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visit MIT OpenCourseWare at ocw.mit.edu. ANDREW LO: So what I want to do

in this lecture is to provide a quick overview of

the equity business, and then talk about a couple

of simple but rather powerful models to price equities– we’re

using the exact same tools that we’ve developed– and then talk a bit about

growth opportunities and growth stocks. OK, so industry overview. What is equity? As I said, it’s an

ownership in a corporation. And typically, when you own

a piece of a corporation, you’re owning that

sequence of cash flows. There are two components

of possible cash flows for a piece of equity security. One is dividends. But, of course, we know

that there are companies that don’t pay dividends. Typically, companies that are

early stage growth companies, they want to conserve

their cash, because they’ve got lots and lots

of investment ideas that they want to implement. And so any cash that’s

generated internally, they’re going to be plowing

back into current operations. So growth companies typically

don’t pay dividends. But you still get value

from the security, because as the firm grows,

as the corporation becomes more valuable, that piece

of paper that you hold becomes more valuable. So in other words,

you get capital gains or price appreciation

of that piece of paper. And if you want to get value

out of that price appreciation, you could always sell it, right? So those are the two

ways of getting value. It’s dividends– and

by the way, there are two different

forms of dividends. Cash dividends or

stock dividends, both of which provide

additional value. But also the fact is

that you could sell it, and so you can get money

from capital gains. Now there are a couple of key

characteristics of common stock that are distinct from bonds. The cash flows we will

be able to analyze using the same tools, but

those tools will ultimately give us different answers,

because the legal structure for equities is

different than for bonds. And I have to say, that

whoever invented equities– this is many, many

centuries ago– really was a brilliant

financial innovator, because equities have just an

enormously powerful ability to provide proper motivation

and incentives for innovation, all sorts of innovation. And let me explain

what that means. First of all, one

aspect of equities that I think you

all probably know is that they are the residual

claimant to a corporation’s assets after the bondholders. In other words,

bondholders have first dibs on the assets of the company,

but their claim on those assets is only equal to the face

value or promised payments of that debt, right? They don’t have access

to any more than what the face value of that

bond is, as well as the coupons along the way. And to say that equity holders

are the residual claimant means that they get

everything else. Now you might say,

gee, that’s not really all that interesting, because

you’re second in line. Well, it’s very interesting

if being second in line means that you get access to

all of the upside of a company’s growth and success. I’m sure that you’ve all heard

of stories of entrepreneurs that have made many hundreds

of times what they put into a company, whereas the

bondholders may have gotten a handsome return

of 10, 15, 20%, but that’s the upper bound

as to what they can get. As a bondholder, your upside

is capped, it’s limited, OK? Whereas, as the residual

claimant, as the equity holder, you have no limit on

your upside, right? Because once the bondholders get

paid, you get everything else. Now the other aspect of

equity that’s really important is something called

limited liability– the fact that, as an equity

holder, the most you can lose is everything. Now that might not seem like

a good deal, but trust me, it’s an amazing deal. By everything, we mean

everything that you put in, so it’s not

literally everything. For example, you

don’t lose your life. You don’t lose your freedom. You don’t lose your pinkie. You don’t lose any other

body parts, or loved ones. All you are at risk of losing is

what you put in to the venture. So that’s what limited

liability means. And the reason that

it’s an innovation is, prior to the

modern-day corporation and limited liability,

it used to be the case that entrepreneurs

faced unlimited liability, or you could be put

in prison if you were to default on your obligations. The fact that there is a

downside limit to what you could possibly lose is a

tremendous boon to innovation, because now it means that

each and every one of you can go out and start

your own company and risk whatever money you

want to put into the company, but no more. And if it doesn’t

work out, well, you can walk away and do it again. And I suspect many

of you know of so-called serial entrepreneurs

that just go from one company to another to another. Many years ago, when I

was at the Wharton School, I heard a talk by the person

who started up Domino’s Pizza. I unfortunately don’t

remember his name, but he was giving a talk

in one of these CEO series and he’s a billionaire, because

of the incredible growth of Domino’s Pizza

in the country. And somebody asked

this fellow, how did you know that having

a national pizza chain was going to succeed

as well as it did? And he’s very honest. He said, you know,

I didn’t know. You know, this was

my ninth company. The first eight went bankrupt. And if this one

had gone bankrupt, I probably would’ve

started a tenth. And I think that’s just

a wonderful expression of the power of

modern capitalism and limited liability, because

here’s an individual that just really wanted to do

something on his own and wanted to make

a success of it, and was willing to

work his heart out time after time after time

until he hit upon something that was really valuable. And that’s the power

of limited liability. Think what innovation

would be if we decided that if your first company

fails, from that point on, you would never be allowed to

start a company ever again. Think how many people

would take the risk or take the plunge to do

something like starting up your own company. So the fact that we

have a security that limits your downside,

and that limits the downside of

other investors that want to join you in

your venture, really allows for capital

formation to occur at a rate and at a scale that would

be impossible without it. Now there’s also voting

rights and the ability to access public markets. What that means is

that you can actually get other people, large

numbers of people, to co-invest with you. So that’s particularly

important when you’re thinking about taking on

very, very ambitious projects. For example, if you want to

start up a biotech company. Biotech companies require more

than a few hundred thousand dollars to get started. I think a few hundred

thousand dollars would maybe buy you a quarter of a

centrifuge these days. Doesn’t really help for

starting up a biotech company. And so if we didn’t

have the ability to access public markets, if

we didn’t have the ability to bring the power

of the public to bear on a particular

investment opportunity, it wouldn’t get done. So that combination of

limited liability and ability to access public markets,

and then voting rights that give investors some say

in how the company is run, is really the

secret to unlocking the power of the masses for

development of innovation and capital formation. Now there’s another point

that I wanted to make here, which is short sales. I think that by

now you should have an appreciation for the

importance of short sales. Short sales allow information to

get into the market price that may not be positive

news, but is nevertheless important for people to have. And so the ability to

short sell a security is a method for

allowing investors to get information

into the market price as quickly and as

easily as possible. Those of you who participated

in the trading game that we did a couple of

weeks ago on that Friday– you know, when we go over

the results towards the end of this course, when we talk

about efficient markets, I’m going to show you

that the prices that occurred in that marketplace

was not very efficient. Part of the reason that

it wasn’t very efficient is because we didn’t

allow you to short sell. And so those of you who had the

information that at one point the stock was worthless,

the most you could have done was to divest yourself of

shares that you already owned. But once you did that,

that was the end, and you’re out of the market. You couldn’t do anything more. If, on the other hand, we

allowed you to short sell, you would have driven that

price down to 0, where it belonged at that point. And so the ability to short

sell is a very, very important aspect of capital

market efficiency and for making prices as

informative as you can. Now there are two markets

for equities– primary market and secondary market. Primary market means the

market where securities are issued for the very first time. Primary, that’s

what primary means. Secondary you could think of as

the market for used securities. We have a market for used cars. You have a market

for used homes. And there’s a market

for used securities. I know you don’t really think

of the New York Stock Exchange as such, but, in fact, it is. It just turns out that

