Hi. I hope you have had a chance to kind of carefully review what we did just before this break I took. And I wanted to remind you that these breaks are more to kind off, give you my sense of where you probably need us need to stop. But remember, this is you in many different ways of learning there, lots of you there. So it's up to you to always take a break. And if you don't understand something, you have other resources. So you don't have to go through these videos till you feel comfortable moving forward. I'm emphasizing this right now because the idea of a stock is not easy to comprehend. So lets just quickly look at this formula. What this formula says is basically, what we know about cash flows is that if you have cash flows going on for a long time, you'll have to discount them at an increasing rate because of a game compounding. So that's all that it's saying. Why dividend? That's just the name with the way the stock base stuff to you, right? Like for example, for a bond, it was coupon and then face well, why is no face value here? Because you expect when you buy a stock that the stock, even if you're going to sell it, is going to have value. And when you sell it, the only way it will have value is if it's expected to move on, not just die. So this inherent built in value coming from looking forward is extremely important to internalize. Okay, so at any point, a stock, unless you know for sure, is not going to last really long has value because of the long longevity there is. So that's it. That's the point that you need to understand and we'll emphasize. What I'm going to do now is I'm going to start giving you examples, and I would I'll stop, take breaks. But you take breaks. As I said whenever it's convenient for you. Okay, the special case off the stock, which is I call a dividend stock, and I think many people in the real world would probably call it the income stock. This is the kind of stock that kind of gives you a steady flow off coat on coat, on the income paired buy stocks is called dividends. So let's look at a special case. Suppose dividends are expected to remain approximately constant. What would be the price off stock? So the notion here is that if you remember I talked about a little while ago, I think it was. But when I was doing, annuities and so on, I just introduced the concept off Richard E. So what is this saying genetically? First, it is saying that you're standing here and you getting approximately the same see cash flow and for a very long period of time. Okay, the only thing twist here is that we'll call this cash flow dividends. So the question is, what is the formula for this? Turns out, and if you have the time, you can do these calculations for yourself and deprivation actually for yourself. But I think it's very cool to derive this. But imagine the formula is the simplest possible. C, over little R actually I apologize because I sometimes use big our little art, but are unqualified means the discount rate or cost of capital and quickly, one more time. Where does it come from? It comes from be a competition. So whenever you're thinking, little are are your cost of capital. You're thinking market. If there was no market, it will be very tough to figure out your value because values are always relative. Okay, so C, in this case, it becomes div over R so this is the formula. What I'm going to do is I'm not going to try to derive it for you. And this is where I think you need to put in some work based on the level of curiosity you have. And you can look at the books I've recommended to you or you can sit down. If you're curious, just derive it. And remember, this is equal to what, Dev one, one plus R plus Dev to one plus R square going on for a long time. In fact, perpetuate T is almost infinity. The only constraint I'm putting on this is these two guys are the same approximately. And why? Why do we use this formulas? Because, remember, a stock you don't even know what the dividend is going to be in the first year. Second year try. So getting to precise can be actually hurtful to your thinking. You're doing a very detailed calculation on stocks. Doesn't make that much sense. So we will use formulas like these because they kind of capture both what's going on and in some sense, what's happened in the real world. Okay, so this is basically the formula and let's go back. So we know that if its dividend stock is a constant level of dividend, whatever it ISS, let's do this. Let's let's spend five minutes and you do it with me and I'm assuming that the problem is relatively straightforward. We kind of do it with each other. Otherwise, just take a break. Do it and we'll come back to it. And I will try my best to make sure that I'm making a good judgment about what is doable together and what is. You want to do a little bit of a break and test yourself. And remember, you have always the opportunity to go to the assessments and assignments to do similar problems and then come back. Okay, so this problem is relatively easy. It says supposed green utility is expected to be a dividend to pay a dividend off 50 cents not to be a dividend, but to pay a dividend or 50 cents per share, for the foreseeable future on the return on the business is 10%. What does this mean? Return on the business? It means another way off saying that the cost of capital belongs not to you, not to anyone but the type of business you're in. And that return is a function off demand supply and everything put together what should be the price of the stock. Now just take a pause. Think about it. I'm going to start scribbling stuff on the bird. So what is it? Timeline wise? Very straightforward. I'm