Understanding Common Stock Valuation Models

So let's now focus on valuation of common stocks. In principle, it's the same story. It's basically the present value of all of the future cash flows generated by the stock. So in order to understand how stock pricing is determined fundamentally, the fundamental value of stocks, all we need to do is just to simply understand the cash flows. Unlike a bond that gives you predetermined cash flow stream right the coupon payments and then face value stocks do not have that feature the value of stock is derived from expectations about future earnings and normally the future earnings will be correlated with future dividend payments so if i am a stockholder i really expect to get dividends and i also expect to get capital gain when i sell the stock because remember unlike a bond stock does not have a maturity so it's reasonable to believe that any stockholder at some point will have to sell it okay it's very rarely that people hold stocks for a very long period of time sure if you're saving for your retirement or contributing to your college fund and as a result you invest in stock portfolio portfolio Of course, you're going to hold those stocks for quite some time, but still in the end, you're going to sell. And when you sell, there is no guarantee that you're going to receive a certain payment. You might get a price that will be much higher than your original purchase price, or you might end up selling at a price that is below the original value. So you might generate capital gain, or you might incur a capital loss. So again unlike a bond that gives you that fixed face value, stocks do not have that feature. So let's just look more carefully about the typical stockholder. So let's imagine that somebody buys a stock in period 0 and sells that stock in period 1. So we are talking about just one period holding. So if that's the case, so here is a period 0, here is a period 1, the maximum price that the stockholder will be willing to pay today will depend on the cash flows that will be received and we can assume that in period one you're going to get dividend we're going to call it dividend one and also you're going to receive p1 p1 is selling price so again dividend one is your dividend and of course p1 is selling price in period one okay so the question is if that's what you're going to get what is the maximum amount of money you're willing to give up today in order to receive that dividend plus the selling price And turns out that that's going to be actually the stock price. So assume the required rate of return is equal to R. So let's say we do know the R, the required rate of return. Again, we will talk later about how it's determined. But for now, let's say you have certain required rate of return in mind. So if you buy a stock, you expect... to receive a certain rate of return on your investment so what you're going to do to figure out the maximum price that you're willing to pay today you are going to discount the dividend payment and the selling price you the discount rate or required rate of return that you want to achieve as a result of that investment so fundamentally the price of a stock I'm gonna call it PS is going to be equal to dividend one okay divided by 1 plus r plus p1. Actually, I'm going to call it p, let me do it this way. Let me just put p0 here. p1 divided by 1 plus r. Okay? So, all right, you have certain expectations about dividends. You have certain expectations about price. So if you're lucky, if the price significantly exceeds what you purchased it for, you're going to generate pretty substantial earnings. But the point is that your price today, A will depend on what you expect about future price and future dividend. And of course, R. R is usually correlated with risk, as always. So the required rate of return, R, is determined by your perception about riskiness of a stock. So now I'm going to do a little bit of substitutions here. So I'm going to claim that fundamentally, even though you at time zero as a stockholder do not plan to hold that stock beyond period one, you are still concerned. about all the future dividends that the stock is going to pay. So again, it might sound a little bit counterintuitive. After all, if you buy a stock today and you're selling it next year, why would you care about dividends in year 2, 3, 4, 20, 50, you know, 100? And the answer is, it's because the amount of money you're going to receive at period 1 when you sell the stock will be determined by expectations of the next buyer about the dividends. And and so on and so forth. So you will have that recursive substitution that I'm going to show you in a moment. So think about it this way again. Even though you don't care about dividends in the future, presumably, you still care about what will be the price in period one. So let's now put ourselves in the shoes of a buyer in period one. So the buyer in period one will price the stock as dividend. 2 divided by 1 plus r plus p2 over 1 plus r. So what you can see is happening here as a buyer in period 1 you anticipate dividends in period 2 and again you're going to sell in period 2. Now what I'm going to do I'm going to take that expression and put it right here for p1. So now my p0 is equal to dividend 1 over 1 plus r plus now I'm going to take out 1 over 1 plus r and for p1 I'm going to substitute dividend 2 over 1 plus r plus P2 over 1 plus R. So now I'm going to do some algebra here. So you have dividend 1 over 1 plus R plus dividend. 2 over 1 plus r squared and p2 over 1 plus r squared so what's interesting here is that it turns out that the price today in period zero already depends not only on dividend one but also on dividend two even though me as a buyer of stock in period zero i don't care presumably i should not care i will not receive dividend two okay i will not get it but in indirectly implicitly i absolutely do care about dividend 2 because dividend 2 will influence p2 and p2 is my direct cash inflow okay so now i'm gonna do one more substitution i promise that would be the last one i'm gonna say okay but now p2 is equal to dividend 3 divided by 1 plus r plus p3 over 1 plus r R so in other words whoever's gonna buy stock in period two will also anticipate dividends in period three and the price in period three so I'm going to substitute it right here so what I'm gonna do now I'm gonna get dividend one or one plus R plus one over one plus R squared okay Actually, let me do it this way. Let me continue first. Dividend 2 over 1 plus r squared. Plus, now I'm going to take out 1 over 1 plus r squared times. And for P2, I'm going to put dividend 3 over 1 plus r. Plus P3 over 1 plus r. So what happens now? I have a sequence here of dividends. Okay, so now you add dividend 3. 1 plus r to the power of 3. And finally, P3. 1 plus r squared. Excuse me, third. And so on. So I can continue this process indefinitely. And as you will see that eventually it turns out that today in period zero the fundamental value of a stock is going to be just the present value of all of the future dividends and it doesn't matter if i plan to sell in one year or in 10 years or in 20 years it does not matter because fundamentally it's still the present value of all the future dividends so you might say wait a minute some stocks don't pay dividends and you will be absolutely right that is why the price today is dependent on on all the future dividends all the expected future dividends so even though there is no dividend in period one no dividend in period two the company might be expected to start paying in dividend in period three or maybe not maybe in period 10 but at some point it must be the case that the firm should be expected to start paying dividends so again My main message for you is don't think that dividends don't matter. A lot of people got carried away. They think, who cares about dividends? As long as the stock price goes up, I should be able to make money. You're right. But the only reason why the stock price is going up is because markets anticipate substantial increase in earnings. And the only way that those earnings will eventually be important for the shareholders is if... they finally start paying dividends. Think of Apple. For a long time, Apple did not pay any dividends, but the stock was going up. And people were wondering, why is it the case? And the answer is very simple. When the stock was, when the company was really growing fast, it did not want to pay dividends because it wanted to reinvest in growth. So on some initial stages, during some initial stages of rapid growth, Some companies choose not to pay dividends because they want to continue investing and growing. But at some point when the company reaches a certain level of size and the growth rate slows down, the company gets more mature, at that point, sooner or later, the cash inflows start exceeding the needs of the firm for investment, and the firm starts paying dividends. And that's when the shareholders start getting a lot of money back. okay but the point is the stock price was still appreciating even though dividends were not paid but again it's not because dividends don't matter it's because people did not expect investors did not expect dividends now they wanted the dividends to be reinvested