Ses 2: Present Value Relations I

The following content is provided under a Creative Commons license your support will help MIT open courseware continue to offer highquality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT open courseware at ocw.mit.edu the other item that I auctioned off that was that's a good question well first of all before I tell You that you'll note that I put those two packages up here in the front of the room for this first section one was bigger than the other and you guys got the smaller one

right and you obviously know what that was the bigger one turns out to have been uh a book um in fact it's a a book that I recently published on hedge funds now it turns out that the bidding of that second item went for $60 the bidding of the item that that I Sold to this section went for $45 five and the fact that it's a smaller package I think makes some sense of why it went for a smaller amount um that shows you the power of information or lack of information in terms of determining

values Yeah question well I don't think so and one of the reasons that I had two different packages and I showed both of you uh both I mean but this entire section the two different packages is to try to Eliminate a bit of that kind of private information I don't believe there was any if I used the same two items then I think there would have been a a concern that there might have been some information spill over so I don't think that was it in fact I think what it was was the size of

the packages believe it or not so anybody that tells you that Size Doesn't Matter I think is uh is not uh being realistic uh was another question Back here question okay yeah how much the book retail the book retails the book retails for $45 now of course I uh I autographed the book so so that probably reduce the resale value but uh and you know we played you know I took the $60 you know no tears fair is fair um so this class you know the individual who bid 45 for that iPod did very very

well indeed and uh the student who bid $60 for the book didn't Do quite as well but that's the point of this example it's that when you don't know what you're bidding for when there's literally no information you're obviously not going to get it exactly right but you have to admit that in the grand scheme of things it's actually not that far off and not that far off in a very particular way I I want to in particular talk about the iPod because we were looking at something like a 70 % discount off of the

retail value of that For this class now I want to comment on that in the context of what's going on today because I I want to spend a few minutes before we start the lecture talking about current events because Finance of course involves current events and right now we are going through an extraordinarily interesting set of times I think that's a a Chinese curse right may you live in interesting times well we're going through some really extraordinary times because what Happened over the weekend is something that has probably not happened since the Great Depression what

happened over the weekend is that the federal government took over two of the largest government sponsored Financial entities in the world Fanny May and Freddy Mack these are two government sponsored entities they're private organizations but they have the the backing of the government in some ambiguous sense and it was ambiguous up until this weekend what That meant what happened was that these large large financial institutions were responsible for purchasing the mortgages from various different Regional Banks and lending institutions why would they do that what was their function anybody know yeah to provide secondary market for

mortgages so that uh the banks are the initial lenders can generate more mortgages and you know make credit more available exactly they're goal was to Really make credit more available in the housing market and the student loan market and the auto loan Market these Consumer Finance markets the purpose of these two organizations was to buy up the various different obligations from Banks and other financial institutions so that the banks and financial institutions could then go out and lend more money to more individuals that wanted these kinds of loans so the purpose of these two organizations

was Really to support and grow these various markets and it turns out that over the last 20 years these markets have grown to Epic Proportions tremendous proportions and now as the housing market has turned down the original lenders uh that made these obligations are facing some severe pressures and that's carried the uh Ripple effects all the way through the financial system to the point where these two organizations literally could not stand on their own And if there had been a default of these two organizations there would be some major repercussions we're going to talk about

that in about four lectures the material that we're going to develop over the next three lectures are going to allow us to analyze the situation and really try to understand what's going on in these markets but I just wanted to alert you to the fact that something really big has happened you won't understand fully what it is you might Read the newspapers and I would encourage you to do so but you won't fully appreciate the importance of of it for another three or four lectures but you're going to see this event unfold before your very

eyes this semester and that will provide the motivation for developing the tools to understand what's going on yeah can I you can ask sure think do you think that was their only option option or do you think that was the right well that's a a very tough Question in terms of the uh the possibilities for the Secretary of the Treasury Paulson and the government um there aren't too many left uh in the sense that these two organizations uh are in a real bind in that they have issued lots of Securities based upon their activities and

in order to maintain the quality of those Securities in order to make good on those promises that it has made to other counterparties very important Counterparties I might add including the governments of India China and a number of sovereign wealth funds that we depend on to loan us the money that has kept us in the style to which we have become accustomed in this country uh in order for us to maintain those kinds of relationships we have to make good on our promises and it's getting harder and harder for these two organizations to do so

because while they've got all of these promises They've made the money that's supposed to be coming in in order to allow them to make good on these promises is dwindling and as they've tried to raise more money in the open market it's become harder and harder because people realize that they're in trouble and it's very difficult for them to raise that money in fact this is related exactly to the point about the iPod auction that we engaged in last time think about how little I received for that $150 item I Received basically 30 cents on

the dollar and why it's because none of you knew what was in that package so now instead of a an iPod that's in a wrapped package imagine if that wrapped package contain paper issued by Fanny May or Freddy Mac and now I'm gonna ask you can you bid on this paper now I don't know whether Fred Freddy Mack or Fanny May will still be around in two years but I'd like you to bid on this paper anyway and by the way what you get for this Piece of paper I don't really know so it's wrapped

up and you don't know either you don't know I don't know you know I don't know and I know you know I know I don't know so what's that piece of paper going to go for well probably less than 30 cents on the dollar right so what we saw happen in this classroom last time is exactly what's happened in Spades to these two large organizations at some point there has to be a Day of Reckoning And the treasury decided rather than waiting for that day of reckoning because if that Day of Reckoning came before they

