 1, what you'll notice is in cell A1, I have minus 2,000. In cell B1, I've 400 and in cell C1 I have 2,400. This is project A. Project B is minus 2,000, 2,000, 625. Let's just try and do the IRRs. IRR function, remember you have to put equal sign, open a parenthesis. Let's do project 1. Remember it's in row 1 where A1-C1. I think I got it. Did I get the colon? Yeah. I'm not going to put in a guess and see if it works. It turns out it does. What is 20 percent? Twenty percent is the IRR of which project? Project Number 1 which means what? Just very slowly, it means the rate of return you earn per year over two years. Let's do project B. IRR, a2:c2. I am just telling it where the numbers are. Twenty-five. Think about this. I would choose which project first. Almost everybody would say go for project Number 2 because it gives you a higher rate of return and this is where problems start. I'm going to now go back to our presentation, and it's very obvious that I've calculated the IRR's and the IRR's I'll just write them down here is 20 percent, 25 percent. Let me just reiterate one thing. What is the IRR? IRR is that rate of return which makes the NPV zero, but that's the rule of thumb for calculating the number because with compounding, the number is very tough to calculate. At 20 percent, NPV is zero. At 25 percent, NPV is zero, but now the question I'm asking you is which of these two projects do you think most people will choose? They would choose Project B, and the answer to this is even though you choose Project B, it may not be the right choice, and why do we call it a short-term bias? Just stare at it. Are they similar in length? Yes. Physical life is two years of both projects, so what short-term bias I'm I talking about? Just stare at these two numbers for the time being. What do you see? You see that Project A is giving a lot of the cash flows later, whereas Project B is giving cash flows early. Which one does IRR favor? It favors B because of that earlier cash flow. Now I'm not necessarily saying therefore Project B shouldn't be taken, I'm just saying that comparing 25 percent with 20 is not the right way to do things, and I'll show you why not in a second. However let me ask you, what's missing when I compare 25 with 20? This is so common in the real world. What's missing is I'm comparing things internally. What is my real benchmark even for IRR? What is the cost of capital outside? I am not even looking at R, so this is key to decision making. Remember all value is relative, so if I just compare internally, my investor is not interested in my internal projects. Even if you are investing in the company, you're interested in how well are you going to do relative to the competition whereas the competition is nowhere there. There is a fundamental problem. Let me just show you now what I mean by the bias. In order to do that, we have to do a couple of things. Let me ask you to do NPV calculations based on five percent, 20 percent or 11 percent. Why I'm I giving you three numbers? Because you can do the analysis of your competitors or your investor will see, and we don't know what the discount rate or little R is. Little R could be five percent, it could be 20 percent or it could be 11 percent. There's a reason why I'm choosing all three and you'll see it in a second, but it should be pretty simple for you to calculate the NPV of both projects using five, 20, or 11, and I'm going to go to Excel to do this but only for a second, because I think you should know how to calculate the NPV of these, and then I'll just put up the numbers for you, but I'd encourage you when you take a break to calculate the numbers. Fair enough, you know how to do the NPV of Project A. What do you do? Minus 2,000 plus what? 400 divided by 1 plus R in parenthesis, plus 2,400 divided by 1 plus R-squared. I'm just saying you don't know your discount rate. Figure out what the value of your project is. What I'm going to do is I'm going to go back and I'm going to use five percent to calculate. Let's do this. Let's do the NPV. Remember NPV has some problems with it. Just remember that for a second. Let's use 0.05, which is the rate of return. Now what is this 0.05? This is not your IRR. What is it? It's that rate of return your investor will look at to compare you to them. We are doing project A. What after that? After that, it's asking for values. Now, remember, don't give value 0 for NPV. That's a little quirk. What do you do? You do b1:c1. Everybody okay? b1 c1, no a1. But then you have to remember that you need a1 to do this project. I've said plus because a1 is already a negative thing. Where does the net come from? From adding back a1, which is almost always negative. You need effort to create something of value. Let's see what the answer is. You get 557.8, so about 558 bucks. Let's do the same thing for project B. I'm going slow here so that we recap calculations. As I said, I promise I'll recap, but I won't spend time on doing for all interest rates. What do you do? You do 0.05 now, where am I? Cash flows. Remember, starting with year 1, so b2:c2 plus what do I add back? A2. Everybody okay? 471.66. What I'm going to do now is I'm going to go back and write out all of these numbers and confirm that we are all on the same page. Just give me a second here and we'll get