excuse me the earnings to be reinvested and they anticipated dividends in the future okay so that's something that that you really need to understand that fundamentally the stock price is just the present value of all the future dividends so that's what we have here okay well a little bit messed up so uh it has to be actually that's interesting why is it like that oh wow Okay, yeah, so looks like the slides are a little bit messed up, but we can fix it. You have the slides in your file that is posted, so hopefully that would be okay. You know what, let me just do one thing. Let me do this. Yeah, looks like it didn't transfer. None of them actually transferred. Okay. All right, I think we have to continue. Let me just see how bad it is. Okay, I can fill it in. I can fill it in while we are talking about it. So anyway, this formula here is not relevant because we just did it. All right, so I could just give you the last one. So dividend 1 divided by 1 plus r, dividend 2 over 1 plus r squared, and dividend 3 over 1 plus r to the power of 3, which is basically the sum of all the dividends from t equal to 1 to 1. to infinity dividend t or 1 plus r to the power of t okay so that's that's not not a big deal that we have some missing signs here that's that's the formula okay or alternatively you could think of it this way if you don't like the summation sign just think about infinite sum of all of the future dividends plus here and plus here now there is a problem here conceptually it's very simple okay just present value of all the future dividends but unlike the bond where you know exactly what the coupon payments are when you know exactly what the face value is with stocks you don't know what those dividends are you can only expect them but there is no any any certainty here because companies earnings might go up they might go down it's also managerial decision what to do with dividends sometimes even if the earnings are going up the company decides not to pay dividends sometimes they decide to increase dividends or just reduce them so what's going to happen there is a lot of uncertainty about dividends and therefore really value in stocks is a very difficult task that is why you see so much variation in stock price targets among the analysts okay there is no confusion about the pricing of bonds it's very obvious you know you just look at future cash flows the only you know divergence of opinions could be as a result of different opinions about yield to maturity the appropriate discount rate with stocks not only are may vary from analyst to analyst some people might believe it's high risk some people might believe it's lower risk but also the cash flows themselves are not determined okay so that's why you know if you look at tesla for example some analysts have target price equal to three hundred dollars some analysts have target price equal to two thousand dollars okay there is huge variation because nobody really knows what the cash flows are going to be nobody really knows what's going to happen with their earnings and they don't know what's going to happen with their dividends as a result so it's very very difficult to value stocks okay but the analysts do the best they can so basically it all boils down to putting some structure on their expected dividends so we are talking about dividend one dividend two dividend three and so on so what analysts normally do they try to forecast earnings once they know the earnings they apply certain percentage and assume that certain percentage of those earnings will be paid out as dividends and that's how they forecast dividends now their forecasting ability might be limited So they may not go beyond X number of periods. So what normally happens, once they forecast the dividends as best as they can up to period N, starting from period N plus 1, they try to assume some constant growth in dividends. So that's called variable growth or differential growth model. So we will talk about it later today. But first, let's introduce a couple of very simple models. stock valuation valuation so the first one is so-called zero growth model so what we do we assume that all dividends are equal okay so what does it mean really it means that it's a perpetuity so dividend one is equal to dividend two is equal to dividend three and so on and so forth if that's the case okay so they're all equal to some just div okay there is no subscript here then the stock price is simply equal to dividend divided by r so that's the present value of perpetuity so it's pv of perpetuity okay so okay very simple model so once you know once you observe your current dividend of a company you assume that that dividend is going to stay at that level forever and the price becomes simply that dividend divided by discount rate the question is why any company would look like this is there any realistic application for that model and the answer is not much but there are some cases one typical case would be a company that is extremely stable in its earnings and it's not expected to grow at all all now why would that happen well because the company does not really have any investment opportunities so you could think of it as the firm that completely exhausted any growth opportunities it operates at a constant zero growth rate in sales so they are not reducing their sales but they're not increasing their sales either again realistically it's very hard to believe that they would be company like that but there are firms that grow very little so the growth rate is very close to zero okay so again you could think of a firm that really just rides it out that pretty much is not growing any sales they are not expected as a result to invest anything in new assets so all they do they just generate their current earnings and they pay all of their earnings to the shareholders because there is no reason to keep those earnings remember they're The reason not to pay dividends is to reinvest so that you can make more money in the future. But if you do not expect to make any more money in the future, if there are no investment opportunities, all you're going to do is just to generate your earnings and pay the amount as dividends. We call it cash cow. Okay, so that would be an example of a cash cow. So think of it as a cow that you milk, all right? And you take all available milk without... any reinvestment okay so that would be an example of cash cow so if that's the case the stock price is very simple it's just dividend divided by r that is required rate of return now i have to say that even though cash cow is a possibility normally those companies don't survive for a long period of time so you could try to approximate their prices dividend divided by r but the assumption that that company will generate those dividends forever or for for any reasonably long period of time is rather unrealistic. So we need a better model. So a better model would be so-called constant growth. So what's going to happen now, you say, no, the dividends are not constant. They are growing, but they are growing at a constant rate. So, for example, your dividend 1 is equal to dividend 0 times 1 plus g, where g is a constant growth rate. Okay, your dividend 2 is equal to dividend 1 times 1 plus g or dividend 0 times 1 plus g square and so on. Your dividend 3 is your dividend 2 times 1 plus g or dividend 0 times 1 plus g to the power of 3 and so on and so forth. So again, what happens is you are dealing with growing perpetuity now. So it's not your regular. perpetuity so dividends are not constant but they are growing at a constant rate so as a result the price today is equal to your next cash flow which is your next dividend dividend one divided by r minus g so that formula comes from your present value of perpetuity if you don't remember you could look back and refresh your memory the present value of growing perpetuity is your c1 cash flow you in your next period in our case is dividend 1 divided by R minus G. Now remember that dividend 1 is equal to dividend 0 times 1 plus G. So very often students forget about that. They just jump. And if I tell you that the company just paid $5 dividend, you need to understand that that is already paid. In your numerator, you need to look at your next dividend. And that would be your $5 dividend. zero times one plus g so you need to have some good assumption about the growth rate so here is an example so let's suppose you have a company that just paid 50 cent dividend and the dividends are expected to increase at two percent annually your r is equal to 15 what is the stock price so again first you need to sort out the information so your dividend zero is equal to 0.5 Okay, but you'll start Price P0 is equal to dividend 1 divided by R minus G. So you need to figure out dividend 1. How do you do that? Well, your G is equal to 2%, 0.02. So your dividend 1... is going to be equal to 0.5 times 1 plus 0.02. Okay? And finally, your r is equal to 15%. So that's why you have this... formula it's 0.5 times 1 plus 0.02 divided by r which is 0.15 minus g which is 0.02 okay and that gives you three dollars and 92 cent So, constant growth model is the workhorse model. It's one of the most common models that actually provides you with the idea about the fundamental value of a stock. Okay, keep