Ses 17: The CAPM and APT III & Capital Budgeting I

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 what I want to do today is to continue where we left off last time in talking about the capital asset pricing model and we're going to finish that off in the next 15 or 20 minutes and then I'm going to turn to applications of the capital asset pricing model in particular I want to focus on capital budgeting that's going to be the last major topic we take on for this course so let me finish capital the capital asset pricing model and then I'll talk a little bit about where we're going to go for the remainder of the the lectures you remember last time where we left off was I decided to estimate the cap down relationship for a couple of stocks Biogen and motorola and we found that the estimated alphas the deviations from the cap M were pretty sizable for both of these companies and the interpretation is either wow these companies are really exceptional values they offer investors much much larger expected return than justified by the appropriate market betas that's one interpretation or the other interpretation is there's something missing with the cap M the cap M doesn't quite capture all of the risks that are giving you these kinds of expected rates of return so I'm going to come back to that debate in just a few minutes but I thought that to continue along these lines let's explore a little bit about the goodness of fit of these measures now I mentioned last time that the R Squared's as a measure of goodness of fit was 17.5% for Biogen and 33 percent for Motorola both of which are reasonably representative of the kind of goodness of fit measures that you're going to see with financial data for the simple reason that financial data is very noisy and so you're not going to get any single theory that can explain 99.9 percent of the fluctuations in any kind of financial series so here's a plot of Biogen versus the market now the market is our reminded you last time is the valuated return including dividends of all stocks on the NYSC Amex and Nasdaq so this market portfolio you can think of as being a broader version than the S&P 500 but it's been meant to capture the market so this is a plot of Biogen versus the market and you can see that there is some slope that fits this scatter of points and of course the equation is one point four two times the market minus a particular value for the Alpha and then r-squared of about 33% over this particular sample period so there is a line that goes through these points but it's not a perfect straight line by any means right you can see there's a scatter and so there's a tendency for Biogen to move together with the market but it's not a perfect linear relationship by any means okay that's why the r-squared is not 100% it's because we're not able to explain all of the fluctuations with a simple linear relationship life is more complicated than that and so the cap M is really just an approximation to a much more complex reality now a particular stock has a lot of idiosyncratic risk right that's what we talked about last time as the the dancing the Irish jig on that catwalk when your window washing on these skyscrapers so you can see that that idiosyncratic risk is really quite significant what happens if we plot not Biogen against the market but another market portfolio against the market like let's say Nasdaq well the next plot shows you look at Nasdaq versus the market as a whole now Nasdaq as you know tends to have smaller stocks stocks that seem to be technology oriented and as a result Nasdaq might be more volatile but nevertheless there is a very strong common relationship between these two market indexes and so now look at this the scatter of points is a lot tighter right it's not still it's not exactly linear but comparing this to that you can see the difference right there's a stronger relationship here and not surprisingly when you put securities into a portfolio what gets averaged out exactly the outliers and what else what other component dealing exactly the videos and Craddock risks the unusual stock specific kinds of randomness that gets averaged out so not surprisingly when you put things into portfolios the noise or the idiosyncratic risks averaged out and what you're left with is whatever common factors remain so I'm going to show you some evidence for how well or how poorly the cap m works by looking not at individual stocks because we know there's a lot of noise with individual stocks I want to show you what happens when you put stocks into portfolios and you look at how those portfolios do okay so let's do one simple example market cap portfolios let's take a look at small stocks and big stocks remember at the introduction of this series of lectures we are showed you some empirical evidence that illustrated the fact that small stocks seem to do really well relative to large stocks the the size anomaly right so let's now take the size anomaly and look at it through the lens of the cap M and asked the question with the cap M can we explain the difference between small and large okay well let's take a look over the 40 years from 1960 to 2000 approximately we see that the small stock portfolio the smallest decile the smallest tenth of stocks in terms of market cap as a group as a portfolio had an average monthly return of 1.3 3 percent and a beta of 1.4 on the other hand the large stock portfolio had an average monthly return of 0.9 percent and a beta of point 94 so that seems like it's sort of consistent lower risk lower expected return but let's plug it in and see if the cat bed relationship actually can tell us something so the expected return of the stock according to the cap M is going to be given by the risk-free rate plus beta multiplied by the market risk premium over the sample period that I'm looking at the market risk premium is about a half a percent per month so roughly 6 percent a year ok and the risk-free rate is also about a half a percent per month during this time period ok so now let's ask the question what is the expected return of a large stock portfolio well according to this it should be 93 basis points per month what about the small stock portfolio according to this it should be one point one six percent per month now this is an amazingly good fit so I wouldn't take this as you know typical in the finance in the finance literature but it just so happens that over this 40-year period the cap M actually works pretty darn well right point nine nine is he expecting the average realized and point nine three is what was predicted for the small cap portfolio one point three three is what was realized and one point one six was what was predicted so that's pretty good now I want to emphasize the point that this is really good because let's take a look at other ways of dividing up the universe and seeing whether or not we can get a better explanation of risk and expected return here's a picture of size sorted portfolios along the security market line so remember security market line is a graph of beta and expected return right the security market line applies to all portfolios and securities unlike the capital market line that applies only to efficient portfolios and securities so in this case we expect the linear relationship and with the exception of this little outlier up here from 1960 to 2001 there's actually a pretty reasonable relationship between beta and expected return in other words the cap M looks like it's actually doing okay for size sorted portfolios the higher the beta the higher the expected return the lower the beta the lower the expected return for size sorted portfolios now what about for beta sorted portfolios suppose you took a bunch of portfolios and you group them into betas and asked the question do the high beta portfolios have higher expected return low betas have low expected return it turns out that again you get a reasonable relationship not exactly what you would expect according to the cap M so the slope of this line remember is going to be given by the risk premium the market risk premium and in fact the realized relationship looks linear but it's at a slightly different slope it doesn't look like the risk premium is the right slope something a little bit less than that seems to be the right slope and it turns out that in 15 for 33 you're going to learn a new theory of the cap M that was developed by Fischer black called the black cap M and the black cap M says that there is no risk-free rate