Welcome back. Regardless of the time you took to review that previous problem, I would recommend that the longer it is, the better. The reason is, it's okay to understand how to calculate things. It's okay to use Excel, but I keep repeating to you that is easy. If you were to just want to know how to calculate stuff, first of all, you could just do it on Excel, learn Excel and you're fine. That's what the real world will push you towards, calculation. But the real value of life is knowing what things are and how they work. I'm going to spend a little more time on IRR, not because I believe it's the tool to use under certain circumstances, it is fine. But it's because it's deceptive as I said. I want to use one more example and it's a silly example, but it happens all the time. Let's do example number 2. Issues with IRR up there. Again, using some numbers. I'm going to show you, this is a simple example, and we don't even need Excel. But it's very important, so project a project, their lives are the same. What are the cashflows? Minus $5,000, $7500. The second project is minus $50,000, $62,500. Which one would you choose? The IRR example, let's do. I'm not going to use a calculator, why? Or an Excel because you can calculate this in your head. So you're spending $5,000, and how much are you making? $7500. What is the real profit, quote and unquote? What's the difference? You're making for A you're making 2500 on 5,000. One period problem. How did I get 2500? FV minus PV. FV is what I get back PV is what I put in, so the answer to this is pretty straightforward 50 percent. What's the answer to this? Well, it's not that bad. It's slightly more complicated. It's $12,500, 625 minus 50, future value minus PV. What I put in divided by $50,000? What is the answer to this? 25 percent. Because if I multiply both by two, I get 25 on top, and I get a 100 on the bottom. You see how cool percentages are if there's one period, very easy. Now, see, I'm following the same rule. What is IRR? IRR is that rate of return that makes MPV 0. Calculate the PV at 50 percent. What do you get? Minus $5,000 plus $7500 divided by 1.5. This divided by 1.5 is what? 5,000 MPV 0. Similarly here, $62,500 divided by 1.25 turns out to be 50,000. That's the rule of thumb because remember. When you're doing the calculation, and you're asking Excel to do it. It doesn't have a clue. What does it start out saying? Suppose it's 0, suppose it's 100, and then it gravitates to 50 and 25 percent respectively. Now here is the problem. Almost everybody will say do this, but the answer is it depends. I recognize that these are not really real-world in the sense that the numbers a little blatant, but you do have $5,000 investment here, 50. Here's another problem with IRR. It likes small things, small ideas. The reason is, look at the denominator. IRR is a ratio. The smaller the investment, the higher the IRR. Everything else is remaining the same. There's a built-in bias of scale that IRR not only favors short term over long term, it likes small over big. To give you an example, suppose you were to figure out the value of getting an educational degree. Forbes Magazine and others do publish this and I'm a little disappointed at that. Why? Because we should understand when popular press publishes all of this, the problem with this number. We say, which university's education gives you a higher rate of return? Well, one thing is pretty obvious; the one with the lowest fee. That doesn't mean the one with the lowest fee creates the most value. So IRR is a problem. It's a percentage and it favors small. Let's see what happens. I'm comparing just simply. If I look at just the IRR, I'm just comparing, again, two projects internally. Let's do the NPV calculations. The first number is 15 percent. I'm not going to do the calculations with you on an Excel, I would encourage you to do them because this is a very simple one-period problems we did a while ago. Let me just write out the numbers. 1,522. Let these be in million. 4,348. At which return? Fifteen percent. Which one will you choose? Fifteen percent 4348. Let me choose 30 percent now. The numbers are 769 and negative 1923. I'll want to write out all of them. Remember I'm copying from here and the calculations, I am doing are NPV. Remember, I'm doing NPV and these are very simple to do. For example, how did I get 1,522? Minus 5,000 7,500 divided by 1.15 and so on. Let me put down the third number. 1,148,1,230. Now let's go over it again. With 15 percent, which will I choose? At 30 percent, which will I choose? At 22 percent, which one will I choose? Yes, a bias towards this, but contending to converge to each other. What's the answer? The answer is, it depends. IRR clearly favors which one? The first one. Remember, what's the IRR of the first one? 2,500 over 5,000 is how much? Fifty percent. What is the IRR of the second one? Twenty-five percent. But these are in isolation. What's the benchmark? What is the competition earning? The competition, if it's earning 15 percent, which one will you choose? Project B. If the competition is earning 30 percent, which one will you choose? Project A. But if the competition is earning 22 percent there about, you're indifferent between the two. I'll do one more thing, I'm going to do a graphic representation of this and hopefully it'll then make sense again. I love graphs. I don't know about you, but there are people they say who like graphic representations more than algebraic. I love equations and stuff like that. That's how I learnt a lot when I was young. So I gravitate towards equations. But graphs are extremely powerful. So let's just do a graph. Now, the question is if the discount rate is zero, what is the NPV? Why? Because I'm trying to guess stuff. Twenty-five hundred. How did I get this? For project A, what is the cash flow in the future? Five hundred. What is the expense? Five thousand, so 2,500 is project A. Project B, and I have not drawing to scale 12,500. I apologize for this. In fact, let's do this. Let's make this 2,500, just to make sure we're at least approximately scale friendly. How did I get the 2,500? If the interest rate is zero I'm just guessing as a calculator or Excel spreadsheet, I just take 7,500 minus 5,000. This is which project? A. This is which project? B. Why is B 12,500? Because I get 62,500 and subtract 50,000. Everybody, okay? Let's take this, and let's take this. What is this number and what is this number? Notice what's true about both these numbers: the NPV is zero. They've got to be the IRRs of the two projects. This is the IRR of which project? Twenty-five percent and this is 50 percent. Luckily, we have done those numbers. What is this project line? B. What is this project line? A. Everybody okay? Fair enough. What is this? This is approximately 22 percent. You can tell the calculator to figure that out or the Excel spreadsheet. What is that rate of return which makes the NPV both the same? Notice the NPVs are the same approximately. The question here becomes as what? Which project do I choose? What is IRR, craving for? It's pushing you towards project A. Whereas the answer depends. Suppose the discount rates are less than 22 percent. You're in this region, meaning the competition is somewhere here. People are earning no more than 22 percent. Now, let me ask you this, how likely is that? Highly likely? This whole notion that you can easily make a lot of rate of return is actually wrong. It's very tough to create value, to make high rates of returns. The competition, if it's here, which is quite likely will, which project will you choose? You'll choose B over A. If the discount rate is somewhere here, beyond this point, you'll reverse this. You'll choose A over B. This again tells you that IRR is really slippery. If interest rates are low, which by low I don't mean super low, I'm saying less than 22 percent, which project would you choose? You choose the one which actually has a low IRR. If our interest rates are very high, which project will you choose? The high IRR. Bottom line is very simple. IRR, again, is favoring what? Short-term projects and small investment projects. I want you to again take a break, think about this. This time, the example is not difficult to calculate, but the issue is as important as the first one. Bottom line is the following: comparing IRR's directly and going in favor of the higher one will make you pick what kind of projects? Small, not impactful, and short-term, which means for a very short period of time. That's not what life is supposed to be. What are we taught ever since we were little? Value creation is most important when it impacts a lot of people and when it lasts for a long period of time. IRR has got a devious bias against it. I'll come and I'll wrap up IRR. This may be a time to take a break and go reflect on the two problems and come back and we'll revisit IRR one last time at a conceptual level and then move on to cashflows. Take a break. See you soon. Bye.