were able to do something it's very hard to put the pieces back together so in my opinion I think they had very little choice but to do something right now before it got out of hand and we're going to talk about this again in fact we're going to run a trading game where all of you are going to get a chance to engage in this kind Of trading it's not exactly the kind that uh involves credit but it'll it'll be a trading game where you'll get to see what it's like to be under pressure and

to have to make decisions and value Securities in real time and you'll have a much deeper appreciation for the kind of issues that uh we're up against yeah sorry what did the government do agreed to pay for all their right all their yes so the government said okay you guys Fanny May and Freddy Mack you Can't make good on your obligations because you've got some problems so we the treasury will stand by all of your claims the government pay that absolutely you know how how can the government pay that what exactly exactly the government they

own the printing presses so they just you want to get paid dollars I'll pay you dollars here how many dollars would you like I'm going to run it here you go So we'll probably in inflation that's that's the concern so the concern is that if you do this too much and you do it without anything backing up the pieces of paper you now print and give to your your debtors then there'll be a problem because pretty soon they're going to realize that the piece of paper isn't really worth as much as they thought it was

so inflation could be a problem it could be a problem we'll have to see but Right now the paper the dollars that are being printed are backed by the full faith and credit of the US government and for the time being that still means something yeah are all the of debt so the question is uh is is all of the debt being guaranteed or is it just how much Freddy and Fanny issued well certainly it's what they've issued so all of the paper that they've issued will be backed by the government in Addition there's some

new paper that they have to issue in order to finance additional mortgages and the government will back that too now this is not for free it's not just printing presses that sounds a little too easy somebody has to pay for it the money's got to come from somewhere or put it another way that money that is spent now backing these instruments cannot be used for other things so if you believe in balancing your budget as opposed to spending on Credit which frankly is what got us into the problems to begin with then there will be

additional Reckoning people have said that the American taxpayer will pay for this well that's true but the question is which set of taxpayers is it us is it your children is it your children's children there are a lot of intergenerational questions about where the burden lies but the fact of the matter is yes we are on the hook that the American taxpayers on the hook for Tens of billions of dollars now in the grand scheme of things tens of billions of dollars is nothing I mean the federal budget is much much larger than that so

this is not a big deal the concern is if if this spreads and ends up costing us more because of Ripple effects and knock on effects that we don't yet know about that could be a problem and that frankly is one of the the reasons why the fed and the treasury decided to step in now to try to contain this problem how good They will be at doing that we don't know read the newspapers over the next few weeks and let's see yeah do you think the common stock basically has to be zero at this

point well it's not worth exactly zero but it's pretty darn close and in fact it's come down quite a lot I think over the last couple of years I don't know what the peak of the price was I haven't looked at it but I think that the the decline has been on the order of 90 to 95% decline of what the peak was over the last couple of years which 83% yeah 83% since when yest yeah that that was just a day ago but I'm talking about since the peak I think it's come down dramatically

so effectively the value of the shareholders Equity is pretty close to zero but that's what happens in a bankruptcy and by the way we're going to talk about bankruptcy too that's going to be a very important part of of what We do when we analyze fixed income instruments so we're going to get to that shortly yeah has there been anything about uh potentially going private again the road there have been discussions about them going private but private in a much smaller way so the discussions that have occurred to the treasury and we don't know which

way things are going to end up because it's a political process as well as an economic one but there's a feeling that These two institutions got too big too quickly and that there wasn't enough oversight to allow them to be able to fail in other words they grew so big so quickly that after a point they were in fact too big to fail and when you're too big to fail all sorts of abuses and improper risk management practices can go on which we will talk about in probably eight or nine lectures okay uh so there's

a variety of proposals that have been put forward and we'll talk About those also over the next six or seven weeks who did the government actually bought the shares from are there federal agencies or is it private compan so Fanny May and Freddy Mack are are called gses government sponsored entities which means that they're not a federal agency but they are backed by the federal government in some manner that has been up until now relatively vague so they're meant to be private Companies they had a CEO both of them had CEOs who who were fired

over the weekend they have separate Boards of directors and they pay pretty attractive salaries private uh you know private uh sector salaries but they were related to the government in the sense that their objectives were to try to support and expand the housing market uh financing which was a government dictated mandate to this their main their main goal is not to earn money To bring a secondary market for mortgages their their main goal was to create uh additional financing to allow the mortgage Market to grow and to allow people to buy homes at reasonable rates

their a secondary goal was to make a profit on top of that so that's why they're not just a government entity but they have a kind of a quasi private uh sector type of mandate and by the way they did a great job they did a great job in the sense that the housing market Has grown tremendously now you could argue that that was irresponsible and that created all these problems that we're facing today but you you talk to somebody who has a subprime mortgage that otherwise couldn't have afforded a house that now has made

every single payment and really enjoys living in their home and has a lifestyle that they couldn't have otherwise had you talk to them and you tell them that it was a mistake so it's Not at all clear that this is a total disaster it's unfortunate and it's a catastrophe from the point of view of the current holders of various pieces of paper that are related to these subprime mortgages but there's a whole group of people out there that have benefited from these subprime mortgages and so you've got to back balance the costs and the benefits

and and we're not doing that right now right now we're just panicking because we're all scared like Hell that something really is going to break but there's a positive side as well as a negative side to every story and so we're going to have to talk about that in a little bit more detail but we can't do that unless we have the framework to think about it so that is going to lead me to today's lecture yeah inv so there are there are two groups of individuals that are involved one are the shareholders of the

companies themselves and these are investors a Number of them are Pension funds institutional investors so therefore you and I in our 401K plans we might actually have an investment in one of these organizations through the plan sponsor that invests in various different entities so like there there a stock that was traded on the exchanges just like any other stock that's one group and those are going to lose most of their Capital they're going to lose their investment Just like when a stock goes belly up the investors of Enron too bad they lose everything they're gone