in mind, we are not talking about models that try to predict the stock price movements. There is a lot of noise in stock price movements. There is a lot of overreaction or underreaction. the reaction to different news markets may not be efficient temporarily in the short run okay especially at high frequency at high frequencies so don't ever think about this model here as the way to forecast the stock price tomorrow okay I rather think about it as a fundamental model that shows the fundamental value of a stock in the long run more importantly The nice feature of this model is that it allows you to see the qualitative effects of changes in different parameters. So again, we are not trying to forecast stock price. Instead, we are trying to understand what factors might influence the stock price. And from this model, you see very clearly, for example, that when R goes up, the stock price goes down. Now, why would R go up? The risk. If somehow the company is perceived as a higher risk, the stock price will go down. Why would company be perceived as a higher risk? Well, we will talk about it later. It turns out that it's a systematic risk, the beta coefficient that matters the most. So we will get to those notions later on. Another obvious parameter is G. When G goes up, the price will go up as well. Now that makes sense. Increase in G means that expectation... about future earnings are rising that's why some companies may suddenly skyrocket in the price due to some positive news okay so let's say it's you know Norwegian cruise lines during coronavirus pandemic so in the heat of the pandemic the stock prices is extremely low because everybody is concerned about future prospects suddenly the cure comes out or back vaccine comes out and everybody's more optimistic about the business. They think that suddenly the Norwegian cruise lines will be able to sail again. So they automatically adjust their G. Okay, so they immediately built in a higher growth rate in earnings compared to what they believe right now. So the price goes up. Also, as a result of that news, R might go down. Thank you. Because not only they expect higher growth and higher earnings, they also expect less volatility in those earnings. As a result, their risk perception of the company is, you know, different. So they think the company is less risky than before. So the price also goes down. So when R goes down, the price, excuse me, goes up. So, again, that's the value of this model. It's not really about just, you know, predicting the stock price. It's not easy. to predict daily movements. It's more about predicting stock price in the long run. That's the model that gives you those target prices, okay? So again, if you're a Goldman Sachs analyst or JP Morgan analyst or Bank of America analyst, you come out and you say, my target for Tesla stock is $680. And it's based on this model right here. you're not saying that it's going to be 680 dollars tomorrow you're saying that that's my target that's what it should be on the basis of fundamentals okay so that's what i want you to understand that all this model that we are doing here are more about fundamental value and they are used in industry extensively for determining the stock price targets okay but not trying to predict short-term fluctuations or movement in the stock prices so finally you have your third case which is so called differential growth that's the model that most analysts use when they come up with it with their targets I told you that that's that's the one that they use but that's kind of the the the basis of it, okay? But more sophisticated model that builds upon the constant growth rate is called differential growth rate model. So what happens in this case? The analyst who wants to, you know, determine the target price for a particular company will have a lot of knowledge about that firm. Therefore, there is no need to assume a particular growth rate right away. You don't know. I mean, you may know a lot. lot more about the company so all you need to do is to forecast actual earnings and as a result actual dividends over a certain period of time but then the more far that the farther distant in the future you're going the less your forecasting ability becomes so no matter how good you are as an analyst no matter for how long you've been following the stock no matter how much knowledge you have about the industry and the company you may not be able to know what's going to happen with the company after 3, 5, 10, 20 years. It's impossible. So what's going to happen? Usually, those analysts look at the stock in the following way. So this is my timeline. Okay Here's my time zero. That's when the stock target is determined the price and It's determined on the basis of your expectations about periods one two Three all the way to period n. So what you do you manually directly forecast? Dividend 1, dividend 2, dividend 3, and so on, all the way to dividend N. How far that N is, how far in the future? Well, it depends. It depends on your forecasting ability. It depends on your confidence about your forecast. You know, it depends on how much you know about the company. And also, it depends on economic conditions. When economy is relatively stable, the forecasting ability gets better. When economy is extremely... volatile the forecasting ability gets shorter and we are talking about only a few quarters forward we cannot know anything that's go beyond that beyond that so anyway so let's say you're the analyst and you're trying to determine the stock price of Tesla your target stock price you say okay I know they're gonna build the plant you know in in in some in Shanghai let's say they did already but let's say you are thinking they're gonna build another one and then another one in Texas and maybe another one in Europe so you have some expectation about what they're gonna do you have your horizon up to two years let's say and you forecast as a result their sales their earnings and hence dividends but then beyond period and you say I don't know I don't know what's gonna happen so starting from period n plus one you assume that the dividends will just be constant growth model. So it's going to be dividend n times 1 plus g. And then, of course, in period n plus 2, it's going to be dividend n times 1 plus g. times n plus g squared, and so on. So again, what you're doing, you end up using constant growth model, as we discussed before, at some point. Because again, there is no way, there is no way to forecast dividends all the way to... to infinity okay so basically what it means it means that for the first end dividends so your stock price zero would be equal to your present value of first N dividends okay that's just your regular PV all the way to period N so here is my dividend N over 1 plus R to the power of N but then starting from period N plus 1 You just say, okay, it's going to be dividend N times 1 plus G divided by R minus G. Okay? That's your constant growth model. The only thing that you should not forget is that this is the present value as of period n. You want it as of period 0. Okay? So, you need to discount that constant growth model, right, by dividing this whole thing by 1 plus r to the power of n. Okay? So... this is basically what you're going to have the only thing that i need to uh i need to fill it in so let me just see p is equal to it's weird what happened with the with all those pluses and minuses so present value of first n dividends which I already showed to you plus dividend n plus 1 okay divided by R minus G and then 1 plus R to the power of n okay now alternatively again you can rewrite it as I did which is dividend 1 or 1 plus R plus dividend 2 or 1 plus r squared all the way to dividend n or 1 plus r to the power of n okay and finally instead of writing dividend n plus 1 you could write it as dividend n times 1 plus g you can do it that way. It's the same thing. And then divide it by r minus g, and then this whole thing, further discount it by dividing 1 plus r to the power of n. So, that's your typical... typical differential growth model that is used by financial analysts okay so again if i'm trying to figure out the uh the price of samsung as of as of today by the way this is p0 so if i'm trying to figure out the price of samsung as of today all i'm gonna do i'm trying to forecast the earnings as a result and as a result dividends for as long as i can and then i will just have to assume some growth rate And that growth rate, by the way, is usually coming from general expectations about growth rate in the industry. Okay. Because normally the companies operate in reasonably competitive environments. So it's hard to say that, let's say, Samsung is going to grow faster than LG in consumer electronics market. Okay. Or that GM is going to grow faster than Ford in automobile industry. Most likely they are going to grow at a similar rate. Now, companies. like Tesla might be very different because nobody knows what their industry is on the one hand they make cars on the other hand they are very high-tech firm okay so you know they are actually you know part of Nasdaq as opposed to S&P 500 or Dow Jones so you know it's it's a gray area but normally normally the company is you know not growing any faster or slower than the