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Until now, we have seen cash flow that end after a certain number of periods.

What if they would to occur forever?

In this video, you see what perpetuities are,

how to calculate the present values, and how they relate to stock valuation.

We will also see how to calculate the present value of a perpetuity whose cash

flows increase at a constant rate forever, which is called a growing perpetuity.

We have talked about annuities, which have a fixed number of periodic payments.

What if the cash flows occurred periodically, but never end?

You wonder what type of cash flows behave like this?

A company pays dividends every year to its shareholders, and

is expected to do so forever.

You can think of this dividend stream as a perpetuity.

The present value of a perpetuity, PVP is PMT divided by r.

Well PMT is the periodic payment of the perpetuity, and r is the interest rate.

The interest rate r is frequently referred to as the discount rate, and

so I'm going to switch to saying discount rate instead of interest rate from now on.

Let's look at a simple example, a stock pays a dividend of $2 every year forever.

The discount rate is 10% per year, how much must the stock be worth today?

The question asks us, what the present value of this perpetuity is?

We know PMT is equal to 2, r is equal to 10%.

Plugging in all the values,

the stock price equals 2 divided by 0.10 which equals $20.

Given the $2 stream of cashflows every year forever and

a discount rate of 10%, the stock price should be $20 to date.

But is it reasonable to assume that a company pays the same dividend

every year forever?

Companies tend to grow in size over time and hence,

are more likely to increase dividends over time.

Let's denote the growth rate in these dividends by little g.

Now we have what is called the growing perpetuity.

With the first payment of the growing perpetuity, being PMT.

The present value of a growing perpetuity is given by PMT divided by r minus g.

When applied to calculating stock prices,

this formula is commonly referred to as the Gordon Growth Model.

Let's apply the Gordon Growth Model to an example.

A stock pays a dividend of $2 every year forever, and

it's expected to increase it at 5% a year forever.

The discount rate is 10% per year, how much must the stock be worth today?

The question ask said what is the present value of this growing perpetuity is?

We know that PMT equal 2 add equal 10% and G is equal 5%.

Plugging in all the values, the stock price equals 2 divided

by 0.10 minus 0.05, which equals $40.

Given the $2 stream of dividends every year forever, growing at a rate of 5%

a year forever, and a discount rate of 10%, the stock price should be $40 today.

Next time, we will start seeing a practical use of this time value of

money framework, which is to use it to value projects.

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