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

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

means and you will just kinda 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 am going to just draw a timeline and you should be able to take a word problem

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

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

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

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

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

finance [laugh] you know? So, so I, I've said this many times you know, and 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 in 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 a PV, present

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

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

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

world 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 will be annual,

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

the, in the, in the beginning what I will 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, I remind you of one thing, just listening to me is, it looks easy,

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

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

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

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

payment, and, 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 forum. But we could do 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, you know, when you are on a

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

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

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

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 the importance of timelines, I am now going to

jump into what I promised I'd do. I am 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 whats going on. Okay. But the mai n insight we

are 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. The 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 up on them. And we are going to assume what

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

today and tomorrow, 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 ten percent

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, you

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

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

simple. I either give you $100 dollars 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? It turns out, if

you talked about it even for a second or even not thinking about it, you'll 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 the future value problem in 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. The timeline is extremely important. Your, I'm giving you two very

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

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

intuitively recog nize 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 time 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, can make fun of. Accounting standing at time zero where we

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

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

effort to create and now a lot of values 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 ten%. 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 come

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

understand this piece. So, the $100 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, right? And then,

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

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

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

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

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

little bit better. So now, what I am going to do is I am 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 then our example, it's 100. And the other is accumulated interest

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

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

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

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

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

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

But the way we write it, which looks, 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 you put in th e brackets is many times called Future Value Factor.

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

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

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

know? I mean, it'll be, 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 only

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

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

want to think about this problem.