Ses 8: Equities

the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu so what I want to do in this lecture is to provide a quick overview of the equity business and then talk about a couple of simple but rather powerful models to price equities we're using the exact same tools that we've developed and then talk a bit about growth opportunities and growth stocks okay so industry overview what is equity as I said it's an ownership in a corporation and typically when you own a piece of a corporation you're owning that sequence of cash flows there are two components of possible cash flows for a piece of equity security one is dividends but of course we know that there are companies that don't pay dividends typically companies that are early-stage growth companies they want to conserve their cash because they've got lots and lots of investment ideas that they want to implement and so any cash that generated internally they're going to be plowing back into current operations so growth companies typically don't pay dividends but you still get value from the security because as the firm grows as the corporation becomes more valuable that piece of paper that you hold becomes more valuable so in other words you get capital gains or price appreciation of that piece of paper and if you want to get value out of that price appreciation you can always sell it right so those are the two ways of getting a value it's dividends and by the way there are two different forms of dividends cash dividends or stock dividends both of which provide additional value but also the fact is that you can sell it and so you can get money from capital gains now there are a couple of key characteristics of common stock that are distinct from bonds the cash flows we will be able to analyze using the same tools but those tools will ultimately give us different answers because the legal structure for equities is different than for for bonds and I have to say that whoever invented equities this is many many centuries ago really was a brilliant a brilliant financial innovator because equities have a just an enormous leap powerful ability to provide proper motivation and incentives for innovation all sorts of innovation and let me explain what that means first of all one aspect of equities that I think you all probably know is that they are the residual claimant to a corporation's assets after the bondholders in other words bondholders have first dibs on the assets of the company but their claim on those assets is only equal to the face value or promised payments of that debt right they don't have access to any more than what the face value of that bond is as well as the coupons along the way and to say that equity holders are the residual claimant means that they get everything else now you might say gee that's not really all that interesting because you're second in line well it's very interesting if being second in line means that you get access to all of the upside of a company's growth and success I'm sure that you've all heard of stories of entrepreneurs that have made you know many hundreds of times what they put into a company whereas the bondholders may have gotten a handsome return of ten fifteen twenty percent but that's the upper bound as to what they can get as a bond holder your upside is capped it's limited okay whereas as the residual claimant as the equity holder you have no limit on your upside right because once the bondholders get paid you get everything else now the other aspect of equity that's really important is something called limited liability the fact that as an equity holder the most you can lose is everything now that might not seem like a good deal but trust me it's an amazing deal by everything we mean everything that you put in so it's not literally everything for example you don't lose your life you don't lose your freedom you don't lose your pinkie you don't lose any other body parts or loved ones all you are at risk of losing is what you put in to the venture so that's what limited liability means and the reason that it's an innovation is prior to the modern day corporation and limited liability it used to be the case that entrepreneurs faced unlimited liability or you could be put in prison if you were to default on your obligations the fact that there is a downside limit to what you could possibly lose is a tremendous boon to innovation because now it means that each and every one of you can go out and start your own company and risk whatever money you want to put into the company but no more and if it doesn't work out well you can walk away and do it again and I suspect many of you know of so-called serial entrepreneurs that just go from one company to another to another many years ago when I was at the Wharton School I heard a talk by the person who started up Domino's Pizza I unfortunately don't remember his his name but he was giving a talk in one of the CEO series and he's a you know a billionaire you know because of the incredible growth of you know Domino's Pizza in the country and somebody asked this fellow how did you know that having a national pizza chain was going to succeed as as well as it did and you know he's very honest he said you know I didn't I didn't know you know this was my ninth company you know the first eight went bankrupt and if this one had gone bankrupt I probably would have started a tenth and and I mean that's just a wonderful expression of the power of modern capitalism and limited liability because here's an individual that just really wanted to do something on his own and wanted to make a success of it and was willing to work his heart out time after time after time until he hit upon something that was really valuable and that's the power of limited liability think what innovation would would be if we decided that if you if your first company fails from that point on you would never be allowed to start a company ever again think how many people would take the risk or take the plunge to do something like starting up your own company so the fact that we have a security that limits your downside and that limits the downside of other investors that want to join you in your venture really allows for capital formation to occur at a rate and the scale that would be impossible without it now there's also voting rights and the ability to access public markets what that means is that you can actually get other people large numbers of people to co-invest with you so that's particularly important when you're thinking about taking on very very ambitious projects for example if you want to start up a biotech company biotech companies require more than a few hundred thousand dollars to get started you know I think that a few hundred thousand dollars we may buy you a quarter of a centrifuge these days it doesn't really help for starting up a biotech company and so if we didn't have the ability to access public markets if we didn't have the ability to bring the power of the public to bear on a particular investment opportunity it wouldn't get done so that combination of limited liability and ability to access public markets and then voting rights that give investors some say in how the company is run is really the secret unlocking the power of the the masses for development of innovation and capital formation now there's another point that I wanted to make here which is short sales I think that by now you should have an appreciation for the importance of short sales short sales allow information to get into the market price that may not be positive news but is nevertheless important for people to have and so the ability to short sell a security is a method for allowing investors to get information into the market price as quickly and as easily as possible those of you who participate in trading game that we did a couple of weeks ago