they knew it they took the risks and the risks don't always work out so that's that the other parties that are involved are the folks that do business with these agencies the counterparties that bought the paper that they issued these IUS and other complex instruments that Freddy May and Fredy Mack issued those individuals we're hoping will be Uh relatively happy about the outcome of the government backing the paper because now the paper that they once held and thought was in trouble will have the full faith and credit of the US government behind them and that

that is a major concern because these counterparties are are very very substantial investors if they decide that this paper is no good and they start getting rid of it wholesale that will create some really significant Market dislocation and mass panic and that's what the treasury stepped in to Stave off this weekend hopefully they will have succeeded in fact if you look at the data it looks like they did succeed but I'm not going to talk about that for another three or four lectures because I want to show you exactly how to think about these instruments

and then we're going to look at the data and see whether or not they've actually done Something significant and you'll be able to tell by looking at market prices by looking at the outcome of auctions like we did last time we're going to be able to tell exactly what happened okay all right well that uh took a little longer than I thought but I think it's useful for motivation for what we're going to do in the class what I want to do today is to start on lectures two and three present Value relations and I

have to tell you this is one of the most interesting lectures of the entire course not because of the the underlying material but rather because of the novelty of the perspective that I want to give you uh about these kinds of of issues this is the very first step in changing the way you look at Financial transactions we're going to start by discussing cash flows and assets I want to Define some terms and I want to change the way you think Of an asset and then we're going to talk about the present value operator and

then we're going to apply that to the time value of money I want to make that concrete so that all of you will start thinking differently now about money today versus money next year and then probably not today but next time we're going to cover two very special kinds of cash flows the annuity and the perpetuity these are two mathematical abstractions that provide Some really interesting insights into this whole notion of present value and then I'm going to talk about a couple of technical issues compounding and inflation and that will lead us right to thinking

about fixed income securities and how to Value them and how the market values them and whether or not the two are the same or or different for the readings I'd like you to start on Brey and Myers Allen chapters two and three you should have already read chapter two From last time I'd like you to reread that and also focus on chapter three for the next couple of lectures okay so first order of business let's define some terms I think you all know what a cash flow is right it's just money that's coming to you

or going away from you a flow of cash and you all know what cash is I presume the next question I want to take on is what is an asset you know we talk About valuing assets but we have to start first by agreeing on a definition for what an asset is and I just put some examples up here of what assets are business entity is an asset if you guys decide to do a startup that startup has value it's an asset property plant and Equipment patents R&D stocks bonds options and even something as difficult

to Value as knowledge and Reputation are assets does anybody know of an example of a really valuable asset that is not physical at all you can't touch it or feel it yeah Al the algorithms that Google is using that's right now how do you know that those are assets they generate Rue they generate Revenue right and has anybody turned them into anything concrete like any type of legal structure to make them Assets a patent exactly a patent and Google has many patents those have value not only are they considered assets but you can actually trade

them you can buy a patent sell a patent license a patent yeah are they patents or are they trade secrets well they're both so Google has patents but they're also a number of Trade Secrets that it uses to protect its intellectual property what's a distinction yeah No what is a trade secret it's secret it's a secret thank you well I'm not sure it's a patent without any kind of legal standing in fact it's sort of an anti- patent isn't it it's not a patent it's a secret specifically like Coke for example the formula for Coke

is a trade secret it is not patented when you when you app for you have to disclose fully what your patent covers and that means that at the end of the patent's life coverage which Well at the end of the life coverage you're out and so I could go and I mean if C would have applied for a patent however many years ago it would have expired I could be making Coke right now but a trade secret is secret forever as long as you take steps to eat secret right so they are taking the risk

of the secret exactly Coke is taking a big risk if in that it has not filed for a patent and frankly if it did it would have expired long ago now what exactly is a Patent what's the motivation for a patent a patent is a legal uh agreement that says that if you tell me everything there is to know about how to construct the item or algorithm that you want to patent if you're willing to disclose that to me and the whole world and I acknowledge that it is new and useful then I will grant

you the ability to be the sole user of that algorithm product or business process for a finite period of time say 17 years So for 17 years if anybody wants to use that algorithm they have to pay you for that privilege so it's a monopoly it's a monopoly that the government grants you for a fixed period of time in exchange for what in exchange for you to will be willing to disclose everything there is to know about it and why is it so that everybody else can learn from it and after 17 years and after

you've made a God awful amount of money somebody else can take that idea and incorporate it Into what they're doing and make money off of that the patent process creates assets out of ideas and it allows you to derive economic value from that in exchange for freely sharing those ideas that's one path to go the other path is I don't want to share because I think that I can do better by keeping it a secret and that's what Coca-Cola has done that's the example that I was thinking of of an idea that has no legal

standing but That's one of the most incredibly valuable ideas in the world today the amount of money that Coca-Cola produces is unbelievable given this simple recipe that apparently people haven't been able to figure out how to reproduce I mean how hard could it be you know you just mix a few things and add some coloring and you know then you get Pepsi I don't know yeah that's right of people who Associate a r do with feeling happy that's true now that's the case they've spent years building the Coca-Cola brand that's one of the most recognizable

brands in the world and that has value too and by the way that value is different from the trade secret so now we see that there's lots of different assets and that's an asset right yeah yeah well that depends at depends on whether or not you think you can keep it A secret right and Coca-Cola apparently has been kept secret pretty well but there are a lot of other people working on the various different kinds of cholesterol reducing drugs not just uh you know the folks that develop lipor so if you can keep it a

