Hi. I hope you had a chance to look at what I did in the last fifteen to twenty minutes because I think what's important about that is. If I could spend hours on it literally it reflects a thinking process and just making things exactly precise to be able to run this stuff. I can do it individual but I encourage you and I will warn you whenever some stuff is easy or not. Remember I told you earlier a joke that you know, if you don't know how to divide, learn how to very quickly. Here I would pause and remember though with one thing, one warning is that don't spend too much time on theory. Theory is only useful in business if it's practical and this stuff is so practically useful to do stuff I'll come to in a second. So, before we jump into an example, let me just wrap up what we talked about another way. When you think of any stock. Any companies equity and for the time being, as you'll know that, you can think of it using this simple formula. P-naught equals EPS / R plus PVGO. Remember one, one, this is a conceptual way. It's not. It's, I'll, I'll tell you what it means in a second. So quickly, definition. What is EPS? As I said, everything is per share, like the prices per share. You don't have the whole company trading. Of course there are, prices these days of companies where your mind starts getting boggled about, how the heck is anybody going to buy one of those shares? Anyway, where EPS is the cash flow per share, and PVGO is the present value of growth opportunities. So it has to do with whatever we did right now. So let me, let me ask you this. What is the price of a stock? The price of a stock is the present value of dividends. Just conceptually, right? Now, there are two formulas that come about. One is when you have no growth and one you have growth, right? Pretty straightforward, and we know where growth is coming from, how it's generated. We spent of some time on it. So let me ask you, which company would have the first piece applicable to? We just did examples. Which of the two examples would have the first piece applicable? Green Utility. So Green Utility, look what I've done. I'm going to assume Green Utility's PVGO is by default, by definition zero and the reason is it's not putting anything back. So, if you're not putting anything back, this formula becomes irrelevant. Why? Because if there's no growth, what is the price of your stock? Dividend over R but remember, if you're not going, putting anything back, this is also EPS over R. So the first piece of this formula is telling you what would you look like that part of a company you can think of which has nothing to do with future growth. Can you think of companies who are not going to grow at all? Sure you can. But what I'm saying is, you can think of every company as having two pieces. One without growth, and one with growth, right? Remember, everything is incremental, right? So, if it is without any growth, you're thinking of the company. And many companies are just that but you can think of any company in that way. What would you think of the formula? Div one / R but because dividend is exactly equal to earnings per share. Why? Earnings per share is being paid out totally as dividends because you're not planning to grow, right? But which comes first? Remember the engine of growth. What comes first? Earnings per share or dividend? Earnings per share. Never put dividend before earnings per share because you're again doing MC Hammer, can't touch this. Cash flow, earnings per share come from whom? Your assets and dividends are payments to your liabilities or the way you're financed. Okay? So this is pretty straightforward. So this is the formula of no growth. What is the formula of growth? What happens with growth? With growth you have your existing assets, but then you have something more and that's called future growth opportunities. And what was the formula for that? P naught = dev one / R - G, right? So how do we figure out PVGO? And this is the point of this exercise. So suppose I want to know if whether there is PVGO or not. The first thing I h ave to recognize is for PVGO to happen you have to be prepared to re-invest in the firm. But to figure out your PVGO, you can do this simple exercise. Think of the firm without any growth and think of the firm with growth, the difference between the two is called PVGO, right? Make sense? Because PVGO. If it's zero, what is G in the formula here? If you are not planning to grow, G is zero. You are not reinvesting and the two formulas collapse. So keep this big picture, I love this. One final question for you, think about it. Suppose I asked you in the 70s, 60s and so on, you looked at the whole stock market of the world. What part of it would belong to the first part? That is, the value of the existing assets with organic growth but not land growth versus what did the future opportunities look like? Relative to after the Internet came through and .coms emerged and after the fall out, right? You don't necessarily have to think of the peak of it. Well, things have flipped. For many companies, it used to be that your business as usual was generating most of your value. But now, what has happened? The growth opportunities reflect value, right? So, so that's what a major breakthrough like the internet does for society, okay? And, and technological innovations. Anyway, so I'm going to now start doing examples and I'm going to do, go a little bit simple, slow. And this is a very good opportunity for you to practice. Suppose you know this about Macrosoft, Inc. Macrosoft, Inc is expected to earn ten% on its existing assets. Questions, what does that ten% mean? Is it the r or is it the IRR of it's existing assets? And remember if some number is reflected as belonging to your assets, it has to be ROI, return on your investment. Has $60 capital per share so what have I done? I've taken Macrosoft and how did I get $60 capital per share? Remember, your starting off, you have say $1,000,000 worth of investment, right? And you divide that by number of shares. That's what the 60 is so let's assume for simplicity. You have $6,000 of inve stment in 100 shares. That 60 is just a function of that division. And why were we doing this? Because remember, everything in stocks is per share. The market capitalization rate is twelve% and please any calculation you do is meaningless unless you know what the heck you're doing, right? And because plus all the numbers are wrong, right? So remember that. What does market capitalization rate mean? And remember, this is another word that I'm now beginning comfortable to throw at you. This guy is also what we usually call the little r. As soon as the word market is used, you know that it is something that is being used to evaluate you, okay? So where did I get this? And with, by the way, the next, rest of this class, almost, at least the next two weeks, are all about this. Because we haven't touched risk and return as yet. Where is it coming from? Similar businesses. I'll let you figure out who is doing similar business to Macrosoft. The company is not planning to grow. What should Macrosoft, Inc's shares trade at? Let's take a five minutes break. Do this problem. Stare at all the concept that I gave you earlier on. The good news here is there is no growth. So tell me, what is the value of this stock? And try to spend some time, and we'll come back and do it together.