on that Friday you know when we go over the results towards the end of this course when we talk about efficient markets I'm going to show you that the prices that occurred in that marketplace was not very efficient part of the reason that it wasn't very efficient is because we didn't allow you to short sell and so those of you who had the information that at one point the stock was worthless the most you could have done was to divest yourself of shares that you already owned but once you did that that was the end and you were out of the market you couldn't do anything more if on the other hand we allowed you to short sell you would have driven that price down to zero where it belonged at that point and so the ability to short sell is a very very important aspect of capital market efficiency and for making prices as informative as you can now there are two markets for equities primary market and secondary market primary market means the market where securities are issued for the very first time primary that's what primary means secondary you can think of as the market for used securities we have a market for used cars you have a market for used homes and there's a market for used securities I know you don't really think of the New York Stock Exchange as such but in fact it is it just turns out that used securities are just as good as new securities in many ways better and so the steps for getting a primary security issued is very different than the steps for dealing with secondary markets for the most part what we're going to be talking about in this course is secondary market transactions and and dynamics however there is obviously a lot more to be said about primary markets I'm going to leave that to other courses in the finance group including M&A and capital budgeting and venture capital those are courses that deal with the dynamics of the primary market these are the markets that you would care about if you're doing an IPO launching a new company and issuing securities for the very first time so I won't spend too much time on that if you're interested you're welcome to read the relevant chapters in the textbook but what we're going to do is to focus on the behavior of secondary markets in particular in the price formation mechanism for secondary market securities here's a little bit of a summary about how these markets have developed you can see that for primary markets the the IPO market goes through cycles there are periods where the market is very very active and there are periods where the market is pretty quiet and not a lot is going on that has to do a lot with the business cycle and with a credit cycle how much money there is out there and it's obviously very important for those of you who are thinking about doing startups because when you do a startup and you get funding from a venture capitalist the way the venture capitalists ultimately gets paid is not by the satisfaction of being part of your wonderful company but rather by having your company go public and having securities be issued so that the venture capitalists can cash out at those public market prices so the venture capital and technology industries are very much caught up in the business cycle and credit cycle as well and so this gives you a little bit of a picture of how that's changed over time on the other hand the secondary market has a somewhat different set of dynamics it's related but not nearly as highly correlated as you might expect this is an example of the dynamics of public secondary markets than NYSC and Nasdaq over the last few years what this displays is the trading volume both measured in terms of shares as well as in a composite refraction on the NYSC volume and you can see that over time that share volume the amount of shares traded has just gone up a year on year and this year will be no different 2008 will be a tremendously significant year for the amount of shares traded on the exchange lots more participation in public markets and the volume while there may be little bits of a dip that are functions of business cycles not nearly as sensitive as the primary market is yeah oh absolutely well there are a number of technological innovations that have made this market increase so quickly so the Internet is one now all of us can trade on the Internet in fact when I was teaching finance back in C was in 2000 or 2001 I remember during the middle of the day one of the undergraduates in the class you know looked at looked at a some kind of cell phone device and then ran out and it came back in shortly before the end of class and at the end of class I asked them you know if everything was all right because he seemed really distressed and then he said that he just had to respond to a margin call on his equity position that he'd put on the day before that this is an undergraduate he's trading on his little cell phone that's a technological innovation that has actually you know increased the volume in these exchanges but there are other technological innovations as well for example something called ECNs electronic communications networks these are essentially they started out as bulletin boards where large buyers and sellers of equities could come together anonymously and transact with each other at relatively inexpensive prices they can cut out the middleman and reduce the bid-offer spread by hitting a transaction price that was right in the middle ECNs have grown tremendously since the early mid-90s when they started and now account for a pretty significant fraction of the volume electronic order routing electronic trading all of these technologies have caused this kind of increase in the equity market trading over the last several years so today as an individual investor you can trade much more quickly you can trade much more cheaply and you can trade much more easily than ever before so consumers have benefited a great deal along the way a number of hedge funds and other investors have ended up going out of business because they have not been able to compete effectively with these kind of technological innovations and this is what I mentioned last time the technology plays a very important role in financial markets now much more so than ever before it used to be that it mattered you know who you knew rather than what you knew that it was the old boys network that mattered instead of the computer network and that the graduates of Harvard and Yale had an advantage over the graduates of MIT and Caltech that's been flipped on its head now over the last several years it's what I call the Revenge of the Nerds so which bodes well for all of you okay so let me now turn to the very first valuation model that was ever developed for equities it couldn't be simpler it's a model that I think all of you are going to immediately understand and yet the implications are going to be really far-reaching it and profound this is called the dividend discount model and it starts with the recognition that when you invest in a company what you're getting for that piece of paper this common equity your getting the rights to the flow of cash forever and what kind of cash we talking about what we're talking about dividends so it's true that not all stocks pay dividends but eventually you would figure the stock will pay dividend at some point right for years Microsoft never paid a dividend but about does it five years ago or six years ago they announced that they're starting to pay dividends why because they accumulated so much cash that they didn't have enough things to invest that cash in so they figured let's give some of it back to the investors in their early days they kept every penny of their earnings to reinvest because they had so many different opportunities to take advantage of but because they became so mature and they had already a number of investment projects that were quite