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In some senses as I said before, if you know how to draw timelines, you have

Â arrived. So, what I am going to do now is, I am going to show you what a timeline

Â means and you will just kinda laugh, because it's kind of silly but I think

Â it's important. So, and by the way, just so that you know my handwriting is nowhere

Â near as perfect as the title on top. So if you expect it to be, you need to grow up.

Â So, I am going to just draw a timeline and you should be able to take a word problem

Â and put it along the timeline. And I will put dots here. Why is this important? I

Â think its important because if you can take a real life problem and put it on a

Â timeline, you achieved probably the most difficult part of taking a real world

Â situation and then using financial tools. So, in some senses, finance requires you

Â to know what life is all about. What the problem is all about before you can use

Â finance [laugh] you know? So, so I, I've said this many times you know, and it was

Â an accident that I got to learn finance. But there is love and then there's

Â finance. The gap is huge, right? I mean, love is somewhere special. But being

Â number two ain't bad. So, you need to understand life, love and so on, and then

Â put in on a timeline and you can put, pretty much anything on a timeline. So,

Â here's the first thing. At this point, we'll typically call this a PV, present

Â value. Then the number of periods are pretty obvious. So this is one, two, three

Â and this is n, n reflects these time periods. The, the important thing to

Â remember is that r is the interest rate that applies to one period and the real

Â world typically that one period is a year. By that I mean, when you see interest

Â rates being quoted for various stuff like a bank loan and so on, it will be annual,

Â and that's just, so that it make sense, you can compare things, kind of. So, in

Â the, in the, in the beginning what I will do is I'll just take PV and I'll try to

Â relate it to FV. So, we'll try to understand these two concepts. How does FV

Â translate to PV, PV translate to FV, go back and forth and become very familiar

Â today. But I, I remind you of one thing, just listening to me is, it looks easy,

Â and that's the challenge of this class. I will make it sound really easy but [laugh]

Â but the challenge is to do the problems and that's when you internalize, right?

Â Because the word problem is the problem. And if you can't figure out the word

Â problem, this is, ain't going to help. So, drawing a timeline, bringing a word

Â problem to it is what it's going to be about. I'll start off with simple problems

Â and then make them more complicated. But today, what we'll stick with is, a single

Â payment, and, I'm sorry, meaning I will transfer something from PV to FV, either

Â for one year, two years, or ten years, and vice versa. We could have stuff coming in

Â here, which is also dollars. Remember, this is dollars, and this is dollars.

Â Could have dollars coming in here, that's what is happening, actually in most

Â projects, most forum. But we could do ignore that for the time being. And the

Â reason is, as I said, I want you to understand time value of money. We'll go

Â slow, in the beginning, and then we'll take off. So, you know, when you are on a

Â plane, the pilot warns you. Okay, fasten your seat belt. I'm gonna take off. I'm

Â going to warn you. I mean, when you hit the assignments in the programs there will

Â be a warning. You better have your seat belt on. So, get on to the problems.

Â That's how you learn. You don't learn by just listening to me or anybody. Okay? So,

Â please recognize the importance of timeline, and I'm going to go back to the

Â notion of how to think about time value of money and how to take timelines and work

Â them forward. We have talked about the importance of timelines, I am now going to

Â jump into what I promised I'd do. I am not going to create a formula and, I mean,

Â pick a formula and just throw it at you. No. To the extent I can, and that's my

Â challenge, is to talk about a problem and then create the formula. Because I don't

Â like formulas without understanding whats going on. Okay. But the mai n insight we

Â are going to worry about is, a dollar today is worth more than a dollar

Â tomorrow. Or in other words, that's the essence of time value of money. The time

Â by itself, the passage of time by itself has value. And there are some reasons for

Â it, as I said, you can go back and read up on them. And we are going to assume what

Â captures the value of money, is the interest rate. The relationship between

Â today and tomorrow, today and the future. And that interest rate we'll assume is

Â positive. So, let me start with an example. Suppose a bank pays a ten percent

Â interest rate per year and you are given a choice between two plans. By the way, I'll

Â be going a lot back and forth, writing and stuff like that, but that will hopefully

Â make it more engaging and as I do a problem, you should do it with me, you

Â know? And then if the problem gets complicated, I will give you more time and

Â then do it together and so on. So this, these are your two choices. It's very

Â simple. I either give you $100 dollars today or I give you $100 one year from

Â now. And for the time being, let's keep our period one year. So the question

Â really is, which one would you prefer? And why? As I said, I just don't want to know

Â what you prefer, I want to know why the heck do you prefer it? It turns out, if

Â you talked about it even for a second or even not thinking about it, you'll choose

Â one of the two. And it's probably going to be the first one, right? So, the goal here

Â is to, use the simple example to motivate something that is fundamental that we'll

Â build on. So, this is the future value problem in an example. So, what I'm going