used securities are just as good as new securities,

and in many ways, better. And so the steps for getting

a primary security issued is very different than

the steps for dealing with secondary markets. For the most part,

what we’re going to be talking about

in this course is secondary market

transactions and dynamics. However, there is

obviously a lot more to be said about

primary markets. I’m going to leave that to other

courses in the Finance group, including M&A and capital

budgeting and venture capital. Those are courses that

deal with the dynamics of the primary market. These are the markets

that you would care about if you’re doing an IPO,

launching a new company, and issuing securities

for the very first time. So I won’t spend too

much time on that. If you’re interested,

you’re welcome to read the relevant chapters

in the textbook. But what we’re going

to do is to focus on the behavior of

secondary markets, in particular, in

the price formation mechanism for secondary

market securities. Here’s a little bit

of a summary about how these markets have developed. You can see that

for primary markets, the IPO market goes

through cycles. There are periods where the

market’s very, very active, and there are periods where

the market is pretty quiet and not a lot is going on. That has to do a lot

with the business cycle and with the credit cycle– how

much money there is out there. And it’s obviously very

important for those of you who are thinking

about doing startups, because when you do a

startup and you get funding from a venture capitalist,

the way the venture capitalist ultimately

gets paid is not by the satisfaction of being

part of your wonderful company, but rather by having

your company go public and having securities be

issued so that the venture capitalist can cash out at

those public market prices. So the venture capital

and technology industries are very much caught up in the

business cycle and credit cycle as well, and so this

gives you a little bit of a picture of how

that’s changed over time. On the other hand,

the secondary market has a somewhat different

set of dynamics. It’s related, but not

nearly as highly correlated as you might expect. This is an example

of the dynamics of public secondary

markets, the NYSE and NASDAQ over the last few years. What this displays is

the trading volume, both measured in terms

of shares as well as in composite fraction

on the NYSE volume. And you can see that

over time that the share volume, the amount

of shares traded, has just gone up year

on year, and this year will be no different. 2008 will be a tremendously

significant year for the amount of shares

traded on the exchange. Lots more participation in

public markets, and the volume, while there may be little bits

of a dip that are functions of business cycles,

not nearly as sensitive as the primary market is. Yeah. AUDIENCE: Is the internet

also, you know, more volume? ANDREW LO: Oh, absolutely. Well, there are a number of

technological innovations that have made this market

increase so quickly. So the internet is one. Now all of us can

trade on the internet. In fact, when I was teaching

Finance back in, let’s see, was it 2000 or 2001? I remember during

the middle of the day one of the undergraduates

in the class looked at some kind of cell

phone device and then ran out. And he came back in shortly

before the end of class, and at the end of

class I asked him if everything was

all right, because he seemed really distressed. And then he said

that he just had to respond to a margin

call on his equity position that he’d put on the day before. This is an undergraduate. He’s trading on his

little cell phone. That’s a technological

innovation that has actually increased

the volume in these exchanges. But there are other

technological innovations as well. For example, something called

ECNs, electronic communications networks. These are– essentially, they

started out as bulletin boards, where large buyers and

sellers of equities could come together

anonymously and transact with each other at relatively

inexpensive prices. They can cut out the middleman

and reduce the bid offer spread by hitting a transaction price

that was right in the middle. ECNs have grown tremendously

since the early, the mid 90s, when they started,

and now account for a pretty significant

fraction of the volume. Electronic order routing,

electronic trading, all of these technologies have

caused this kind of increase in the equity market trading

over the last several years. So today, as an

individual investor, you can trade much more quickly. You can trade much more cheaply. And you can trade much more

easily than ever before. So consumers have

benefited a great deal. Along the way, a number of

hedge funds and other investors have ended up going out of

business because they have not been able to compete

effectively with these kind of technological innovations. And this is what I mentioned

last time, that technology plays a very important role

in financial markets now, much more so than ever before. It used to be that it

mattered who you knew, rather than what you knew. That it was the old boys

network that mattered, instead of the computer network. And that the graduates

of Harvard and Yale had an advantage over the

graduates of MIT and Caltech. That’s been flipped

on its head now over the last several years. It’s what I call the revenge

of the nerds, which bodes well for all of you. [LAUGHTER] OK, so let me now turn to

the very first valuation model that was ever

developed for equities. It couldn’t be simpler. It’s a model that

I think all of you are going to

immediately understand, and yet the

implications are going to be really far-reaching

and profound. This is called the

Dividend Discount Model, and it starts with

the recognition that, when you invest in a

company, what you’re getting for that piece of paper,

this common equity, you’re getting the rights

to the flow of cash forever. And what kind of cash

are we talking about? Well, we’re talking

about dividends. So it’s true that not

all stocks pay dividends, but eventually you would figure

the stock will pay dividend at some point, right? For years, Microsoft

never paid a dividend. But about, was it five

years ago or six years ago? They announced that they’re

starting to pay dividends. Why? Because they had

accumulated so much cash that they didn’t have enough

things to invest that cash in, so they figured, let’s give some

of it back to the investors. In their early days, they kept

every penny of their earnings to reinvest, because they had

so many different opportunities to take advantage of. But because they

became so mature and they had already a

number of investment projects that were quite

valuable, and yet were still generating

so much cash, they decided to return

some of it to investors. So at some point, you’re

going to get dividends. And if a company never,

ever pays dividends, well, then, it should

be worth 0, right? If it pays you no cash

forever, then that seems like a very bad asset. Yeah. AUDIENCE: What stops the

board of directors [INAUDIBLE] really depends on [INAUDIBLE]

issuing dividends [INAUDIBLE].. ANDREW LO: Well, first of

all, if they issued dividends to pay themselves,

that’s fine, as long as they pay all the other

shareholders at the same time. So the answer is, in

principle, nothing stops them, but what makes them

decide against that is if they have uses

for the cash other than paying themselves. If, as a company, you have no

idea what to do with the money you are generating,

well, first of all, that suggests that

maybe you’re not doing your job,

because as a company, you’re supposed to be coming up

with valuable ways of earning money for your investors. However, it may be that your

company is very mature, stable, there’s no growth,

there’s nothing going on, and all the cash that

you’re generating you don’t know what to do with. In that case, you may very

well return all of that money to investors. That’s nothing wrong with that. The idea behind

having a vote though, is that you want to make sure

that the board of directors, who typically do own or are

responsible to shareholders that own large blocks of shares,

will be deciding in the best interests of the shareholders. And it could be that the best

interest of the shareholders is to give them

back their money, because we, the mature

company that we are, don’t have any other

uses for the money. Yeah. AUDIENCE: [INAUDIBLE]

that, if the company never pays dividends, [INAUDIBLE]. What about the [INAUDIBLE]? Is there no value [INAUDIBLE]? ANDREW LO: Well,

but think about it. If a company keeps on

appreciating in value, but never pays out a dividend,

what’s happening to the cash? You know, when I say

never, I mean never. So I don’t just mean like

in 10 years or in 20 years. I mean never. So can you think

of a company that appreciates in

value all the time, but never, ever,

ever pays a dividend? There’s no cash, so

you’ll never get any cash. That’s– AUDIENCE: Well, then,

wouldn’t you make a profit by selling [INAUDIBLE]? ANDREW LO: Oh, yes, you could

make a profit by selling, but if you sell a

security to somebody else and they know for a

fact that it never, ever, ever, ever pays any

money, well, then, that’s called a

Ponzi scheme, right? In other words, you’re

selling a piece of paper that’s worthless to

somebody and hoping that they are a bigger fool than

you are for having bought it. So when I say it never pays

any cash, I really mean it. If it never– if you know

for sure that it never, ever pays any cash, then it can’t

be worth anything, right? If you don’t believe that,

then I have a piece of paper that I would like you

to take a look at, and I would like

to sell you, OK? Yeah. AUDIENCE: Could it be like

coupons and, like, the company dissolves? ANDREW LO: What’s that? AUDIENCE: Even if it