valuable and yet we're still generating so much cash they decided to return some of it to investors so at some point you're going to get dividends and if a company never ever pays dividends well then it should be worth zero right if it pays you no cash forever then that seems like a very bad asset yeah well first of all if they issue dividends to pay themselves that's fine as long as they pay all the other shareholders at the same time so the answer is in principle nothing stops them but what makes them decide against that is if they have uses for the cash other than paying themselves if as a company you have no idea what to do with the money you're generating well first of all that suggests that maybe you're not doing your job because as a company you're supposed to be coming up with valuable ways of earning money for your investors however it may be that your company is very mature stable there's no growth there's nothing going on and all the cast that you're generating you don't know what to do with in that case you may very well return all of that money to investors nothing wrong with that the idea behind having a vote though is that you want to make sure that the board of directors who typically do own or are responsible to shareholders that own large blocks of shares will be deciding in the best interest of the shareholders and it could be that the best interest of the shareholders is to give them back their money because we the mature company that we are don't have any other uses for the money yeah well but think about it if a company keeps on appreciating in value but never pays out a dividend what's happening to the cash you know when I say never I mean never so I don't just mean like in 10 years or in 20 years I mean never so can you think of a company that appreciates in value all the time but never ever ever pays a dividend there's no cash that you'll never get any cash that's oh yes you could you could make a profit by selling but if you sell a security to somebody else and they know for a fact that it never ever ever ever pays any money well then that's called a Ponzi scheme right in other words you're selling a piece of paper that's worthless to somebody and hoping that they're a bigger fool than you are for having bought it so when I say it never pays any – I really mean it if it never if you know for sure that it never ever pays any cash then it can't be worth anything right if you don't believe that then I have a piece of paper that I would like you to take a look at and I would like to sell you okay yeah what's that even well well then it does pay something that's a liquidating dividend then that violates my condition that it never ever ever pays anything right and that's the point if the company is growing and it has value then you know for a fact that either a it will pay you a dividend at some point or B if it doesn't and it gets liquidated then when it gets liquidated you'll get a pro rata share of whatever's in the company in which case that's a payment so to say that a company never ever pays a dividend I literally mean it will never ever pay anything okay and in that case it can't be worth anything if you know that but if you can find somebody who will buy it anyway then that's an example of an arbitrage that's a free lunch and so you can do that a lot if you can find people like that okay so we're going to apply the very basic principles of present value analysis to a security that pays dividends so let's let the price of a stock PT today be given by that let DT be the cash dividend that gets paid at time T and by the way DT could be zero for many many years and at some point become positive all right DT can never be negative right we're not talking about taking money from investors it pays either positive amount or zero and I'm going to let P sub T be the expectation operator at time T so now I'm going to explicitly recognize that these dividends are not known in advance unlike bonds where you know the coupons in advance I don't know the dividends in advance so I'm going to have to guess I'm going to have to make a forecast as to what they are and let me let our sub t be the so-called risk adjusted return that is commensurate with the risks of the dividends that are there I'm going to wave my hands at this point as to how we get the dividend discount return the appropriate risk-adjusted return but I'll come back to that in a few lectures when we go over a methods for determining the appropriate risk adjustment okay but for now let's assume that we have it and we get it from the market place right just like we got the yield from the market place it's a sum total of everybody's fears expectations hopes and so on so with these components defined I'm now going to simply write the price of my instrument as this value function of the future cash flows right that's the most general expression we started with on day one and given what we now know about present value and valuing cash flows that come in the future it's not a big leap of faith to put some structure on this valuation operator okay the value of this sequence of future cash flows is simply equal to the expectation today time T of future dividends out into the infinite future discounted back by the appropriate risk-adjusted rate of return now you'll notice that the rate of return this R I've put a subscript T plus 1 and T plus 2 and so on I'm explicitly recognizing the fact that the appropriate risk adjustment changes over time as market conditions change and as the business changes ok so it could be that the risk adjusted return for a 1-year cash flow is this but the risk-adjusted return for a two-year cashflow is different just like we have a yield curve for riskless bonds we may have a yield curve for risky cash flows okay and if I really want it to be a masochist when it comes to notation what I could do is to have a double subscript that says that this is the appropriate risk-adjusted return between years T and T plus one and then this is between years T and T plus two and so on because these discount rates may be completely different tomorrow in other words tomorrow's discount rate for a 1 year cash flow may be different than today's discount rate for a 1 year cash flow right so I can have a whole string of discount rates for today and a completely different string of discount rates for tomorrow and for every day in the future these things change all the time I think you'll see now why I told you earlier equities is a lot more complicated than fixed income instruments it's because there are two sources of uncertainty one is the discount rate and the other is the cash flows and moreover the discount rate that we're talking about it's not the risk-free discount rate but it's the risk adjusted discount rate and if risks change over time as certainly they have over the past even few days then the discount rate should change so in addition to the term structure effect of different yields we also have the risk effect of looking out into the future given current market conditions so while this expression is tidy and it looks nice and clean in order to turn this into an actual number that you can look at and decide gee do I want to invest in this stock is it undervalued or overvalued it's going to take a lot of work so before we get to that word I want to spend some time thinking about simpler things and try to come up with relatively simple implications of this relatively robust model question the answer is yes both it's the riskiness of the company as well as the riskiness of the aggregate set of market conditions it's both and so we have to figure out how that factors into into this equation that's going to take us a few lectures to get there but it's the answer is both yeah would you say it's related to the riskiness of the expectation of the dividend being whatever it is