secret great keep it for yourself but very often you won't be because other people are working on the same research also there's a certain cache to having a patent and it provides You with a certain kind of business uh business viability you can go to an investor and say here I've got this idea the idea has been certified by the US patent office it is patent number XYZ and that's why you should give me money versus you go to an investor and say hey I got a secret I can't tell you what it is you

know what you're back to the iPod okay Andy question oh no I was just gonna I was gonna say the same thing yeah okay so now we we know that there All sorts of assets even intangibles even things that you can't hold in your hand can be an asset I want you to forget about all of that I want you to think about an asset in a completely different way I want to reduce an asset to its fundamental core properties and to do that here's my definition of an asset an asset at a given point

in time T is simply equal to a Sequence of future cash flows CFT CFT plus1 CFT plus2 dot dot dot that is the definition of an asset that I would like to adopt for the next 12 weeks okay now this might seem trivial to you but trust me it's not it's a very subtle idea and it's going to have all sorts of interesting implications that we're going to discuss over the next few lectures but I want to make sure that everybody fully appreciates what I mean When I say an asset is a sequence of current

and future cash flows let me just describe a couple of interesting things about this definition first of all it doesn't involve past cash flows so when I Define an asset I have to Define it relative to a point in time that in in of itself I think is something new right so it's not enough to say an asset is Coca-Cola you have to say that the asset is Coca-Cola to today versus Coca-Cola 10 years ago versus Coca-Cola 100 years from now those are different assets the point in time actually matters in other words right this

is like the Zen Paradox you can never step into the same river twice right because water's moving it's always a different River in that sense an asset as at every point in time is a different asset and that's not that surprising because if you believe from my definition that an asset is equivalent to its current and future Cash flows then those cash flows are very different depending on where you stand so for example the stock of Fanny May and Freddy Mack as an asset was very different five years ago than it is today they're both

assets they're both cash flows but the cash flows are very different depending on what point time you're talking about so when I think about a cash flow I'm thinking about a particular sequence that occurs given market conditions and An asset is comprised of those cash flows they are one and the same when you tell me that you have an asset I immediately think of okay what's the sequence of cash flows that's all I care about from the purposes of financial analysis that's all that matters Okay so over the next few weeks we're going to be

building up a theory of financial analysis the basic building blocks of that theory are assets so you can think of Assets as the molecules or atoms of a unified field theory of finance and the protons and electrons those are the cash flows okay yeah the cash flows have to be positive no nope they don't have to be positive or negative but they do have to be real numbers so no complex numbers here okay positive or negative that's what an asset is now you might think well gee if all the cash flows are negative then I

don't really want that asset well that's the nature of an asset Maybe then you call it instead of an asset you call it a liability exactly but from my perspective developing this atomic theory of Finance I'm going to focus on this as the basic building blocks and I don't care whether they're positive or negative for the moment okay we're going to talk about their characteristics later but I just want to agree on the definition of what an asset is question yeah so it's a sequence cash flows it's not a summation it's right It's not a

summation it's a sequence meaning it's basically just a list of cash flows at different points in the future including the present but not the past so according to my definition the past doesn't matter when you talk to me about an asset all I'm looking at is current and future cash flows okay and it's a sequence of cash flows so that means they're ordered in time and I'm not even telling you whether or not you know what the cash Flows are so it could be that the future cash flows I'm writing them as letters but who

knows what the letters stand for you might not know what the future cash flows are but you can still nevertheless acknowledge that they exist as an abstraction okay that's what an asset is I don't care what you use to value your various different cash flows but the definition of an asset is simply a sequence of Current and future cash flows all right that's what we're going to talk about as an asset so all the things that I listed up there knowledge reputation can reputation be considered a sequence of future cash flows does that make sense

how what Goodwill how would you use that Goodwill yeah your reputation is such that you Know people choose you instead of a competitor and so that additional cash flow from from from that choice is coming from reputation exactly right the additional cash flow that you get based on that reputation that's the value of the asset or that is the asset right there assets have common elements absolutely no reason why you can't have common cash flows across different assets right but nevertheless a single asset is a Collection of present and future cash flows yeah but as

you said like if I have one asset or building and if she has a building and if I'm A lender that means like I have a different cash want yes but however there's a maret of the building yeah so if like sequence of the cash flow yeah how can how can you like we're going to get to that that's actually a very deep question that will require Three more lectures before we get to but I will answer that exact question in three lectures if not before okay before we talk about how to Value these assets

I want to make sure we agree on what a definition of an asset is so I think we agree right any any questions about that yeah have of but they any incremental flows EX well not to be not to be anal about this but you know mathematically a sequence of 0000000000 is a Bonafide cash flow Right so the zero asset is possible too all right so this is absolutely General now and you might you might argue at this level of generality it's useless well not not quite not quite because I think it helps us to

formulate a perspective and the perspective is when you start thinking about various different kinds of assets I'm talking really complicated assets assets with all sorts of you know options and triggers and various Contingencies the more complicated it gets the more important this framework is because no matter how intimidating the problem you are faced with the bottom line is an asset is a sequence of cash flows it's simple conceptually the hard part part is figuring out what those cash flows are but the conceptual framework is what I want you to start with because that will clear

your mind of a lot of cobwebs that really don't belong in any kind of financial analysis So we start cash flows sequence of cash flows is an asset okay now that I've told you that there's lots of examples that you can come up with so I've given you some in the notes please take a look at them each one of these is an asset and each one of these represents a certain SE sequence of cash flows some may be more subtle than others but they are nevertheless cash flows so I want you to think about