in fact what you ought to be using is the rate of return of something called a 0 beta portfolio well it turns out that if you do that you would actually get a line that fits this line almost exactly so the black 0 beta cap M seems to be a better approximation but for now the cap M is actually a pretty reasonable first approximation so let's let's finish off that first and I'll come back to the black zero beta cap in a minute okay so this is a plot of the expected return of beta sorted portfolios higher beta higher average return lower beta lower average runs so it seems like the cap M is actually pretty reasonable right not perfect but it gets at the heart of what risk really means now in order to emphasize the point let me show you a couple of other graphs this is volatility sorted portfolios so now I'm sorting stocks based upon their total volatility not just their beta remember the beta measures a part of their total volatility right the beta is the systematic component of the risk volatility is the entire amount of risk of a security if you use volatility as a way of sorting stocks then look at the expected rate of return there is no systematic relationship between volatility and return the higher the volatility you don't get necessarily the higher the return so in other words volatility is not the right measure of the risk reward trade-off one of the first things I talk to you about in this course is that if we've learned anything in modern finance we've learned that you don't get something for nothing and in particular if you are going to bear more risk you have to be paid to bear more risk but you have to define risk appropriately in this case this diagram shows that volatility is not the right measure of risk you might have to bear more volatility for whatever reason but you won't always get rewarded right because volatility is not the relevant measure of risk from the capital markets point of view what you get rewarded for is the risk that you cannot get rid of by diversification and that kind of risk is not Sigma its beta so beta you do get rewarded Sigma you do not get rewarded necessarily right higher risk does not mean necessarily higher expected rates of return when you measure risk with volatility higher risk in the form of beta does seem to be associated with higher expected rates of return okay now in the most recent literature there have been questioned the beta is the ratio of a covariance to the variance it's not the ratio of standard deviations in the case of a efficient portfolio it's the ratio of two standard deviations other questions okay so what I was going to tell you now is about the most current research the most current research suggests that while beta does seem to have some impact on explaining expected returns there are other factors out there that seem to contribute to that explanation in other words the cap M while it's a very interesting and compelling first approximation it is only an approximation there are other factors like book to market like liquidity like trading volume that seems to also add to the explanatory power of these kinds of relationships so what we're we're at today is that we think there are multiple betas out there not just one market beta so the basic vanilla-flavored theory of finance and what you're going to be learning how to use over the next few lectures remaining in this course is the single beta cap but where we are at the cutting edge of research or some would argue the bleeding edge of research is that there are multiple betas out there multiple sources of common risk so it's not just the market risk that is by far the biggest but there is liquidity risk there is currency risk there's term structure risk there's a variety of risks that cannot be diversified away with a large portfolio of very very different kinds of assets and so a better version of the cap m1 that you might use if you were becoming an expert in finance theory is to try to identify other sources of betas other sources of expected return that have risks attached to them and to use these multiple factors in your analysis okay so these are some references that you can take a look at but the fact is that the cap M is used almost universally among portfolio managers among venture capitalists and project managers and chief financial officers so the cap M is a very very powerful framework for thinking about risk and return and so it's important to understand it but just keep in mind that like any other finance theory it's just the theory it's just meant to be an approximation to a much more complex reality ok so what we're going to do now yeah question so that's a great question let me repeat that the question is does factors that are useful for the cap M always have to be associated with some kind of a tradable market portfolio or index or can it be some other factor like macroeconomic factor like unemployment well there's a big difference between factors that are economically relevant and factors that are financially relevant and let me explain the difference factors that are economically relevant may well explain the returns of certain securities a good case in point is unemployment unemployment is a factor that does seem to have some explanatory power for stock market returns the reason that we don't focus on those kinds of factors from a financial decision-making point of view is that while they may identify interesting economic relationships between certain parts of one one part of the economy and other it doesn't really allow you to make any kind of market decisions in other words if you can't trade it then you can't manage it so from the perspective of financial applications most of the factor models that you will see our factor models where the risk factors are portfolios of securities or in some other sense tradable right so for example if I had a particular beta exposure for example if I'm holding a portfolio over here and this is more bata than I want I can get rid of that beta by trading in sp futures contracts to decrease the beta you can't trade unemployment all right so at least not as easily as you could market betas so while there are many research papers out there that try to document the relationship between all sorts of economic indicators and financial markets from the applications perspective the kind of models that we will be dealing with will be factors that are associated with portfolios of marketable securities that you can trade purely from a practical perspective okay so the key points for this series of lectures lectures 15 through 17 what I want you to take with you is that there are two critical relationships that you must understand the first is the risk reward trade-off for efficient portfolios that's the capital market line and the second is the risk-reward relationship for all other kinds of portfolios that's the security market line of the Kappa the cap M requires equilibrium that's a departure from everything we've done in this course up until now all of the pricing relationships that I've argued have to hold things like present values of bonds of stocks of futures of forwards of options all of those pricing models all of them rely just on this notion of no free lunch that people prefer more money to less money but with the cap M I actually had to invoke a much stronger condition I actually had to require that supply equals demand it was through supply equaling demand that I was able to identify that the tangency portfolio is equal to the market portfolio okay so what we've done is to look into the heart of the market and try to infer from that what the market is actually doing by coming up with a particular discount rate that is a that is consistent with those market views and that now provides us with a complete theory of Finance from your perspectives you now know how to value 99.9 percent of anything that's out there you've got the tools to do that so what I'm going to do with the remainder of the course is I'm going to force you to apply those tools in several different context until you understand how the tools work okay so that's we're going to do for the rest of the course let me just pull up the syllabus amazingly we're actually on schedule despite the crisis and all our discussions thereof we are to be focusing on capital budgeting today next lecture and the third lecture where we take the tools of net present value calculations and risk adjustments and it just apply them to a bunch of different contexts we're going to apply