never pays dividends, you could still

get something back if the company

dissolves [INAUDIBLE].. ANDREW LO: Well, then

it does pay something. That’s a liquidating dividend. Then that violates my

condition that it never, ever, ever pays anything, right? And that’s the point. If the company is

growing and it has value, then you know for a

fact that either A, it will pay you a dividend

at some point, or B, if it doesn’t and

it gets liquidated, then when it gets

liquidated, you’ll get a pro rata

share of whatever’s in the company, in which

case, that’s a payment. So to say that a company

never, ever pays a dividend, I literally mean it will

never, ever pay anything, OK? And in that case, it

can’t be worth anything if you know that. But if you can find somebody

who will buy it anyway, then that’s an example

of an arbitrage. That’s a free lunch. And so you can do that a lot if

you can find people like that. OK, so we’re going to apply

the very basic principles of present value analysis to a

security that pays dividends. So let’s let the

price of a stock, Pt, today, be given by that. Let Dt be the cash dividend

that gets paid at time t. And by the way, Dt could

be 0 for many, many years and at some point become

positive, all right? Dt can never be negative, right? We’re not talking about

taking money from investors. It pays either a

positive amount or 0. And I’m going to let E

sub t be the expectation operator at time t. So now I’m going to

explicitly recognize that these dividends are

not known in advance. Unlike bonds, where you

know the coupons in advance, I don’t know the

dividends in advance. So I’m going to have to guess. I’m going to have to make a

forecast as to what they are. And let me let r sub t be the

so-called risk-adjusted return that is commensurate with the

risks of the dividends that are there. I’m going to wave my

hands at this point as to how we get the

dividend discount return, the appropriate

risk-adjusted return, but I’ll come back to that in

a few lectures, when we go over methods for determining the

appropriate risk adjustment, OK? But for now, let’s

assume that we have it, and we get it from the

marketplace, right? Just like we got the yield

from the marketplace, it’s a sum total of

everybody’s fears, expectations, hopes, and so on. So with these

components defined, I’m now going to simply write

the price of my instrument as this value function of

the future cash flows, right? That’s the most

general expression we started with on day one. And given what we now know about

present value and valuing cash flows that come in the future,

it’s not a big leap of faith to put some structure on

this valuation operator, OK? The value of this sequence

of future cash flows is simply equal to the

expectation today, time t, of future dividends out

into the infinite future, discounted back by the

appropriate risk-adjusted rate of return. Now you’ll notice that the

rate of return, this r, I put a subscript, t, plus

1, and t plus 2, and so on. I’m explicitly

recognizing the fact that the appropriate

risk-adjustment changes over time as market

conditions change and as the business changes, OK? So it could be that the

risk-adjusted return for a one-year

cash flow is this, but the risk-adjusted return

for a two-year cash flow is different. Just like we have a yield

curve for riskless bonds, we may have a yield curve

for risky cash flows, OK? And if I really wanted

to be a masochist when it comes to notation,

what I could do is to have a double

subscript that says that this is the

appropriate risk-adjusted return between years

t and t plus 1, and then this is between

years t and t plus 2, and so on, because these

discount rates may be completely different tomorrow. In other words,

tomorrow’s discount rate for a one-year cash flow may be

different than today’s discount rate for a one-year

cash flow, right? So I can have a whole string

of discount rates for today, and a completely different

string of discount rates for tomorrow and for

every day in the future. These things change

all the time. I think you’ll see now why I

told you earlier equities is a lot more complicated than

fixed income instruments. It’s because there are two

sources of uncertainty. One is the discount rate, and

the other is the cash flows. And moreover, the discount

rate that we’re talking about, it’s not the risk-free

discount rate, but it’s the risk-adjusted

discount rate. And if risks change over

time, as certainly they have over the past

even few days, then the discount

rate should change. So in addition to

the term structure effect of different

yields, we also have the risk effect of looking

out into the future, given current market conditions. So while this

expression is tidy, and it looks nice

and clean, in order to turn this into

an actual number that you can look

at and decide, gee, do I want to invest

in this stock? Is it undervalued or overvalued? It’s going to take

a lot of work. So before we get to

that work, I want to spend some time thinking

about simpler things, and try to come up with

relatively simple implications of this relatively robust model. Question? AUDIENCE: Yes, sir. Does rt take into

account the riskiness of the company itself, or

is it of the marketplace? ANDREW LO: The answer is yes. It’s both. It’s the riskiness

of the company, as well as the riskiness

of the aggregate set of market conditions. It’s both. And so we have to figure

out how that factors into this equation. That’s going to take us a

few lectures to get there. But the answer is both. Yeah. AUDIENCE: Would you

say it’s related to the riskiness of the

expectation of the dividend being whatever it is at time t? ANDREW LO: Well– AUDIENCE: If I were to know that

the first dividend is absolute certain, but after

that, not so much, then could I replace rt

with a risk-free rate, but rt plus 2 with something

else, and so forth? ANDREW LO: Yes, assuming

that that dividend really was risk-free. Yes, that’s right. So the idea behind

the discount rate– and, by the way, I’m going to

ask you to explain this to me. So I’m going to

make a statement, and then I’m going to ask

you to justify it, OK? The statement is this– the discount rate that’s used

in the denominator of each of these fractions,

that discount rate has to be risk-adjusted

in a way to reflect the risks of the numerator,

as well as general market conditions. It has to be commensurate

with the risks of that particular numerator. So if this numerator is much

less risky than this numerator, I would argue that

you would have to use a different

discount rate, one that’s higher for the

more risky numerator than for the less risky. Now justify that for me. Why is that a reasonable

thing to want to do? Yeah. AUDIENCE: Because you’re getting

more return on [INAUDIBLE].. ANDREW LO: That’s right. AUDIENCE: Your discount

rate would be [INAUDIBLE].. ANDREW LO: That’s right. You get more return

on your capital for something of

greater risk on average, because you’ve got to be

rewarded for bearing that risk. And if you’re not

rewarded, you’re not going to take on that risk. How do you know that? How do you know that you’re

going to get rewarded for taking on that risk? Where did you get

that from, besides me? AUDIENCE: That’s just the law

of the jungle, I don’t know. [LAUGHTER] ANDREW LO: You’re right. It’s a law of the jungle. But in this case,

what is the jungle? AUDIENCE: [INAUDIBLE] ANDREW LO: Exactly, thank you. The market. Excellent. The market. The market is the