that read through these Examples and make sure you understand why they are assets now valuing an asset that's the question that yungun was asking about how do you value a sequence of cash flows because you and I we might have a very different perspective on what that cash flow is worth so for the moment I'm not going to answer that question or rather I'm going to answer it with a typical device that economists Use all the time which is I'm going to just create some notation to answer the question and the notation I'm going to

give you is v in particular V subt that's a function that takes as its input a sequence of cash flows and spits out a number which I'm going to call the value of the asset at time T So how do you value a cash flow well you use the value operator V subt you stick In a cash flow and out pops a number okay we're going to have to spend the next three lectures figuring out what V is but I can tell you one answer right away in fact all of you know what V is

or one definition of v what is it can anybody tell me what V is where do you get V from yeah that's right but you're close where did that come from what you pay for it what do you Mean by that market price what Market what Market yeah exactly any Market this is what you were getting at what you pay for it any Market if there's a market you've got your V so V one example of a VT is a market at time T right that's what we did last time we had a value operator

stick in a a gift wrapped box and you get out $45 that's an example of a v what we're going to try to do though is to take apart that box and see how it works and whether or not it does work Market Market well we don't know what best means so for our discussion right now any Market will do but then you can have a separate discussion as to whether or not there are better markets or Worse markets and we have to Define what that means so we're going to get to that when We

start talking about how the V operators work yeah so we don't we don't know what a perfect or imperfect Market is yet and I'm going to hold off on that for quite a few more weeks all we know is it's a market so let me put it to you this way the last lecture when I auctioned off that iPod and I only got a third of the price would you consider that a perfect Market it didn't feel that way to me but on the other hand it Worked I had something that I wanted to unload

and I unloaded it at a price that two mutually consenting adults agreed to so you know that worked that that was pretty good but in order for us to understand whether or not it really works we've actually got to take apart the Box we got to open up VT I'm not going to do that just yet I want to First acknowledge that there exist VTS out there and more often than not when you Let the market dictate what that VT is you actually get some pretty interesting results results that will require a little bit more

structure to interpret one way to interpret the structure is to acknowledge that there's a time element to the cash flows so when I ask you to analyze a VT or an asset the first thing you're going to want to do is to draw this picture right here and I'm serious about this in order for you to understand the value of an asset you Have to know the timing of the cash flows time means everything in finance okay a cash flow today is not the same as a cash flow next year yeah so are we going

to divorce the the accounting defin of an asset from Finance for instance land right has to be recorded at B value at all yes right so what I'm asking you to do is to think abstractly in terms of the cash flows themselves I haven't talked about Accounting practices at all I'm going to come back to how we actually implement this and at that point it'll be important to bring in the accounting elements but for now let's set them aside okay so these are actual cash flows that you will receive at different points in time and

by the way I want you to use this exact same framework for analyzing accounting practices because financial analysis can actually be used to ask the question are accounting Conventions good or bad some accounting conventions are favorable some are unfavorable but the only only way to analyze them is by using this kind of a framework first okay so I would argue that this will be certainly useful for looking at accounting practices but it won't necessarily be the same so you'll need to have to make that distinction okay so so far nothing I've said is all that

controversial I don't think I've simply defined that there's a Value Operator Operator means function you stick in a sequence of cash flows out pops a number and when you analyze the value of an asset I want you to always draw a timeline and make sure you understand the sequence of cash flows okay without the timeline I don't know that you really understand what's going on so F first of all as a tip for your midterm and final exams anytime you have a calculation which you have to do a present value or valuation Exercise I want

to see this I want to see that you know when things are going to happen because nine out of 10 times when you make a mistake in valuation it's because you line this up incorrectly okay now what is V well we said that one example of a v is the market but is that objective is it subjective does it work well how is value determined and what we're going to do in this lecture and the next one is to take apart this function V in the case of no uncertainty so remember I told you the

two important factors in financial analysis that makes Finance interesting and exciting is time and uncertainty right and we've seen both of those things happen this weekend a lot of time has passed in resolving the uncertainty with regard to Fanny May and Freddy Mack what I'd like to do is to abstract from the uncertainty part for the next couple of Le There's no uncertainty okay I'm going to get rid of the randomness and I'm only going to focus on figuring out the value operator this V subt function for cases where we have cash flows at different

points in time but where the cash flows are known for sure so there's no uncertainty about whether they're going to happen or not happen Okay after we do that after we do the no uncertainty case for which we have a complete solution I will then come back and introduce Uncertainty in a somewhat more natural way and then we're going to focus on valuation with uncertainty as well okay so let me start with the perfect certainty case about how to figure out what the V subt is and I'm going to start with a very simple example

that has to do with manipulating cash flows and I'm going to talk in particular about foreign currencies so I want to ask you what happens when You add 150 yen to 300b what do you get when you add those two 150 Yen plus 300b is equal to 450 what $450 if if uh if you believe that please see me after class and uh we'll need to do some transactions well look obviously 450 makes no sense right it's like you know adding your weight to your age that number might be interesting but there's No interpretation for

it right so 150 and 300 you would never add those two and talk about 450 watt right there you don't even have a unit to be able to ascribe to it well well that natural reaction that you have that natural aversion you have to adding up dollars or or Yen and you know in different currencies I want you to develop that exact same attitude towards cash flows at different points in Time so let me continue on with this obviously if you want to add the to you know that you have to convert them to the

same currency right so 300 lb converts to a certain number of Yen and so when you add that up you get 46,50 Yen or if you want to convert it to pounds it converts to 3.98 Pounds Sterling right those numbers make sense the reason they make sense is because they're in the same units so Apples to Apples is the familiar adage that we use right you can't add apples to oranges actually in Theory you could right you could make fruit salad and you need apples and oranges and pears and all that but for the for

argument sake when it comes to money it really doesn't tell you much that you've got you know 450 blah you need to have a set of units well it turns out that this actual uh analysis requires that we pick a base currency we pick what's called a Numer rare a numer is a unit of account or a standard by which we measure everything okay so either Yen or pounds will work just fine it doesn't matter which if you're a British investor you might care about pounds if you're a Japanese investor you might care more about