general industry trend So forecasting that G usually boils down to figuring out what's the general growth rate, expected growth rate in the industry. Okay. All right. So, okay. So, okay. So where's the where the parameters are coming from? So, as I mentioned, your R is going to be, you know, coming from. actually you know let's start with g uh your growth rate g will be coming from the industry standard but but in order to figure out that industry standard what you do you look at the roe excuse me roe right here on average industry return uh return on return earnings or roe and you multiply by retention ratio on average okay you can do it for companies specifically specifically that's fine as well you could just look at companies roe and multiply by retention ratio so why is this the growth rate think about it my return on earnings shows to me what percentage of my earnings become my new earnings okay so roe is my return on equity basically so it shows to me again what percentage of my earnings um are retained excuse me uh how much i make per dollar of investment in my of my shareholders okay so that should be the growth rate in my earnings but not all of my earnings are retained so what i need to do i need to multiply by retention ratio okay so you can do it for individual company or you can do it for industry in general you could just figure out average roe you could figure out average retention ratio and and do it that way okay excuse me the r is basically coming from a model that we're going to describe later okay so you know for now let's not worry about estimation of r so r needs to be estimated Okay, one of the ways to do it is to use capital asset pricing model, CAPM. It's not the only model that can be used. There are various models. There is factor model. There is no arbitrage model. But we're going to focus on CAPM, capital asset pricing model. pricing model that will use some kind of risk estimate of a stock and use it as an ingredient to figure out the expected required rate of return okay so don't worry about it now we will talk about that later on that would would be uh uh actually uh you know our next section of the course when we're going to start turning to a risk and return discussion that's where the capital asset pricing model will be developed and we're going to use it in order to estimate r so again there is a lot of estimation going on but for now just take it as given now what you can do is to simply decompose r into two pieces okay so uh let me me uh yeah let me let me follow you through here uh so again we are not talking about we are not talking about estimating future r again that is coming from cap m model but once you observe r okay so let's say you held a stock for several periods and now you're wondering where your return is coming from okay how did you get that return the answer is it comes from two components one is your dividend yield and another component is the growth rate in value of the stock okay so that's kind of our decomposition it's not the forecast of future r the future r needs to be forecasted using more sophisticated tool but if you simply want to decompose your observed rate of return into two components you can do it that way so let me show you why Well, remember that P0 is equal to dividend 0 times 1 plus g divided by r minus g, which is equal to dividend 1 divided by r minus g. So what I'm going to do now, I'm going to solve for r. Okay? And I can show you that r would be equal to dividend 0 over 1 plus g divided by P0. Okay? Uh... let me just see plus g okay and let me just see that would be equal to so dividend zero times one plus g that's your dividend one okay divided by p zero and then plus g okay so i have a feeling that it might not you be clear so let me just you know what let me just do a better job here okay because it might not be clear that quickly so again P zero is equal to dividend one divided by R minus G so R minus G is equal to dividend one divided by P zero therefore r is equal to dividend 1 over p0 plus g. Okay? So that's basically what I wanted to do. We missed one step, so I just wanted to make sure that you understand. Okay, that's basically the decomposition, the decomposition of rate of return. So what it tells you is that the stock return is coming from two sources. First one is dividend yield, which is dividend divided by stock price. And the second component is growth, or we can call it, we can call it. stock price appreciation okay And that's not surprising. It should not be surprising for you because if you ever traded stocks or if you ever considered trading stocks, you need to understand that you have two sources of return. In order to make money on stocks, you should be able to get either stock price appreciation or you should get some dividends. And that dividend divided by the purchase price gives you so-called dividend yield in percentage terms or both. Okay, ideally, you would like to have a stock that that pays dividends and also growth grows in value okay but it doesn't have to be historically for most companies especially faster growing company it's g that derives that actually drives most of the returns only the mature company that don't grow fast but pay a lot of dividends those would be the ones that actually you know have heavy dividend yield component but for most companies you most of the return is coming from the growth rate okay but again i want you to understand this decomposition is not an estimate of r okay you're not going to estimate future r by trying to forecast dividends and future growth rate you can do it that way okay but it's not the common model a better way of doing it is to use capital asset pricing model All right, so and we will talk about capital asset pricing model a little bit later. So finally, let's look at the stock market reporting. It's very simple. Just like with bonds, stocks are traded. and some of the stocks actually are not you know heavily traded and sometimes the trading volume is extremely low those would be so-called over-the-counter stocks sometimes we call them pink sheets so the pink sheets are over-the-counter stocks they're listed on over-the-counter brokerages so there is no much volume so the stock quotes are not very reliable they're outdated okay so you got to be very careful with those so whenever you are interested in dealing with over-the-counter stocks keep in mind that the stock price may not be really reflecting the true demand and supply but if the stock is widely traded like gap in this case right we're talking about gap gap gap incorporated so okay you have company the name is gap incorporated then you have the unique identifier it's called ticker or symbol in this case is GPS for let's say Tesla is TSLA for Walmart I think it's WM I might be wrong for Ford it's F uh for bank of america i think it's uh boc uh bank of america corp or bac i i'm not sure 100 but anyway you just need to understand that any company has that unique three four or one two letter identifier it's just easier that way because once you know identifier you can search for that stock very quickly you don't need to worry about name okay let's look at other parameters here so the first one right here that's your highest observed price over the last 52 weeks in dollars and cent then you have the lowest observed price and from that you could see the range so you know looks like in this case the range is uh quite substantial from 9.4 to 21.9 so it's almost you know more than 100 difference then you have div div that's your dividend in terms of cent per share so 0.34 is the last observed dividend okay 34 cent per share the next one is dividend yield so yld percentage that's dividend yield so it's obtained by taking that dividend 0.34 and dividing by the last observed price in this case it's 1106 so you could verify if you take 0.34 and divide by 1106 you should be able to get roughly 3.1 percent dividend yield okay the next one is pe price earnings ratio we talked about it before the higher the price earnings ratio the more valuable the firm relative to dollar of its earnings so normally high pe firms are the ones that are expected to grow faster okay so in this case the price earnings ratio is equal to eight it's not too high it's not too low it's it's reasonable But again, there is no benchmark. You just need to compare to industry standard. Then you have volume in hundreds. So it looks like it's almost 9 million shares that were traded on the last day. Then we already mentioned the last observed closing price. So that as of close of previous day. And finally, there is net change, 45 cents. That's basically by how much the price went up or down from... yesterday right from the previous day so 45 cent change that's by how much the price appreciated over the previous day compared to the closing price at the end of that day okay so that's pretty much it in terms of stock price valuation so we talked about bonds we talked about stocks now we are ready to talk about that are what determines the required rate of return on stock stocks, what determines the required rate of return on bonds, and ultimately what determines the overall weighted average required rate of return on financing that the company needs to get in order to invest in its projects.

