0:10

And I want to remind you that these breaks are more to kind

of give you my sense of where you probably need to stop,

but remember this is you, and many different ways of learning.

There are lots of you there.

So it's up to you to always take a break.

And if you don't understand something, you have other resources.

So you don't have to go to these videos until you feel comfortable moving forward.

I'm emphasizing this right now,

because the idea of a stock is not easy to comprehend.

1:08

So that's all that it's saying.

Why dividend?

That's just a name for the way the stock pays stuff to you, right.

Like for example, for a bond it was coupon and then face value.

Why is there no face value here?

Because you expect when you buy a stock that the stock,

even if you're going to sell it, is going to have value.

3:37

Turns out, and if you have the time, you can do these calculations for yourself,

and data for yourself, but I think it's very cool to derive this.

But imagine the formula is the simplest possible c over little r.

Actually I apologize because I sometimes use big r and little r but

r unqualified means the discount rate or cost of capital.

4:34

So this is the formula.

What I'm going to do is I'm not going to try to derive it for you.

And this is where I think you need to

put in some work based on the level of curiosity you have.

You can look at the books I've recommended to you or

you can sit down if your curious, just derive it.

Remember this is equal to what?

5:12

The only constraint I'm putting on this is these two variables are the same,

approximately.

And why do we use these formulas?

Because remember, a stock, you don't even know what the dividend is going to be in

the first year or the second year.

So getting too precise can be actually hurtful to your thinking.

You're doing a very detailed calculation of stocks.

Doesn't make that much sense, so

we will use formulas like these because they kind of capture both

5:52

So we know that if it's dividend stock is a constant level of dividend,

whatever it is.

Let's do this.

Let's spend five minutes and

you do it with me, and I'm assuming the problem is relatively straight forward.

We can do it with each other.

Otherwise, just take a break, do it.

6:13

And we'll come back to it, and I will try my best to

make sure that I'm making a good judgement about what is doable together and

what is you want to do a little bit of a break and test yourself.

And remember, you have always the opportunity to go to the assessments and

assignments to do similar problems and then come back, okay?

So this problem is relatively easy.

It says suppose Green Utility is expected to be at dividend

to pay a dividend of 50 cents.

Not to be a dividend but to pay a dividend of 50 cents per share for

the foreseeable future.

And the return on the business is 10%.

What does this mean, return on the business.

It means another way of saying that the cost of capital belongs not to you,

not to anyone, but the type of business you are in, and

that return is a function of demand, supply, everything, but together.

What should be the price of the stock?

7:34

And I'm asking you what would the price of the stock be?

And I'm calling it a utility because it turns out utilities are regulated.

And it's very common to view them as income stocks,

as opposed to another example I'm getting to which is

at the heart of the rest of the session this week.

It's called Growth Stocks and I just love that stuff because

it'll convey what really is going on and how growth is good.

How growth could be bad and so on.

But let's stick right now with the stock that's not planning to grow but

is planning to pay $0.50.

9:13

the assumptions behind the ease of the formula.

You just suddenly realize, how cool it is.

You know how people are so comfortable with numbers, seemingly,

in the financial world.

It's because they use formulas like this.

That's what's ingrained at the back of my head.

And therefore, I can feel very comfortable.

It's not that I'm very comfortable calculating complicated

formulas with numbers in Excel.

In fact, I shouldn't be and I have better things to do.

Okay, so let's just see,

what does forever mean?

Now many people get caught up in, nothing is forever, how could it be forever?

Let's just, this is not quite real,okay?

So let me ask you the following question.

Let me assume that forever means 30 years.

And by the way, that's not terribly long, right?

A lot of companies do survive 30 years.

That's not the important point though.

We are trying to price a stock that

is not expected to die tomorrow because there's no point in doing that, right?

So let's take this example, same example and

say, okay Gautham, forget about this perpetuity stuff.

It doesn't make sense.

So let's just assume it lasts for

30 years and the dividend is 0.50.

11:03

So just to recall what was the value of the perpetuity,

it was $0.50 divided by 0.1, very simple.

So 50 cents multiplied by 10 was 5 bucks.

Keep that in the back of your mind.

Now let's do this on a calculator.

You see what's going to happen, you can't do this in your head.

And that's part of the value proposition I was talking about.

So let's go to an Excel.

Let's do =, and what are we figuring out?

PV, I'm actually much slow than you probably, by now.

And you guys are just rolling along with this stuff and

saying, Gautham, come on, get, go fast.

I don't type very fast, that's the way I am.

Well anyways, so the rate is .05, that can't change.

And how much of my, sorry, rate is 0.1.

Right, there you go.

I'm talking and I'm messing up numbers.

The rate was 10%.

I think I got it right, 0.1.

The number of periods was what?

Not infinity, I don't like that, but 30 is fine.

And how much was my money?

$0.50, and I hope my fingers haven't done anything bizarre.

What's the answer or what's the value?

Look, it's $4.71.

Why did I do this?

Let's go back.

12:44

Are you sure for the next 30 years, you'll get that dividend?

Because if it was exactly true, that you expected it and

you got it, there's something really magical about you.