well if I were to know that the first dividend is absolutely certain yeah but after that not so much huh then could I replace RT with the risk-free rate but RT plus 2 with something else umm yes assuming that that dividend really was risk-free yes that's right so the idea behind the discount rate and and by the way I'm going to ask you I'm going to ask you to explain this to me so I'm going to say I'm going to make a statement and then I'm going to ask you to justify it okay the statement is this the discount rate that's used in the denominator of each of these fractions that discount rate has to be risk adjusted in a way to reflect the risks of the numerator as well as general market conditions it has to be commensurate with the risks of that particular numerator so if this numerator is much less risky than this numerator I would argue that you would have to use a different discount rate one that's higher for the more risky numerator than for the less risky now justify that for me why is that a reasonable thing to want to do yeah that's right that's right you get more return on your capital for something of greater risk on average because you've got to be rewarded for bearing that risk and if you're not rewarded you're not going to take on that risk how do you know that how do you know that you're going to get rewarded for taking on that risk where did you get that from besides me you're right you're absolutely it's the law of the jungle but in this case what is the jungle exactly thank you the market excellent the market the market is the jungle from which you compete for scarce resources and in order to get your pet project funded you've got to provide the right incentives for people to buy into your project so that's the logic and the justification now let me go one step farther and say suppose that you want to replicate these cash flows suppose that you want to create a portfolio that gives you these kind of cash flows well then you've got to go to the marketplace and figure out what the appropriate opportunity cost is for each of those cash flows and then discount them because that's what the market is charging for those cash flows so that's why you have to get the appropriate discount rate matched to the appropriate cash flow right it comes straight out of what we learn about bond pricing but now we're adding an extra dimension risk and I'm not going to be able to talk about it in any more detail than this until we put more quantitative structure on what we even mean by risk I mean you you all take for granted when I say risk you say yes you understand what risk is but in order for us to justify a particular expression for how to make that kind of adjustment we have to be very specific about how to measure risk so in about 3 or 4 lectures I'm going to actually propose a method for measuring risk and once we have that method in hand we can then make that risk adjustment extremely explicitly I'm going to give you a formula that you can actually compute in an Excel spreadsheet that will tell you exactly whether the number should be six point five percent or seven point three percent or eight point nine percent you're going to actually see how to do that yourself yeah the time between correct correct it doesn't have to be the same uh and if it's not the same then the difference in horizon should be reflected by the implicit size of that discount rate yeah well you tell me can we use the company's bond yield to use as a discount rate for the equity well that depends it depends on whether or not the equity in the bond are a comparable risk right remember it's not the company that determines the discount rate it's not the company or rather it's not determined by Fiat or by announcement of a company's particular policies what determines the yield is the riskiness of that yield and the market place the market determines that particular price not the individual or not the uses or not the sources of those funds yeah of course they do but they reflect in a very specific way we're going to talk about that when we get to the capital structure companies that have very high leverage are going to have more risky equity than companies with very low leverage so the leverage does have an impact on the equity we're going to come to that in a little while there is a relationship all right but for now let's look at these securities in isolation and not worry about it and I'm going to keep coming back to the idea that it's not the company that gets to determine the discount rate but rather it's the company's riskiness or rather the riskiness of the cash flows and the markets assessment of the cost of that riskiness that determines the interest rate a few years ago there was a faculty member at Carnegie Mellon who won a Nobel Prize and and you know it ended up that you know he was one of the highest-paid professors at the time and so he was being interviewed by the school newspaper and they said professor so-and-so do you think it's appropriate that even though you've won a Nobel Prize that that you should get paid twice as much as some of the other faculty who are in you know Nobel prize-winning physicists and fields medalists in the math of mathematics department and so on I mean do you think it's fair that your salary is twice as high as other people in the the school and the faculty member who is an economist said you know listen son the university does not determine my equilibrium salary they only determine what city I work in in other words the salary of an individual is not determined by that particular institution it's determined by the market place the market place bids on that faculty member and the highest bidder presumably will be able to get that faculty member the same thing with these cash flows it's not the company's debt or the company's weighted average cost of capital which we don't know what it is yet but I'll define little later on it's not the company that gets to choose what the discount rate is the question is given the riskiness of that cash flow what does the market tell me is the fair rate of return for that cash flow that's the number I want to plug into that denominator yeah question market may determine the discount rate but the company determines the growth rate of the dividend right they get to decide what they did within there well they get to decide what the dividend is subject to their ability to pay that dividend but if it turns out that they make a bad decision and they pay out all the dividends and they have no more money and they can't grow the company anymore then who determines what's worth what's worth what ultimately the market the market is the final arbiter in all of these calculations at least that's the theory of finance that's the basic plain vanilla frictionless model okay it's the market that determines these interest rates later on after we go through the basics and you understand the frictionless model I'm going to introduce frictions and then you'll see what impact corporate policies have on these implications in some cases corporate directors can actually do a lot of harm by making suboptimal decisions that go against the market in other cases you could argue that corporate decision makers know more than the market and are able to make bets that the market is not capable of doing that's certainly possible because who knows the company better than you do although a markets expert would say it's not knowing the company that will determine the value of the company it's knowing how that company compares to all the other companies that are out there that determines the value of the company and you as the corporate insider may know your business very well but you don't know how you stack up against the 25 other businesses in your industry and we the market know better than you the individual that that's the argument that