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So now the next concept which probably is more talked about is

present value then is future value.

So again, let me start with a problem.

So, the question says, what is the present value of receiving 110 one year from now,

and I think some of you or all of you are smiling,

because you know why I'm asking this question with these specific numbers.

The interest rate is 10% and I'm giving you $110 one year from now.

So think about this problem like something like this.

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You're going to receive 110 dollars in the future, one year for now, and

are trying to figure out what does it mean to you today, and

this is a very important problem to solve right.

Because most problems in life you make effort today and

you get money or pleasure in the future.

Right?

So you want to figure out what is the value of that today?

And present value, therefore, is a little bit more important than future value for

decision making.

However, future value, I think, is easier to understand.

And it forces you to be a finance person.

Finance people look forward.

Finance people don't look back.

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Right?

So hopefully, that's ingrained in you.

I'll tell you a little bit about what that has done to me, you know?

Because finance has changed me in good ways, mostly.

But there are some elements of it which are pretty hilarious,

which I'll get to in a second.

Okay.

So let's do this problem.

And I'm going to use, again just a simple way of doing it.

And so, here you go.

You have zero, you have one.

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I think if you've paid attention and

you've gone back which you can do at any time, you know the answer to this,

because I know what the future value of $100 is at 10%.

It's $110.

So what is the value of $110 in the future today?

Answer has to be $100.

Recall again the first problem I did with you.

I asked how much would $100 become after one year.

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And we realized that $100 would become $110.

And I'll ask you exactly the same question, but in reverse.

I'm saying suppose you had $110, how much would it be worth?

Obviously, to get the same $100 the interest rate has to be the same, right?

And I've kept it the same.

So the reason I find this problem very interesting is it's easy to do.

However, how do you go from $110 to 100 bucks?

So this is where I would recommend very strongly is that we try to

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do the concept before the formula.

So, if you look at my notes.

I'll just go ahead one bit.

Is that I never do the formula before the concept.

So if you saw me toggle, I went to the next page, and

I showed you the formula after I did the concept.

So, let's do it again.

Simple.

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However, dividing something by one plus r, if I said it to you the first time

you would have said, why the heck am I dividing something by one plus something?

And the reason is that one plus something is a factor

that anything can be multiplied by.

So the future value factor is one plus r.

What is the present value factor?

One divided by one plus r, right?

Because I'm taking the future value.

And multiplying it by one,

which is missing here, because it doesn't matter, divided by one plus r.

This guy is telling me what?

This guy is telling me, What is the present value of one buck,

if I got it one year from now?

I have to divide that by one plus r, and if r

in our examples is greater than zero, what will the value become?

Less.

So it's very straight forward that something in the future

will become lesser in magnitude or value when I bring it today.

That's why this whole process is called discounting.

When you read about finance, we'll say discounted cash flow or discounted money,

and the reason is your lessening and the key to that lessening is what?

This. R being greater than zero creates present

to become larger in the future, but it also therefore implies by

definition that the larger in the future becomes less today.

So that's the concept, right?

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But in doing the concept, what have I also done?

I have to redo the formula.

So I have to redo the formula, which we can rewrite, and you can write now.

You created the formula.

Present value is equal to, in our case,

100 bucks, sorry $110, I apologize,

which was the future value divided by 1.1.

Why?

Because r equals 10%.

So 110, pardon the this is a 1, you know what I mean?

I can make mistakes, too.

110 divided by 1.1, and this becomes hundred bucks.

How do you double-check that?

Well, it's straightforward.

That's what I love about finance.

Ask yourself, how much would 100 become in the future?

And the answer you know is 110.

So, future value and present value are kind of checking each other.

They have to be consistent with each other,

because one is simply looking at the other in reverse, if you may.

So I hope this is useful to you and this itself is easy to calculate because I am

dividing by 1.1 and the value is if you notice was 110.

However let's do this problem, suppose you will inherit $121,000 two

years from now and the interest rate is 10%.

How much does it mean to you today?

In other words, ask yourself the following question.

If you were to put 100 bucks, right, $100,000

in the bank how much would it become 121,000?

I'm giving you the answer already, and the reason is I know, because I've created

this problem, that the answer to this question turns out to be $100,000.

So let's see how I got that.

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And I'm keeping the problem simple because you need to understand the concept

better than the actual calculations.

Because the calculations, if they're simple, you focus on [INAUDIBLE].

So let me ask you this.

Can you tell me the value of this,

121, in year one?

Can you?

And I hope you say yes why?

Because we have done it.