Yen it just depends upon your perspective but either one will do for the purposes of analyzing how much money you have at a point in time well that exact same exercise has Has to be applied to money today versus money tomorrow because those two things are not the same it's like Yen and pounds they're not the same they can't buy the same things they aren't used in the same way they have different markets the markets are related but they're different so once you know the exchange rate and once you pick a base currency you can

combine the thing the same idea holds true for cash flows at different points in time Cash flows at different points in time are like different currencies in order to add them together you've got to use the appropriate exchange rates okay once you do then all of the valuation that we're going to conduct over the next couple of lectures becomes absolutely trivial so let me give you an example of that here's my timeline and my timeline has payoffs at various different dates now I'm arguing that the past and The future cannot be combined without converting them

so we have to have a set of exchange rates that convert all the various different currencies into a numer rare or single base currency and for the sake of argument I'm going to just pick time zero dollars today as my base currency so in other words I want to convert every cash flow into the single currency that is today's dollars okay so in particular over the Course of T days days one through T how many different currencies do I have apart from my base currency of Time Zero money yeah I've got T different currencies T

dates every single date it's a different currency and I need to convert them in order to add them up okay so I'm going to argue that the cash Flow uh the sequence of cash flows cf1 cf2 dot dot dot if I want to figure out what it's worth in a single currency date Zero currency I've got to multiply the cash flows by the appropriate exchange rate what's the exchange rate the exchange rate is how many dollars at date one per dollar at date Zero how many dollars at date two per date zero dollar how many

dollars at date three per date Zero and so on I'll have t exchange rates for the T different kinds Of currencies that I have each currency is dollars denominated as of a particular date any questions about that pretty straightforward you think it's straightforward but you're going to have to think about it for a little while and do some problems to really make sure you appreciate this perspective all right now we're ready to talk about what this value operator is I'm going to argue that once you've got the exchange Rates across the various different currencies then

the value of the collection of cash flow is just the sum of all of the values of the cash flows denominated in the same currency but instead of currency meaning pounds or dollars or Yen the currency is going to be date zero dollar okay questions about this this is important now so I'm going to define something called The Net Present Value operator npv as the date Zero value of the cash flows now why is this called Net Present Value because typically when you are valuing uh an investment you have to pay some money UPF front

and then you get cash flows later on and so your net investment is going to be given by some summation of those pieces but it's not a a simple sum you can't just add the numbers that would be like adding 300 Yen to 150 Pounds or whatever you have to figure out how to convert all the currencies to the same unit of account dollars today and so that's why it's called present value that's the value at the present today and the reason it's net is your netting out any initial investment which is the cash flow

at Time Zero okay so v0 is equal to cf0 notice there's no exchange rate because we're doing it in today's dollars so that's the base Currency plus the cash flow tomorrow multiply by the exchange rate between dollars tomorrow and dollars today and so on if there's an initial investment then the initial cash flow is negative that just means you have to put money in to the project or the investment and then over the course of the next T periods you get cash flows which could also be positive or negative and you have to convert them

into today's Dollars and once you do you look at that number and you see whether or not you like it that's the value the net present value of the cash flows now I have one un unanswered question for you what's the unanswered question in all of this analysis sounds good right this pretty simple stuff but I pulled something out of the air what did I pull out of the air the exchange rate exactly exactly where do I get the exchange rates you should be asking me Where do you get the exchange rates and you know

what I'm going to tell you what what what's the answer I'm going to give you where do I get the exchange rates from the market exactly from the market I get it from the Market how do I get it from the market well we did it last time you know how we're going to auction it off you want to see how I've got a security that pays a dollar a year from Today pays a dollar a year from today who will offer me a penny for that piece of paper who will offer me 50 cents

for that piece of paper 75 cents 80 cents 90 cents 95 cents 97 cents 98 cents well all right 97 cents to the dollar there you go that's the exchange rate right there we're done by the way I appreciate that that's A lot of confidence in my creditworthiness it's only a 3% discount all right well that's the exchange rate between today and next year what about today and five years from now where do we get that from exactly the market okay I've got a piece of paper pays a dollar five years from now how many

people will pay me a penny for that we'll go through the whole motion and come up with come up with the same kind of process and we'll get a Number so the market now in a few weeks we're going to have to question whether or not that is a good way of getting the exchange rates I'm not going to talk about that just yet but that's where we get it from okay so I've begged the question a little bit but I think I've actually made some progress in providing a framework to think about valuation once

we establish the exchange rates you will agree with me that I can value any any cash flow whatsoever where the cash Flow payments are known with certainty in advance right so that's a pretty impressive achievement in the space of 45 minutes right we've actually figured out how to Value any cash flow whatsoever under perfect certainty given the exchange rates and I've told you where to get the exchange froms you get them from the marketplace that's why financial markets are so important it's because we require those inputs into our valuation process for Doing the analysis we

rely on financial markets if financial markets didn't exist we can't do this I'd have to wave my hands and say well you can get it from some kind of theoretical Source you just make it up just come up with some numbers that doesn't sound very compelling and in fact it's not the power of financial markets is the wisdom wisdom of the crowds and like it or not you're the wisdom that we're tapping on you know we're tapping your wisdom to Come up with these exchange rates okay so we know now that the value of a