getting 50 cents evident for long, long time and I'm asking you, what would the price of the Stock B and I'm calling it to utility because turns out utilities I've regulated. And it's very common to view them as income stocks, as opposed to another example I get into which is at the heart off the rest of this session this week. Is called growth stocks. And I just love that stuff because it will convey to you what really is going on and how growth is good, how growth could be bad and so on. But let's stick right now with the stock that's not planning to grow, but it's planning to pay 50 cents. You know, the formula for this is what, 0.50 over 0.10 which is Div1 over r we just did, right? What is that? 0.5 over 0.1 is the same as what? Multiplying by 10. Why? Because one over 0.1 is same as multiplying by 10 when you're dividing, right. So this is five bucks. So this was pretty straightforward, right. Whatever they encourage you to do is think about how easy this is to value, right. So you took 50 cents and you just multiplied by 10 and you've got five bucks, and it's basically that and people do this when you're comfortable with this level of the assumptions behind the ease of the formula. You just suddenly realizes how cool it is. You know how people are so comfortable with numbers seemingly in the financial world. It's because they used formulas like this. That's what ingrained at the back of my head and therefore I can feel very comfortable. It's not that I am very comfortable calculating complicated formulas with numbers in excel. In fact, I shouldn't be. I have better things to do, okay, so let's just see what does forever mean? Now many people get caught up in nothing is forever. How could it be forever? Let's just this is not quite real. Okay, so let let me ask you the following question. Let me assume that forever means 30 years. And by the way, that's not terribly long, right? A lot of companies do survive 30 years. That's not the important point though. We're trying to price the stock that is not expected to die tomorrow because there's no point in doing that, right. So let's take this example. Same example and say, okay, got them coming forget about this perpetually stuff. Doesn't make sense. So let's just assume it lasts for 30 years and the dividend is 0.5. And so what am I doing? I'm, what is this called? Have we done this before? I think we have, right? What is it called? This is called an annuity of 30 years. The only difference between annuity of 30 years and the perpetuity is the perpetually is going to go beyond the year 30. Okay, so just recall, what was the value of the perpetuity? It was 50 cents divided by 0.1. Very simple. So 50 cents multiplied by 10 was five bucks. Keep that at the back of your mind. And now let's do this on a calculator. You see what's going to happen? You can't do this in your head. And that's part of the that proposition value proposition I was talking about. So let's go to an Excel. Let's do equal sign. And what are we figuring out? PV. I'm actually much lower than you, probably by now. And you guys were just rolling along with the stuff and saying, awesome, come on, get go fast. I don't type very fast that's the way I am. All right any way, so the rate is 0.5. That can't change and how much of my sorry rate is 0.1, right. There you go. I'm talking and I'm messing up numbers. The rate was 10%. I think I got it right, 0.1. The number of periods was what? Not infinity. I don't like that, but 30 is fine. And how much was my money? 50 cents. And I hope my fingers haven't done anything bizarre. What's the answer or what's the value? Look, it's $4.71. Why did I do this? Let's go back. So what's the value if I use an annuity? Value is 4.71. Let me ask you this. Are you sure for the next 30 years you'll get that dividend because if it was exactly true that you expected it and you got it, there's something really magical about you are the real world. The real world doesn't operate like that. It's approximately that, right? So getting very precise about five bucks for 30 I mean, 50 cents for 30 years would make sense if you were exactly show that is going to happen. But why be so precise about something that you feel will happen? So this is a very powerful way of showing you the value of a perpetuity. How much did we calculate the actual perpetuity? And this is, by the way, seemingly a very simple example. But its a very deep issue, right. So this shows you wife finances both art and science. All your numbers are wrong. So what's the point getting very precise about being wrong, right? So let's compare these two, am I close when I did a perpetually or five bucks. Yes, I'm pretty close, which was easier. Heck, I could do the five bucks in my head. I just multiply 50 cents by 10, right? Okay, now annuity of 4.71. It's for 30 years, right? So tell me, what is 29 cents five minus 4.79 is 29 cents. If you could think for a minute, tell me what that is and it'll make you pause about what's going on. It's the present value off the 50 cents in the year 31 after that, forever. So getting 50 cents forever on the face o It should be what? Infinity. But you see now the power of powers again compounding at a 10% rate of return. The money that you get after 31st year is almost trivial. It's only 29 cents, even though it's forever so recognizing that the interest rate is positive. And for stocks, stocks are risky relative to bonds. They're likely to be high. You know that formulas like perpetual teas will bring you so close that you don't need to necessarily be very precise. I am not saying don't use Excel. I'm saying most of value of the frame book comes from your