Â to do is I'm going to try to work with you. So, try to think through this. So, A

Â is, remember, A was $100 now. This is A. And B was $100 in the future. And that's

Â what I meant. The timeline is extremely important. Your, I'm giving you two very

Â simple choices to actually recognize. Now, this is where even popular financial press

Â screws up and you wouldn't believe it, but it's true. What we'll do in our head is we

Â intuitively recog nize that just the passage of time has an effect and will

Â have an effect on the value of the money we are talking about or whatever it is,

Â but we directly compare these two. And that's not the right thing to do. In other

Â words, if you were to do this, and I say this in my class, and I'm going to say

Â this to you, if you start comparing money across time directly with each other, it

Â would be better if you stabbed me. Because you're basically telling me, whatever

Â you're teaching in finance is useless. So, remember the first principle is, you

Â cannot compare money across time. That would only be meaningful if time had no

Â value. And what captures the value of time in this one scenario, is what? The

Â interest rate. So, let's try to work it a little bit better. At this point in time,

Â let's do the future value, right? So, what is already in the future? We know that

Â this is already in the future. So, the question is, I cannot compare this to this

Â at time zero, but what can I do? I can either bring this back to time zero, so

Â take this. Or, carry this forward to the future. And the reason I'm going to do

Â carrying forward the future value first, is I think It is easier to understand

Â finance if you do that. And it also makes you think about the future. And that's

Â very important. Every decision that you make, every value creating decision that

Â you make should force yourself to look into the future. And this is where I think

Â accounting can make, can make fun of. Accounting standing at time zero where we

Â are today, is looking backwards. So that's, it's, you know, it's, it's done.

Â The, the past is over. So, while you can derive very interesting implications from

Â the past and I don't mean to demean anything, all decisions ultimately involve

Â your capability to look into the future. And that's what's challenging about it and

Â that's what's awesome. Every decision has an impact on the future. And typically,

Â the painful part happens today. The better the idea the more the pain today. But

Â benefits, lot in the future. You know? So like Go ogle, I mean it took a lot of

Â effort to create and now a lot of values been created. So, sticking to the simple

Â problem, I think you know the answer to this. The answer to this will be $110. And

Â the reason is very simple, r is ten%. So, let me just walk you through, talk you

Â through and then we'll do the formula. I know right now many of you are saying come

Â on, this is just too easy. Well, it will build on itself and so we got to

Â understand this piece. So, the $100 that you had, you could put in a bank, right?

Â And that 100, because the interest rate is positive, will be part of this 110.

Â Because the interest rate is positive you can't lose that $100, right? And then,

Â you're earning ten percent interest. So, what is ten percent of $100? $ten. So,

Â it's very obvious what's going on that you, in the end will have $110. So, as I

Â promised you, what I am not going to do is I am not going to throw a formula at you

Â until at least you have some sense of where I am going and hopefully this simple

Â example has motivated you to, motivated you to try to understand future value a

Â little bit better. So now, what I am going to do is I am going to throw the concept

Â at you. In this concept, what it says is the following, that the future value of

Â anything that's carried forward has to have two components. One is the initial

Â payment, and then our example, it's 100. And the other is accumulated interest

Â which in our example is $ten. So, the problem becomes very straightforward. You

Â put in $100, you get a $100. But then you get ten%on the 100 which is $ten. So you

Â get 110. So, this is the formula. So, if I were to ask you, what does it related to

Â the problem that we just did. So, what is this P? P is your initial payment of $100.

Â What is the r? R is the ten%. But the ten percent is on what? Is on the P of $100.

Â So, I know that ten percent of $100 is a fraction one-tenth and this will be $ten.

Â But the way we write it, which looks, is very straightforward, is we take P out of

Â the picture. So, the P is common to the first one, therefore, the one. And rP, r

Â P. So, what you put in th e brackets is many times called Future Value Factor.

Â It's a factor because, what does this one + r reflect? Let's do it in our case. One

Â + r in our case is 1.10. And what's cool about this number is, it tells you the

Â future value of $one. So, if you know the future value of $one in this case is 1.1,

Â which is very simple, one plus the interest. You know the future value of any

Â number. Because if the number is 100, you multiply 1.1 by a 100, you get 110. If

Â it's a million, you get 1.1 million and so on and so forth. So, many people

Â conceptually emphasize that Future Value Factor. And I'm going to just do it this

Â one time. But you can go back to the notes, and think about it like that, you

Â know? I mean, it'll be, it'll be very helpful to you. So, right now, what I'm

Â not going to do is, I'm not going to use any tool to elaborate on this formula, by

Â that I mean, you don't need Excel to do this, right? Actually, you need Excel only

Â to do when the problem becomes difficult to compute, not think about. Okay. So, the

Â initial payment is P and the accumulated interest is r P. So, that's the way you

Â want to think about this problem.

Â