sequence of cash flows is simply equal to today's dollars when you discount when you use these exchange rates to convert them to present dollars dollars today and that's often called present value notice that these exchange rates are sometimes called discount factors the reason they're called discount factors is because typically They are numbers that are less than one like what we saw today a dollar next year I was able to auction off for 97 cents today that number is smaller than a dollar because people are impatient a dollar today is worth more than a dollar next

year so if I promise you a dollar next year you're only willing to pay me a little bit less than that for that privilege okay so it's a discount over what it would be on the day that it gets paid yes what you Discounting like my that's a great question let me repeat it for everybody to hear the question is what are you discounting if there's no uncertainty why should a dollar next year be worth less than a dollar today because there's no uncertainty I've I've ruled out uncertainty right so there's no default risk it's

impatience people want to consume Now versus later and therefore if you're going to force somebody to consume later you've got to Somehow offer them some incentive to do that so in order for me to have you give me a dollar so that I can take the dollar now and I'll pay you back a year from now so that you can't consume that dollar today you have to wait a year to consume that dollar in order for me to do that I actually have to make it interesting for you which means you give me 97 cents

now and I give you back a dollar next year I pay you extra for that time that you Have to wait yeah also an arum that I my absolutely absolutely we we haven't we haven't talked about the mechanism for determining what that exchange rate is and I'm going to come to that but before we even talk about that I want to acknowledge that it exists and it's real and we can figure out what it is just from a simple auction a market and we can use it okay but I'm going to get to exactly what

it means and how we arrive at those exchange rates that's going to Be a very important part of this for inflation we know that comp1 today is less than1 that's right I'm going to get to that the end of this lecture that's another reason why there might be some kind of discounting it's not just the time preference that's right exactly yep so we're going to come back to that as well is there deflationary environment deflation can Occur negative real interest rates can occur during certain unusual periods of Economic Development so that's a possibility it's it's

not a possibility that we've seen in the United States in recent years but other countries have experienced that and when that happens there's some really serious repercussions so we're going to come to that in fact in 2004 the US government early on in that year was very concerned about the Possibility of deflation and it was only towards the end of 2005 that inflation became more of a concern so we're going we're going to come to that as well would you separate the concept of inflation from the time value of money all those two different fundamental

concepts yes I would and let's hold off on inflation for now because I don't want people to get confused by it it's something I'm going to bring in at the very end all right so I will come that To that that is a topic for uh for lectures two and three okay so we now know how to Value uh cash flows at least using this very simple framework with exchange rates and here's an example just a very very simple one where I've got the two discount rates or exchange rates for next year and the year

after it's 90 cents to the dollar and 80 cents to the dollar notice that the farther you go into the future the more of a discount These exchange rates require that's also human nature having to do with impatience and possibly inflation and other kinds of phenomena but we're and again I'm not going to tell you how we got those numbers I got them from the marketplace Okay now what's the net presson value of a project requiring a current investment of $10 million with cash flows of 5 million in year one and seven in year two

that's Trivial right here you go minus 10 million today 5 million next year but next year's dollars is not the same as today's dollars so you got to convert it to the right currency so that's 90 cents to the dollar multiplied by five and then 80 cents of the dollar multiplied by seven when you add it up you get 100 ,000 of today's dollars that's what this investment is worth so the first question is should you take this investment is it a good Project well let me ask you do you want $100,000 yeah if you

don't again see me afterwards I will help you with this problem remember the first day I told you that once you figure out valuation management is Trivial well I wasn't just kidding this is an example what we've been able to do is to take a problem what's the net present value of a project requiring the sequence of cash flows we've been able To take that problem that management problem should you do this or not we've been able to reduce that to a simple question do you want $100,000 I think the answer is yes so that's

the management part okay let's do this done the valuation part is the hard part the management part the decision is easy once you have the right numbers in front of you second question suppose a buyer wishes to purchase this project but pay For it two years from now how much should you ask for this project now the first thing you need to do is what well that's the second thing the first thing you need to do draw a timeline okay draw a timeline so you know exactly what's going on two years from now is that

next year or is that two years from today so draw a timeline and you can figure out once you have the timeline what the present values and Future values are okay so when you work out the numbers you can actually make a decision and figure out exactly what you ought to charge for that okay that's it for the time value of money but I want to summarize by telling you what we've learned so far we've learned that we can value cash Flows assets which are sequences of cash flows and the way we value that is

by making some implicit assumptions the assumptions are we know the cash flows in advance so there's no uncertainty about what the cash flows are second we know the exchange rates and if you don't know them go get them where do you get them you get them from the marketplace okay and finally there are no frictions in the currency conversions One thing you didn't ask me about is that typically when you go abroad and you have to convert your currencies what do you have to do you have to find somebody that converts it for you and

typically they will charge you a fee for that conversion right I've been talking as if the conversions happen without any kind of frictions that's an assumption that could be tested so we're going to talk about frictions later in the course but for now we're going to assume that There are no frictions okay now of course these are all hypotheticals they're all approximations to a much more complex reality but once we understand how the model works with these simplifying assumptions we can then go back and say okay let's make the assumptions more realistic and let's see

how that affects the implications so I'm going to first do the plain vanilla version of this and then after we fully understand it I'm Going to come back and make this more complex okay so for until lecture 12 that's a long ways away but until lecture 12 I'm going to assume that these assumptions hold and after lecture 12 I'm going to go back and systematically question and expand and revise each one of these so when I told you during the first day of class that you can't handle the truth this is what I mean we're