going. Remember the two numbers we just did. We did 558 and 472. Let's go back and let's work with this now. NPV, I'm going to start writing here, at five percent was what? 558 and 472. The first question I'll ask you is, so suppose you do your analysis in your projects A and B, your are responsible for the cash flows, but now you go and judge them at five percent, which one will you choose? Suppose this is millions of dollars. Which one will you choose? Because if it's just dollars, you would say, "Come [inaudible] , you're still wasting my time. It's not worth my time to put in the effort to calculate". Suppose this is millions and believe me, corporations use millions of dollars to make decisions. Which one will you choose? You'll choose A. Now what is the second percentage? Twenty percent. Now you go and say, suppose my best alternative for the investor and for me, my competition is earning 20 percent, 1t 20 percent, I know this is zero, because I just calculated the IRR. It turns out the answer to this is 101. What's happening now? I just flipped. I've made at 20 percent rate of return. I will now choose project B. You see what's going on? My IRR rule always said, if you were using it blindly, choose B over A. But now I'm giving you two scenarios where it depends. At five percent go with A, at 20 percent go with B. Finally, I gave you an 11-percent rate of return. What was the scenario there? Turns out the numbers are 308, 309. What's going on here? I've chosen these numbers to show you three things. One, at a rate of return that's relatively low for the competition, I should choose project A. At very high rates of return for this kind of project, I would choose B, but at about 11 percent, what's true? I'm roughly the same. I'm indifferent between A or B. I'll put this or this. This is also one way of thinking about what we call in the real world is a break-even analysis. Eleven percent is the point at which you're indifferent between the two. I would really like you to draw graphs. To emphasize this, I'm going to now draw graphs, but remember the graph will be NPV versus rate of return, and I'll show you all the numbers. Let's get started. This is very cool stuff actually, and it's not that difficult to do. We have done this before. I'm plotting NPV here, which is value zero and returns rs. Let's start off trying to plot the two projects. If the IRR is zero, can I do the two? Very straightforward. If IRR is zero, I can easily figure out the NPVs of both projects. The first project's NPV is 800. Why? Because the cash flows, if you go back are minus 2,000, 400, and 2,400 and at r of zero, which is usually not the case. The calculator is trying to guess what it is. What is the NPV of project B at r 0? Turns out to be it is minus 2,625. You know the second point. What is this and what is this? These are the points at which the two projects have what? Zero NPV. These are the points at which the two projects will give you the IRRs. This graph is a way of figuring out what the IRRs is and what is this point? Remember what's true at this point? The NPVs are the same and they were about what? Three hundred and nine. What is this graph telling you? That at 11 percent, you don't care between the two projects. But at five percent, which one would you choose? A, and at 20 percent, which one would you choose? B. The 11 percent tells you a benchmark or a cutoff point, and the point here is very simple. You will choose project A if the competitors are earning anything up to 11 percent. After that, you will choose B if then other competition is earning more than 11 percent. Let me ask you a simple question and then we'll take a break. When would you choose neither? It's very simple. Stare at this graph. When would you not choose either one? Well, at what rates of return that the competition is operating at are both projects negative NPV? Answer is more than 25 percent. Because if the discount rate is more than 25 percent and remember the discount rate, little r is what the competition is earning. It's not easy to calculate. We'll spend a whole bunch of time on that when we do risk and return. But the point I'm saying is that it's the most important ingredient to decision-making. If the discount rate is more than 25 percent, you won't choose either. I have just shown you with a very simple example that the problem with IRR is it's not clean. It's biased in favor of short-term projects. It's biased in favor of projects that show you early cash flow. Let's take a break now. Think about this. Take even a few hours thinking about it because it's extremely important. I genuinely believe that there are two kinds of people out there, those who do not understand IRR and can therefore learn, and I learn, hopefully, you are learning or you already know these issues. But the second set of people who know the issue with IRR, it's very smart way seemingly of calculating things. It's very natural. But there's a built-in bias and the bias in favor of myopia, short-term payback. But it's very sophisticated bias. If you want things in the short term for whatever reason, and I'll talk about that in a second, what will you tend to do? You'll tend to favor IRR as a decision-making rule. Take a break, we'll do one more example and then we'll move on to cash flows. See you soon. Bye.
