So, let's spend some time on understanding the intuition. So, we have cash flows, we have very simple cash flows. What were the cash flows? -1000 today, signifying our effort. The cost of what it took to start the project and what was the cash flow next year? 1320. Where do these cash flows come from? And I'll later use the following language. Who do they belong to? Please recognize one thing extremely important and I will keep emphasizing this, but it's very important. Cash flows belong to the project, to your idea. You are responsible as the person generating this idea to come up with the cost and benefits, you know, because if you can't do it, then the idea is not obvious to anybody. So, this is the first step in recognizing what are the cost and benefits of your own idea. Now, it's not easy to do. It involves Accounting, it involves Finance, and so on. So, I'll spend an entire session next time on how do you come up with these. But I must warn you, that's the one part of this class that I cannot spend a lot of time on, because it will require you to do a class at Accounting. Remember, the language that we use is Accounting? We'll use, if you don't understand Accounting, we cannot take business plans and convert them into cash flows. But don't worry, it's not that difficult. I'll introduce you to enough part so that you can do some basic stuff yourself. So, what our cash flow then come from? The most important point is think of them as profits, not revenues, not cost of doing same thing. Profits. Right? What is left in the end. Those what we call cash flows and they are current at various points in time. In this case, 1320 in the future and the cash outflow today is -1000. The key point, however, is it's your ideas signature. It's unique to your idea. So, the idea and cash flows to me are the same thing. Idea and benefit and cost are the same thing because if you can't combine the two, it's, an idea is meaningless. Okay? Now, here's the important point. What is r is our problem? The interest rate. It's ten %. And this is something that's really critical to understand. So, if the cash flows come from what your sense of the idea is, your ability to. Figure out the cash flows, and it obviously ultimately the cash flow also depending on the customer to buy your product or not. But what I'm saying is it's your responsibility to do all the hard work to show what the cash flows and benefits of the idea are. Where does r come from? R is an extremely critical aspect of finance. R captures the opportunity cost of investing in this idea. Opportunity cost is easily said, everybody nods their head when it is said, but it is very tough to understand. And PhD's take tests on opportunity cost, people have been working on the real world for years and they screw up. And the reason is, it's a very easy concept to say, yes I understand it, but it's very tough to actually figure out. So, let me tell you why r is tough. You would imagine, as most of the world does, is that r comes from thin air. In fact, most of the time, I'm really frustrated where people pull r out of thin air and say, you know, it is twenty%. Why? So, here's something very important to understand. R comes from the next best use of even your own investment, leave alone other people's on a similar project. So, think of r as not belonging to your project. R is that return, that is coming from, investing, in say, a competitor. So, imagine you are going on, you've a great idea, but similar ideas usually exist, right? It was the internet boom that threw us off, because we had never seen things like that. But typically, your idea's not brand new. Something similar is going on. So, imagine if you have the money to start your own idea. I think it would behoove you to look at existing people doing the same thing. And if they are getting a better return than you are, it doesn't make sense for you to do it, right? So, it helps society to use r as the return or the possibility of making money in a similar venture with a competitor, that becomes your r. Because when you go to r, you should be thinking like the investor in you or in other people. What will an investor do if you show me your cash flow, cost and benefits, what's the first thing that will strike me? How could I do better? But in the same type of business, because I can't compare businesses that are making rocket engines with selling bananas. And you'll say, why not? Because they are not the same thing. One is much riskier than the other. We'll get to that. Okay? What does the final number mean? So, what was our NPV? Our NPV was what? $200 dollars, right? What is the unit of, unit of measurement? Dollars. It is the measurement of value, in, I am not saying dollars can measure all values. What I am saying is the unit of measurement is the unit used by everybody, right? So, here's the cool thing, you will add $200 or 200 million if you may, If you want to put everything in million, in net value to you and hopefully to society, by this idea, right? So, so, the final number has a very cool number as well. It says, how much value have you created? You've created 200 million worth of value, why? Because you invested a 1000, and you got 1200, you got 1320 but when you discounted it back today, by what the competitor could have done, you are making 200. Should you pursue this idea? What do you think? Answer is yes and the reason is very straightforward. You're creating positive value, right? One caution. One caution. If you do not have the resources to do so, should you not do it? And why am I using this conscience, caution, caution? Is because there could be situations in the world where you have a great idea but don't have the resources. And what comes in to your rescue? Markets. Competitive, fair, not money lenders dressed as banks, whatever. It's fair resources available to you. Why will that happen? Because most of us don't have great ideas, I mean it's okay not to, right? I don't come up with great ideas all the time. It's very tough to come up with great ideas. So, what do we do? And we have mostly savers in society if you ha ve the resources, of course, and we want them to go to the people with the ideas. And the people with the ideas, don't have ideas, great ideas all the time, right? So, at some point, they also want their resources to go elsewhere. So, if the resources are not there, then ideas are not implemented. Therefore, the importance of markets. So, I'm going to assume, if you have a good idea, resources will come, regardless of whether you have the resources or not. That clearly depends on the availability of a market, right? Okay. Net Present Value, the essence. Value is always incremental, and I'am going to emphasize this because this is extremely important, it puts everything together, to what. So, lets get started and let me ask you the following cool thing. Suppose you have a $1,000, and you're going to invest it at times zero. What is the option? The option is clearly, very simple. Your idea is being practiced elsewhere. So the r of ten%, as