would be made against that pre-film can I use the thing tell me oh we're gonna get to that we're going to talk about preferred stocks that's separate issue preferred stocks have a different priority of claim and that's going to require some slightly different modifications to this formula yep so what kind of question expected value so yesterday the example yes you discounted a thousand to nine hundred yeah if everybody to Luther what else you need to discount to account for there is well I mean you have to take into account the fact that there are other competing opportunities for this particular project of the marketplace and so it's not just the risk of this project but rather how the risk of this project stacks up against the risks of all other possible projects that you would be competing for in the open market let me put it you this way let's do a simple thought experiment suppose that instead of of these as being dividend streams for a given company let's do the following thought experiment let's imagine doing a strip okay you all know what strips are now right so let's think about stripping out dividends okay it's a very weird thought experiment granted but just bear with me let's suppose that instead of one company I generate an infinity of companies each company lives only for one dividend payment after which it gets liquidated so each of these cash flows DT plus one dd+ do each one of these things isn't separate and independent company that gets liquidated right after it pays a dividend okay now how would you value a portfolio of all of these companies well you would do this right for each company you would figure out what the appropriate discount rate is and the appropriate discount rate reflects not just the time value of money but the appropriate riskiness of that cash flow for example if I took that company let's let's actually do a thought experiment of how we do that let's go through the motions okay I've got a piece of paper that is something that funds nanotechnology I in a very specific application and this company is going to require a certain amount of investment and then it'll pay off all of its earnings in 2013 December and then it'll liquidate and be done with okay that's the company how do I figure out the price of the company today anybody how do I figure out the price I have this piece of paper that says in 2013 the company will liquidate and I want to know what the prices what's the first thing you would do with that proposal if you got it in the mail what would you want to know yeah I want to know like if there is a security I can buy in the market yeah their company but a paper yeah the same risk return profile yeah I look at the microfiber why would you do that because there's no reason I would go through the hassle fiction and utility of yanking a new company if I can just go online and buy right that's one logic but another logic is that you have your money looking for a home you can put it in this new venture or you can put it in this existing company and if they're comparable then at least you have some sense of what it's worth exactly in order to figure out whether or not you can get a comparable security you need to know what the cash flow is for that nanotechnology startup right so so you might think first about estimating the expected cash flow in the liquidating dividend in 2013 okay so you you calculate the numerator all right and you find a company out there that has that same kind of cash flow you have to find one that has the same profile so it does it in 2013 at which point it gets liquidated but let's even forget about suppose we didn't have such a company suppose we didn't have an existing security so this is literally a fresh start you've got a piece of paper that gives you the claim to a company that liquidates in 2013 with one cash flow only and now you've estimated that cash flow to be approximately twenty seven million dollars okay so now we've got the numerator a piece of paper that pays twenty seven million dollars how do you figure out its price what would you do yeah calculate the risk that is gonna I do now okay and you've done that that's the 27 million dollars tonight right the 27 million dollars includes the probability that it actually zero so the expected value is 27 million how would you go about yeah the liquidation value is the 27 million on average so no no it's just one payment 27 million on expectation oh it may be two possibilities maybe you either get you know fifty four million with 50 percent probability or nothing with 50 cent probability so the expectation is 27 million what would you do yeah yeah suppose you don't know what to use suppose you want to figure out what the price is yeah I know what you mean but suppose that you didn't have that what would you do either risk-free security or okay with that scene yeah credit okay this guy you could do that but now we're getting more and more complicated isn't there an easier way to figure out what the price is exactly you know let's let the market decide auction it off now when you option it off you take the highest bidder right and you get a number I don't know what that number is but let's just say the number is I don't know 15 million you've got somebody who's willing to pay 15 million today for a cash flow that gives them tight expected twenty seven million in 2013 with those two numbers that gives you are doesn't it that's how R is established it's established in the exact same way that we establish our for riskless bonds the way that US Treasuries ended up being three basis points on September 18th was basically tons of people wanted to buy these securities bidding down the yield and bidding up the price so if we had this piece of paper that paid only one dividend in 2013 and we auctioned it off we would get a yield the yield would be a risk-adjusted yield I don't know how the risk adjustment got made so you could be quite right that you take the base the risk for yield and you add on top of that a credit spread and who knows what the point is the market did it for us okay so what I'm getting after with this formula is I want to use those discount rates that are determined by the market place because if ever I have to sell my company if ever I have to take this company and break it apart and get rid of it and the market is going to pay me for it the way that the market is going to evaluate the different pieces is just the that I described they're gonna look at each cashflow look at how risky it is look at the opportunity cost of other investments that they could get the same risk return profile for and they'll pay that amount which will implicitly give me the appropriate yield yeah listen to me purchasing a stock miscalculation yeah do I have to assume that this calculation is wrong because why would I pay out money for something that's going to be exactly the same kind of discounted so that's a good point let me repeat the question the question is why in order for you to buy the stock would you have to assume that this is wrong or rather that the market price is not equal to this well the answer is no you don't have to although if you did that would provide a motivation for you to want to do want to do that but it could be that you simply want the risk and reward of this particular cash flow what's wrong with that suppose that the security is fairly priced so this equation at the very bottom says that the price of the security is equal to the present value of all the future expected cash flows discounted at the fair rate of return that's a perfectly reasonable thing for somebody to want to invest in if they like that kind of risk reward combination so some people want to put their money in Google and some people want to put their money in IBM and some people want to put their money in US Steel those are different companies