So let's go back to what we were talking about, because we were talking. We now know how to do NPV, and the NPV of this is 1400, right? What is the generic formula? So the generic formula, just stare at it for a little while, and I would encourage you to write it out. It's right there for you. It's very simple. NPV starts off at the negative number, your investment and once you get your investment. You put a negative sign in front of it, because that's how the world works usually. Then, what does C1 stand for? C1 stands for the cash flow in the first period. What does C2 stand for? C2 stands for the cash flow in the second period. In our problem, we just stopped there. What did we have, -1,000, 1,320, 1,452. Numbers were changing, but very conveniently in multiples that were easy to calculate and then you can go on to n. Important point, this framework can be used for any length of time and as the time gets longer. Refining your numbers too much doesn't pay off, and we talk about it later. Don't try to think about the number you're getting as an exact number. Try to think about the process. Properties of NPV and then we'll take a break. I want to go through the properties of all three criteria in discussing today at the end. because I just want to remind myself about what's good, what's not so good about it, within the context of what we know. And within the larger context of how the world should operate, there is a should here. Does it make sense? Think about it for a second. What are you trying to do? You're trying to figure out whether this is a value creating idea or not. Does this make sense? I think so for the most part, right. So what are you doing? Are you discounting for the fact that the time has passed? Answer's yes. How are you discounting it? Remember, how did you get the 10% and by the way, they'll be spend three classes on how you calculate that 10% I gave you. Because risk will be coming in and so and so forth. But for time being, you need, you already know what's the most important thing about R. Which is, the discount is coming not from your business per se, but from similar businesses that are already exist. Why? Because even if you have the resources, $1,000 or millions of dollars, you would like to put it in a value creating idea, right. So if it's a better value creating ideas where you may want to think about investing there even yourself, okay. Unit of measurement. Now the make sense part, in some sense this captures all the following parts. So, I'm just going to highlight the one or two issues and make sense and then, you look at a feeling for irritative measurement. What is it? So, let's just make some notes as we go along. Benefits minus costs time value of money, makes sense. What is the unit of measurement? It is our unit of measurement of measuring value, dollar. Now, you may use cows to value things or smiles or whatever. The point here, is not the dollar. Again it's, you recognize it, you're able to say, yep, so I made $1400 NPV. Two things to remember about this is this. One, this number is not right. It's as right as it's wrong, because it's based on my predictions of the future, so there's a lot of art involved in judging NPV. If it's 1,400, sound like a good number, big number, it could be 700, it could be 2,100. Because of uncertainty and we'll deal with that as we come later, okay. Next point, is the benchmark obvious? So, what is the benchmark of value I'm pausing here [LAUGH]. When will you do a project? When the NPV's greater than, right. Now here's some, I hope you don't mind the next bit I'll talk about. Most people think they understand zero. Zero was the last number created, as far as I can tell. Imagine imagining nothing, nothingness is not easy to imagine, but for the time being, we'll pretend we know what zero is. I think when you say zero, almost everybody nods their head. They don't have a clue like me, but that's okay. We know that This 1,400 is greater than zero. Easy to communicate. I would say it is the easiest thing to communicate. Why? Because of all of the. I've taken the benefits into account. I've taken the class into account and I'm saying on a neck basis, you are creating positive value. The tough part here to communicate is time value money. But I think people intrinsically understand that $100 today versus $100 in the future is not the same. Next, easy to compare ideas and projects. Turns out yes, so if you have two ideas One is 1,400 and one is 1,200 and four. Just because you don't have the time to do both or whatever, there's something making you choose between the two. Which one should you choose? This one, so look at the beauty of it. Because of all the things that we talked about, in the end, after you have done all the discounting and after you've used the right discount rate. You can compare similar ideas and pick the one that's creating the most value, right. So, that's so cool, I mean, that's exactly what common sense dictates, right. Is it easy to calculate and here, I'm going to put maybe a question mark and then say, mm-mm, not right. Why did I do that? Okay, so if you went 40 years ago, 50 years ago, right. Calculating NPV in a real world context with not just two cash flows, with multiple cash flows is a challenge. And the culprit is what? Pause again, compounding. So, it's not easy to do, I agree, but in today's world, with Excel being your slave. And you being in charge of machines rather than the other way around, this is not a legitimate answer, this is not. You have so much power in a laptop that you could send the first rocket to the moon using just your laptop, right. Don't try to do it though, but you know what I mean. There's absolutely no need to tell me I understand NPV but I can't calculate it, it's not easy to calculate. Yes, ss a person, I would encourage you to do divisions of something raised to power n, but a laptop can do it for you. Any other benefits? I think when you take them all, I would encourage you all to talk amongst yourselves. The forum that is created is great for talking about issues like this, because I do think that it has a weakness. And I'm only going to talk about that weakness right now. Just give you a hint. NPV unfortunately, though very, very good, misses one component. It has a static view of the world after today. So, you make a decision today and you say yes, if it's positive I'll do it. No, if it's zero or negative, I won't do it. But what happens is, you are in charge, you're making good decisions in the future too. You have the flexibility to change the world as the world changes in the future. So npv, because it predicts all the future cash flows, does an analysis up and down once. Is missing out on something called flexibility and in a more advanced class, we'll do something called Reloc Options. You must have heard of option pricing. It got a Nobel Prize. It's a very powerful way to think, but NPV is a necessary ingredient of that idea. It's not separate. It just adds flexibility, so let's do this. I think I've spent a fair amount of time on probably the most useful, practical way of measuring value and of comparing ideas. I want you to think about it, I want you to even go take the time, do some problems from the assessment. Don't wait until the whole video is over, because that's not a good way to learn. So, I'm going to take a break here and you take a break to do significant work or whatever. But let's pause here and you pick up whenever next you're able to. What are we going to do next? We're going to talk about a couple of other ideas. Criteria that are used in the real world and we'll come back to this session. We're still, please remember, we're still in week three and may the force be with you. Whether you're drinking coffee, doing yoga, going for a walk, or taking a nap. See you soon. Bye.