them left and right and what I'd like to do after that is to put it all together in the very last lecture I'm going to try to give you a sense of where we stand today in terms of how to apply these tools more broadly given the market conditions that prevail so I'm going to talk about market efficiency versus behavioral finance psychology and I'm going to bring in some evidence from the cognitive neurosciences that will integrate all of the different parts of the course okay so make sure you if you're going to come for one lecture you've got to come to that one because that's where I'm going to put it all together for you okay so we're going to turn out to this notion of capital budgeting I'm going to take the perspective that we now understand how markets work we understand how pricing works we know how to make risk adjustments and we're going to take those ideas and apply them to very practical settings and so in that respect I'm going to ask you to change your focus up until now we've been looking at markets from the perspective of an investor you know either wire Buffett or the investor that steep in portfolio theory now I want you to change your perspective and say that you are a corporate financial officer or you're a project manager and you're trying to make financial decisions about various different alternatives you're not principally trying to beat the market or you're not principally trying to invest your wealth you're trying to make a decision about whether or not to take on certain projects and the question is how do we use the tools that we've developed to do that so we're going to start with the NPV rule which is the rule that we've developed at the very beginning of this course it's suit it's very appropriate that we end the course with the discussion on this rule but now with a much more sophisticated understanding of how to apply it I'm going to talk about cash flow computations because it'll turn out that cash flows are what you need to discount with NPV not accounting earnings which have all sorts of conventions that are not necessarily realistic or relevant for economic decision-making but rather I want you to focus on actual dollars and cents that you're going to be getting period by period I'm going to talk about discount rates applying them over time project interactions alternatives the NPV role and how capital budgeting is currently done there are going to be three different main points to this sequence of lectures the first main point is to use proper risk adjustments in doing NPV calculations that's something that I think by now should be already ingrained in your way of thinking but I want to make sure that that's true the second main point I want to get across is that there are lots of different ways of doing capital budgeting but in this case there's only one right way to do it from the perspective of economic analysis now economic analysis may not be the only consideration when you make a decision about whether take on a project there are economic considerations but there are also political social practical cultural all sorts of other considerations I'm not going to say anything about those because that's outside the purview of this finance course but from the business and financial decision-making perspective NPV is always the right thing to do and I want to emphasize that by showing you three wrong ways of doing capital budgeting these are ways that people still we make use of today so things like using IRR or using payback or using profitability indexes I'm going to go through each of those and argue why those are not the correct way of making financial decisions but because they're so prevalent I want you to at least be aware of them and understand how they relate to NPV okay and the last thing I want to do is to tell you about the complexities of financial decision making by talking about time as an element in other words the fact that decisions are being made over time makes these kinds of interactions among projects very very complicated and I'm not going to be able to solve all of those for you that's what 15 for 30 for this course on capital budgeting and corporate financing will do but I want to give you a taste of it so you are aware that there's a whole nother world out there where you've got to take these tools and understand how to apply them okay so let's talk about the NPV rule we started this course with a statement that all assets are nothing more than a sequence of cash flows that's what I call an asset right every single asset can be reduced essentially to a sequence of cash flows so this is a sequence of cash flows for a particular project or asset and the current market value is simply the NPV where now you've got a discount by the appropriate cost of capital that is an appropriate risk-adjusted cost of capital where you're adjusting the risk relevant to that particular cash flow okay so you'll notice that I use R 1 for cash flow 1 and I use RT for cash flow t what that means is that you can have two different discount rates for two different cash flows of the same project because those two different cash flows may actually have to risks okay so now when you see this expression which is exactly the same expression I showed you at the very beginning of this course it should have much more meaning to you because now you understand what amount of effort goes into coming up with that appropriate discount rate it turns out that because of something called value additive 'ti we can make decisions about how to allocate our resources simply by picking those projects with big positive NPV s in other words you don't have to worry about project interactions unless there are interactions that are explicitly involving your decisions all right having a firm and combining high NPV projects is the best way to increase the value of that firm so you look at each project on a standalone basis and if there are project interactions you then evaluate those interactions separately and I'll give you examples of that okay so we're all familiar with this this is just a standard approach to calculating market value now the investment criteria that I'm going to propose for capital budgeting for project selection is this for a single project if you've got one project you're trying to decide upon take it if and only if the NPV is positive right if it's positive take it if it's negative do not take it or sell it short it if you can okay it's hard to short projects it's not that hard to short securities for many independent projects take all of them with positive NPV if they're independent meaning that taking one doesn't preclude you from doing another or there's no project interactions take them all as long as they have positive NPV if there are project interactions then you have to take that into account so one simple example of a project interaction is you can only take one of many and if that's the case then you pick the one that's got the highest npv okay where you have to use the proper risk adjustment for that particular project alright so in order to compute NPV you need three things you need cash flows obviously you need the discount rates and you need to consider strategic options the first and the third I'm not going to help you with that's your business that's the business of business you've got to identify what those cash flows are and you've got to identify what your options are what I can help you with in the context of this course is evaluating the market value of those possibilities the strategic options you now understand how to use option pricing analysis and for discount rates you now know how to use risk adjustments to calculate the appropriate discount rates okay but the other stuff is domain-specific expertise that you bring to the table and so I told you the very beginning of the course that finance is the language of business this is what I mean you can't even talk about making a decision unless you speak the language of Finance unless you evaluate projects in this kind of a framework okay so in terms of cash flow calculations I'm going to give you some examples in a few minutes but let me summarize what I'm going to tell you and then we can talk about the specifics through that example the first point is you should use cash flows not accounting earnings because again accounting earnings are meant for purposes other than decision making accounting is really meant as a kind of a check-up to see how you've done how you've done is not the same thing