that have different rates of return based upon their different risks and cash flows and even if those things are fairly priced it's not like you're going to make no money you're going to make money based upon the fair market rate of return for that security now if you think you've got a better mousetrap and you can identify mispriced securities that gives you a whole nother reason for investing but even without any mistakes being made even with if market prices are perfectly fair people want to invest because they want the return that those kind of investments give them right okay so let's consider some simple cases in order for us to really make use of this formula which at this level of generality really is useless let's try to simplify and see what we get and we're going to simplify in the ways that we've done before let's assume that dividends are fixed throughout time and given by a number D okay and let's assume that the risks don't change over time and are given by a discount rate R well if you fix D and you fix R magically what you get is that the price of the security is equal to our old friend the perpetuity formula D over R okay not that surprising if you have a constant stream of dividends with a constant discount rate then the price is equal to D over R now again this may seem totally trivial to you but it does provide a very interesting observation number one the price of common stock is an increasing function of the expected cash flows in the form of future dividends so if you expect there to be higher dividends going forward the price should go up and if you expect lower dividends going forward the price should go down so that's a nice insight another insight though is that the price of a stock is inversely proportional to its discount rate if interest rates go up in general if interest rates go up what should happen to the stock price exactly it should go down there are two ways of thinking about it one is that future cash flows are going to have to be discounted at a higher price or two the demand for stocks will not be as great because now the opportunity for earning higher return exists in other securities like bonds and so that will reduce the demand for stocks the price will come down right so that's a very nice model but we can make it a little bit nice sir by allowing the dividends to grow so now suppose you have a growth company a company where the dividends are expected to grow at a rate of G every period well then once again we have our old friend the perpetuity with growing coupons right D over R minus G and now as I think I alluded to earlier on when we went through this formula we have in this very very simple expression one explanation for the technology bubble both how it got so big and secondly how it burst if R is close to G if the growth rate is very large you're going to get a very big price and if there are rapid changes and what people expect G to be or what people estimate G to be you can get very rapid shocks in the level of prices including price run ups and then crashes right yep yes so is R greater than G Omega G is necessary in order to get that closed form expression but is that is there any more meaning to that or is this just a mathematical thing there is meaning to that the meaning is actually quite simple and we alluded to it when we first went through this formula suppose that our we're not greater than G suppose R were less than G what that's telling you is that the rate of growth of this security or this cash flow or this dividend the rate of growth is much faster than the interest rate right so you've got wealth that's growing over time faster than the interest rate which means that if it really is true that it'll last out into perpetuity then in very short order you should become bigger than the entire planets GDP right because you're going to be bigger than the interest rate so the rate at which assets in the future are being deflated to the present is actually less then the rate of which you're growing your wealth pretty soon you're going to become you know richer than God himself and we know that that can't happen so right now the interest rate the inflation rate for example that's right now that's right now but this is out of the perpetuity do you believe that that's sustainable out of the perpetuity well then this formula doesn't work this formula is a formula that's predicated on infinity not ten years not 20 years you know as we mentioned when we went over the formula China has been growing at a rate of 10% for the last 15 years do you think 10% growth rate is sustainable if China continues to grow at 10% you know pretty soon we're all going to be speaking Mandarin I mean you know it's it's just not possible for a country to both be reasonably sized and not totally dominant and to have rate of growth so much larger than what can be sustained over a long period of time and and so that's the key this is a formula that's about infinity it's not about five years or ten years okay other question no okay so in this case the gordon growth model allows us to get an expression that tells us if there are very very significant growth opportunities that can actually push up the price of a stock dramatically if somehow all of us decide that those growth opportunities no longer exist because we have new information then boom it disappears okay a good example of this is cold fusion I don't know how many of you remember 15 or 20 years ago there was a big controversy about the the pons and Fleischmann experiment where they did in it they did an experiment where it seemed like they generated heat but heat not from a chemical reaction but from a nuclear reaction in a standard laboratory setting and typically you need very very unusual conditions to generate thermonuclear reactions that can that can create that kind of heat now in the end they were discredited and apparently although you know it's there still controversy out there it doesn't seem like it was a nuclear we but if it were if it was possible to generate a nuclear reaction at room temperature what that could have meant is that it would eliminate all of the energy problems of the world because you'll be able to run your car on tap water and the amount of energy and an ounce of tap water is enough to fill your car for about a year so think about it if that technology really were to have worked out what do you think the value of that would be what's the G in that case and you can understand why people would have invested hundreds of billions of dollars into that kind of an opportunity if it were in fact a real opportunity there was a short time where we didn't know and during that time our – G look pretty small G look big relative to our uh and so that created very very large swings in prices of both traditional energy companies like oil companies you can imagine what all companies would be worth if we figured out how to run cars on water right that would you know maybe be justifiable you know in light of how much they've made over the years but the point is that it creates enormous opportunity and potential dislocation so that the expectations of the market matter a great deal and this is why this is how it actually gets incorporated now I'm going to take that equation and turn it around turn it on its head and it will give us another insight into how to think about the discount rate and the value of corporations if the price of a stock today is given by D over R minus G then I can flip things around and say that R minus G is equal to D over P right the dividend price ratio is equal to R minus G or R the discount rate that I'm using for the cash flows is given by the dividend yield plus the rate of growth implicit in that that company's investment opportunity set now why is this interesting well in order for you to understand the importance of this