We have done a one year problem.

So that's why I have said in finance you can time travel.

Watch Star Trek, watch Star Wars, watch Matrix,

if that's part of who you are finance will be easy.

So let's time travel to period one, how much will hit be?

Well I know it'll be 121,000 divided by how much?

1.10, that's the amount it will be after how much?

One year, but you're looking at two years from now, 121.

This is very easy to divide that's why I took it.

So what is 1.1 into 121?

How much will I be left with?

Well one, one, 110.

So this is 110,000, but that's not what I'm asking you.

I'm not asking you what is the value of $121,000 inheritance one year from now.

I'm asking you today, so what do you do?

You take 121,000 divided by 1.1.

And then I divide it again by 1.1.

Right?

So how much does that become?

I know this guy is 110.

And I know how to divided 110 by 1.1.

The answer has to be 100,000.

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So just the simple example tells you how

hurtful present value process can be, and why do we call it discounting?

If you're thinking the future 121, and boiling it down to only a hundred bucks.

A hundred thousand dollars.

And the reason if very simple, the interest rate is pretty high.

But a lot of people in business in particular tend to

use high interest rates, and I find that a little bizarre at times.

But anyway, just wanted to give you a flavor of what's going on, and

now, I'm going to do what I promised you.

Is I'm going to tell you the concept formula together.

So let's do it.

What's the formula's present values.

The present formula value turns out to be

future value, of, in our case 121,

divided by 1 plus r raised to the power what?

In our case it was two because future value of 121 was occurring when?

Two years from now.

In this case it'll be raised to the power n.

Where n in our example was two.

But could be anything, right.

You could be getting an inheritance 50 years from now.

You could be retiring 30 years from now.

So this problem doesn't have to be two or three, right?

So that's why I wanted to emphasize that,

and I'm going to do one more thing before we go today.

And what I'm going to do is,

before I get in multiple payments, that's what next time is.

So just to give you a sense of what where we are headed.

We've talked about a single payment carrying back and forth.

Now I will do something else much closer to reality.

Which is multiple payments, but before I do that,

what I want to do is show you Excel again.

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So let's show you Excel again, and the problem I will do is the two year problem.

So let's do.

Now what is it that you are trying to calculate?

The critical thing to remember is put the function that I'm trying to solve for.

So I'm doing PV, right?

And the rate was what?

10%, number of periods was 2.

PMT, remember, is a flow every year, we don't have any of that.

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And now, I'm supposed to tell you the feature value.

I'll tell you, meaning the Excel, okay?

So 121,000.

I think I got it, if I didn't, shame on me.

And let's see.

$100,000, right?

So, I want you to see if one last thing, and

I'll show you the power of compounding in reverse.

Right?

So let's make this 121,000 stay the same.

Let's keep 10% interest the same.

But then let's just mess with this number two.

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So I'm going to make the two, ten.

So am I saying?

Instead of giving you $121,000, your inheritance,

suddenly you realize that there was a typo.

Sorry?

Not two years, but ten years.

Now, you're thinking, no big deal.

Well, you're probably wrong, by a huge amount.

The amount of money you're left with, if I've gotten all the numbers right.

And by the way, a part of your problem is to double check what I'm doing.

Not to kind of second guess me, but to get the problem right, right?

So hopefully, we have a relationship now.

We are not waiting for

me to make a mistake, [LAUGH] because I will make mistakes.

Your goal here is to try to learn for yourself, even if I am.

So what's happened?

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power of thinking and bringing it all together.

I hope you also recognize that we are going to go slow in the beginning and

part of the reason is so that you feel comfortable with time value of money.

And to do that slowness the major way I am going slow

is by keeping risk out of the picture.

If I through risk in and

we started messing with that at the same time, life would become quite complicated.

But just so that it satisfies your curiosity remember high risk high return.

High risk, high return.

Tend to go together.

So even though we're not talking about risk right now, that being at the back of

your mind in that simple, powerful way is not a bad thing.

I'm really excited about this class and the reason is, believe it or not,

I feel like I'm teaching each one of your separately.

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And I think the power, if that has power, that's awesome.

Because even when I teach classes like I cannot do that.

I feel I struggle many times,

because I feel like I wish I could be a perfect teacher for everyone, but I'm not.

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And I'm hoping that online though, it has limitations obviously,

online has this huge benefit that I feel like I'm talking to you, you're there

I can feel you and remember whatever beats here is the same thing that beats there.

So if I see you or I don't see you, I can feel you.

Take care and [INAUDIBLE]