as how you're going to do one of the things that I think has is apparently not emphasized enough is that when you look at accounting data you're looking at numbers that are not random variables they have been realized there's no uncertainty in what a balance sheet or an income statement says right it's about the past and accountants hate uncertainties I don't know how many people are accountants here or how many accountants you know but if you know that you know there's a certain personality type that gets drawn into that profession and these are not big risk takers they want to see order and certainty in what they're doing that's what a good accountant will do is to try to understand where to put all the expenses and revenues into the proper boxes so that it all adds up accounting is incapable it is not designed to manage and reflect uncertainty you've heard the term off-balance sheet item right like for example I've spoken before about a credit default swap or a futures contract if you engage in a futures transaction the moment you engage in that transaction what's the NPV of a futures contract zero exactly and as a result that does not go on the balance sheet because it is neither an asset nor is it a liability it's both or neither depending on how you look at it it's an off-balance sheet item because it doesn't where do you put it it has zero value but the point is that entering into one of those agreements has a big impact on your future risk so accounting the language of accounting is not ideally suited for thinking about the future it's a wonderful method for understanding what happened in the past and you need to understand that in order to plan for the future you need to know what your current assets are and what your current liabilities are but that doesn't tell you where your risks are going to be and it doesn't allow you to speak about the dynamics of cash flows because that's not what an accountant job is that's not what accounting is designed to do right this is not meant to be a critique of accounting but simply that you can't use it for purposes that it wasn't ideally designed to serve so the first point is you've got to use cash flows not accounting earnings second point you have to use after-tax cash flows why because you have to pay taxes that's one of the you know along with death and you know some other unavoidable aspects of life you have to pay taxes so if you have to pay taxes then you may as well look at after-tax cash flows the reason this is important is because there are certain things that show up as cash flows that you wouldn't ordinarily think of as cash flow because of the tax code for example depreciation depreciation is an accounting technique for attributing the decline of capital assets when you buy a machine it's new on day one but after 15 years it's not new anymore and it's not worth the same after 15 years as it is on day one now how you account for the loss in value of that machine how you account for how the machine gets used up over 15 years that's a matter of accounting practice that may have no bearing on the actual economics of the machine but it has absolute bearing on the cash flows that you are going to receive because you get to deduct depreciation expenses off of your taxes so after tax cash flows is important and finally this Third Point sounds simple but it's anything but simple unless you practice with it and do a lot of examples use cash flows attribute tribute to the project in other words you got to compare the firm with and without the project and look at the cash flows okay it's very very easy to forget certain cash flows that either come along with the project or have to be spent if you take on the project and you'll end up missing one element or another and in many cases those kinds of omissions can have a huge impact on whether or not you decide to take on the project all right so there are lots of examples about how you might do that here but in the end practice practice practice is going to get you to understand how to take into account each of the features okay so I'm going to just go through a few of these now and then I'm going to talk about the the point that I started with earlier which is I want to show you some techniques for capital budgeting that are incorrect and how they relate to the NPV rule okay so let me just tell you a little bit more about accounting earnings versus cash flows cash flows are what you need to use for calculating end because in the end what matters is the cash that you get not the accounting profits that may or may not be realizable so cash flows are simply equal to cash inflows – cash outflows that's how simple right it's not simple because you've got to figure out what those cash inflows or outflows are from in many cases accounting data and so you need to know a little bit about how the accounting interacts with these kinds of calculations so I'll just give you a little bit more detail and I'll leave it up to you – to focus on specific applications because the accounting rules first of all they change fairly often and actually right now at the heart of the debate in the financial crisis is this notion of fair value accounting faz 157 which says that you've got to use market values for updating your assets and liabilities and that's a new ruling that has created some problems because market values during times of distress can drop precipitously and this is why I told you early on that accounting is not ideally suited to deal with a lot of issues having to do with risky assets because risk is not an element that accounting frame the accounting framework is well-suited to to deal with ok so how do we get cash inflows – cash outflows well operating revenues is typically what cash inflows involve for a given project operating revenues and then you subtract from that operating expenses without depreciation the reason you don't take into account depreciation is I told you depreciation is one of these magic accounting concepts that has no bearing on reality it's a mechanism for simply accounting for a decline in the market value of a particular kind of equipment or asset and there are a lot of different accounting conventions that are a function of tax code changes for example in some cases you can accelerate the depreciation of an asset even though a machine is working fine there are certain situations where you can assume that half of the Machine evaporated after one year how does that happen well it's an accounting tool that Congress passed years ago to allow companies businesses to accelerate the depreciation and therefore get a tax advantage question yes that's right and so we're going to take that into account but the point is that for the purposes of cash flow the depreciation schedule will impact the cash flow only in terms of the actual tax shields that it generates not that it will decrease the value of the machine when the accountants tell you that it will okay so the idea is that your operating expenses are expenses you have to pay irrespective of what the depreciation schedule is okay so accounting expenses without depreciation is what you're paying out in cash it's the actual cash outflow every single year capital expenditures is what you spend on new equipment and then income taxes so this is this is your point Louis all of the effect of the appreciation on your income tax gets included in here income taxes you have to pay every year so that's a cash outflow right so if there's something that could reduce your cash outflow you better take that into account and that's where depreciation comes in it's a tax shield that allows you not to pay as much taxes so it reduces your tax burden it reduces your income taxes but again the focus is on cash flows money in versus money out that's what you're trying to measure okay and once you get the measure of money in – money out then you can start discounting using your appropriate cost of capital but you've got to get the cash flows right and so you know there are a number of other subtleties for example the project income taxes that you pay for your project is going to be the corporate tax rate times the operating profit minus the tax rate time's your depreciation so your depreciation doesn't actually affect the profitability of the particular piece of equipment or the project except insofar as it affects the taxes you have to pay so project income taxes the income taxes associated with your particular project are going to simply be the tax rate