I said, is what is gotten on, say, a similar or a competitive idea that exists. So, you are investors, say even your dad [laugh], says look, I have a thousand dollars or a million, whatever and I can figure out how much can I make in the market place, the important thing is apples to apples. So, if you set up a banana stall, your dad should be comparing it to a banana stall. If he set up a rocket engine machinery factory, he should compare you to something similar. Because risk, apples versus apples, oranges versus oranges. So, suppose he took this money, and put it in an existing business that was similar. How much would he make? Its very simple, you've got to calculate the future value of a $1,000 one year from now. Don't tell me you can't do it, you can. It is 1100. Do you get it? Take a 1000, you get the 1000 back plus the ten percent return so what is this? This is = P(1+r). This is the first thing we did and what is P? $1,000. Why is it negative and this positive? Because incomes and then you get a gain. So, the $1,000 grows into 1100. This is the existing idea. Somebody is already doing this kind of business. Obviously, sometimes, you have a brand new idea, and it is tough to evaluate and that's why we screw up. [laugh] when new things come because, after all, we are human. So now, what does your idea say? Your idea saying is, give me the thousand. This is the, your alternative. And I'll give you how much? Well, somehow you are so cool, that you're able to generate 1320 instead of 1100. Why am I emphasizing this? And the reason is value is not created in absolute amounts. This is extremely important, value is always created in a relative amount. So, look at this. This is the same investment, so I'am not having an investment of 500,000 versus 1,000. But look at what's happening. That's why [inaudible] problem is so simple. How much am I creating? Yes, I am creating 1320 but that's not the right way of figuring out a value. The right way of figuring out a value is how much I have created additional to what already would have existed. So, take 1320 and subtract 1100, how much are you left with? 220. Everybody gets this? I have been able to with my ingenuity, in a very similar business with a similar risk, able to create value of 220. By the way, this is happening all the time. Let me give you a very simple example that we'll come back to, Walmart. Is Walmart doing something that was never done before? Heck no. I mean, not to take anything away from their efforts, they don't sell something that we have never seen before. Walmart is not like Apple, which has created something new that we like. It is selling stuff that we already wanted to buy, right, but in a different way and created value to that process. So you have 220, but when is the 220, which year? Now, look at the beauty of this. Well, if I bring this back today, how much is it? Very simple. 220 divided by 1.1. Why? Because the interest rate is ten%, and I am discounting for one year. How much am I left with 200, which is also what, NPV. This is something that is so important to recognize that the process of discounting that we did, r ight, the process of discounting that we did, takes care of the opportunity cost of capital. Another way to think about it is everybody else was making zero, then everything is green, right? But everything, everybody, else in this example is not making zero, they are making ten%. I hope this was useful and I hope that you remember that net present value is always incremental. And value creation is always incremental because that's how life is. There's no such thing as absolute value. It's always relative value. Okay, let's do another example and then I promise we'll take a little bit of a break after we do the NPV. So, what's the NPV of this? So, we, let's go a little bit faster. Why? Because we can. What's the value of this? -1000. What's the value of the next guy? We already know this, 1320 / 1.1. Remember, ten percent is the discount rate. And note, now that you know how to do present values, I'm going a little bit faster. And we just did this. What is the NPV? Now, this is a little bit tricky and I'll do Excel in a second. How much would you, so this one, how did I get? I took 1320 and divided it by one+r which was 1320 / 1.1, right? And I got 1200. Now, look. If this is apples, this is oranges, what is this? Bananas. [laugh] Because one year has passed, that's [inaudible]. However, the interest rate is very high. So, what do you I to do? I have to take this amount. Take 1,452 / 1.1^2. Which turns out to be I'm going to go sideways here now, 1.21. If you do this, I believe you get 1,200 again. I set up the problem so that I can, you know, get wrong numbers and so on. So what is the NPV, 2400, -1000, right? So, 200 was the first periods value creation and so it's 1400. So, let me just make sure I've got this number right, and I believe I have. But I want to do one last thing before we talk about NPV overall. And what I'm going to do is I'm going to use Excel to generate these, these numbers so I am going to rehearse. And there's a trick and unfortunately there's a little bit of a hassle in doing NPV which I want introduce also, so let's do this problem. So, in cell one, I'm going to put -1000. Please remember it's an A cell, A1. And I'm putting all these numbers in there because eventually when you're doing a more complicated problem, the beauty of Excel is you can put all the numbers in and then, you know, you can modify it and so on and so forth. What is the next number? The next number is 1320. And remember, I'm doing exactly the same problem that we just did. What is the last number? 1,452. So, these are the cash flows. You have - 1000, 1320, 1452. Now, what I want you to recognize about NPV is there is a little bit of an issue with it. So, I'm going to do NPV, open parenthesis, the first number that always jumps out at you is always rate, right? So, 0.10. Now, here's the thing that already is on the website, a resource saying how to use Excel, which Nate, my [inaudible] has created for you. And he has highlighted this issue, but I wanted to do it real time too. You do not want to put the investment there. It is set up to do PV, so the first payment is starting in cell B1, right? So, the first payment in the future is one year from now, so you look B1: C1, alright. But then you recognize that this is just a PV. So, what do you have to do? You have to take account of the NPV part of it. So, what I'll do is I'll add A1. Why did I add A1? Because I know if I add A1 and A1 is already negative, as it should be, because it's an investment, what, what do I get? I get 1400. So, this allows you to use Excel, the only thing that I would encourage you to remember is Excel NPV is a rarely doing PV of future cash flows so don't give times 0's information or the cell, the first cell information in your cash flows. Of course, please remember how do you get cash flows, we'll do next time. But think of these as profits and the first period times zero is an investment, okay?