We're talking about how we figure out, firms might be sole proprietorships. That's like Larry's tree trimming shop. Larry keeps the cash, any profits that are made, they accrue to me. I'm the sole owner of that firm. And we talked about partnerships Larry's tree trimming and Tim's landscaping form Larry and Tim's garden shop. They're partners and they split the profits and they split the cost. But corporations are different, corporations are entities where the ownership is very diverse. The ownership is people who have those little sheets of paper. They don't really have a little sheets of paper anymore, but they have shares in that particular company. There can be millions of outstanding owners for some large companies. But we have to think about, who determines the price of those? Who determines what the price of a share of stock is? What we're going to do today is we're going to think about that. We're going to think about the price of a share of stock. A share of stock is simply an ownership right. To go back to my little Larry's tree-trimming shop, I could in fact incorporate, the state of Illinois is not that expensive. I could incorporate, so I'd be Larry's Tree-Trimming Inc, I have to issue some shares. Maybe I'll put ten shares out there. Each share is worth $100, and I would sell those shares. That's how I get money. We have an equity market, I would those shares, people will give me a hundred bucks for an ownership right. When I sell the ten shares, I now have $1000, that allows me to buy two or three chainsaws and I can really get my operation going. Then at the at the end of the year, all the profits I made would be divided amongst the ten shareholders. By the way, I kept a couple shares for myself. So there's really eight shareholders out there, plus the two in my pocket. So I have some desire to make this company more efficient. We want to think about the price of a share of stock and we're going to put it this way. We're going to say the price of a share of stock is equal to and we're going to write an equation out there to think about it. If you own a share of IBM, just to pick one company at random. If you own a share of IBM, that means you have an ownership right, a right to some cut, your fair share of the total profits that goes out to them. And you're going to get some of that every year. What we're going to do is we're going to think about basically what economists call a net discounted value. We're going to bring that money future valued back today's value. So the price of that stock is going to be equal to your per unit profits that you get in the current period. Just suppose that you own 1% of the IBM stock. If IBM has $1 million, you would get 1% of that $1 million, because you have 1% of the shares. And you would get that today, but you also get some profits in the next period. So you get some profit next year down the road, but now we have to divide these by 1 plus r. This number here, r is the interest rate. Think about it, suppose this numerator is $100. You're expecting next year that your shares are going to be worth $100, your profit from that. A hundred dollars a year from now is the same as about $98 today. How do I know that? I could take $98 today, put in the bank and 365 days from now, that will be worth $100. Because the bank has posted interest that they would pay me. What I have to do in order to think about what's to devalue in today's world. What's the value of that profit a year removed? I have to what we economists call discount that. So we divide it by what the interest it would have earned by sitting in the bank. The problem is, it's not a problem, but you're also going to have this, it's an asset in perpetuity. You're going to get profit from two years down the road. And now you have to divide that by the interest that you would get in one year plus the interest you would get in the second year. Which is really the same thing as saying 1 plus r squared, you have two years of sitting in the bank. So now if I think I'm going to get $100 two years from now, if my expectations are that I'm going to get $100 two years from now. That's the same thing as saying gee, all I really need to do is put $95 in the bank today. If I put $95 in the bank today, after 365 days plus another 365 days, that'll be worth $100. Of course, you're going to do this in year three. Now I just going to put 1 plus r to the power of 3, you're going to do it in year four you expect to earn. Nobody expects IBM to be broke. Sometimes big firms like Enron do suddenly vanish, but for the most part, your expectations are they're still going to be around. And then plus on, so forth. This is what's known as an infinite sequence but it converges, that's nice. Some infinite sequence don't. It converges and you can see that you're each year, farther down the road. If you think you're going to get expectations of $100 four years from now, you probably only need to put about $88, $84, $83 in a bank today. And four years from now that will have grown to exactly $100. And that's how you are able to what we call discount back the future value of that money. Now this is a stream of expectations, your expectations. On any given day, over a billion shares, there's a b there. Over a billion shares are going to trade hands in the New York Stock Exchange. Today, a billion shares are going to trade hands. Now every time that happens, somebody walks up with a pile of cash and says, I want to buy some of your shares in that company. And somebody else says, okay, I'll sell them. Nobody puts a gun to anybody's head. Suppose I go up to my friend and I say hey, I know you got some shares in XYZ company. I'd like to buy them and my friend says okay, here's the price and I say, I'll pay that. Now as soon as I transaction happens, the person who sold them turns around and goes I'm glad I got rid of that stock. I don't have very good expectations about the future stream of numerators for that company. I don't think they're managed very well, I'm glad I got out. At the same time, no one put a gun to my head and said buy that stock. I did it because in my mind, this company is poised for a big growth spurt. And I want to be a member of that team, I want to be an owner that's going to go going forward. On any given day, again, a billion shares are going to trade hands. That means there's lots of people who think this company's stock has probably run its course. I want to get away from being an owner now, I'm going to go to some other company. At the same time, definitionally, somebody else says I'm glad to get in this company. I really want to put my money and be an owner in this company. So there are expectations out there and that's what drives these ups and downs in stock value. If you hear a report, like a few years ago, it was reported that Volkswagen got in a little bit of trouble. Because they discovered that they were giving fraudulent data on emissions tests. What happened is that the stock price for that company basically went down by 25% overnight. Because all those numerators of what people thought they were going to be getting back by being a part owner of Volkswagen have now taken a depressing downturn. Because no, they said for we're going to pay fines. We're going to have brand image problems. There's all sorts of stuff that's going to make these little numerators not as good as I thought they were. Lots of people felt that in one night and so the stock price took a big dump.