>> Like bonds and preferred stock,
the value of common stock is equal to the present value
of all future expected cash flows, meaning dividends.
Unlike bonds and preferred stock,
dividends are neither fixed nor guaranteed,
which makes it harder to value common stock compared to bonds and preferred stock.
Meaning because of the uncertainty in timing and the amount of dividends,
common stock valuation is less accurate than bonds or preferred stock pricing.
But dividends generally tend to increase with the growth of corporate earnings,
and we will use this idea in our calculations.
Let's briefly consider how companies grow.
Two primary ways are through capital infusion,
which means issuing new stock,
or through internal growth,
which means retaining profits to grow and expand the business.
Internal growth is the factor that is used for valuation purposes.
So let's look at the formula to calculate internal growth.
The formula is the growth rate equals return on equity
times the percentage of earnings management intends to retain.
The formula is written as g equals ROE times percent pr.
Most of the time in common stock valuations,
you are just given a growth rate,
but let's look at an example in case you have to calculate it.
Assume that a firm return on equity is
14 percent and management plans to retain 37 percent of earnings for investment purposes.
What is the firm's growth rate?
Well, we take 14 percent times 37 percent, and we get a growth rate of 5.18 percent.
So let's learn the dividend growth model,
which is often called Gordon's growth model.
These names are interchangeable.
The formula is, common stock value equals dividend amount in year 1,
which means next years dividend,
and we divide that by the difference between the required rate of return
minus the growth rate or often, D_1 divided by r minus g.
So let's look at an example.
A company pays a two dollar dividend at the end of last year
and is expected to pay a cash dividend in the future.
Dividends are expected to grow by at four percent
and investors require a rate of return of 14 percent.
So step 1, what is the amount of dividend next year?
Step two, using the new dividend amount,
what is the value of common stock?
We predict the future dividend by taking
the current dividend and multiplying it by the growth rate.
The current dividend is two dollars,
and the growth rate is four percent.
We can assume that the dividend next year will be
four percent greater than this year, which is $2.08.
Now, that we have next year's estimated dividend, we can solve for the common stock value,
using the formula D_1 divided by r minus g.
We take $2.08 and divide it by the difference between 14 percent rate of return
and four percent growth rate to get $20.80.
This is the intrinsic value of the stock.
If it is selling for less, we should buy it.
If it's selling for more, we should sell it if we own it already.
Finally, let's look how to calculate the expected rate of return.
We learned how to do this with preferred stock already.
The formula is very similar except common stock grows in value,
so we need to add the growth rate.
The formula is the annual dividend divided by the market price.
Then we add to the result the growth rate.
For example, current market price of a stock is $45
and the stock pays a dividend of two dollars with a growth rate of six percent.
What is the expected rate of return?
Two dollars divided by $45 is 4.44 percent,
add to that the six percent growth rate, and the expected rate of return is 10.44 percent.