The Dividend Discount Model - YouTube

Hello and welcome back.

And today we're going to look at the dividend discount model,

which is a way of computing a value of a stock.

So in the previous video Anders showed you how to value bonds, and bonds are debt for the company.

In this video we will find the stock value from the cash flows coming to a stock.

And the cash flows coming to a stock are called dividends.

So when a company pays money to the shareholders, it's called dividend.

And this model then,

that we're going to use is called a dividend discount model.

Here's some short repetition.

When you had bonds

it was fairly simple to compute then because

when you buy the bond it's pre-specified what you're going to pay.

So you're given a coupon every year.

So the coupon here, coupon here

coupon here, coupon here and coupon until the end of the bonds life.

And they are all equally large, so you could take them all at once.

Use the present value of an annuity

and get the value of them and then in the end, as the bond matures

you receive a face value which is a single cash flow, so you move that alone.

And then you can compute the present value of all these

and you find the price of the bond.

But today we're going to look at stock or equity shares.

And we start by talking a little bit about what it is so.

Common stock, which is what we will focus on today, represents ownership in a company.

So you have a part of the ownership of a company.

It usually gives you voting rights and therefore some control of the company,

so you can, for example, vote on who is going to sit on the board

and in that way affect the management of the company.

And also from the company perspective,

equity or stocks represents a permanent source of funds.

So when you start by investing equity in a company,

they don't have to repay it,

then they probably can't repay all of it either.

So it's a fund, which they always will have.

And they can also choose never to repay anything.

If you own a common stock, then you have the right to income.

So if the company makes profits year after year,

you are entitled to a share that.

But they have what is called a residual claim,

and that means that everyone else who claim money

from the company will receive the money first.

So for example, if the company take a loan at the bank,

then you need to pay the interest rate to the bank first before you can give

anything to the shareholders.

And this also means in case of trouble.

So let's say that the

company lose all its value and goes bankrupt.

Well then everyone else has a priority of getting money from the company

and only if there's anything left after that

then the shareholders can get anything.

So this is what we need by residual claim.

Like I said, the company has no obligations

to pay dividends, so dividend is the only real cash flow

that you get from the company

and the company can choose to simply not do it.

Of course you can select the managers and that way influence it, but

in general, they don't have to pay the dividends.

But if you invest money in stocks, then you have what is called a limited liability.

So if you invest your money then you can lose all of your investment,

but you cannot be liable, you cannot be forced to pay for anything beyond that.

So let's say I invest 1000 SEK in a company and it goes bankrupt.

Well, I lose my investment,

but in case there's not enough left to honor the depth holders, like bond holders or banks,

then me as an owner doesn't have to step in with more money to provide to them.

So I have limited liability in that sense.

And other names, they can be called equity shares, equity securities, equities,

and probably some other names as well.

Let's take some more terminology, but with an example in this case.

Assume that you buy a stock today for $50.

In one years time you receive a dividend of 150

and you then sell the stock for 50.5.

What is your return here?

So this is general terminology

That we will use so P0 here is the price at time zero.

So the price today

P1 is the price next year in one years time.

So in this case it was 50.50, and P0 was 50.

And Div 1, div stands for dividend and 1 is dividend in year one, or period one.

So in our case we had here was P0

50 was P0, and 1.50 was the dividend in year one.

So what kind of returns do we make it?

Well, first of all, we can see

how much money do we get in period one.

So we get 50

from selling the stock.

And then we get 1.50 from the dividend,

so that's a total of $52.

And it costs 50 when we bought it, so the total return to us is

52 minus 50

So that's a gain of 2, and we divide it by what we purchased it for

And it gives us a return of 4%.

But we can divide this

so we can take the dividend part for itself and the increase in price for itself.

So how much was the dividend part?

The dividend part was 1.50

We divide it by 50 and we get 3%

and then we had the price increase.

So the price in one years time was 50.50.

When we purchase it, it was 50 so the price increased by $0.50.

And we divide that by 50 and find that this increase was 1%.

So we see that this total return 4%

consists of a dividend part of 3% and increase in the price of 1%.

This is called the dividend yield.

So the dividend yield is the return you get from the dividend and it simply equal to

the dividend, the next dividend, divided by the current price.

Then we have the capital gain.

And capital gain then represents the increase in price.

So in this case, the capital gain that we received was P1 minus P0 divided by P0.

So it's simply, if you have a price increase then you have a capital gain

and then we have something called the total return.

And the total return is just the sum of them.

The dividend capital gains.

So how much money did you make on this investment?

Now we're going to look at one period at a time.

So we say that if you buy a stock, then you buy it today and you hold it for one period.

After that you sell it again to someone else.

So what do we get in that case?

We pay a price which we call P0 today, so that is what we pay.

And then in one years time we might receive a dividend, or maybe it's zero

and we also receive the selling price.

So this could of course be lower than what we buy it for.

And then we make a loss, perhaps, but it could also be positive.

It's a positive inflow in year one.

Who buys this?

So when I sell it, I sell it to someone else

and that someone else pays for something.

What does that person pay for?

Now we can do the same thing in year one.

Someone pays a price P1

in order to receive something one period ahead in the second year.

And they receive a dividend that year as well as a selling price P2.

And whoever is buying it in P2 is also buying to receive something.

What does that person receive?

Well, it's the same argument, you pay a price P2 in period 2

to receive 1 dividend in the next period as well

as a selling price in the third year,

and I mean I could go on doing the same thing,

but I think you get the picture by now.