And when you sell, there is no guarantee that you're going to receive a certain payment. You might get a price that will be much higher than your original purchase price, or you might end up selling at a price that is below the original value. So you might generate capital gain, or you might incur a capital loss.

So again unlike a bond that gives you that fixed face value, stocks do not have that feature. So let's just look more carefully about the typical stockholder. So let's imagine that somebody buys a stock in period 0 and sells that stock in period 1. So we are talking about just one period holding. So if that's the case, so here is a period 0, here is a period 1, the maximum price that the stockholder will be willing to pay today will depend on the cash flows that will be received and we can assume that in period one you're going to get dividend we're going to call it dividend one and also you're going to receive p1 p1 is selling price so again dividend one is your dividend and of course p1 is selling price in period one okay so the question is if that's what you're going to get what is the maximum amount of money you're willing to give up today in order to receive that dividend plus the selling price And turns out that that's going to be actually the stock price.

So assume the required rate of return is equal to R. So let's say we do know the R, the required rate of return. Again, we will talk later about how it's determined. But for now, let's say you have certain required rate of return in mind.

So if you buy a stock, you expect... to receive a certain rate of return on your investment so what you're going to do to figure out the maximum price that you're willing to pay today you are going to discount the dividend payment and the selling price you the discount rate or required rate of return that you want to achieve as a result of that investment so fundamentally the price of a stock I'm gonna call it PS is going to be equal to dividend one okay divided by 1 plus r plus p1. Actually, I'm going to call it p, let me do it this way.

Let me just put p0 here. p1 divided by 1 plus r. Okay? So, all right, you have certain expectations about dividends.

You have certain expectations about price. So if you're lucky, if the price significantly exceeds what you purchased it for, you're going to generate pretty substantial earnings. But the point is that your price today, A will depend on what you expect about future price and future dividend.

And of course, R. R is usually correlated with risk, as always. So the required rate of return, R, is determined by your perception about riskiness of a stock. So now I'm going to do a little bit of substitutions here.

So I'm going to claim that fundamentally, even though you at time zero as a stockholder do not plan to hold that stock beyond period one, you are still concerned. about all the future dividends that the stock is going to pay. So again, it might sound a little bit counterintuitive.

After all, if you buy a stock today and you're selling it next year, why would you care about dividends in year 2, 3, 4, 20, 50, you know, 100? And the answer is, it's because the amount of money you're going to receive at period 1 when you sell the stock will be determined by expectations of the next buyer about the dividends. And and so on and so forth. So you will have that recursive substitution that I'm going to show you in a moment.

So think about it this way again. Even though you don't care about dividends in the future, presumably, you still care about what will be the price in period one. So let's now put ourselves in the shoes of a buyer in period one.

So the buyer in period one will price the stock as dividend. 2 divided by 1 plus r plus p2 over 1 plus r. So what you can see is happening here as a buyer in period 1 you anticipate dividends in period 2 and again you're going to sell in period 2. Now what I'm going to do I'm going to take that expression and put it right here for p1.

So now my p0 is equal to dividend 1 over 1 plus r plus now I'm going to take out 1 over 1 plus r and for p1 I'm going to substitute dividend 2 over 1 plus r plus P2 over 1 plus R. So now I'm going to do some algebra here. So you have dividend 1 over 1 plus R plus dividend. 2 over 1 plus r squared and p2 over 1 plus r squared so what's interesting here is that it turns out that the price today in period zero already depends not only on dividend one but also on dividend two even though me as a buyer of stock in period zero i don't care presumably i should not care i will not receive dividend two okay i will not get it but in indirectly implicitly i absolutely do care about dividend 2 because dividend 2 will influence p2 and p2 is my direct cash inflow okay so now i'm gonna do one more substitution i promise that would be the last one i'm gonna say okay but now p2 is equal to dividend 3 divided by 1 plus r plus p3 over 1 plus r R so in other words whoever's gonna buy stock in period two will also anticipate dividends in period three and the price in period three so I'm going to substitute it right here so what I'm gonna do now I'm gonna get dividend one or one plus R plus one over one plus R squared okay Actually, let me do it this way.

Let me continue first. Dividend 2 over 1 plus r squared. Plus, now I'm going to take out 1 over 1 plus r squared times.

And for P2, I'm going to put dividend 3 over 1 plus r. Plus P3 over 1 plus r. So what happens now? I have a sequence here of dividends. Okay, so now you add dividend 3. 1 plus r to the power of 3. And finally, P3.

1 plus r squared. Excuse me, third. And so on. So I can continue this process indefinitely.

And as you will see that eventually it turns out that today in period zero the fundamental value of a stock is going to be just the present value of all of the future dividends and it doesn't matter if i plan to sell in one year or in 10 years or in 20 years it does not matter because fundamentally it's still the present value of all the future dividends so you might say wait a minute some stocks don't pay dividends and you will be absolutely right that is why the price today is dependent on on all the future dividends all the expected future dividends so even though there is no dividend in period one no dividend in period two the company might be expected to start paying in dividend in period three or maybe not maybe in period 10 but at some point it must be the case that the firm should be expected to start paying dividends so again My main message for you is don't think that dividends don't matter. A lot of people got carried away. They think, who cares about dividends?

As long as the stock price goes up, I should be able to make money. You're right. But the only reason why the stock price is going up is because markets anticipate substantial increase in earnings. And the only way that those earnings will eventually be important for the shareholders is if... they finally start paying dividends.

Think of Apple. For a long time, Apple did not pay any dividends, but the stock was going up. And people were wondering, why is it the case?

And the answer is very simple. When the stock was, when the company was really growing fast, it did not want to pay dividends because it wanted to reinvest in growth. So on some initial stages, during some initial stages of rapid growth, Some companies choose not to pay dividends because they want to continue investing and growing. But at some point when the company reaches a certain level of size and the growth rate slows down, the company gets more mature, at that point, sooner or later, the cash inflows start exceeding the needs of the firm for investment, and the firm starts paying dividends.

And that's when the shareholders start getting a lot of money back. okay but the point is the stock price was still appreciating even though dividends were not paid but again it's not because dividends don't matter it's because people did not expect investors did not expect dividends now they wanted the dividends to be reinvested excuse me the earnings to be reinvested and they anticipated dividends in the future okay so that's something that that you really need to understand that fundamentally the stock price is just the present value of all the future dividends so that's what we have here okay well a little bit messed up so uh it has to be actually that's interesting why is it like that oh wow Okay, yeah, so looks like the slides are a little bit messed up, but we can fix it. You have the slides in your file that is posted, so hopefully that would be okay.

