In some sense as I said before, if you know how to draw a Timelines you have a rights. So what I'm going to do now is I'm going to show you what a Timeline means and you'll just kind of laugh because it's kind of silly. But I think it's important. So, and by the way, just so that you know, my handwriting is nowhere near as perfect as the title on top. So if you expect it to be, you need to grow up. So, I'm going to do just draw a Timeline, and you should be able to take a word problem and put it along, the Timeline. And I put dots here. Why is this important? I think it's important because if you can take a real life problem and put it on a Timeline. You achieve probably the most difficult part of, taking a real word situation and then using financial. So in some senses, finance requires you to know what life is all about, what the problem's all about, before you can use finance. [LAUGH] So I say this many times. It was an accident that I got to learn finance. But there is love. And then there's finance. The gap is huge, right? I mean love is somewhere special, but being number two ain't bad. So you need to understand life, love, and so on, and then put it on a Timeline. And you can put pretty much anything on a Timeline. So here's the first thing, at this point, we'll typically call this FPV, Present Value. Then the number of periods are pretty obvious. This 1,2,3 and this is n. N reflects these time periods. The important thing to remember is that r, is the interest rate that applies to one period. And the real word, typically that one period is a year. By that I mean when you see interest rates being quoted for various stuff, like a bank loan and so on, it'll be annual. And that's just so that it makes sense, you can compare things kind of. So, in the beginning what I'll do is, I'll just take PV and I'll try to relate it to FV. So we'll try to understand these two concepts. How does FV translate to PV, PV translate to FV, go back and forth and become very familiar today. But I remind you of one thing. Just listening to me it looks easy. And that's the challenge of this class. I'll make it sound really easy, but the challenge is to do the problems and that's when you internalize, right? Because the word problem is the problem. And if you can't figure out the word problem this ain't going to help. So drawing a Timeline, bringing the word problem to it, is what it's going to be about. I'll start out with simple problems and then make them more complicated. But today what we'll stick with this, a single payment. I'm sorry, meaning I will transfer something from PV to FV. Either for one year, two years, or ten years, and vice-versa. We could have stuff coming in here, which is also dollars. Remember this is dollars, and this is dollars. Could have dollars coming in here, that's what is happening, actually, in most projects. Most. But you can ignore that for the time being. And the reason is, as I said, I want you to understand time value of money. We'll go slow in the beginning and then we'll take off. So when you are on a plane, the pilot warns you. Okay, fasten your seat belt, I'm going to take off. I'm going to warn you. I mean, when you hit the assignments and the problems, there'll be a warning. You better have your seat belt on. So get on to the problem. That's how you learn. You don't learn by just listening to me or anybody, okay? So please recognize the importance of Timeline and I'm going to go back to the notion of, how to think about time value of money and how to take Timelines and work them forward. We have talked about importance of Timelines. I'm now going to jump into what I promised I'd do. I'm not going to create a formula. And I mean, pick a formula and just throw it at you, no. To the extent I can, and that's my challenge, is to talk about a problem and then create the formula. Because I don't like formulas without understanding what's going on, okay. But the main insight we're going to worry about is, a dollar today is worth more than a dollar tomorrow. Or in other words, that's the essence of time value of money. That time by itself, the passage of time by itself has value. And there are some reasons for it as I said, you can go back and read upon them. And [INAUDIBLE] going to assume, what captures time value of money. Is the interest rate, the relationship between today and tomorrow, or today and the future, and that interest rate we'll assume is positive. So let me start with an example. Suppose a bank pays a 10% interest rate per year and you are given a choice between two plans. By the way, I'll be going a lot back and forth writing and stuff like that. But that will hopefully make it more engaging and as I do a problem, you should do it with me. And then, if the problem gets complicated, I'll give you more time, and then we'll talk together, and so on. These are your two choices. It's very simple, I either give you $100 today, or I give you $100 one year from now. And for the time being, let's keep our period one year. So the question really is which one would you prefer, and why? As I said, I just don't want to know what you prefer, I want to know why the heck do you prefer it? Turns out if you have thought about it even for a second or even without thinking about it you will choose one of the two. And it's probably going to be the first one. Right? So the goal here is to use the simple example to motivate something that is fundamental that we'll build on. So this is a future value problem and an example. So what I'm going to do is I'm going