Okay, we just did a simple example, now let's do the real deal. This is an ugly looking formula, I totally recognize that. But I think it's also very intuitive, and we're going to do some examples of this, don't worry. But let's kind of try to struggle with the formula just a little bit and understand what's going on. The denominator of this thing looks like something you have seen before. It looks exactly like the denominator from the net present value calculation. And you know why it looks like it? because basically that's what it is. It's really no different than that. So you've got 1 + i, which is the discount rate per period, and then you've got it raised to the power of t-1. Now why t-1? Well, the reason it's t-1 is recall that in the first period when we first acquire a new customer, let's say in this point called that t=1. I know in my previous example I started with 0, I was just trying to keep it simple, this is more the industrial strength version. So, let's call the t=1. What is anything raise to the power of 0? Math test, 1, anything raise to the power of 0 is 1. So, when we raise that to the power of 0, that whole denominator becomes 1. Why? Because in the first period we don't want to discount their profits because they come in immediately, right? And then in the subsequent periods after that that's when MPV effect kicks in. It's discounting the future cash flows. Now where are the cash flows here? They're in the numerator. What is this M of t? Well, that is just like the GP minus the marketing spend that I had in that simple little example. It's the total amount of money you make on a customer per period, whatever that period happens to be. Whether it be a month or a year, that's the total bucks in the door minus all your costs. Now, what's this r to the t minus 1? r is the retention rate we just talked about. And why is it to the t-1? For the exact same reason the denominator is t-1. Because in the first period, what do you want to happen to r, it to go to 1. Why? Because you get the m of t. You the money come in the door, right? And it comes in with probability equal to 1. It's only in the future that you have the discounts or the probability that you're going to get that money in the door. So that's when that rate starts kicking in, that retention rate. And as you move farther and farther out, what's going to happen? That's going to be raised to a higher and higher power, and so that overall retention is going to fall. We're going to see that in a relay case. We're also going to see it in some examples. So taken in totality, what you have here is, on the top, you have a stream of profits that is reduced because of the probabilities in the future that it doesn't show up. And then the denominator, what you have is the same as the NPV formula. That's just taking into account interest rates, or discounts rates, and saying there's profits that may show up in the future. We gotta discount those back, too, because money tomorrow is not as valuable as money today. And that is the basic structure of this thing, and it's used in all kinds of applications and I'm going to show you some examples of it.