You know what, let me just do one thing. Let me do this. Yeah, looks like it didn't transfer. None of them actually transferred.

Okay. All right, I think we have to continue. Let me just see how bad it is.

Okay, I can fill it in. I can fill it in while we are talking about it. So anyway, this formula here is not relevant because we just did it. All right, so I could just give you the last one.

So dividend 1 divided by 1 plus r, dividend 2 over 1 plus r squared, and dividend 3 over 1 plus r to the power of 3, which is basically the sum of all the dividends from t equal to 1 to 1. to infinity dividend t or 1 plus r to the power of t okay so that's that's not not a big deal that we have some missing signs here that's that's the formula okay or alternatively you could think of it this way if you don't like the summation sign just think about infinite sum of all of the future dividends plus here and plus here now there is a problem here conceptually it's very simple okay just present value of all the future dividends but unlike the bond where you know exactly what the coupon payments are when you know exactly what the face value is with stocks you don't know what those dividends are you can only expect them but there is no any any certainty here because companies earnings might go up they might go down it's also managerial decision what to do with dividends sometimes even if the earnings are going up the company decides not to pay dividends sometimes they decide to increase dividends or just reduce them so what's going to happen there is a lot of uncertainty about dividends and therefore really value in stocks is a very difficult task that is why you see so much variation in stock price targets among the analysts okay there is no confusion about the pricing of bonds it's very obvious you know you just look at future cash flows the only you know divergence of opinions could be as a result of different opinions about yield to maturity the appropriate discount rate with stocks not only are may vary from analyst to analyst some people might believe it's high risk some people might believe it's lower risk but also the cash flows themselves are not determined okay so that's why you know if you look at tesla for example some analysts have target price equal to three hundred dollars some analysts have target price equal to two thousand dollars okay there is huge variation because nobody really knows what the cash flows are going to be nobody really knows what's going to happen with their earnings and they don't know what's going to happen with their dividends as a result so it's very very difficult to value stocks okay but the analysts do the best they can so basically it all boils down to putting some structure on their expected dividends so we are talking about dividend one dividend two dividend three and so on so what analysts normally do they try to forecast earnings once they know the earnings they apply certain percentage and assume that certain percentage of those earnings will be paid out as dividends and that's how they forecast dividends now their forecasting ability might be limited So they may not go beyond X number of periods. So what normally happens, once they forecast the dividends as best as they can up to period N, starting from period N plus 1, they try to assume some constant growth in dividends. So that's called variable growth or differential growth model. So we will talk about it later today.

But first, let's introduce a couple of very simple models. stock valuation valuation so the first one is so-called zero growth model so what we do we assume that all dividends are equal okay so what does it mean really it means that it's a perpetuity so dividend one is equal to dividend two is equal to dividend three and so on and so forth if that's the case okay so they're all equal to some just div okay there is no subscript here then the stock price is simply equal to dividend divided by r so that's the present value of perpetuity so it's pv of perpetuity okay so okay very simple model so once you know once you observe your current dividend of a company you assume that that dividend is going to stay at that level forever and the price becomes simply that dividend divided by discount rate the question is why any company would look like this is there any realistic application for that model and the answer is not much but there are some cases one typical case would be a company that is extremely stable in its earnings and it's not expected to grow at all all now why would that happen well because the company does not really have any investment opportunities so you could think of it as the firm that completely exhausted any growth opportunities it operates at a constant zero growth rate in sales so they are not reducing their sales but they're not increasing their sales either again realistically it's very hard to believe that they would be company like that but there are firms that grow very little so the growth rate is very close to zero okay so again you could think of a firm that really just rides it out that pretty much is not growing any sales they are not expected as a result to invest anything in new assets so all they do they just generate their current earnings and they pay all of their earnings to the shareholders because there is no reason to keep those earnings remember they're The reason not to pay dividends is to reinvest so that you can make more money in the future. But if you do not expect to make any more money in the future, if there are no investment opportunities, all you're going to do is just to generate your earnings and pay the amount as dividends.

We call it cash cow. Okay, so that would be an example of a cash cow. So think of it as a cow that you milk, all right?

And you take all available milk without... any reinvestment okay so that would be an example of cash cow so if that's the case the stock price is very simple it's just dividend divided by r that is required rate of return now i have to say that even though cash cow is a possibility normally those companies don't survive for a long period of time so you could try to approximate their prices dividend divided by r but the assumption that that company will generate those dividends forever or for for any reasonably long period of time is rather unrealistic. So we need a better model.

So a better model would be so-called constant growth. So what's going to happen now, you say, no, the dividends are not constant. They are growing, but they are growing at a constant rate.

So, for example, your dividend 1 is equal to dividend 0 times 1 plus g, where g is a constant growth rate. Okay, your dividend 2 is equal to dividend 1 times 1 plus g or dividend 0 times 1 plus g square and so on. Your dividend 3 is your dividend 2 times 1 plus g or dividend 0 times 1 plus g to the power of 3 and so on and so forth.

So again, what happens is you are dealing with growing perpetuity now. So it's not your regular. perpetuity so dividends are not constant but they are growing at a constant rate so as a result the price today is equal to your next cash flow which is your next dividend dividend one divided by r minus g so that formula comes from your present value of perpetuity if you don't remember you could look back and refresh your memory the present value of growing perpetuity is your c1 cash flow you in your next period in our case is dividend 1 divided by R minus G. Now remember that dividend 1 is equal to dividend 0 times 1 plus G.

So very often students forget about that. They just jump. And if I tell you that the company just paid $5 dividend, you need to understand that that is already paid.

In your numerator, you need to look at your next dividend. And that would be your $5 dividend. zero times one plus g so you need to have some good assumption about the growth rate so here is an example so let's suppose you have a company that just paid 50 cent dividend and the dividends are expected to increase at two percent annually your r is equal to 15 what is the stock price so again first you need to sort out the information so your dividend zero is equal to 0.5 Okay, but you'll start Price P0 is equal to dividend 1 divided by R minus G. So you need to figure out dividend 1. How do you do that? Well, your G is equal to 2%, 0.02.

So your dividend 1... is going to be equal to 0.5 times 1 plus 0.02. Okay? And finally, your r is equal to 15%.

So that's why you have this... formula it's 0.5 times 1 plus 0.02 divided by r which is 0.15 minus g which is 0.02 okay and that gives you three dollars and 92 cent So, constant growth model is the workhorse model. It's one of the most common models that actually provides you with the idea about the fundamental value of a stock.