to try to work with you so try to think through this. So A is, remember A was $100 now. This is A and B was, $100 in the future. And that's what I meant, a Timeline is extremely important. I'm giving you two very simple choices to actually recognize. Now, This is where even popular financial press screws up, and you won't believe it but it's true. What we do in our head is we intuitively recognize that just the passage of time has an effect and will have an effect on the value of the money we are talking about or whatever it is. But we directly compare these two and that's not the right thing to do. In other words if you were to do this, and I say this in my class and I'm going to say this to you, if you start comparing money across time, directly with each other It would be better if you stabbed me, because you're basically telling me, whatever you're teaching in finance is useless. So remember the first principle is you cannot compare money across time. That would only be meaningful if time had no value. And what captures the value of time in this one scenario, is what? The interest rate. So let's try to work it a little bit better. At this point in time let's do the future value right? So what is already in the future? We know that this is already in the future. So the question is I cannot compare this to this at time zero but what can I do? I can either bring this back to times zero so take this, or, carry this forward. To the future. And the reason I'm going to do carrying forward, the future value first, is I think, it is easier to understand finance if you do that. And it also makes you think about the future and that's very important. Every decision that you make, every value creating decision that you make should force yourself to look into the future. And this is where I think accounting can make fun of. Accounting standing at time zero, where we are today, is looking backwards. [LAUGH] So, it's done. The past is over. So while you can derive very interesting implications from the past and I don't mean to demean anything, all decisions ultimately involve your capability to look into the future. And that's what's challenging about it and that's what's awesome. Every decision has an impact on the future and typically the painful part happens today. The better the idea, the more the pain today. But benefits a lot in the future, so like Google. I mean, it took a lot of effort to create, and now a lot of value has been created. So sticking to the simple problem, I think you know the answer to this. The answer to this will be $110. And the reason is very simple, r is 10%. So let me just walk you through, talk you through, and then we'll do the formula. I know right now many of you are saying let's go on. This is just too easy. Well, it'll build on itself. And so, we kind of understand this piece. So the $100 bucks that you had, you could put in a bank, right? And that $100, because the interest rate is positive, will be part of this $110. Because the interest rate is positive, you can't lose that $100 bucks, right? And then, you're earning 10% interest. So what is 10% of $100 bucks? $10 bucks. So it's very obvious what's going on, that in the end you will have $110. So as I promised you, what I'm not going to do is I'm not going to, throw a formula at you until at least you've had some sense of where I'm going and hopefully this simple example has motivated you to try to understand future value a little bit better. So, now, what I'm going to do is, I'm going to throw the concept at you. In this concept; what it says is the following. That the Future Value of anything that's carried forward has to have two components. One is the Initial Payment. And in our example it's 100. And the other is Accumulated Interest. Which in our example is $10 bucks. So the problem becomes very straightforward. You put in $100 bucks, you get $100 bucks. But then you get 10% on the $100, which is $10 bucks. So you get $110. So this is the formula. So if I were to ask you, what is it related to the problem that we just did? So what is this P? P is the Initial Payment of $100 bucks. What is the r? R is the 10%. But the 10% is on what? It's on the P. Of $100. So I know the 10% of $100 bucks is a fraction 1/10 and this will be $10 bucks. But we will write it is very straightforward is we take P out of the picture. So the P is common to the first one therefore the one. And rP, r*P. So what do you put in the brackets is many times called Future Value Factor. It's a factor because what does this 1 + R reflect? Let's do it in our case. 1 + R in our case is (1.10). And what's cool about this number is it tells you the future value of $1.00. So if you know the future value of $1.00, in this case it's 1.1 which is very simple, one plus the interest, you know the future value of any number. Because if the number is 100, you multiply 1.1 by 100 you get 110. If it's a million, you get 1.1 million and so on and so forth. So many people conceptually emphasize that Future Value Factor. And I'm going to, just do it this one time but you can go back to the notes and think about it like that. I mean it'll be very helpful to you. So right now, what I'm not going to do is I'm not going to use any tool to elaborate on this formula. By that I mean you don't need Excel to do this right? Actually you need Excel to do only when the problem becomes difficult to compute. Now to think about. Okay. So the Initial Payment is P and the Accumulative Interest r*P. So that's the way you want to think about this problem.