multiplied by the operating profit minus the tax rate times whatever depreciation you can claim and so this is how you can get the appreciation into your cash flows it affects the amount of income taxes you're paying and that's it all right so the bottom line what's your cash flow it's going to be one minus your tax rate times the operating profits operating profits is operating revenues minus operating expenses without depreciation without depreciation depreciation comes in later when you're talking about the taxes so here is where the depreciation comes in so your cash flow is operating profits multiplied by one minus the tax rate minus your capital expenditures and by the way your capital expenditures notice that you're not getting taxed on that right nor do you get a deduction for that you don't get to deduct capital expenditures the way you get to deduct ordinary expenses from running a company because capital expenditures are treated differently by the tax code does that make sense who knows that's that's for the tax experts to decide upon the fact is that capital expenditures have a different tax treatment and you have to know that that's why you need accountants tell you how they get treated the way they get treated is you get to depreciate the capital expenditures as the accountants tell you you're using them up so if you buy a piece of equipment for twenty five million dollars you don't get to deduct it right away because you're not using all of it right away you're using part of it every year how much are you using that's where the depreciation schedule come relevant so here what you're getting in terms of cash flows what you're getting is the depreciation that you report every year multiplied by the tax rate you're getting that as a positive cash flow why is that who can tell me why that is yeah that's not quite right it's along those lines but not exactly that's not exactly the mechanism code you write depreciation is an expense you get to deduct so you're right about that but you're getting to deduct it purely because of the tax code and because you get to deduct it you don't have to pay this much tax in other words without the depreciation you would be out this much money but because you have that deduction it's like I get out of jail free card you basically take this card and say here I don't have to pay this much tax how much is that card worth well it's worth this so this is actually the amount of cash you're going to get to keep in your pocket if you have this depreciation tax shield that's what it's called a tax shield it prevents you from paying a certain amount of taxes you actually get to keep that money in your company so it's actual cash flows to you okay so the accounting impact of depreciation is here and it's important I know it seems like it's a waste of time for us to spend time for my telling you how to do accounting but this is an important enough point that people forget when you're doing NPV calculations that I want to hammer this home what matters from an economic perspective is the cash that you're getting for your project year in and year out keep your eyes on the cash don't keep it on the accounting numbers keep it on the cash and if you do that you'll never go wrong okay here's an example just to make the point a machine is purchased for a million dollars with a life of ten years and it generates annual revenues of three hundred thousand and operating expenses of a hundred thousand if you assume that the machine gets depreciated over ten years using straight-line depreciation what does that mean straight-line yeah exactly so the machine is worth a million bucks and you're depreciating it over ten years straight line what do you deduct every year a hundred thousand yeah yeah that's right be a hundred years if you did ten thousand that would be a long a long life of the machine yes right ten thousand dollars hundred thousand dollars a year for ten years that's how much the accountants are telling you you're using up the machine and so every year you get to deduct a hundred thousand dollars from that kind of depreciation so what is your after-tax cash flow now your accounting earnings the way that an accountant would accrue the earnings would be this it's three million minus 100 K minus 100 K 300 K minus 100 K minus 100 K that's 100 K of earnings so an accountant would tell you that your earnings for this situation is a hundred thousand a year right however that's not the cash flows let's look at the cash flows the cash flows on an after-tax basis assuming a forty percent corporate tax rate is okay one minus 0.4 times revenue of three hundred minus operating expenses of a hundred so you're making two hundred cash every year before tax but then you got to pay tax but then you're getting a depreciation deduction of a hundred thousand a year so you're actually getting one hundred and sixty thousand dollars of cash every year not a hundred but one hundred and sixty okay so when you do an NPV calculation it makes a world of difference whether your NPV this guy or your NPV ting this guy they're not the same right and from an economic decision perspective this is what you ought to focus on not on this yeah it worked yeah that's right so there are other other considerations that you might want to bring into the analysis but my point is simply using accounting earnings versus after-tax cash flows will give you a different number in both cases I'm not I'm not taking into account the the upfront outlay of a million right right agree that's right and and that's part of the problem that's one of the reasons by the way why certain companies are incentivized to acquire other companies it's because the acquisition costs aren't accounted for in the same way that the operating costs so if you've got a company that's generating a lot of profits it's very profitable but it costs you a lot of money to acquire from the accounting perspective it can make you look really good because your earnings are going to get a big boost but in fact the NPV of the situation may not be as attractive the bottom line from shareholder wealth if you are doing this for your own personal account you'd want to be making decisions not on accounting earnings alone but rather on cash flows alright and PVS yeah slow me in what sense you're looking at the net incremental impact on your working capital and this takes that into account yeah that's right so I haven't talked about what the NPV is if you want to do the NPV you've got to ask the question does the after-tax cash flow just the five million dollars I haven't talked about that yet so if I'm not I'm not suggesting that we've got an answer for what you should do with this particular situation I'm simply using this as an illustration to point out that accounting earnings is not the same thing as after-tax net cash flows okay yeah well no I didn't I did not say that the question about whether or not you care about the solvency of company of the company is a question about what the ultimate costs of bankruptcy are but from a shareholders perspective if you asked the question what does the shareholder want you the corporate manager to do the answer is simple the shareholder wants you to maximize the net present value of the business okay if there are dramatic costs of bankruptcy or financial distress then you're going to have to incorporate that into your calculation for what you should do absolutely but the point is that when you're looking at net present value net present value gives you the appropriate data to make that trade-off okay always use net present value to at least calculate the implications of the various different investments in the case of bankruptcy costs if there are dramatic costs of financial distress then you don't want to go there because then you're not going to be serving the best interest of the shareholders but if on the other hand there are very little risks of financial distress and there's an incredibly good opportunity for you to take on certain risk that looks more than worthwhile relative to the compensation you're getting then I would argue that it makes sense to do so so the question is one about magnitude what are the bankruptcy costs versus the value of the upside for the particular project at hand and you've got to make that decision with the all the various different data properly computed what I'm telling you how to do is to compute that data okay all right here are some other calculations that describe what went on in the