When I say t = 0 here, I mean at the time that you acquire the individual customer.

So t = 0.

We have t = 1, t = 2, t = 3.

These are just time periods.

They could be months.

They could be years.

It really depends on your particular business situation.

We will talk about how to select time periods in the retail relay case.

But for right now just think of those as time periods.

Then we have GP, remember that's the amount of money that you're making on

an individual customer in any different period.

Then you subtract from that that retention spend.

So any money that you use to try to keep a customer being a customer has to

be taken out of the gross margin that you make on the products that they buy, right?

So you have to subtract that out.

And this becomes the totality including marketing spend

that you make on a customer in any given period.

Okay, so understand that.

Now what's right below it?

It's the same thing but it's multiplied by r, now what is that r?

That is the retention rate and what this is trying to get at is the following,

I make, let's say I make a certain amount of money when I acquire a customer.

Now I'm going to make some more money if they buy from me again.

However there's some probability that they're never going to buy from me again.

Sometimes that's called attrition, right?

And then the opposite of that attrition is what we're measuring here.

Which is that retention rate.

So let's say if someone buys from Amazon for the first time,

what's the probability that they're going to buy the next month?

And let's just say that's 90%.

Then what you have to do, if you're Amazon, is say,

how valuable are they to me?

Okay, they bought from me today, I get to count that money, all of that money.

But I only get to count 90% of the money that they might spend next month.

Because there's some chance that next month they just won't be there.

And then the month after that what do we have to do?

Well we have to square that retention rate.

Because maybe only 90% of

the people that ordered the second time will also order the third time.

So this will drop that to 81.

And then three months later, we'd have to take that 81 and do what?

We'll multiply that by 0.9 again.

And that's saying,

three months down the road are they likely to still be my customer?

What's that probability?

That's about 0.73.

And Amazon has to take those probabilities into account,

just like really you think about a net present value calculation.

In order to discount those future cash flows because

they realize they simply just might not be there.