jungle from which you compete for scarce resources. And in order to get

your pet project funded, you’ve got to provide the

right incentives for people to buy into your project. So that’s the logic

of the justification. Now let me go one

step farther and say, suppose that you want to

replicate these cash flows. Suppose that you want to create

a portfolio that gives you these kind of cash flows. Well, then, you’ve got

to go to the marketplace and figure out what the

appropriate opportunity cost is for each of those cash flows

and then discount them, because that’s

what the market is charging for those cash flows. So that’s why you have to

get the appropriate discount rate matched to the appropriate

cash flow, all right? It comes straight out of what

we learned about bond pricing, but now we’re adding an

extra dimension– risk. And I’m not going to be able

to talk about it in any more detail than this until we put

more quantitative structure on what we even mean by risk. I mean, you all take for

granted, when I say risk, you say, yes, you

understand what risk is. But in order for us to justify

a particular expression for how to make that kind

of adjustment, we have to be very specific

about how to measure risk. So in about three

or four lectures, I’m going to actually propose

a method for measuring risk. And once we have

that method in hand, we can then make that

risk adjustment extremely explicitly. I’m going to give you a

formula that you can actually compute in an Excel spreadsheet

that will tell you exactly whether the number should

be 6.5% or 7.3% or 8.9%. You’re going to actually

see how to do that yourself. Yeah. AUDIENCE: The score

wasn’t implying that those time structured

to when dividends paid out. Like, the time between

t plus 1 and t plus 2 doesn’t have to be the same

as t plus 2 and t plus 3. ANDREW LO: Correct, correct. It doesn’t have to be the same. And if it’s not the same,

then the difference in horizon should be reflected by the

implicit size of that discount rate. Yeah. AUDIENCE: [INAUDIBLE]

the company’s bond yield [INAUDIBLE]? ANDREW LO: Well, you tell me. Can we use the

company’s bond yield to use as a discount

rate for the equity? Well, that depends. It depends on whether or

not the equity and the bond are of comparable risk, right? Remember, it’s not

the company that determines the discount rate. It’s not the company– or rather, it’s not

determined by fiat, or by announcement of a

company’s particular policies. What determines the

yield is the riskiness of that yield and

the marketplace. The market determines

that particular price, not the individual, or not

the sources of those funds. AUDIENCE: Whenever [INAUDIBLE]

of the company’s bonds do not reflect on

the company’s equity? ANDREW LO: Oh, of

course, they do, but they reflect in

a very specific way, and we’re going to

talk about that when we get into capital structure. Companies that have

very high leverage are going to have more

risky equity than companies with very low leverage. So the leverage does have

an impact on the equity. We’re going to come to

that in a little while. There is a

relationship, all right? But for now, let’s look at

these securities in isolation and not worry about it. And I’m going to keep

coming back to the idea that it’s not the company that

gets to determine the discount rate, but rather it’s

the company’s riskiness– or rather the riskiness of the

cash flows and the market’s assessment of the cost

of that riskiness– that determines

the interest rate. A few years ago, there

was a faculty member at Carnegie Mellon

who won a Nobel Prize, and it ended up that he

was one of the highest paid professors at the time. And so he was being interviewed

by the school newspaper, and they said,

Professor So and So, do you think it’s appropriate

that even though you won a Nobel Prize,

that you should get paid twice as much as some

of the other faculty who are Nobel Prize-winning

physicists and fields medalists in the Mathematics

department, and so on? I mean, do you think it’s

fair that your salary is twice as high as other

people in the school? And the faculty member, who is

an economist, said, listen son. The university does not

determine my equilibrium salary. They only determine

what city I work in. In other words, the

salary of an individual is not determined by that

particular institution. It’s determined by

the marketplace. The marketplace bids

on that faculty member, and the highest

bidder, presumably, will be able to get

that faculty member. The same thing with

these cash flows. It’s not the company’s

debt, or the company’s weighted average

cost of capital, which we don’t know

what it is yet, but I’ll define a

little later on. It’s not the company

that gets to choose what the discount rate is. The question is, given the

riskiness of that cash flow, what does the market tell me

is the fair rate of return for that cash flow? That’s the number I want to

plug into that denominator. Yeah, question. AUDIENCE: The market may

determine the discount rate, but the company determines the

growth rate on the dividend, right? They get to decide

what the dividend is. ANDREW LO: Well,

they get to decide what the dividend is

subject to their ability to pay that dividend. But if it turns out that

they make a bad decision, and they pay out

all the dividends, and they have no more

money, and they can’t grow the company

anymore, then who determines what’s worth what? Ultimately, the market. The market is the final arbiter

in all of these calculations. At least that’s the

theory of finance. That’s the basic, plain

vanilla, frictionless model, OK? It’s the market that determines

these interest rates. Later on, after we

go through the basics and you understand the

frictionless model, I’m going to

introduce frictions, and then you’ll see what

impact corporate policies have on these implications. In some cases,

corporate directors can actually do a lot of harm

by making suboptimal decisions that go against the market. In other cases, you could argue

that corporate decision-makers know more than

the market and are able to make bets that the

market is not capable of doing. That’s certainly possible,

because who knows the company better than you do? Although a market

expert would say it’s not knowing the

company that will determine the value of the company. It’s knowing how

that company compares to all the other companies that

are out there that determines the value of the company. And you, as the

corporate insider, may know your

business very well, but you don’t know

how you stack up against the 25 other

businesses in your industry, and we, the market, know better

than you, the individual. That’s the argument that

would be made against that. AUDIENCE: In the case

of refinanced stocks, can I use the same formula? ANDREW LO: We’re

going to get to that. We’re going to talk

about preferred stocks. That’s a separate issue. Preferred stocks have a

different priority of claim, and that’s going to require

some slightly different modifications to this formula. Yeah. AUDIENCE: So I had a question

about the expected value. So yesterday in the example,

you discounted the 1,000 to 900 [INAUDIBLE] Et. So what else do you need

to discount in the r to account for the risk? ANDREW LO: Well,

I mean, you have to take into account the fact

that there are other competing opportunities for this

particular project in the marketplace. And so it’s not just the

risk of this project, but rather how the

risk of this project stacks up against the risks

of all other possible projects that you would be competing

for in the open market. Let me put it to you this way. Let’s do a simple

thought experiment. Suppose that instead of

these as being dividend streams for a given company,

let’s do the following thought experiment. Let’s imagine doing a strip, OK? You all know what

strips are now, right? So let’s think about

stripping out dividends, OK? It’s a very weird thought

experiment, granted, but just bear with me. Let’s suppose that

instead of one company, I generate an

infinity of companies. Each company lives only

for one dividend payment, after which it gets liquidated. So each of these cash

flows, Dt plus 1, Dt plus 2, each one of these things is

a separate and independent company that gets

liquidated right after it pays the dividend, OK? Now how would you

value a portfolio of all of these companies? Well, you would do this, right? For each company,

you would figure out what the appropriate

discount rate is, and the appropriate

discount rate reflects not just the

time value of money, but the appropriate

riskiness of that cash flow. For example, if I took

that company– let’s actually do a thought

experiment of how we do that. Let’s go through

the motions, OK. I’ve got a piece of

paper that is something that funds nanotechnology in

a very specific application. And this company

is going to require a certain amount of

investment, and then it’ll pay off all of its

earnings in 2013, December, and then it’ll liquidate

and be done with, OK? That’s the company. How do I figure out the

price of the company today? Anybody? How do I figure out the price? I have this piece of

paper that says in 2013, the company will

liquidate, and I want to know what the price is. What’s the first thing you

would do with that proposal if you got it in the mail? What would you want to know? Yeah. AUDIENCE: I would want