expression you have to realize that for many years stock analysts would look at a company's discount rate or cost of capital by simply using the dividend yield so in the exact same way that if you have a bond and you see what the coupons are and you take the coupon and divide it by the price that gives you a sense of what your rate of return is over a given period when you look at a stock and you want to ask the question how much am i earning on that stock what is the rate of return on that stock for me the investor you take the dividends that you get paid every quarter and you take that dividend you divided by the stock price and that gives you a sort of rate of return right because if you think about buying the stock for a price P and then getting cash flows of D every quarter or every period then your yield your rate of return is D over P that's called the dividend price ratio or dividend yield what this expression says is something that every MIT graduate knows in his or her heart which is that technology adds value above and beyond what you observe in current cash flows it's not just a dividend that gives a company value it's the ability for companies to grow over time it's not just the company's current plant and equipment and operations that give it value it is all of the interesting wonderful innovative creative ideas that are locked up in that company that may one day be implemented and allow it to grow far beyond the founders wildest dreams that also has to be factored into the rate of return of the company and this simple little dividend yield model tells us this it says that the required rate of return the risk adjusted discount rate the cost of capital the user cost whatever you want to call it this R has two pieces to it one is the cash that you get on a regular basis the dividends that the current operations generate plus plus the growth opportunities of those dividends out into the infinite future okay now remember the way that we structured this dividend payment the way that we had our formula set up the dividends are the dividends that get paid next period right if you go back and look at the formula this is the price today and it's given by the dividends paid at time t plus 1 so this price that I'm using in my notation is the current ex-dividend price meaning this periods dividend has been paid already and now the value to this piece of paper is the future dividends starting next period t plus 1 so this when I say D is fixed it's fixed but it's getting paid next period ok so in this expression this d is actually next periods dividend but remember that when I'm trying to value the company today I don't observe next periods dividend which is random but I know how much was just paid in the most recent period so if I want to use D and there's growth I actually have to take the most recent dividend the one that just got paid and multiply that by 1 plus G to get the value of next periods dividend so that's why this expression I corrected not corrected it's not that it's wrong it's just I've changed the the expression so that it is d sub 0 which is the most recent dividend that was just paid multiplied by 1 plus G divided by P so I just do that you know when you if you want to use this formula and by the way you can actually go out and use this now I would actually encourage you to use it go out and take a look at your favorite stock and take a look at its dividend yield you can find it on Yahoo Finance comm as well as other websites and then you make a guess as to what the appropriate growth rate is and try to figure out whether it fits this equation okay you can observe dividends you can observe today's price and you you have to make an assumption about what you think the growth rate is and when you plug that in that will give you an estimate of what the cost of capital is for that particular company yeah I did this exercise without fun but with just the perpetuity formula yeah okay yeah and in terms I mean every stock that I look at yeah seems to be over tempo it seems to be more than the dividends / that's right exactly that's because why why is it if you just use D over P every single stock looks like it's overvalued what are you missing exactly right you're missing G but then G turns out to be higher than well no no well how did you get R okay okay we don't know we don't know all right that's what we're trying to figure out right so if you just said you're looking at D over P and you're trying to figure out implicitly what that implies for the growth rate of stocks take a look at this expression in light of future growth opportunities and you'll see that dividend yield is not the only story you've got to use other expressions yeah well it should be on an annual I well it should be on whatever cycle the dividends get paid so if dividends get paid quarterly then it's a quarterly growth rate if it's an annual payment then it's an annual growth rate so the benefit of this expression is that there is no timing that's been assumed it's just whatever the periods are so if its quarterly dividends used quarterly growth rate yeah yes well yes so if it doesn't have dividends then this formula is not going to be all that interesting right D is going to be zero but remember this is not the current D this is the the steady-state D and if companies are in the early part of their growth phase it's going to be hard to estimate what that steady-state D is so there'll be other expressions that we're going to derive in a few minutes where we use accounting identities to relate dividends to earnings or the cash flows it used to be the case that instead of using dividends you would use earnings because even though companies that don't pay out dividends they still have earnings well that is until the internet came about right then you had companies that actually had no earnings so how do you value how do you evaluate a company that has no dividends it has no earnings and has negative cash flows in fact if you use those models the more negative the cash flow the higher the value so something weird is going on it has to do with the fact that these are meant to be steady-state formulas and not formulas for individual time periods if there are individual time periods where you have zero cash flows or negative cash flows because of growth you will have to make adjustments in the formulas and I'll show you how to do that in a few minutes yeah well again this formula is really very steady state dividends right so if they change the dividends what you should not use is this what you should go back and use which is going to be a bit more complicated is this the bottom equation right so this equation is always correct because this is completely general dividends at time T plus K added to the future and so if you know the future path of dividends or you have an expectation of what that future path is you can use this formula but look how difficult this is I mean you don't think about how an equity analyst has to make his living they've got to figure out not only what the appropriate discount rate is which is hard enough but they've got to figure out what the appropriate path of dividends are not just what the dividends will be in steady state because they may not be able to do that they may want to figure out what the dividends are going to be next year the year after the year after that so there's a lot of work to be done it's hard it's hard work but more importantly it's not just hard work it's actually very inaccurate work in other words it's really hard to estimate this thing with any degree of accuracy so what do you know you know you're going to be wrong most of the time imagine a job where you go into the job knowing that if you do really well you're a genius you're the top of your class you're the best that's ever been that that's ever done this thing and in that