previous this is a case of accounting earnings after-tax cash flow after-tax at the bottom line is that they're different so for the perspective of NPV calculations you ought to focus on the particular calculation that gives you net cash flows okay so now I'm going to turn to focusing on the denominator discount rates we already went through an analysis about how to pick the discount rate the discount rate that you use is the one that adjusts for the risk of the project but keep in mind that a projects discount rate the required rate of return is the expected return demanded by investors for the project the way you ought to think about it is the project think of it like a stock and ask the question for people who are going to buy that project they're going to buy the stock what kind of a discount rate are they going to place on the riskiness of that stock it's just like Gillette versus General Motors we talked about that last time depending on how risk-averse the population is that will determine a particular market risk premium the market risk premium and the beta is going to determine what the appropriate discount rate is for that particular stock and the idiosyncratic risk is going to be assumed away because nobody has to bear that risk right everybody can be diversified if they want to be the second thing is that the discount rate in general depends on the timing and the risks of the cash flows I'm gonna give you an example in a few minutes that'll throw you off a bit because there's going to be two different kinds of risks and you're going to have to between the two so let me come back to that point with an example that'll be much clearer and the last couple of points is that the discount rate is usually different for different projects now this is something that again a lot of corporate managers miss they feel that if they're in a particular division then that division has a particular cost of capital and from that point on you should always use the cost of capital for anything that the division does what if it's the case that the division is doing something so different from what it originally started with and I'm gonna give you an example of that okay an example is something that happened just a couple of years ago I don't know how many of you realize but Bloomberg you know the maker of those nice terminals that everybody uses Bloomberg has actually a publishing company yeah that's right there's a Bloomberg Business press they publish books and this particular business just got launched a couple of years ago they already have a whole bunch of books in fact they're publishing a book that I've been working on with a former student of mine a series of interviews of technical analysts and so as part of this idea of setting up a business press they had to figure out what the appropriate cost of capital is for that activity and then ask for money from the parent company to launch this okay so the question is how do they do that do they use the appropriate cost of capital for Bloomberg Bloomberg's business is not publishing right there an information vendor and they're a technology company and as such they have a certain multiple right those of you who are in venture capital project financing you know about multiples right if you have a company with a particular kind of earnings then the value of the company is typically stated as a multiple of those earnings okay the multiple for an IT company a technology company a financial services company a multiple there is not the same as the multiple for a publishing company by the way which which multiple is hires anybody know can actually multiple for publishing is hired and why is that what's the logic foot IT being higher higher higher growth potential that's one also market profit margins tend to be higher publishing is not a growing business I don't know how many of you realize that because of the internet because of text messaging all all sorts of of innovations have really hurt the publishing business and that's why a lot of publishers have either gone out of business or have combined so now we have a few mega publishers yeah so you know if you're an entrepreneur that's looking to set up bloomberg press and now Bloomberg is using a particular cost of capital you may say well hey wait a minute if that's not the right cost of capital because publishing is a different multiple how would you do that then how would you figure out what to use in order to fit in order to calculate the value of a venture for Bloomberg press Courtney exactly so let's look at other companies that are in the business that we want to get into and see what kind of beta they have and what the appropriate cost of capital is Anand okay so let's let's hold off on that discussion for it for a moment I'm not going to try to justify why they get into it I just want to understand what the mechanics of how they decide on whether or not to get into it I'll come back to why later let's come back to that in just a few minutes though before we get to that let's figure out how they even evaluate all right so I've suggested here that they might use the beta of John Wiley & Sons that's a publicly traded publishing company but they could also use the beta of mcgraw-hill which should we pick mcgraw-hill or John Wiley Lois why exactly mcgraw-hill has lots of other businesses besides publishing so while they do do a lot of publishing they also do a lot of other things give me another business that mcgraw-hill is involved in it anybody yeah exactly boo girl hell own Standard & Poor's and Standard & Poor's does a lot of things including publishing ratings as well as indexes so those businesses are not the same as publishing books mcgraw-hill has lots of other subsidiaries whereas John Wiley & Sons all they do is publishing but they are what is known as a pure play company so let's take a look this is the revenues of mcgraw-hill of John Wiley & Sons sorry in 2007 if you look at the core business 39% professional trade 17% higher ed 44% scientific technical and medical that's not a perfect match for Bloomberg but that's not bad right that's you know within the same general area what we would really prefer is if it were just this slice that we could carve out and figure out what that business looked like but that's not so easy to do because of the the fact that it's one company that's doing all of it well so I guess I would be lying if I told you that size didn't matter that's usually the case size matters in in the sense that you want to have a company that's representative of what you're trying to do and smaller companies bear certain risks that larger companies don't vice-versa a larger companies have access to certain benefits and technologies that smaller companies don't so the point is that we don't always get to choose what's available you got to look at the various different alternatives out there and the best way to approach it is to get a range so if you're going to be doing this in a more serious fashion what you do is to make a study of the publishing business find companies at both ends of the spectrum the small ones and the big ones the pure plays and the conglomerates and estimate the cost of capital for all of them and then say given this spectrum of results we think that the appropriate cost of capital should be here and basically make a choice after having looked at the evidence so what I'm giving you is not a simple recipe that will work in every circumstance but rather an approach that with sufficient study and analysis will yield an intelligent answer so let's actually take a look at the answer here all right so we've got John Wiley & Sons we've got their performance over a period of time the share price and so on if you take the beta of John Wiley & Sons series a shares and you can get that from Yahoo it's a beta of 1.2 9 as of last year then with the risk-free rate of 5% and a market risk premium of 6% which is when Bloomberg was trying to decide when to go into the business about about two years ago it turns out that the cost of capital is twelve point seven percent so that's actually a pretty reasonable cost of capital which says that that's the number you use in figuring out whether or not the cash flows from a publishing business make sense okay now to Ananse question why are what you do that when you can invest in you know a business that may have a higher cost of capital or a higher rate of return we don't know that they do in other words at this point Bloomberg may