Welcome to finance in Excel video number 65.
Hey, if you want to download this workbook for chapter seven
or the PDFs, the PowerPoints for chapter seven,
just click on the link directly below the video,
and scroll all the way down to the finance Excel class
section.
Hey, in this video here, we want to talk about calculating
a stock price at time t.
Let's look at our model we've been using,
the dividend growth model.
Here's our price at time 0.
If we know the current dividend and there's a constant growth
rate, we can use this model or this.
Now, this is a time 0.
What if you want to predict into the future?
Can we use this model?
Well let's think about this.
Time 0, as long as we know the next dividend,
we just do R minus g.
Well, let's look ahead.
By the way, these slides are at the very end.
There's one slide for each math model we're using.
Just as with time 0, but here we have time t.
The price at time t is?
Well, of course it's just the next dividend, right?
So we have this.
If we know dividend exactly at time t,
we do 1 plus the growth rate.
Or simply if we know the dividend one period ahead.
So that's the concept here for this model.
Any time you know the dividend for the next period,
you can use this model, whether it's at time t or time 0,
like we saw here.
Now let's look at an example.
I'm going to go to slide 18.
And then we'll do this over in Excel.
XYZ company's expected to pay a dividend of $5 next period.
And dividends are expected to grow at 5% per year.
The required return is 15%.
Current price?
Well, we can do that.
$5 divided by our discount rate minus constant growth rate,
we get $50.
And of course, as we mentioned, if it was selling for $51,
we wouldn't buy.
If it was selling for $49, we would.
Now, we'll take this information.
And now we want to ask, what is the price expected
to be in four years.
Well, as we just mentioned, if we wanted price at time 4,
we just need to figure out time 5 dividend, right?
Now, this 5 right here, that 5 is next period.
So we already have D 1.
So there's D 1.
So we simply multiply it times the growth rate
to the fourth exponent.
5 times 1.05 constant growth rate raised to the fourth.
And that gives us what?
It gives us D 5.
Once we know D 5, we simply divide it
by required return minus constant growth rate.
And ding, ding, ding, we have our stock price
at time 4 for us.
Now let's go over to Excel.
And I'm going to calculate this example here.
We were given, we know, or we calculated previously
the dividend at time 1 divided by R minus g.
Now we need to figure out the dividend at time 5.
Well, we know our dividend at time 1.
So just like anything with a constant growth
rate, 1 plus whatever that growth rate is.
And in our case, we're going 4 periods into the future.
Notice we start at 1, go 4 into the future, that's 5.
There is our 5.
We could then take next period's dividend,
since we're trying to figure out the price at time
4, next period's dividend, D 5, divided
by required return discount rate minus the growth rate.
And so there's our value.
Now I'm going to go back over to the PDFs
and go to this next slide, number 20.
Now let's just take a look here.
Here's our model for time 0.
Next dividend divided by R minus g.
And here's our model for time t.
So it's always just, go to the next dividend,
and then divide it by that.
Well, let's break this apart.
How did we get dividend at time t plus 1?
Well, if we knew dividend at time t,
we just 1 times g to get to the next period.
Well, how did we get dividend at time t?
Well, if we know dividend at time 1,
we just do 1 plus g raised to the t, which
is what we did over in Excel just a moment ago.
But let's look at this right here, this little piece
right here.
That's multiplication in the numerator.
If two things are multiplied in the numerator,
we can break that apart.
We could say D 1 divided by R minus g
and take that right there and simply multiply times this.
Well, let's take a closer look here.
What in the world is that?
Does that look familiar?
That's just price at time zero.
You mean price at time 0 times 1 plus the growth
rate raised to the t?
That's how we can calculate it.
That's an even easier way to calculate price at time t.
This also assumes that-- and it makes sense,
because if we have constant growing dividends,
the stock's value is based on this dividend growth rate.
So that means also the stock value at any time t
is based on that growth rate.
All right, let's go over here.
So the easier way to do this is simply to say =--
if we know price at time 0 times 1 plus the growth rate.
And then we're going 4 periods out.
We want it at that period.
So we simply exponent 4.
Oh, the same answer.
So that one depends on the fact that we know price at time 0.
All right, a little bit more about the dividend growth
model.
When we come back, we'll talk about the dividend yield
and the capital gains yield.
All right, see you next video.