So let's make this a little bit more formal.

We always said that if we want to value something like the bonds we took,

the future cash flows and then we discount it back until today.

So in the case of our stock.

We pay a price P0 and that price should be the present value of the expected dividend

plus the expected value of the price that we receive.

So these are the two things that we get, so that was

the dividend yield.

And this was the, well, that's not actually the capital gain, but it's the part.

In the same way we can find what is the person in period one paying for

whoever is paying P1, does it to receive the dividend in year 2

and the selling price in year two.

And again we discount it by 1 + rE, I should mention that this rE is the cost of equity

so its the discount rate used by the owner of the shares.

But since we only have a one period model,

we don't take this to the power 2.

So the dividend comes in year 2, but you buy it in year one,

so there's only one year between when you pay for it

and when you receive it.

Therefore there's no to the power to here.

But what we can do now

we have an expression for P1 here,

and we have P1 here, so we could take this entire expression for P1.

And if you insert it, or replace P1 here by the value of P1 as it is expressed down there

if we do that, it looks like this.

So this now here

this is the old P1.

This part corresponds to the old P1

and then, by some mathematical manipulation or mathematical magic maybe you think

we can rewrite this so it looks like this instead.

So the price today should be equal to the present value of the dividend in one years time

plus the present value of the dividend in the second year.

And now as you see here, there's suddenly to the power two

since it's the price today, and we discounting the dividend in two years time,

we have to take it to the power of two.

And then we also have the selling price in the second year.

That's also received two years from now,

which is why we take to the power two when we're discounting it.

But why can't we do this one more time?

This selling price here P2, it should also be equal to the dividend received the year after

and the price received year after, as we showed in the picture earlier.

And again, this is discounted from year three to year two,

so it's only one year,

and therefore there's no to the power of 3 here or anything.

What can we do then?

Well, we can take this whole expression and

we can replace P2 with this expression.

If we do that and simplify it again, we get an expression here.

So the price today is equal to the present value of the dividend year 1,

the present value of the dividend year 2

The present value of the dividend year 3, and the present value of the price year 3.

But the price year 3 should be equal to the dividend in year 4 and the price in year 4.

So I can continue this as long as I want.

And we can show this may be in the picture instead,

so the price today should equal to the present value of the dividend next year

and the price next year.

But this price could be replaced by the dividend year 2 and the price in year 2.

And this price could be replaced by the dividend in year 3

and the price in year 3, and this price could replace...

We can go on and go on and go on,

and eventually we find that the price today

should be equal to the present value of all dividends that will ever be received from this company.

So that's basically what the dividend discount model says.

The value or the price of a stock today

is the present value of all future dividend payments.

So we have a little bit of assumptions here.

We assume that the firm will exist forever when we're going to do the calculations later.

And we're also going to assume that at some point we have a constant growth in the dividend.

So there's an annual percentage growth every year.

Otherwise it would be very hard to actually calculate the price.

So we can end with an example.

Let us estimate the value of a stock which has the following estimates

and the cost of equity equal to 13%.

So the dividend in one years time it's going to be $1.00

and it will grow by 10% the next year.

And after the second dividend it will grow at a constant rate of 2% per year.

So we can compute then, the first year was $1.00.

The next year it should grow by 10%, so it would be 1 times 1 + 0.10, which is 1.1.

So I've already done it here.

I don't know yet what the dividend in year 3 and year 4 is,

but I do know that I will have a growth rate of 2% every year.

So what is the present value of this one?

Well, I said we should compute the present value

of all of them discounted to today.

So for the first one we will take it alone because it's only $1.00.

The second one we will also take alone.

And then from year 3 and onward, we have a constant growth rate of 2% per year.

So this is what you call a growing perpetuity, and you've seen how to compute the value of that

so we can take all of these at once with one step.

And then we'll take it all the way back until today.

So the present value of the first two

So let's take the dividend 1 and dividend 2

Then the present value would be 1/1 + 0.13 to the power of 1, this is from the first year.

We add 1.10 divided by 1 + 0.13 to the power of 2

It's from here.

And if you compute the present value of that, it will turn out to be 1.746.

What is then the third dividend, the dividend 3, well

Dividend 3 is found by

we knew that the second years dividend was 1.1

and we also knew that it would grow by 2% per year.

So we take 1.1 times 1.02 and we find this dividend to be 1.122.

How did we compute the present value of a growing perpetuity?

Well, we took the cash flow, so the dividend is 1.122

We divide it by the interest rate, or the cost of equity

Minus the growth rate of 2%.

And we find this to be 12.466...

And this is then given in year 2.

So that's the first jump when we go here.

So we need to move this from year 2 until today.

So we take the value which was then 12.4666

and then we divide it by 1 plus the cost of equity to the power of 2,

since we need to move it two years.

And this is then 9.763.

So the total value of this stock is then, so P0 is equal to 9.763

Plus, the value of these two first dividends which we had in the previous slide

It was 1.746.

So plus 1.746 and we say that the total value of this stock is 11.51, approximately

So then we know what the value of this stock is and we have now learned

how to compute the price of a single stock using the dividend discount model.

A short summary, stocks represents ownership in a firm.

So if you own a stock, you have a part of the ownership.

The value of a stock according to this model,

is the present value of all future dividends.

And that's it for this video.

See you in the next one.