to know, like, if there’s a security I can

buy in the market, is the company

going to pay for it? Because it’s the same

risk return profile. And I look at the

marketplace for that. ANDREW LO: Why

would you do that? AUDIENCE: Because

there’s no reason I would go through the hassle,

or friction, as you call it, of pricing a new

company if I could just go online and buy it. ANDREW LO: Right,

that’s one logic, but another logic is that you

have money looking for a home. You can put it in

this new venture, or you can put it in

this existing company. And if they’re

comparable, then at least you have some sense

of what it’s worth. Exactly. In order to figure

out whether or not you can get a

comparable security, you need to know what the cash

flow is for that nanotechnology startup, right? So you might think first about

estimating the expected cash flow in the liquidating

dividend in 2013. OK, so you calculate the

numerator, all right? And you find a company

out there that has that same kind of cash flow. You have to find one that

has the same profile, so it does it in 2013, at

which point it gets liquidated. But let’s even forget about– suppose we didn’t

have such a company. Suppose we didn’t have

an existing security. So this is literally

a fresh start. You’ve got a piece of

paper that gives you the claim to a company that

liquidates in 2013 with one cash flow only. And now you’ve estimated

that cash flow to be approximately $27 million, OK? So now you’ve got the numerator. A piece of paper that

pays $27 million. How do you figure out its price? What would you do? Yeah. AUDIENCE: Calculate the risk

that it’s going to [INAUDIBLE],, also you have the

time [INAUDIBLE].. ANDREW LO: OK, and

you’ve done that, and that’s the $27 million. AUDIENCE: That’s included

in the valuation. ANDREW LO: Right,

the $27 million includes the probability

that it actually is 0, so the expected

value is 27 million. How would you go about– yeah. AUDIENCE: Wouldn’t it

actually be two [INAUDIBLE],, so when the 27

million liquidates, you get the value of the assets? ANDREW LO: The liquidation value

is the 27 million on average. AUDIENCE: [INAUDIBLE]

two payments for that. ANDREW LO: No, no, no,

it’s just one payment– 27 million on expectation. Oh, it may be two possibilities. Maybe you either get 54

million with 50% probability, or nothing with 50%

probability, so the expectation is 27 million. What would you do? Yeah. AUDIENCE: I think

if you’re already weighted in the probability

[INAUDIBLE] 0 [INAUDIBLE] ANDREW LO: Suppose you

don’t know what to use. Suppose you want to figure

out what the price is. AUDIENCE: [INAUDIBLE] discount. ANDREW LO: Yeah, I

know what you mean. But suppose that you

didn’t have that. What would you do? AUDIENCE: [INAUDIBLE]

at the yield curve just to get an idea of

what in 2010, at least either a risk-free

security or a security with that same credit risk. You know, what discount

rate that would go in there, discounting by that [INAUDIBLE]. ANDREW LO: You could

do that, but now we’re getting more and

more complicated. Isn’t there an easier way to

figure out what the price is? Exactly. You know, let’s let

the market decide. Auction it off. Now when you auction it off, you

take the highest bidder, right? And you get a number. I don’t know what

that number is, but let’s just say the number

is, I don’t know, 15 million. You’ve got somebody who’s

willing to pay 15 million today for a cash flow that

gives them expected 27 million in 2013. With those two numbers, that

gives you r, doesn’t it? That’s how r is established. It’s established

the exact same way that we establish r

for riskless bonds. The way that US

treasuries ended up being three basis points

on September 18th was, basically, tons of people

wanted to buy these securities, bidding down the yield

and bidding up the price. So if we had this piece of

paper that paid only one dividend in 2013 and

we auctioned it off, we would get a yield. The yield would be a

risk-adjusted yield. I don’t know how the

risk adjustment got made. So you could be quite right that

you take the risk-free yield, and you add on top of

that a credit spread and who knows what. The point is, the market

did it for us, OK? So what I’m getting

after with this formula is I want to use those discount

rates that are determined by the marketplace. Because if ever I have

to sell my company, if ever I have to

take this company and break it apart

and get rid of it, and the market is

going to pay me for it, the way that the market

is going to evaluate the different pieces is just

the way that I described. It’ll look at each cash flow,

look at how risky it is, look at the opportunity

cost of other investments that they can get the same

risk return profile for, and they’ll pay that amount,

which will implicitly give me the appropriate yield. Yeah. AUDIENCE: So let’s

say that me purchasing a stock with this

calculation, do I have to assume that

this calculation is wrong? Because why would I pay

out money for something that’s going to be exactly the

same, kind of discounted, cash flow back to right now? ANDREW LO: So

that’s a good point. Let me repeat the question. The question’s why– in order

for you to buy the stock, would you have to

assume that this is wrong, or rather, that

the market price is not equal to this? Well, the answer is

no, you don’t have to. Although if you did, that would

provide a motivation for you to want to do that. But it could be that you

simply want the risk and reward of this particular cash flow. What’s wrong with that? Suppose that the security

is fairly priced. So this equation

at the very bottom says that the price

of the security is equal to the present value

of all the future expected cash flows discounted at

the fair rate of return. That’s a perfectly

reasonable thing for somebody to

want to invest in, if they like that kind of

risk/reward combination. So some people want to

put their money in Google, and some people want to

put their money in IBM, and some people want to put

their money in US Steel. Those are different

companies that have different rates

of return based upon their different

risks and cash flows, and even if those things

are fairly priced, it’s not like you’re

going to make no money. You’re going to make money

based upon the fair market rate of return for that security. Now if you think you’ve

got a better mousetrap, and you can identify

mispriced securities, that gives you a whole

another reason for investing. But even without

any mistakes being made, even with if market

prices are perfectly fair, people want to

invest, because they want the return that

those kind of investments give them, right? OK, so let’s consider

some simple cases. In order for us to really make

use of this formula, which at this level of generality

really is useless, let’s try to simplify

and see what we get. And we’re going to

simplify in the ways that we’ve done before. Let’s assume that dividends

are fixed throughout time, and given by a number D, OK? And let’s assume that the

risks don’t change over time and are given by

a discount rate r. Well, if you fix D and you

fix r, magically, what you get is that the price

of the security is equal to our old friend, the

perpetuity formula, D over r, OK? Not that surprising. If you have a constant

stream of dividends, with a constant discount

rate, then the price is equal to D over r. Now, again, this may seem

totally trivial to you, but it does provide a very

interesting observation. Number one, the

price of common stock is an increasing function

of the expected cash flows in the form

of future dividends. So if you expect there to be

higher dividends going forward, the price should

go up, and if you expect lower dividends

going forward, the price should go down. So that’s a nice insight. Another insight, though, is

that the price of a stock is inversely proportional

to its discount rate. If interest rates

go up in general, if interest rates

go up, what should happen to the stock price? AUDIENCE: [INAUDIBLE] ANDREW LO: Exactly,

it should go down. There are two ways

of thinking about it. One is that future

cash flows are going to have to be

discounted at a higher price. Or two, the demand

for stocks will not be as great, because now the

opportunity for earning higher return exists in other

securities like bonds, and so that will reduce

the demand for stocks and the price will

come down, right? So that’s a very

nice model, but we can make it a little

bit nicer by allowing the dividends to grow. So now suppose you have a

growth company, a company where the dividends are

expected to grow at a rate of g every period. Well, then, once again, we have

our old friend, the perpetuity, with growing coupons, right? D over r minus g. And now, as I think I

