Find stock price - "constant" vs "constant growth" dividends - YouTube

In this video I would like to explain how to calculate the price for one share

of stock, if we know what the future dividends would look like. And we are

going to consider two cases. One: we call it a "constant dividend" case. Two: we call it

a "constant growth dividend" case. Let's say we have... let's say we have our time

line. And we want to mark year 0, which is today, year 1, year 2, year 3, year 4, dot

dot dot. What we know is that the company will pay a $10 dividend next time it

pays a dividend. So you buy a stock share now, your first dividend will be in a

year in the amount of $10 on your one share. Let's say we also know that the

interest rate, or the discount rate, is 12%. This is what we are given. Here, in

the second case, we have exactly the same thing except we will have one additional

piece of information. So let's mark our years again. If you buy a share of stock

today, year 0, your first dividend will be $10 paid in a year. Same interest rate, or

discount rate, 12%. And there's one thing we add to case two, which is the rate at

which the dividends will be growing every year in the future (2%). Okay. What we want

to find - let's change the color to red - is two things. So, what's the price

today and, second, what's the price in two years. And we want to do the same

calculations here: what is the price today and what will be the price in two

years. Okay. Let me switch to blue, which is my favorite color for all my

calculations! "Constant dividend", case one. "Constant dividend" means the dividend amount

will not change, so it will stay at $10 every year forever.

It's a perpetuity. If it's a perpetuity, to find the price (so, Price 0) we need

to take Year 1 dividend, so "D1", and divide it by the interest rate. Right?

So, we take this dividend, put it in the numerator. Now plug in the numbers: 10

divided by 0.12, and we get

$83.33 for the price that you will be paying today that correctly represents

all the future $10 dividends that you will be receiving in perpetuity. Price in

two years - same exact approach! Price in Year 2

should be calculated using the present value of a perpetuity formula that says:

take the dividend one year from this time, which is for Year 3, and divide

by the interest rate. But in our case it's the same dividend amount. It's still

$10. Every year it's $10. So the calculations will be identical:

10 divided by 12% which gives

$83.33 for the price in Year 2. Now we want to do the

same thing in the second case, except now we added another number, right? The growth

rate in dividends. Why? Because this is what "constant growth dividend" looks like.

It means the dividend will not be the same, it will be growing at a constant

rate every year, every year, forever. What will the dividend be two years from today?

Well, it's $10 in Year 1. We can actually use the financial calculator.

Let's turn it on. Let's increase the decimals: "2nd", "format", let's make it

4. Let's begin! 10 dollars, negative, is our "Present

Value". That's in Year 1. We wanna find what it will be one year after that, if

it grows by 2%. So 2% is our interest rate equivalent at which

the money grows. I press "2", "I/Y". I wanna find the Future Value after one

year. I press "1", "N", and I want to "compute" the "Future Value". $10.20. Let's

put it here. So what we did was essentially taking $10 from Year

1, multiplied by 1 plus 2% growth rate in dividends, and that's how

we got $10 and 20 cents. 10.2. Now the same way we can

calculate future dividends except we're gonna only do maybe one more since it's

going to be another perpetuity with endless cash flows. For the third year

dividend essentially we would need to do the same thing: $10.20 from Year 2

multiplied by 1 plus the 2% growth rate in

dividends. So, 1.02, which gives 10.404. And we can double-check

that. So, this becomes our Present Value... 2%

growth rate... after 1 year... gives us... "compute", "FV"... 10 dollars 404

cents. Right? So we have that number. And let me put dot dot dot and call it a

growing perpetuity. Growing perpetuity. And this one here was a regular

perpetuity. Perpetuity means $10 forever, every year, forever. It keeps

going. Okay. Now let's find the two prices.

Exactly the same approach! To find the price in Year 0 we need to take the

dividend in Year 1 and divide by "R". But this time we need to use the growing

perpetuity Present Value formula, which is a little bit different. On the bottom

in the denominator we put "R" minus the growth rate in dividends. "R" minus "g". So

12% minus 2%. Okay. So, we do: 10 divided by 0.12 minus

0.02, which is $10 divided by 0.1, and that gives $100.

That's the price

today. Now, the price in two years is found exactly the same way again! We take

the dividend from Year 3 and divide by "R" minus "g". See how for "Price 0" we

need "Dividend 1", for "Price 2" we need "Dividend 3". We did the same thing

above except it didn't matter, all dividends were the same, they were all

$10. Here they are different amounts, right? Here dividend in Year 3 is 10

dollars and 40 and a little bit cents (404, divided by 0.12

minus 0.02, which is 10.404 divided by 0.1, or $104.04,

right? And you see how the price is higher two

years from today compared to today's price. And this is how it will always be

with a stock with dividends increasing at a constant rate. And

that's because at any point of time the price per share of stock is nothing but

the present value of all future dividends after that time. And if all

future dividends are larger dollar amounts that will result in a higher

price at that time. Now, one thing we can notice is that this is the price today (

$100), $104.04 is the price in two years.

Let's do something. 100... Let's clear everything... Start out fresh... Increase the

decimals. Let's say to four. 100 dollars, negative, is our "Present Value".

That's the price today. Let's say that the price in two years is two years in

the future, so that's our "Future Value". That's $104.04. That's

our "Future Value". They are two years apart, Year 0 and Year 2. That's our "N". "2", "N".

Let's compute the implied growth rate in the price: "compute", "I/Y". 2. 2% per year.

which is exactly like the growth rate in the dividend amount. And this will always

be the case! Right? So, going from Price 0 to Price 1

implies that the price increases by 2% per year, which is just like the

growth rate in dividends. And it's an important detail to remember. So, the

price goes up at the same rate at which the dividends will be increasing.