case you're going to be right 52% of the time 52% of the time that means you're wrong 48% of the time that's pretty discouraging but that's really the nature of this task it's really hard you know it's like trying to do weather forecasting but weather forecasting over the next 30 years and then taking the sum total of all of those decisions putting it into a portfolio and then investing your life savings in that that's kind of tough right but but it's also exciting yeah question okay oh yeah yes the Givaudan is going to change the future yeah who did this probably like into the annuity yes equation so that point in time when he changes yes you would use the annuity discount formula in pieces so for example if the cash flows for the first ten years look like one thing and then the next 20 years look like another thing and then the next 30 years look like something else what you could do is apply the annuity discount formula to the first ten years and then apply the annuity discount formula with a different discount rate and a different cash flow to the next 20 and then discount that back and then discount that back ten more years and then do the to the next 30 and then discount it back to the very beginning so exactly that that's that's the way to do it which is effective effectively doing it like this but it's hard I mean it's hard enough to estimate cash flows next year and I can tell you there are a lot of firms that have forecasted this year's cash flows last year are scratching their heads wondering how they can be so far off now imagine doing it 30 years hence I mean it's an impossible task but at the end of the day it has to be done in other words whether you want to make those forecasts or not people are going to trade your stock and so if you're not making those forecasts well somebody else is going to because they got to trade the stock so what we want to do is to figure out a slightly better mousetrap of understanding what those forecasts are telling us and if we can literally get 52 percent correct rates we're going to be rich beyond our wildest expectations that's really hard to do and it's just the nature of this particular endeavor it's very difficult to estimate cash flows discount rates and risk conditions so far out into the future question yes these formalized puzzling the copy down yes I'm wondering why would we do that why do I care about the tips because I think it's much more interesting to to calculate its growth rate well in order to calculate the cost of capital you need the growth rate but I would I think it's easier to get the cost of capital and against the growth rate I just don't understand why I would be interested in the cost of capital okay well you're gonna have to wait about another seven lectures for that because there is a reason why you care about the cost of capital and that is that if you're trying to decide how to spend your firm's money if you're a CFO and you're allocating cash across different activities you need to know what your firm's cost of capital is so that that you get a sense of what the opportunity cost versus taking that money and investing it in other opportunities outside the firm so in order to make decisions you need that number well you do in the sense that you want to know whether you're going to get your money's worth I mean if you're investing in one company versus another in order to make that decision you need to know what the rate of return is right so it's actually quite important it's very very important for decision making what that number is far yeah so let's call it the rate of return that's right yeah well and by the way the reason that I always use four or five names for the same quantity is to sensitize you to the fact that people look at these numbers from different perspectives so when I use the term cost of capital I'm thinking about it as a corporate manager who has internal funds that is going to are going to be deployed in different activities and the cost of that capital as a CFO is given by are now as an investor external to the company I'm thinking about how to invest my money I want to know what my rate of return is and as a regulator that wants to understand what the appropriate capital charge is for different kinds of activities that are going to be appropriate for borrowing and lending I also need to know what the appropriate risk adjustments are to that particular number yeah I was I was wondering how frequently the companies actually changed their dividend policy does it every year every few years and and also other exceptions like is there a reason sometimes for a company who's like growing to issue dividends or for company that's not a non-cash – no – oh so that's a great question the question is how companies set their dividend policy the short answer is that companies don't like to pay dividends unless they know for a fact that they can maintain the level for a good a good long period of time and the reason is simple when a company cuts dividends that's considered bad news no matter how you slice it when a company decides to reduce its dividends the typical response is oh it's cash-strapped or it's in trouble there's a problem so once you know that then as a corporate financial chief financial officer you will not recommend to the board to cut dividends unless there's a really significant issue with the firm and therefore as a result you're not going to either pay or raise dividends unless you think you can support that level for a good long time so because of that reason you're right dividends don't get changed very often and actually it's quite costly in some senses to change that dividend policy not just from the corporate perspective but from shareholder perception a good company apparently do do some different from there are exceptions because of certain circumstances that are unique to the company for example a company could be in a cash crunch like right now because of some kind of capital charge due to certain on you know underperforming securities in which case they may declare a temporary suspension of dividends the other side of the equation is that a company may have gotten a big windfall they just decided to sell a division and they've got a large amount of cash they don't know what to do with all the cash so what they'll do is that they'll pay out an extraordinary dividend extra ordinary dividend which means that it's a one-time thing and then from that point on they'll go back to a regular dividend policy yeah yeah yeah well it depends on how much money you have it depends upon you know what your shareholders want to have done I mean that's certainly a decision that a corporate financial manager would have to make in concert with the shareholders as well as the the CEO and that's a strategic decision but in order to make that decision you've got to have a few things at your fingertips you've got to have the opportunity cost of capital you've got to figure out what your borrowing cost is and in order to figure out your borrowing cost what do you need to know about your debt how risky and how do we measure risk for corporate debt and just talked about it last class in in yeah you need a rate right so you you have to figure out whether or not the cost of funds from internally generated sources is cheaper or more expensive than going to the external capital markets right now I would say that it's extremely expensive to go out the capital markets if you could do it at all if you're going to raise money you're going to be paying up through the nose General Electric credit default swap today was priced at 700 basis points this is triple-a rated security at 700 basis points Fred that it's it's crazy but people don't want to lend right now so if you want to borrow in capital markets today good luck

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