Oh the real world, the real world doesn't operate like that.

It's approximately that, right?

So getting very precise about 5 bucks for 30, I mean, $0.50 for

30 years would make sense if you were exactly sure that it's going to happen.

13:27

And this, by the way, seemingly a very simple example, but it's a very deepish,

right, so this shows you why finance is both art and science.

All your numbers are wrong.

So what's the point of getting very precise about being wrong, right?

So let's compare these two.

14:41

Infinity.

But you see now the power of, pause again, compounding.

At a 10% rate of return,

the money that you get at the 31st year, it's almost trivial.

It's only $0.29, even though it's forever.

So recognizing that the interest rate is positive, and

for stocks, stocks are risky relative to bonds.

They're likely to be high.

You know that formulas like perpetuities will bring you so close,

that you don't need to necessarily be very precise.

I am not saying don't use Excel, I'm saying most of value

of the framework comes from your thinking not from your answers, they are wrong.

I hope you found this little example very useful because

formulas like c over r are used all the time.

They are bases of are what are called multiples in finance.

Venture capitalists, people in I banking,

people who value stocks, don't try to get too precise.

On the other hand, bond pricing, I just touched upon a little bit,

can get very, very technical and precise.

And the reason is.

There's uncertainty only in one thing.

Fundamentally, in government bonds, for example.

If you expect the cash flow to be paid,

the uncertain interest rates is driving everything.

So you can get really precise in trying to model that.

But anyways, here in stocks, everything's uncertain.

[LAUGH] So what's the point getting too precise about?

Pretty much everything, because you can't.

16:35

And this is called a growth stock.

And I'm sure you have seen examples of these and

things happening as we speak, which is the biggest company in the world

right now in terms of value of their stock?

Remember, when I say, value for company, I could mean many things.

The first thing I could mean is being a finance guy,

what is the market cap, which is the value of their stocks.

But companies also have debt.

So when I say a value of the whole company,

people would want to include that, which makes sense.

So anyway, so which is the company whose stock value is the most in the world?

It's Apple.

Apple has almost gone and survived, almost died and

survived and then grown rapidly in different phases.

So I would call it a growth stock, but it depends on where is it in its lifecycle or

new idea generation, regeneration or whatever.

So let's see how this would be priced.

Look what I am saying here.

Your Po here, where the first dividend is DIV1.

You can also call this generically, C1.

You see, that's what I told you, the nice thing about finance.

Once you know time, value and money, then we'll do risks at a fundamental level.

You can do any problem.

Because the beauty is the same framework, same tools, just the symbols change.

The names change.

So the first is C1.

18:26

And in this case, DIV2

is DIV1(1+g) and so on.

Now obviously, we'll see and I'll show you the formula again.

It looks very similar to the previous one.

Let me first show you the formula.

But remember genetically, what will DIV2 be called?

C2 and so on.

So let me write the formula down and then we'll, by the way,

this is the only form of it, I haven't derived it for you.

And the reason, it'll just take up too much time.

The generic formula is C1 over r-g.

What is g?

19:16

In this case, expected dividends.

What is C1?

The first cash flow.

So this is very important.

First cash flow is C1, the g is the growth in the cash flows not in r.

R is already a percentage.

So these are both percentages.

R and g are both percentages.

So, I'm not subtracting dollars from a percentage.

19:53

You'll have to go the long way to do C1 divided 1 plus r,

C2 divided by 1 plus r square till such point that r is greater than g.

And that will always happen, think about it.

If g was greater than r, you would own the world.

It's not possible in a steady state, but

those are things that you get to practice in your assessment.

So let's call this the formula and

replace it by DIV1 over r-g.

And I'm going to use examples where r is greater than g.

But as I said, again don't use the formula when it doesn't make sense to use.

For example, if r is equal to g, what are you going to do?

Sit there, stare at the formula.

You have something divided by zero, go figure.

We use the long method.

And that's another thing I don't like about the way we get taught math and

algebra is we are never taught in a context.

I shouldn't say, never.

I was lucky in high school.

I was taught math always in a context and I've benefited so much by it, instead many

times we are taught stuff and all we see is the backside of the person teaching.

And that's not very interesting, anyways.

So let's get started with the formula and

I'm going to now let you take a little while to do it.

This is a good time to take a break, but let's first read the formula.

Suppose Moogle, Inc, I apologize my sense of humor is limited.

Is expected to pay, Ryan is laughing with me.

Is expected to pay dividends of 20% next year.

You see how I have to specify the first dividend?

And the dividends are expected to grow indefinitely at a rate of 5% per year.

Again, the word indefinitely doesn't literally mean forever.

Remember, it's reusing formulas as an approximation.

Stocks of similar firms are earning an expected rate of return of 15% per year.

Why am I saying this?

Because I want to repeatedly remind you

that the 15% is not owned by you.

In fact, it doesn't belong to anybody, it belongs to the marketplace.

Businesses get different rates of return due

to a fundamentally different set of risks.

What should be the price of a share of Moogle, Inc?

So just take a minute and try to do it in your head.

When we come back, we'll do it together and see how easy it is.

Take a break.

See you soon.