alluded to early on when we went through this formula, we

have in this very, very simple expression one explanation

for the technology bubble, both how it got so big,

and secondly, how it burst. If r is close to g, if the

growth rate is very large, you’re going to get

a very big price. And if there are rapid changes

in what people expect g to be, or what people

estimate g to be, you can get very rapid shocks

in the level of prices, including price one-ups

and then crashes, right? Yeah. AUDIENCE: What kind of confuses

me is that, I mean, yeah, so is r greater than g? And r greater than

g is necessary in order to get that

[INAUDIBLE] efficient. But is there any

more meaning to that, or is this just a

mathematical thing? ANDREW LO: There

is meaning to that. The meaning is

actually quite simple, and we alluded to

it when we first went through this formula. Suppose that r were

not greater than g. Suppose r were less than g. What that’s telling you

is that the rate of growth of this security, or this

cash flow, or this dividend, the rate of growth is much

faster than the interest rate, all right? So you’ve got wealth that’s

growing over time faster than the interest rate, which

means that if it really is true that it’ll last out

into perpetuity, then in very short order you

should become bigger than the entire

planet’s GDP, right? Because you’re going to be

bigger than the interest rate. So the rate at which

assets in the future are being deflated

to the present is actually less

than the rate of what you’re growing your wealth. Pretty soon, you’re going to

become richer than God himself, and we know that

that can’t happen. AUDIENCE: But isn’t it that– I mean, so right now,

the inflation rate is greater than the interest

rate, for example, right? ANDREW LO: That’s right now. That’s right now, but this

is out of the perpetuity. Do you believe that

that’s sustainable out of the perpetuity? AUDIENCE: No. ANDREW LO: Well, then,

this formula doesn’t work. This formula is a formula

that’s predicated on infinity, not 10 years, not 20 years. As we mentioned, when we

went over the formula, China has been growing at a rate

of 10% for the last 15 years. Do you think 10% growth

rate is sustainable? If China continues

to grow at 10%, pretty soon we’re all going

to be speaking Mandarin. I mean, it’s just not

possible for a country to both be reasonably-sized

and not totally dominant, and to have a rate

of growth so much larger than what

can be sustained over a long period of time. And so that’s the key. This is a formula

that’s about infinity. It’s not about five

years or 10 years. OK, another question. No. OK, so in this case,

the Gordon growth model allows us to get an

expression that tells us if there are very,

very significant growth opportunities that

can actually push up the price of a

stock dramatically. If somehow all of us decide that

those growth opportunities no longer exist because we have

new information, then boom, it disappears, OK? A good example of

this is cold fusion. I don’t know how many of you

remember, 15 or 20 years ago, there was a big controversy

about the Pons and Fleischmann experiment, where they did

an experiment where it seemed like they generated heat,

but heat not from a chemical reaction, but from

a nuclear reaction in a standard

laboratory setting. And typically, you need

very, very unusual conditions to generate thermonuclear

reactions that can create that kind of heat. Now in the end, they were

discredited and, apparently, although there’s still

controversy out there, it doesn’t seem like it

was a nuclear reaction. But if it were, if it

was possible to generate a nuclear reaction at room

temperature, what that could have meant is that

it would eliminate all of the energy

problems of the world, because you’d be able to

run your car on tap water. And the amount of energy

in an ounce of tap water is enough to fuel your

car for about a year. So think about it. If that technology really

worked to have worked out, what do you think the

value of that would be? What’s the g in that case? And you can

understand why people would have invested hundreds

of billions of dollars into that kind of

an opportunity, if it were, in fact,

a real opportunity. There was a short time

where we didn’t know, and during that time, r

minus g looked pretty small. g looked big relative

to r, all right. And so that created

very, very large swings in prices of both

traditional energy companies like oil companies. You can imagine what oil

companies would be worth if we figured out how to

run cars on water, right? That would maybe be justifiable

in light of how much they’ve made over the years. But the point is that it

creates enormous opportunity and potential dislocation

so that the expectations of the market matter a

great deal, and this is why. This is how it actually

gets incorporated. Now I’m going to

take that equation and turn it around,

turn it on its head, and it’ll give us

another insight into how to think about the discount rate

and the value of corporations. If the price of a stock today

is given by D over r minus g, then I can flip things

around and say that r minus g is equal to D over P, right? The dividend price ratio is

equal to r minus g, or r– the discount rate that I’m

using for the cash flows– is given by the dividend

yield plus the rate of growth implicit in that company’s

investment opportunity set. Now why is this interesting? Well, in order for

you to understand the importance of

this expression, you have to realize

that, for many years, stock analysts would look

at a company’s discount rate or cost of capital by simply

using the dividend yield. So in the exact same way

that if you have a bond, and you see what the coupons

are, and you take the coupon and divide it by the

price, that gives you a sense of what your rate of

return is over a given period. When you look at a stock, and

you want to ask the question, how much am I earning

on that stock? What is the rate of return

on that stock for me, the investor? You take the dividends that

you get paid every quarter, and you take that

dividend and you divide it by the stock price,

and that gives you a sort of rate of return, right? Because if you

think about buying the stock for a price, P, and

then getting cash flows of D every quarter, or every

period, then your yield, your rate of

return, is D over P. That’s called the dividend

price ratio, or dividend yield. What this expression

says is something that every MIT graduate knows

in his or her heart, which is that technology

adds value above and beyond what you observe

in current cash flows. It’s not just the dividend

that gives a company value, it’s the ability for

companies to grow over time. It’s not just the company’s

current plant and equipment and operations

that give it value, it is all of the interesting,

wonderful, innovative, creative ideas that are locked

up in that company that may one day be

implemented and allow it to grow far beyond the

founders’ wildest dreams. That also has to be factored

into the rate of return of the company. And this simple little dividend

yield model tells us this. It says that the

required rate of return, the risk-adjusted discount rate,

the cost of capital, the user cost, whatever you want

to call it, this r, has two pieces to it. One is the cash that you get on

a regular basis, the dividends that the current

operations generate, plus the growth opportunities

of those dividends out into the

infinite future, OK? Now remember, the way that

we structured this dividend payment, the way that we

had our formula set up, the dividends are the

dividends that get paid next period, right? If you go back and

look at the formula, this is the price

today, and it’s given by the dividends

paid at time t plus 1. So this price that I’m

using in my notation is the current

ex-dividend price, meaning this period’s dividend

has been paid already, and now the value to

this piece of paper is the future dividend,

starting next period, t plus 1. So when I say D is

fixed, it’s fixed, but it’s getting

paid next period, OK? So in this expression,

this D is actually next period’s dividend. But remember that

when I’m trying to value the company today,

I don’t observe next period’s dividend, which is random,

but I know how much was just paid in the most recent period. So if I want to use

D, and there’s growth, I actually have to take the most

recent dividend, the one that just got paid, and

multiply that by 1 plus g to get the value of

next period’s dividend. So that’s why this

expression I’ve corrected– not corrected,

it’s not that it’s wrong– it’s just I’ve changed

the expression so that it is D sub 0, which is the most

recent dividend that was just paid multiplied by 1

plus g divided by P. So I just do that– if you want to use this

formula, and by the way, you can actually go

out and use this now. I would actually

encourage you to use it. Go out and take a look

at your favorite stock, and take a look at

its dividend yield. You can find it on

yahoofinance.com as well as other web sites. And then you make a guess as

to what the appropriate growth rate is, and try to

figure out whether it fits this equation, OK? You can observe dividends. You can observe today’s price. And you have to make an