Okay, keep in mind, we are not talking about models that try to predict the stock price movements. There is a lot of noise in stock price movements. There is a lot of overreaction or underreaction.

the reaction to different news markets may not be efficient temporarily in the short run okay especially at high frequency at high frequencies so don't ever think about this model here as the way to forecast the stock price tomorrow okay I rather think about it as a fundamental model that shows the fundamental value of a stock in the long run more importantly The nice feature of this model is that it allows you to see the qualitative effects of changes in different parameters. So again, we are not trying to forecast stock price. Instead, we are trying to understand what factors might influence the stock price.

And from this model, you see very clearly, for example, that when R goes up, the stock price goes down. Now, why would R go up? The risk.

If somehow the company is perceived as a higher risk, the stock price will go down. Why would company be perceived as a higher risk? Well, we will talk about it later. It turns out that it's a systematic risk, the beta coefficient that matters the most. So we will get to those notions later on.

Another obvious parameter is G. When G goes up, the price will go up as well. Now that makes sense.

Increase in G means that expectation... about future earnings are rising that's why some companies may suddenly skyrocket in the price due to some positive news okay so let's say it's you know Norwegian cruise lines during coronavirus pandemic so in the heat of the pandemic the stock prices is extremely low because everybody is concerned about future prospects suddenly the cure comes out or back vaccine comes out and everybody's more optimistic about the business. They think that suddenly the Norwegian cruise lines will be able to sail again.

So they automatically adjust their G. Okay, so they immediately built in a higher growth rate in earnings compared to what they believe right now. So the price goes up. Also, as a result of that news, R might go down.

Thank you. Because not only they expect higher growth and higher earnings, they also expect less volatility in those earnings. As a result, their risk perception of the company is, you know, different. So they think the company is less risky than before. So the price also goes down.

So when R goes down, the price, excuse me, goes up. So, again, that's the value of this model. It's not really about just, you know, predicting the stock price.

It's not easy. to predict daily movements. It's more about predicting stock price in the long run.

That's the model that gives you those target prices, okay? So again, if you're a Goldman Sachs analyst or JP Morgan analyst or Bank of America analyst, you come out and you say, my target for Tesla stock is $680. And it's based on this model right here. you're not saying that it's going to be 680 dollars tomorrow you're saying that that's my target that's what it should be on the basis of fundamentals okay so that's what i want you to understand that all this model that we are doing here are more about fundamental value and they are used in industry extensively for determining the stock price targets okay but not trying to predict short-term fluctuations or movement in the stock prices so finally you have your third case which is so called differential growth that's the model that most analysts use when they come up with it with their targets I told you that that's that's the one that they use but that's kind of the the the basis of it, okay? But more sophisticated model that builds upon the constant growth rate is called differential growth rate model.

So what happens in this case? The analyst who wants to, you know, determine the target price for a particular company will have a lot of knowledge about that firm. Therefore, there is no need to assume a particular growth rate right away. You don't know.

I mean, you may know a lot. lot more about the company so all you need to do is to forecast actual earnings and as a result actual dividends over a certain period of time but then the more far that the farther distant in the future you're going the less your forecasting ability becomes so no matter how good you are as an analyst no matter for how long you've been following the stock no matter how much knowledge you have about the industry and the company you may not be able to know what's going to happen with the company after 3, 5, 10, 20 years. It's impossible. So what's going to happen?

Usually, those analysts look at the stock in the following way. So this is my timeline. Okay Here's my time zero.

That's when the stock target is determined the price and It's determined on the basis of your expectations about periods one two Three all the way to period n. So what you do you manually directly forecast? Dividend 1, dividend 2, dividend 3, and so on, all the way to dividend N. How far that N is, how far in the future?

Well, it depends. It depends on your forecasting ability. It depends on your confidence about your forecast. You know, it depends on how much you know about the company.

And also, it depends on economic conditions. When economy is relatively stable, the forecasting ability gets better. When economy is extremely...

volatile the forecasting ability gets shorter and we are talking about only a few quarters forward we cannot know anything that's go beyond that beyond that so anyway so let's say you're the analyst and you're trying to determine the stock price of Tesla your target stock price you say okay I know they're gonna build the plant you know in in in some in Shanghai let's say they did already but let's say you are thinking they're gonna build another one and then another one in Texas and maybe another one in Europe so you have some expectation about what they're gonna do you have your horizon up to two years let's say and you forecast as a result their sales their earnings and hence dividends but then beyond period and you say I don't know I don't know what's gonna happen so starting from period n plus one you assume that the dividends will just be constant growth model. So it's going to be dividend n times 1 plus g. And then, of course, in period n plus 2, it's going to be dividend n times 1 plus g.

times n plus g squared, and so on. So again, what you're doing, you end up using constant growth model, as we discussed before, at some point. Because again, there is no way, there is no way to forecast dividends all the way to... to infinity okay so basically what it means it means that for the first end dividends so your stock price zero would be equal to your present value of first N dividends okay that's just your regular PV all the way to period N so here is my dividend N over 1 plus R to the power of N but then starting from period N plus 1 You just say, okay, it's going to be dividend N times 1 plus G divided by R minus G. Okay?

That's your constant growth model. The only thing that you should not forget is that this is the present value as of period n. You want it as of period 0. Okay? So, you need to discount that constant growth model, right, by dividing this whole thing by 1 plus r to the power of n. Okay?

So... this is basically what you're going to have the only thing that i need to uh i need to fill it in so let me just see p is equal to it's weird what happened with the with all those pluses and minuses so present value of first n dividends which I already showed to you plus dividend n plus 1 okay divided by R minus G and then 1 plus R to the power of n okay now alternatively again you can rewrite it as I did which is dividend 1 or 1 plus R plus dividend 2 or 1 plus r squared all the way to dividend n or 1 plus r to the power of n okay and finally instead of writing dividend n plus 1 you could write it as dividend n times 1 plus g you can do it that way. It's the same thing. And then divide it by r minus g, and then this whole thing, further discount it by dividing 1 plus r to the power of n. So, that's your typical...

typical differential growth model that is used by financial analysts okay so again if i'm trying to figure out the uh the price of samsung as of as of today by the way this is p0 so if i'm trying to figure out the price of samsung as of today all i'm gonna do i'm trying to forecast the earnings as a result and as a result dividends for as long as i can and then i will just have to assume some growth rate And that growth rate, by the way, is usually coming from general expectations about growth rate in the industry. Okay. Because normally the companies operate in reasonably competitive environments. So it's hard to say that, let's say, Samsung is going to grow faster than LG in consumer electronics market.

Okay. Or that GM is going to grow faster than Ford in automobile industry. Most likely they are going to grow at a similar rate.

Now, companies. like Tesla might be very different because nobody knows what their industry is on the one hand they make cars on the other hand they are very high-tech firm okay so you know they are actually you know part of Nasdaq as opposed to S&P 500 or Dow Jones so you know it's it's a gray area but normally normally the company is you know not growing any faster or slower than the general industry trend So forecasting that G usually boils down to figuring out what's the general growth rate, expected growth rate in the industry. Okay.