not have any ability to invest in its current business or others that have a higher rate of return so one could argue that a cost of capital of a lot 12.7% is actually a pretty reasonable hurdle rate for a new business so in other words I would only invest in this business if it yielded a positive NPV now a positive NPV means it's earning more than 12.7% on average right that's a pretty good rate of return for a new business now there's another business that Bloomberg could get into which is the hedge fund business right I mean why not they got all this data they mayor's will make use of it and you know turn into a hedge fund now that business I suspect that the cost of capital is a lot higher higher because the riskiness is more substantial and there you have to start talking about the riskiness of bankruptcy you know would it really be a good idea to jeopardize Bloomberg's entire franchise on one mega hedge fund I don't know maybe but you know probably not if you're if you really are serious about preserving the franchise value of the company might well so that's the project interactions that I haven't talked about up until now I'm assuming this is a standalone subsidiary and I'm evaluating as positive NPV or not okay the next step in the capital budgeting process is to then ask the question okay as a standalone entity I think I understand it I got the cash flows down I got the discount rate down I know what the comparisons are I've evaluated the NPV and it looks positive now let me ask what does this do strategically for the firm that's the third question the strategic options is it good or is it not so good and if so can I put a number on that now from Bloomberg I wasn't involved in any discussions internally so I can't tell you what Bloomberg came up with but from what I gather they decided that there are some positive synergies between a business press and their other media type of access that they felt that there are some cross-selling opportunities so that when there was a good book that could put it on the Bloomberg screen and advertise free basically and and then the print media would actually help to support attention to Bloomberg as an outlet for for news so in that case they determined that this interaction was all good that there wasn't a downside to it and part of the reason I think is because they were able to assemble a team of very experienced publishers and editors they pulled them out of other publishing firms to start this new venture and they ended up getting some really good people involved and you know I've had the pleasure to work with some of them they are very very professional so Bloomberg actually made a pretty good decision at least from the perspective of getting this thing launched whether or not it'll be profitable who knows it's only been around for a couple of years but so far they've developed a pretty impressive list of authors yeah they go to this I said it pulls everything up to go 11 yeah rest their businesses now more expensive include the value destruction their business well so if there's any kind of value creation or destruction you're implicitly assuming some kind of of market irrationality right because what you're assuming is that if they pull this thing up they pull up the cost of capital for the entire firm they lower the valuation of the entire firm you're assuming that people in the industry can't see through the fact that they've got a subsidiary and in some cases you may be right but I would argue that a better perspective is to say that analysts are going to be able to do division by division valuation and say okay they got a publishing division these are the revenues these are the costs they're segregated and it makes sense for them given the synergies blah blah blah so I would expect that those considerations may not be as significant now if if on the other hand this publishing operation were really big in other words if it ended up that it grew so big that it accounted for half of the revenues of Bloomberg press a Bloomberg the entity then I think your point would be well taken would be much more serious right now it's a tiny little you know blip in the grand scheme of things that may turn into something big but for example if you're an investment bank nowadays we don't have any more of those but at one point we did if you're an investment bank and you've got a franchise based upon customer driven business very well reliable very high multiples you know very very valuable kind of franchise and then the question is should you get involved in prop trading prop trading proprietary trading basically being a hedge fund carries in the marketplace no multiple actually in some cases the multiple is negative I mean that is less than one right because if you're thinking about acquiring a hedge fund the typical hedge fund will provide you with whatever earnings they have this year but next year they could blow up so there is no multiple assigned to hedge funds typically not always I can give you examples over the couple of years where hedge funds have sold for multiples but they're not many of them and typically a hedge fund when you look at the value of the future earnings the multiple that's applied can be less than one if they're there's a concern that the hedge fund can drag down the value of the parent company so there are situations where for a distress sale people have paid 50 cents on the dollar of assets of a hedge fund of the actual cash that the hedge fund is generated for its shareholders they paid less than a dollar for dollar because of that kind of effect on the parent company Goldman Sachs after they went public they really had a lot of difficulty internally thinking about prop trading because prop trading accounted during certain years for such a large fraction of the Goldman franchise that it ended up having the effect that Mike was talking about that is people said gee Goldman is nothing but a prop trading firm I'm not going to give it a multiple of seven let's try a multiple of two and a half that is value destruction so that's that's a concern but for small projects that aren't about the entire corporation that aren't likely to affect the perception of the entire corporation you don't have to worry about that so size does matter in another way yep see today I use 1% so this is the time element that I mentioned to you before when you take on a project you've got to have the right time it's got to be the right time and so things change the cost of capital changes so right now I would use 1% for this particular project so you might think it'd be easier to get it launched but try getting cash in a setting like today to your project and you started at 1% and then all of a sudden the risky rate goes up so that mean that you might economically need to cancel your project yeah absolutely yeah at one point john maynard keynes was criticized for flip-flopping on the gold standard and mccain's had a very very sensible reply which i think i may have mentioned in class which is that when the facts changed sir I changed my mind what do you do so absolutely if cost of capital changes gear from now you may have to cancel your project or you may wish you had taken two of the projects but you didn't get to these kinds of project interactions over time make it really complicated that's one of the reasons why we have a whole separate course on capital budgeting is to come up with tools to deal with these kind of interactions so absolutely fact I'm gonna give you an example of that in just a minute we're that time element actually is very important let's let's actually go over that right now so sorry so here's an example that you don't know how to do yet we're going to figure out how to do it together all right and has to do with time and with risks so a firm is investing in an oil exploration project all right we're going to drill a bunch of holes in a particular area we're trying to find oil and it's going to take time to drill these holes so it's going to take at least a year and at the end of the first year there's going to be a probability of 1/3 that we find 3 million barrels of oil but there's a probability of 2/3 that we find nothing we come up dry ok 1/3 2/3 probability now if we are successful with that 1/3 probability then the 3 million barrels of oil will be pumped out of the ground by the end of the second year so at the end of the first year if we're successful we'll find oil and then it'll take a year to extract it and barrel it put