assumption about what you think the growth rate is. And when you plug that

in, that will give you an estimate of what

the cost of capital is for that particular company. Yeah. AUDIENCE: So like this exercise

without the [INAUDIBLE],, with just the perpetuity

formula, D over r, incurs– I mean, every stock

that I look at seems to be more than the

dividends divided by– ANDREW LO: That’s right. Exactly. That’s because why? Why is it, if you

just use D over P, every single stock looks

like it’s overvalued. What are you missing? AUDIENCE: g. ANDREW LO: Yeah, exactly. Right, you’re missing g. AUDIENCE: But then g turns out

to be higher than r, right? ANDREW LO: Well, no, no, no. How did you get r? AUDIENCE: OK, OK. We don’t know r ANDREW LO: We don’t know r. That’s what we’re trying

to figure out, right? So you just said you’re

looking at D over P, and you’re trying to

figure out implicitly what that implies for the

growth rate of stocks. Take a look at this expression

in light of future growth opportunities and you’ll see

that dividend yield is not the only story. You’ve got to use

other expressions. Yeah. AUDIENCE: So looking at

that [INAUDIBLE] about it on an annualized basis or

between dividend payment? ANDREW LO: Well it should

be on an annualized– well, it should be on whatever

cycle the dividends get paid. So if dividends

get paid quarterly, then it’s a quarterly

growth rate. If it’s an annual payment, then

it’s an annual growth rate. So the benefit of

this expression is that there is no timing

that’s been assumed. It’s just whatever

the periods are. So if it’s quarterly dividends,

use quarterly growth rate. Yeah, question. AUDIENCE: We can’t just

go out and use this model on just about any

company, right? Doesn’t the company

have to, I guess, pay dividends and use

dividends as, perhaps, a way to represent the

[INAUDIBLE] of the company? ANDREW LO: Well, yes. So if it doesn’t have

dividends, then this formula is not going to be all

that interesting, right? D’s going to be 0. But remember, this

is not the current D. This is the steady state

D. And if companies are in the early part

of their growth phase, it’s going to be hard to

estimate what that steady state D is. So there’ll be other

expressions that we’re going to derive

in a few minutes, where we use accounting

identities to relate dividends to earnings or to cash flows. It used to be the case that

instead of using dividends, you would use

earnings, because even though companies that

don’t pay out dividends, they still have earnings. Well, that is until the

internet came about, right? Then you had companies that

actually had no earnings. So how do you valuate a

company that has no dividends and has no earnings, and

has negative cash flows? In fact, if you use those

models, the more negative the cash flow, the

higher the value. So something weird is going on. It has to do with

the fact that these are meant to be steady

state formulas, and not formulas for individual

time periods. If there are individual

time periods where you have zero cash flows or

negative cash flows because of growth, you’ll have to make

adjustments in the formulas, and I’ll show you how to

do that in a few minutes. Yeah. AUDIENCE: Do you have

to change the formula if, let’s say, the board decides

to change dividend [INAUDIBLE]?? ANDREW LO: Well,

again, this formula is really meant to be steady

state dividends, right. So if they change the dividends,

what you should not use is this. What you should go

back and use, which is going to be a bit

more complicated, is this, the bottom

equation, right? So this equation

is always correct, because this is

completely general. Dividends at time t plus

k out into the future. And so if you know the

future path of dividends, or if you have an expectation

of what that future path is, you can use this formula. But look how difficult this is. I mean, think about

how an equity analyst has to make his living. They’ve got to figure

out, not only what the appropriate discount rate

is, which is hard enough, but they’ve going

to figure out what the appropriate path

of dividends are, not just what the dividends

will be in steady state, because they may not

be able to do that. They may want to figure

out what the dividends are going to be next year, the year

after, the year after that. So there’s a lot

of work to be done. It’s hard. It’s hard work. But more importantly,

it’s not just hard work, it’s actually very

inaccurate work. In other words, it’s

really hard to estimate this thing with any degree of

accuracy, so what do you know? You know you’re going to

be wrong most of the time. Imagine a job where you go into

the job knowing that if you do really well, you’re a genius. You’re at the top of your class. You’re the best that’s

ever done this thing. And in that case, you’re going

to be right 52% of the time. 52% of the time. That means you’re

wrong 48% of the time. That’s pretty discouraging. But that’s really the

nature of this task. It’s really hard. You know, it’s like trying

to do weather forecasting, but weather forecasting

over the next 30 years, and then taking the sum total

of all of those decisions, putting it into a portfolio,

and then investing your life savings in that. That’s kind of tough, right? But it’s also exciting. Yeah, question? OK, oh yes. AUDIENCE: [INAUDIBLE]

If dividend is going to change

in the future, wouldn’t this formula be

likened to the annuity equation? So that point in time when

it changes, for which– [INTERPOSING VOICES] ANDREW LO: You would use

the annuity discount formula in pieces. So for example, if the cash

flows for the first 10 years look like one thing, and

then the next 20 years look like another

thing, and then the next 30 years look like

something else, what you could do is apply the annuity discount

formula to the first 10 years, and then apply the

annuity discount formula with a different discount

rate and a different cash flow to the next 20, and then

discount that back and then discount that back

10 more years, and then do that to the next

30, and then discount it back to the very beginning. So exactly. That’s the way to do it,

which is effectively doing it like this, but it’s hard. I mean, it’s hard enough to

estimate cash flows next year. And I can tell you

there are a lot of firms that have forecasted this

year’s cash flows last year are scratching their

heads, wondering how they can be so far off. Now imagine doing

it 30 years hence. I mean, it’s an impossible task. But at the end of the

day, it has to be done. In other words, whether you want

to make those forecasts or not, people are going to

trade your stock. And so if you’re not

making those forecasts, well, somebody else is

going to, because they’ve got to trade the stock. So what we want to

do is to figure out a slightly better mousetrap

of understanding what those forecasts are telling us. And if we can literally

get 52% correct rates, we’re going to be rich beyond

our wildest expectations. That’s really hard to do. And it’s just the nature of

this particular endeavor. It’s very difficult to estimate

cash flows, discount rates, and risk conditions so

far out into the future. Question, yes. AUDIENCE: You said we could

use this formula to calculate the firm’s cost of capital. I’m wondering why

would we do that? Why do I care about

the firm’s cost? I think it’s much more

interesting to calculate the growth rate [INAUDIBLE]. ANDREW LO: Well, in order to

