Welcome back. Regardless of the time you took to review that previous problem, I would recommend that the longer it is, the better. And 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, calculations, calculation. But the real value of life is knowing what things are and how they work. And 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 its kind of a silly example, but happens all the time. So let's do example number two, issues with IRR are up there. Again, using some numbers, I'm going to show you this is a simple example. And we don't even almost kind of don't even need Excel. But it's very important. So, project A, project B. Their lives are the same. What are the cashflows -55,000, 7500 and the second project is -50,000, 62,500. Which one will you choose? So the IRR example let's do and I'm not going to use a calculator. Why? Or on 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 end quote, what's the difference really, you're making for A, A you're making 2,500 on 5,000, right? One period problem, how did I get 2,500? FV minus PV. FV is what I get back. PV is what I put in. So the answer to this is pretty straightforward, 50%. What's the answer to this? Well it's not that bad. It's slightly more complicated. It's $12,500. Right? 62,500 minus 50,000 future value minus PV. How about I put in divided by 50,000? All right? What is the answer to this? 25%. Because if I multiply both by 2 I get 25 on top and I get 100 on the bottom, so percentage. You see how cool percentages are. If there's one period very easy. Now C, I'm following the same rule. What is IRR? IRR is that rate of return which makes NPV zero. Calculate the NPV at 50% what do you get? Minus 5, 000 plus 7,500 divided by 1.5. This divided by 1.5 is what? 5, 000 NPV zero. Similarly here 62,500 divided by 1.25 turns out to be 50, 000 and that's the rule of thumb because remember, when you're doing a calculation and you're asking Excel to do it it doesn't have a clue. So what does it start off saying? Okay, suppose it's 0, suppose it's 100, and then it gravitates to 50% and 25%, respectively. Okay, now here's the problem. Almost everybody will say do this. But the answer is, it depends. And I recognize that these are not really real-world in the sense that the numbers are a little blatant. But you do have 5,000, investment here, 50. Here's another problem with IRR, it likes small things, small ideas. And the reason is, look at the denominator. IRR is a ratio, so the smaller the investment the higher the IRR. Everything else remaining the same. So there's a built-in bias of scale that IRR not only favors short term over long term, it likes small over big. So 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's pretty obvious, the one with the lowest fee. That doesn't mean the one with the lowest fee creates the most value, right? So IRR is a problem. It's a percentage and it favors small. So let's see what happens. Okay? 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. Okay. The first number is 15%. And I'm not going to do the calculations with you on an Excel, I would encourage you to do them. Because these are very simple one period problems, we did a while ago. Let me just write out the numbers. 1522, and let these be in million. 4348, at which return? 15%. So which one will you choose? 15%, 4348. Let me choose 30% now. And the numbers are 769 and negative 1923 okay? I want to write out all of them. And the third number, remember I'm copying from here. And the calculations I am doing are NPV, remember I am doing NPV and these are very simple to do. So for example, how did I get 1522 minus 5000, 7500 divided by 1.15 and so on. Okay, so let me put down the third number, 1148 1230, so now let's go over it again. With 15% which will I choose? At 30% which will I choose? At 22% which one will I choose? Kind of yes, a bias towards this, but tending to converge to each other. So again, what's the answer? The answer is, it depends. So IRR clearly favors which one? The first one, right? Remember, what's the IRR of the first one? 2500 over 5000 is how much? 50%. What is the IRR of the second one? 25% but these are in isolation. [LAUGH] What's the benchmark? What is the competition earning? So the competition, if it's earning 15%, which one will you choose? Project B. If the competition is earning 30%, which one will you choose? Project A. But if the competition is earning 22%, thereabouts, you're kind of 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 like, I don't know about you, but there are people that say who like graphic representations more than algebraic. I love equations and stuff like that. That's how I learned a lot when I was young. So I gravitate towards equations, but graphs are extremely powerful. Let's do a graph, okay? Now the question is, when NPV is zero, sorry, what is the IRR, what is the, if the discount rate is zero, what is the NPV? Why, because I'm trying to guess stuff, so 2500. How did I get this? For project A what is the cash flow in the future? 7500. And what is the expense? 5000. So 2500 is project A. Project B and I've 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 are at least approximately scale-friendly. So how did we get the 2,500? If the interest rate is 0, I'm just guessing, as a calculator or an Excel spreadsheet. I just take 7,500- 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? Okay. So, 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 their NPV is zero so they've got to be the IRRs of the two projects. So this is the IRR of which project? 25%. And this is 50%. Luckily we have done those numbers. And what is this project line, B. What is this project line, A. Everybody okay? Fair enough. What is this? This is approximately 22%. And you can tell the calculator to figure that out. So it's on the Excel spreadsheet. What is that rate of return which makes the NPV both the same? Notice. The NPVs are the same, approximately. So 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. So suppose the discount rates are less than 22% so you're in this region. Meaning the competition is somewhere here. People are earning no more than 22%. 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. So the complication of itself, is quite likely. Which project will you choose? You'll choose A. Sorry B over A. If the discount rate is somewhere here beyond this point you'll reverse this. You'll choose A over B. So this again tells you that IRR is really slippery. If interest rates are low, which I'm not by low, I don't mean super low. I'm saying less than 22%. Which project will you choose? You'll choose the one which actually has a low IRR. If our interest rates are very high, which projects will you choose? The high IRR. So 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. And bottom line is the following. Comparing IRRs 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. And that's not what life is supposed to be, right? 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. And IRR has got a devious bias against it. So 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 cash flows. Take a break, see you soon, bye.