it in barrels and sell it and we'll have three million barrels to be able to do that ok and then after that the field will be depleted ok now the expected after-tax profit per barrel is 20 bucks we're going to make 20 bucks a barrel after tax not now but a year from now the risk-free rate is 5% the industry discount rate of oil production is 20% that's a very high cost of capital but the oil production is a high beta activity as you can sort of tell right market prices are down oil prices down when the market was up oil prices were pretty high oil has a high beta okay so the discount rate is 20% but the exploration risk this 1/3 2/3 probability that has a beta of zero what's the NPV of this project how do you figure that out believe it or not you actually have all the tools to solve this problem but it's hard and not only is it hard for all of you it's actually hard for for professionals a couple of years ago I taught the Sloan fellows program during the summer I don't know how much you know about the Sloan fellows program but this is a program where we bring executives who've worked for 15 20 30 years made their fortunes and have decided to take a year off to get a degree and so these are very seasoned senior professionals so teaching them is a whole other challenge they're very they know a lot and they know a lot about virtually anything and everything you ever care to talk about it's a case in point I gave this example to the Sloan fellows class somebody in the back of the room said excuse me for a little bit I I don't recall that we actually use this analysis when we were doing oil exploration and I said well what you tell us about what you did who you are and so on and the fellow said that well I'm the senior vice president for oil exploration at Saudi Aramco this is the biggest oil company in the world and he was the man in charge of drilling those holes and he actually said that they didn't do this analysis but that he actually was going to try it out because he thought it made a lot of sense so that was that was a little scary I have to tell you very intimidating audience but the point is that this is a very subtle idea let me tell you what what it is let me tell how it works okay there are two risks going on here there is the market risk of pumping the oil out of the ground and selling it and that we understand quite well that has a beta given by this particular cost of capital twenty percent so we already know what the discount rate is in that second year but we need to figure out how to discount from the second year to the first year what should the appropriate risk risk adjusted discount rate is from the first year back to Year Zero that's the key right that's the hard part at the end of the second year we're going to have three million barrels of oil each priced at $20 a barrel for a profit of sixty million dollars right or six million dollars here yeah so sixty million dollars at the end of two years now we're going to discount it back to the beginning of that two-year period so in other words we're going to discount it from the end of the second year to the beginning of that second year or the end of the first year and that's what we get as 50 million right 60 million discounted back by twenty percent discount rate that's 50 million at year one if we strike oil but there's a one-third probability that we strike oil there's a 2/3 probability that we don't the question is what do we discount this possibility back to Year Zero and I'm going to argue you discount it back not at 20 percent but at 5 percent 5 percent that's the risk-free rate now why on earth would you do that this is the oil industry we're talking about the reason you discount the first year back to Year Zero at risk-free rate is because the risk of coming up dry that risk is completely diversifiable that is complete idiosyncratic risk there is no beta right the oil deposits underground don't know whether it's a bull market or a bear market they couldn't care less they're either there or they're not there and you're drilling for it so your risk of not striking oil has no bearing on the market if you are well diversified then that risk is actually not something that you're going to get rewarded for and therefore you need to discount it at the risk-free rate so in fact the NPV of this project is fifteen point nine million dollars which is a lot bigger number than if you were to discount it by twenty percent both years it's because the risks are different so to Brian's point when risk changes over time you've got to use the appropriate discount rate for that particular kind of risk now it just so happens that here ahead of time we actually understood where the risks were coming from so we know that the risks between year zero and year one are different from the risks between year one and year two you've got to use the appropriate discount rate for that kind of risk this is a very subtle problem that you have to think about carefully in order for you to understand it fully okay but it's an important one so that's why I spend time on it any questions about this any any debate any argument you agree with this does this make sense to you if it doesn't make sense speak up now or forever hold your peace right because it's important that you absorb the lesson from this particular example yeah Andy and so suppose that you know for a fact that there's a third you consider the same project that has the exact same that's right that's right absolutely because there you have no uncertainty and you're just simply taking the expected value and assuming that you're getting the expected value and it's because the uncertainty of this project in the first year is completely diversifiable it's a coin flip it's a coin flip and you're not going to get rewarded for bearing that coin flipped because if you diversify put it another way suppose you were Saudi Aramco and instead of doing one of these fields you did 100 well then you've diversified across all sorts of possible coin flips and then the law of large numbers would actually reduce your payoff to something very very a riskless or close to riskless right okay sure the first year is the 5% because I told you hear that the exploration risk is completely non systemic it's zero beta so when you're drilling 4 holes whether or not you find oil you don't find oil has absolutely no bearing on whether the market is up or down there's no correlation if there's no correlation then that means that it's a kind of risk that you're not going to get reward for this is the Irish jig dance you know the dancing on that platform you're not going to get paid extra for dancing an Irish jig on that platform when you're window-washing okay so the key here is this statement right here the exploration risk is non-systematic if the exploration risk were systematic for any reason then of course you'd have to use a discount rate that would be commensurate with the appropriate beta and there's no telling that that beta is going to be the same as pumping the oil out oil exploration is not the same thing as oil production there are two different kinds of activities that carry with it different kinds of risks okay other other questions or comments yeah show right yeah so the answer is it depends on the industry you know for certain industries where you cannot identify discrete changes in the riskiness of the activities then it makes sense the only thing you can do is to come up with one discount rate but for industries like this where there are discrete phases of these different projects then you actually do use different discount rates because the uncertainty resolves in a different manner depending on the industry so if you keep in mind a lesson that the appropriate discount rate should be commensurate with the risks of that particular cashflow think of each cashflow as a piece of paper that you're auctioning off to people in a marketplace and ask the question what would those folks in the marketplace demand in terms of the appropriate compensation for that kind of risk you'll be able to make the right decisions okay and if you can't tell then you may as well use one discount rate if you can't tell one cashflow from another then what you're telling me is that effectively it's the same kind of project okay we're out of time I wish you all a Happy Thanksgiving we'll see you on Monday where we're going to continue on with capital budgeting and do some more applications

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