thinking, not from the answers. They're all wrong. I hope you found this little example very useful, because formulas like c over r, are used all the time. They're basis of what are called multiples in finance. Venture capitalists, people in I bank, in I banking people who value stocks don't try to get to precise. On the other hand, bond pricing I just touched upon a little bit can get very, very technical and precise. And the reason is There's uncertainty only in one thing, fundamentally writing government bonds. For example, if you expect the cash flow to be paid uncertainty, interest rates is driving everything. So you can get really precise in trying to model that. But anyways, here in stocks, everything is uncertain, right. So what's the point getting too precise about pretty much everything because you can't. Okay, now let me move on to something that's much more interesting in my book. Suppose dividends are expected to grow at the rate of g per year. What is the price of the stock? And this is called a growth stock. And I'm sure you've seen examples of these and things happening as we speak. Which is the biggest company in the world right now in terms of value of the stock? Remember when I say value for company, I could mean many things, the first thing I could mean as being a finance guy. What is the cap market cap, which is the value of their stocks? But companies also have debt. So when I say value of the whole company, people would want to include debt, which makes sense, okay. So anyway, so which is the company whose stock value is the most in the world? It's Apple. Apple has almost gone and survived, almost died and survived and then grown rapidly in different phases. So I would call it a growth stock. But it depends on where is it in its life cycle or new idea, generation regeneration or whatever. Okay, so let's see how this would be priced. Look what I'm saying here, your p0 here where the first dividend is, Div1. You can also call this genetically C1. You see, that's I told you, the nice thing about finances once you know, time, value of money and then we'll do risk. At a fundamental level you could do any problem because the beauty is the same framework, same tools, just the symbols change. The names change. Okay, so the first to C1, what is the second one? DIV2. So why am I labeling them now with one and two? And I didn't do so before? Because the numbers are changing, right. And in this case, Div2 is Div1 times one plus g and so on. Now, obviously, we'll see and I'll show you the formula again. It looks very similar to the previous one. Let me first show you the formula. But remember, genetically, what will they div2 be called? C2 and so on. So let me write the formula down and then we'll, by the way, this is the only for formula where I haven't derived it for you. And the reason it will just take up too much time. The generic formula is C1 over R minus g. What is G? It's the growth rate in your cash flows in this case, expected dividends. What s C1? The first cash flow. So this is very important. First cash flow is C1. The g is the growth in the cash flow is not an r, r is already a percentage, right. So these are both percentages r and g are both percentages. So I'm not subtracting dollars from a percentage, okay. And what this to use this formula, it makes sense to the world. If r is greater than g. If r is not greater than G, what will you have to do? You have to go the long way. So do C1 divided by one plus r, C2 divided by one plus r square until such point that r is greater than g and that will always happen. Think about it. If g was greater than r, you will own the world it's not possible in steady state, but those are things that you get to practice in your assessment. So let's call this the formula and replace it by Div1 one over R minus g. Okay, and I'm going to use examples where r is greater than Jz. But as I said again, don't use the formula when it doesn't make sense to yours. For example, if R is equal to G, what are you going to do? Sit there, stare of the formula? You have something to add by zero. Go figure. You use the long method. Okay. And that's what another thing I don't like about the way we get taught math and algebra is we have never thought in a context I shouldn't say never. I was lucky in high school, I was taught math always in a context, and I benefited so much by it instead. Many times we're taught stuff and always see is the backside of the person teaching. And that's not very interesting anyways. Okay, so okay, let's get started with the formula, and I'm going to now let you take a little while to do it. Well, this is a good time to take a break, but let's first read the formula. Suppose Moogle Inc on apologize. My sense of humor is limited, is expected to pay. Ryan is laughing with me. Is expected to pay dividends of 20 per share next year. You see how I'm have to specify the first dividend and the dividends expected to grow indefinitely at the rate of 5% for the year. Again, the word indefinitely doesn't literally mean forever. Remember, it's we're using formulas is an approximation. Stocks off. Similar firms are earning an expected rate of return of 15% per year. Why am I saying this? Because I want to repeatedly remind you that the 15% is not owned by you. In fact, it doesn't belong to anybody. It belongs to the marketplace. Businesses get different rates of return due to a fundamentally different set of risks. What should be the price of a share of Moogle Inc. Okay, so just take a minute. Try to do it in your head. When we come back, we'll do it in our with together and see how easy it is. Okay. Take a break. See you soon. Yeah.