going to start simple and try to understand the Implications of these simplistic assumptions and then little by little we're going to make these assumptions closer to the truth okay now more examples once we understand how this exchange rate mechanism works we can look at all sorts of other alternatives to calculating value so in particular one question that you might ask that was asked is a dollar today should be worth more than a dollar In the future because of impatience because of inflation because of all the reasons we described but the bottom line is supply and

demand more people want money today than money tomorrow and so supply and demand bottom line dictates that there is this difference between the two so we can actually figure out what that difference is by looking at the exchange rates so in particular a dollar in year zero uh if you hold it for a year it'll turn into a dollar Times something the reverse of the exchange rate of a dollar in year one brought back to year zero but I'm going to write it in this format one plus something because remember when we're going the other

way when we have a dollar in year one and we want to figure out what is it worth in today's dollars that's a discount right it's a number less than one so if you want to go the opposite direction if I have a Dollar today and I'm I want to know how much is that dollar worth a year from now it should be greater than one in fact it should be the reciprocal of the exchange rate going the other way right instead of looking at pounds you look at Yen and so it's the opposite of

the same exchange rate but the way I'm going to write it is 1 + r because it'll be greater than one typically so R will be a number typically greater than zero what about for two years I'm going To Simply write it as 1 + r quantity squared and the reason I do that is because I'm thinking about taking that same growth rate and applying it two years in a row okay I could have written 1+ Z and Z then would be the rate of growth over a 2-year period but I like to think in

terms of annual frequencies so I'm going to just simply assume that the year is my unit of account and then looking at a one-ear 2year threeyear kind of growth period I'm going to Simply take powers of this Factor 1 plus r okay so a dollar in year zero is going to be worth a dollar times one + r to the teth power in year t this R is often called the opportunity cost of capital in fact there are like five different names for this R it's called the interest rate it's called the growth rate it's

called the cost of capital it's called the opportunity cost of capital John Mayor and KES called it The user cost there are tons of names for this quantity but the basic idea is it's the it's the reverse of the exchange rates that we were looking at before when we were trying to bring everything to today's dollar now the reason I'm showing this to you is because it turns out that we're going to want to move money back and forth through time and in order to do that we need to sometimes multiply and sometimes divide and

I want to come up with just One set of notation as opposed to all these exchange rates floating around so remember when we had T periods and I wanted to figure out what the value of an asset was today given T periods we had to have t exchange rates that's a pain in the neck to carry around t numbers and moreover there are exchange rates that you have to deal with between dates t plus k and t plus J so any two dates you got to have an exchange rate between them so pretty soon the

number Of exchange rate you got to keep in your head is ridiculous right that's why they came up with the Euro right to try to unify some of these exchange rates so here is a way to unify all the exchange rates into one number little r once you know little r you know everything you know all the exchange rates for every possible two dates that you care about now where do we get little r From exactly you're learning so we get it from the market now it's going to be a little bit more complicated than

that it turns out that the Market's going to give us many different RS so we're not going to get to that yet so for now let's just assume that the market gives us one R this R once you have this one number R it will allow you to do all of these calculations back and forth you can move money back and forth through time Because you will know what the exchange rate is between any two points in your cash flow sequence okay now that we have the r let's go back and figure out what the

exchange rates are what we were talking about in terms of bringing stuff back to date Zero okay and it turns out that there's a really simple form it turns out that a dollar in year one if you paid me a dollar in year one and I wanted to Figure out what it was worth today given this R number that I used it's actually just equal to a dollar divided 1 plus r so what's the exchange rate oh what's that oh that's not the exchange rate what's the exchange rate that allows us to take a dollar

next year and bring it to a dollar today it's one over 1 plus r one over 1 plus r remember R is a number greater than zero so one over 1 plus r is a Number less than one like 97 cents to the dollar so the exchange rate between next year's dollar and today's dollar is 1 over 1 plus r what about the exchange rate between a dollar two years from now and today what is that one over 1+ R squ that's right and so on so the exchange rates or discount factors are simply related

to the little RS in this Manner okay that's the mechanics and Mathematics of present value now this might seem intuitive and when I say it you might understand it or you might think you do please go back between today and Wednesday go over this and test yourself you know try to figure out for a given R if you have $100 today and R is 7% what is a $100 worth three years from now or if you have $180 three years from now and you want to figure Out what it's going to be worth not three

years from now but a year from now and the r is 8% what is it equal to test yourself by coming up with little examples to challenge your own understanding of this concept because it's going to be critical we have to get this right because everything that we build from here on in is going to rest on the foundations of these calculations okay now with these RS I'm Going to leave you with this one last concept which is that the value of the cash flows that we've been talking about at Time Zero is simply equal

to the cash flows multiplied by the exchange rates and now with this definition of little r this opportunity cost of capital this interest rate this uh discount rate we then have an expression for what this value operator ought to be right using this expression any cash Flow in the world can be valued under perfect certainty and and under the assumptions that we described any cash flow can be valued therefore any asset can be valued so what we've done in the space of a lecture is to create a valuation operator that works for virtually anything under

the sun in certain simplified circumstances that's a major achievement you can congratulate Yourself that we've reached this level but we're going to have to do some more work to think about how to use this so we're not done yet we have some additional analysis to do but this is a wonderful starting point next time we're going to focus on how to take this and apply it to two very very special cash flows an annuity and a perpetuity and you know what this is going to do this is going to allow you to figure out what

your mortgage payments are every month When you go apply for a mortgage you'd be surprised at how subtle that calculation is and how many Bankers don't know how to do it well you will all right I'll see you next time [Applause]