calculate the cost of capital, you need the growth rate. AUDIENCE: OK but,

I mean, I think it’s easier to get

the cost of capital and guess the growth rate. I just don’t understand why I

would be interested in getting to know this firm’s cost– ANDREW LO: In the

cost of capital, OK. Well, you would have to wait

about another seven lectures for that, because there

is a reason why you care about the cost of

capital, and that is that if you’re trying to

decide how to spend your firm’s money, if you’re a CFO

and you’re allocating cash across different

activities, you need to know what your

firm’s cost of capital is so that you get a sense

of what the opportunity cost versus taking that

money and investing it in other opportunities

outside the firm. So in order to make decisions,

you need that number. AUDIENCE: If I’m in [INAUDIBLE],,

as an investor outside, like, looking at the

stock market, [INAUDIBLE]?? ANDREW LO: Well,

you do, in the sense that you want to know

whether you’re going to get your money’s worth. I mean, if you’re investing

in one company versus another, in order to make

that decision, you need to know what the

rate of return is, right? So it’s actually

quite important. It’s very important

for decision-making what that number is. AUDIENCE: Right after return. It’s not cost of capital. If I look it that way. ANDREW LO: So let’s call

it the rate of return. That’s right, yeah. Well, and by the way,

the reason that I always use four or five names

for the same quantity is to sensitize you to

the fact that people look at these numbers from

different perspectives. So when I use the

term cost of capital, I’m thinking about it as

a corporate manager who has internal funds that

are going to be deployed in different activities. And the cost of that capital

as a CFO is given by r. Now as an investor

external to the company, I’m thinking about how

to invest my money. I want to know what

my rate of return is. And as a regulator that

wants to understand what the appropriate

capital charge is for different kinds of

activities that are going to be appropriate for

borrowing and lending, I also need to know what the

appropriate risk adjustments are to that particular number. Yeah. AUDIENCE: I was

wondering how frequently the companies actually

change their dividend policy. Is it every year,

every few years? And also are there exceptions? Like is there a

reason sometimes where a company who is, like,

growing to issue dividends, or for a company that’s got

a lot of cash to not do so? ANDREW LO: So that’s

a great question. The question is how companies

set their dividend policy. The short answer

is that companies don’t like to pay dividends

unless they know for a fact that they can maintain the level

for a good long period of time. And the reason is simple. When a company cuts dividends,

that’s considered bad news. No matter how you slice

it, when a company decides to reduce its dividends, the

typical response is uh oh, it’s cash-strapped, or it’s in

trouble, there’s a problem. So once you know that, then

as a corporate financial– chief financial officer– you will not

recommend to the board to cut dividends unless there’s

a really significant issue with the firm. And therefore, as

a result, you’re not going to either

pay or raise dividends unless you think you

can support that level for a good long time. So because of that

reason, you’re right, dividends don’t get

changed very often. And actually, it’s quite

costly in some senses to change that dividend

policy, not just from the corporate perspective,

but from shareholder perception. AUDIENCE: What about exceptions? Like why would a

company currently do something that

is different from– ANDREW LO: There are

exceptions because of certain circumstances that

are unique to the company. For example, a company

could be in a cash crunch, like, right now, because of

some kind of capital charge due to a certain underperforming

securities, in which case they may declare a temporary

suspension of dividends. The other side of the

equation is that a company may have gotten a big windfall. They just decided

to sell a division, and they’ve got a

large amount of cash. They don’t know what to

do with all the cash, so what they’ll do is

that they’ll pay out an extraordinary dividend. Extra ordinary

dividend, which means that it’s a one-time thing,

and then from that point on, they’ll go back to a

regular dividend policy. Yeah. AUDIENCE: What

does a [INAUDIBLE].. How you want to invest

in billions of dollars. Do you borrow money to invest

versus [INAUDIBLE] dividend [INAUDIBLE]? ANDREW LO: Well, it depends

on how much money you have. It depends upon what your

shareholders want to have done. I mean, that’s

certainly a decision that a corporate

financial manager would have to make in concert

with the shareholders, as well as the CEO. And that’s a strategic decision. But in order to

make that decision, you’ve got to have a few

things at your fingertips. You’ve got to have the

opportunity cost of capital. You’ve got to figure out

what your borrowing cost is. And in order to figure

out your borrowing cost, what do you need

to know about your debt? AUDIENCE: [INAUDIBLE] ANDREW LO: How risky. And how do we measure

risk with corporate debt? We just talked

about it last class. Hint, hint. AUDIENCE: You got to rate it. ANDREW LO: Yeah, you

need a rate, right. So you have to figure

out whether or not the cost of funds from

internally-generated sources is cheaper or more

expensive than going to the external capital markets. Right now, I would say that

it’s extremely expensive to go out into capital markets,

if you could do it at all. If you’re going to

raise money, you’re going to be paying

up through the nose. General Electric credit

default swap today was priced at 700 basis points. This is AAA-rated security,

at 700 basis points credit. It’s crazy! But people don’t want

to lend right now. So if you want to borrow

in capital markets today, good luck.

I watched them land on the moon..It didn't mean I was there..

This is great,but i prefer physics In MIT.

This is fantastic. Extremely informative videos.

you don't lose your pinky, haha hilarious. Such a great teacher.

1:06:47 lol

At 1:01:17, the professor encouraged us to apply the equation in the real stock trading , but how can we actually identify the growth rate g here in a practical sense?

It is an incomplete video… the lecture notes contain 22 slides and from which only 9 are dealed here… http://ocw.mit.edu/courses/sloan-school-of-management/15-401-finance-theory-i-fall-2008/video-lectures-and-slides/MIT15_401F08_lec07.pdf

Min 21:40….hmmm I could think of a whole bunch of companies that never paid anything to shareholders, at least not publicly, and yet their values went down.

Could someone guide where to find the second half lecture , thanks.

The J&J stock is one of the most consistent dividend payers, which increase for more that half a century each single year. So I decided to use it as a homework to implement the Gordon growth model formula. If we take J&J 10-K 2014 form or 2014 Annual Report with dividend payments known for three consecutive years (2012, 2013, and 2014) and the forecast (already a fact) for 2015, we see a rather smooth dividend growth ($3.00 in 2015/$2.40 in 2012^(1/3)=7.72% on an annual basis). During the weeks following the 10-K 2014 publication on Feb 24, 2015, the stock price moved around $100.00 (I actually adore J&J stock for having such a convenient price 🙂 ). So having $3.00 annual dividend forecast for 2015 (which we, of course, can discount since it is paid quarterly by $0.75) gives us slightly less than 3.00/100.00=3.00% + 7.72% of dividend annual growth. The calculated expected discount for J&J stock during late Feb-early March 2015 was approximately 10.7%. Seeing virtually no stable stock appreciation since then, this seems to give us a rather "pure" expected discount. I highly appreciate Professor Lo's very informative lectures and his fantastic teaching style.

The "cc" button under right side of the screen is gorgeous. The translation is so accurate.

I don't understand lol

what about political scenarios, which inturn going to change the economics and which inturn the earnings and dividend. so how can the dividends or earnings be right so much in to the future?

7:40 describes the way it is in AUSTRALIA, australia is terrible and it is a ruiner of free spirit and development, take this from me, i am born , bred here, its terrible , they destroy your life here. !

superb

Fantastic – I had never previously known the importance of short selling in price discovery. Simply put, if short selling is not possible or not allowed, then the market price is only getting half the information. I still need to think about the ethics and incentives of short selling though.

You can send spaceships to them moon with those formulas!

Where can I find the solutions of Brealy Myres and Allen 10th edition?

cool