All right. So, okay. So, okay.

So where's the where the parameters are coming from? So, as I mentioned, your R is going to be, you know, coming from. actually you know let's start with g uh your growth rate g will be coming from the industry standard but but in order to figure out that industry standard what you do you look at the roe excuse me roe right here on average industry return uh return on return earnings or roe and you multiply by retention ratio on average okay you can do it for companies specifically specifically that's fine as well you could just look at companies roe and multiply by retention ratio so why is this the growth rate think about it my return on earnings shows to me what percentage of my earnings become my new earnings okay so roe is my return on equity basically so it shows to me again what percentage of my earnings um are retained excuse me uh how much i make per dollar of investment in my of my shareholders okay so that should be the growth rate in my earnings but not all of my earnings are retained so what i need to do i need to multiply by retention ratio okay so you can do it for individual company or you can do it for industry in general you could just figure out average roe you could figure out average retention ratio and and do it that way okay excuse me the r is basically coming from a model that we're going to describe later okay so you know for now let's not worry about estimation of r so r needs to be estimated Okay, one of the ways to do it is to use capital asset pricing model, CAPM. It's not the only model that can be used.

There are various models. There is factor model. There is no arbitrage model.

But we're going to focus on CAPM, capital asset pricing model. pricing model that will use some kind of risk estimate of a stock and use it as an ingredient to figure out the expected required rate of return okay so don't worry about it now we will talk about that later on that would would be uh uh actually uh you know our next section of the course when we're going to start turning to a risk and return discussion that's where the capital asset pricing model will be developed and we're going to use it in order to estimate r so again there is a lot of estimation going on but for now just take it as given now what you can do is to simply decompose r into two pieces okay so uh let me me uh yeah let me let me follow you through here uh so again we are not talking about we are not talking about estimating future r again that is coming from cap m model but once you observe r okay so let's say you held a stock for several periods and now you're wondering where your return is coming from okay how did you get that return the answer is it comes from two components one is your dividend yield and another component is the growth rate in value of the stock okay so that's kind of our decomposition it's not the forecast of future r the future r needs to be forecasted using more sophisticated tool but if you simply want to decompose your observed rate of return into two components you can do it that way so let me show you why Well, remember that P0 is equal to dividend 0 times 1 plus g divided by r minus g, which is equal to dividend 1 divided by r minus g. So what I'm going to do now, I'm going to solve for r. Okay?

And I can show you that r would be equal to dividend 0 over 1 plus g divided by P0. Okay? Uh...

let me just see plus g okay and let me just see that would be equal to so dividend zero times one plus g that's your dividend one okay divided by p zero and then plus g okay so i have a feeling that it might not you be clear so let me just you know what let me just do a better job here okay because it might not be clear that quickly so again P zero is equal to dividend one divided by R minus G so R minus G is equal to dividend one divided by P zero therefore r is equal to dividend 1 over p0 plus g. Okay? So that's basically what I wanted to do. We missed one step, so I just wanted to make sure that you understand. Okay, that's basically the decomposition, the decomposition of rate of return.

So what it tells you is that the stock return is coming from two sources. First one is dividend yield, which is dividend divided by stock price. And the second component is growth, or we can call it, we can call it.

stock price appreciation okay And that's not surprising. It should not be surprising for you because if you ever traded stocks or if you ever considered trading stocks, you need to understand that you have two sources of return. In order to make money on stocks, you should be able to get either stock price appreciation or you should get some dividends.

And that dividend divided by the purchase price gives you so-called dividend yield in percentage terms or both. Okay, ideally, you would like to have a stock that that pays dividends and also growth grows in value okay but it doesn't have to be historically for most companies especially faster growing company it's g that derives that actually drives most of the returns only the mature company that don't grow fast but pay a lot of dividends those would be the ones that actually you know have heavy dividend yield component but for most companies you most of the return is coming from the growth rate okay but again i want you to understand this decomposition is not an estimate of r okay you're not going to estimate future r by trying to forecast dividends and future growth rate you can do it that way okay but it's not the common model a better way of doing it is to use capital asset pricing model All right, so and we will talk about capital asset pricing model a little bit later. So finally, let's look at the stock market reporting. It's very simple.

Just like with bonds, stocks are traded. and some of the stocks actually are not you know heavily traded and sometimes the trading volume is extremely low those would be so-called over-the-counter stocks sometimes we call them pink sheets so the pink sheets are over-the-counter stocks they're listed on over-the-counter brokerages so there is no much volume so the stock quotes are not very reliable they're outdated okay so you got to be very careful with those so whenever you are interested in dealing with over-the-counter stocks keep in mind that the stock price may not be really reflecting the true demand and supply but if the stock is widely traded like gap in this case right we're talking about gap gap gap incorporated so okay you have company the name is gap incorporated then you have the unique identifier it's called ticker or symbol in this case is GPS for let's say Tesla is TSLA for Walmart I think it's WM I might be wrong for Ford it's F uh for bank of america i think it's uh boc uh bank of america corp or bac i i'm not sure 100 but anyway you just need to understand that any company has that unique three four or one two letter identifier it's just easier that way because once you know identifier you can search for that stock very quickly you don't need to worry about name okay let's look at other parameters here so the first one right here that's your highest observed price over the last 52 weeks in dollars and cent then you have the lowest observed price and from that you could see the range so you know looks like in this case the range is uh quite substantial from 9.4 to 21.9 so it's almost you know more than 100 difference then you have div div that's your dividend in terms of cent per share so 0.34 is the last observed dividend okay 34 cent per share the next one is dividend yield so yld percentage that's dividend yield so it's obtained by taking that dividend 0.34 and dividing by the last observed price in this case it's 1106 so you could verify if you take 0.34 and divide by 1106 you should be able to get roughly 3.1 percent dividend yield okay the next one is pe price earnings ratio we talked about it before the higher the price earnings ratio the more valuable the firm relative to dollar of its earnings so normally high pe firms are the ones that are expected to grow faster okay so in this case the price earnings ratio is equal to eight it's not too high it's not too low it's it's reasonable But again, there is no benchmark. You just need to compare to industry standard.

Then you have volume in hundreds. So it looks like it's almost 9 million shares that were traded on the last day. Then we already mentioned the last observed closing price. So that as of close of previous day.

And finally, there is net change, 45 cents. That's basically by how much the price went up or down from... yesterday right from the previous day so 45 cent change that's by how much the price appreciated over the previous day compared to the closing price at the end of that day okay so that's pretty much it in terms of stock price valuation so we talked about bonds we talked about stocks now we are ready to talk about that are what determines the required rate of return on stock stocks, what determines the required rate of return on bonds, and ultimately what determines the overall weighted average required rate of return on financing that the company needs to get in order to invest in its projects.

Transcript for:Understanding Common Stock Valuation Models

Transcript for:
Understanding Common Stock Valuation Models