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Learning Outcomes.
After watching this video you will be able to use various versions of
the dividend discount model to calculate the stock price.
Define what dividend yield and capital gains are.
Dividend discount models.
Let's look at how to value stocks.
This will help us tie together the concept of expected returns with
current stock prices.
Valuing stocks will help us identify those stocks that appear to be mispriced.
Let's say that you know that a stock would pay the dividend
of one dollar after one year.
At which point the stock will be worth $55.
Denote D sub 1 equals one dollar and P sub 1 equals $55.
What must this stock be worth today?
To answer this question, we'll need to know the expected return on the stock.
We will discount these future cashflow
back to today using the expected return to get today's stock price.
In other words, today's stock price P sub 0 equals
D sub 1 plus P sub 1 divided by 1 plus R sub E.
Where r sub e is the stock's discount rate which comes
from an asset pricing model like the APT or CAPM.
Rearrange this equation and solve for r sub e.
We now have r sub e equals D sub 1 plus
P sub 1 divided by P sub 0 minus 1.
This can further be arranged to r sub e = D sub
1 over P sub 0 + P sub 1- P sub 0 divided by P sub 0.
The first term is the derivative of the stock and
the second term is the capital gains rate of the stock.
This tells us that the expected return on a stock must equal its
dividend yield plus it's capital gains rate.
Let's complete this example by saying that P sub 0 is $50.
Then the dividend yield is 1 over 50, which is 2%,
the capital gains rate is 55 minus 50 over 50, which is 10%.
So the expected return on the stock is 2% + 20%, which is 12%.
We can extend this example to a stock that pays end dividends.
It's price today, P sub 0, will be D sub 1,
divided by 1 + r sub e to the power one + D sub 2
divided by 1 + r sub e to the power 2, + so
on until d sub n divided 1 + r sub e to the power n,
+ p sub n divided by 1 + r sub e to the power n.
Each D sub i is the annual dividend paid by the stock and
P sub N is the stock price at the end of year N.
This is a simple dividend discount model where the current stock price is arrived
by discounting future dividends and the stock price and the end of N years.
But we expect companies to last forever.
So a better way to estimate today's stock price is that it is equal to
the present value of all expected future dividends that it will pay.
Now we have p sub zero equals d sub one divided by one
plus r sub b to the power of one Plus D sub two divide
by 1 + r sub E to the power two plus so on forever.
This is a very cumbersome calculation as we are to calculate dividend every
year forever.
That is estimate and infinite number od dividend.
One way to simplify this calculation,
is to assume that the expected dividend is the same every year forever.
That is dividends form a constant payment by maturity.
In this case, the stock price today,
p sub zero, would be d sub 1, divided by r sub e.
Let's say that you expect the company to pay a dividend of $5.00 every year
forever.
And it's expected return or discount rate is 10%.
The stock price today must be five divided by 10%.
Which is $50.00.
Assuming that dividends stay a constant seems unrealistic
as companies typically grow over time.
So what if we assume that dividends grow at a constant rate every year forever?
Now we have a growing perpetuity.
The stock price today, D sub zero, will be D sub one,
divided by the difference between R sub E and growth rate of dividends, G.
This is referred to as the dividend growth model or the Gordon Growth Model.
Let's build on our previous example.
Where the stock pays a dividend of $5 in the first year and
has a discount rate of 10%.
Let's now assume that the dividend grows at 5% every year, forever.
This tells us that the dividend in the first year is going to be $5,
that in the second year will be 5(1 + 0.05) Which is 5.25.
That, in the third year, will be 5(1+0.05) squared,
which is 5.5125 and so on forever.
The stock price today would be 5 /
(0.10-0.05), which is $100.
Taking a step back, how do we determine the growth rate of dividends?
We'll answer this question the next time.
Ramabhadran ThirumalaiAssistant Professor
