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110 Chapter 5. Uncertainty, Default, and Risk.
CHAPTER 6
Dealing With Imperfect Markets

Opinions, Market Depth, Transaction Costs, Taxes, and In¬‚ation
last ¬le change: Feb 23, 2006 (14:21h)

last major edit: Mar 2004, Dec 2004




So far, we have assumed no di¬erences in information (which we might call “opinions”), no
transaction costs, no taxes, and a large market with many sellers and buyers”the “perfect
market.” In one sense, it is precisely these perfect market assumptions that have allowed
modern ¬nance to become the “science” that it is today. Most of the important concepts of
¬nance have been derived in perfect markets ¬rst.
Why is it that these perfect markets assumptions are so important? It is because of what they
have done for us: They have given us one unique appropriate expected rate of return”whether
you want to borrow someone else™s money to ¬nance your projects or lend your money to
someone else undertaking projects.
As convenient as this may be, you know that perfect markets do not exist. They are a concept,
not reality. Thus, you must now learn how to think about ¬nance in “imperfect markets.” So
we now leave this frictionless, utopian world. You will see that if markets are imperfect, it is
di¬cult to attach a unique value to goods. Instead, the value depends on who the seller and
who the buyer might be. Fortunately, most of your tools (and speci¬cally NPV) still work! But
you need to apply them with more caution.




111
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112 Chapter 6. Dealing With Imperfect Markets.

6·1. Causes and Consequences of Imperfect Markets

So far, we have not drawn a distinction between the cost of capital at which you can borrow
money to ¬nance your projects, and the rate of return at which you can save money. In “perfect
markets,” these two rates were the same. Let us ¬rst cover broadly what market imperfections
are and how they make our lives more di¬cult, and then discuss each imperfection in greater
detail in its own section.


6·1.A. Perfect Market Assumptions

A perfect market is de¬ned by the following assumptions:

No Di¬erences in Information Everyone holds the same opinion. How can this assumption be
violated? Here is one example. If your bank believes that there is a 50% chance that you
will go bankrupt and default, and you believe that there is only a 0.1% chance, then your
bank will lend you money only if you pay a much higher expected interest rate than it will
pay you if you deposited your money with it.
This is why our perfect markets assumptions includes one that everyone has the same
information and agrees on what it means. (It does not mean that there is no uncertainty,
however. The important point in a perfect market is that everyone interprets the uncer-
tainty identically.)

A Deep Market You can easily ¬nd a buyer or a seller. How could this assumption be violated?
Say there is only one bank that you can do business with. This bank will exploit its
monopoly power. It will charge you a higher interest rate if you want to borrow money
from it than it will pay you if you want to deposit your money with it”and you will have
no good alternative. (There is one nitpick quali¬cation: if a project is worth more if it is
owned or ¬nanced by a particular type”e.g., if a golf range is owned by a golf pro”then
there must be a large number of this type of owner.)
This is why our perfect markets assumptions includes one that there are in¬nitely many
buyers and sellers.

No Transaction Costs You can trade without paying any transaction costs. How can this as-
sumption be violated? If it costs $1,000 to process the paperwork involved in a loan, you
will incur this cost only if you need to borrow, but not if you want to save. This will make
your e¬ective borrowing interest rate higher than your e¬ective savings interest rate.
This is why our perfect markets assumptions includes one that there are no transaction
costs.

No Taxes There are no tax advantages or disadvantages to buying or selling securities. Specif-
ically, there are no asymmetric tax treatments to the seller divesting or to the buyer
purchasing. How can this be violated? If you have to pay taxes on interest earned, but
cannot deduct taxes on interest paid, your de facto savings rate will be lower than your
borrowing rate.
This is why our perfect markets assumptions includes one that there are no taxes.

We will soon tackle each of these issues in detail. However, the e¬ect of violating any of these
assumptions is really the same. Any violation that breaks the equality between the borrowing
and the savings rate also breaks the link between value and one unique price (or cost). In fact,
the value of a project may not even have meaning in imperfect markets”a project may not
have one unique value, but any from among a range of possible values.
¬le=frictions.tex: RP
113
Section 6·1. Causes and Consequences of Imperfect Markets.

6·1.B. Value in Imperfect Markets

In a perfect market, the value of the project depends only on the project, and not on you If savings and
investment interest
personally or on your cash position. This is often called the “separation of investments and
rates differ, the project™s
¬nancing decisions.” You could make investment choices based on the quality of the projects value (NPV) depends on
themselves, not based on how you would end up ¬nancing them. The NPV formula does not the owner™s position
have an input for your identity or wealth”its only inputs are the project™s cash ¬‚ows and the
rate of return on alternative investments.
But if the borrowing and lending rates are not the same, then the value of the project depends An example.
on your cash holdings. For example, assume that you can lend money (invest cash) at 3%, and
borrow money (receive cash) at 7%. What is the present value of a project that invests $1,000
today and returns $1,050 next period?

• If you have $1,000 and your alternative is to invest your money in the bank, you will only
get $1,030 from the bank. You should take this project to earn $20 more than you could
earn from the bank.

• If you do not have the $1,000, you will have to borrow $1,000 from the bank to receive
$1,050 from the project. But because you will have to pay the bank $1,070, you will lose
$20 net. You should not take the project.

The proper project decision now depends on how much cash you have. The separation between
your project choice and your ¬nancial position has broken down. Taking your current cash
holdings into account when making investment choices of course makes capital budgeting
decisions more di¬cult. In this example, it is fairly easy”but think about projects that have
cash in¬‚ows and out¬‚ows in the future, and how decisions could interact with your own wealth
positions in the future. Equally important, in imperfect markets, the project value is no longer
unique, either. In our example, it could be anything between +$19.42 ($1,050 discounted at
3%) and ’$18.69 ($1,050 discounted at 7%).
Solve Now!
Q 6.1 What are the perfect market assumptions?


Q 6.2 What does the assumption of a perfect market buy you that would not be satis¬ed in an
imperfect market?


Q 6.3 Evaluate whether supermarkets are competitive markets.



6·1.C. Perfect, Competitive, and E¬cient Markets



Do You Always Get What You Pay For?
Let us expand on this insight that projects may not have unique values. Have you ever heard Are there any good
deals?
someone say “it™s only worth what people are willing to pay for it” and someone else that “it™s
worth much more than it™s being sold for”? Who is correct? Are there any good deals?
The answer is that both are correct and neither is correct. The ¬rst claim is really meaningful Let™s waf¬‚e a little.
only to the extent that markets are perfect: if a market is perfect, items are indeed worth exactly
what buyers are willing to pay for them. The second claim is really (sort of) meaningful only
to the extent that markets are imperfect: if a market is imperfect, items have no unique value.
Di¬erent people can place di¬erent values on the item, and you may consider an item worth
much more than what it was sold for.
¬le=frictions.tex: LP
114 Chapter 6. Dealing With Imperfect Markets.

In ¬nance, we often “conveniently” assume perfect markets. Although not perfectly accurate,
For PepsiCo shares,
other perfect market this is often reasonably justi¬able. For example, take the market for trading shares of stock in
assumptions are not
PepsiCo. It de¬nitely appears to be a competitive market, i.e., a situation in which there are
perfectly true, but not
many competing buyers and sellers, so that no single buyer or seller can in¬‚uence the price.
too far from the truth.
There are lots of potential buyers willing to purchase the shares for the same price (or maybe
just a tiny bit less), and lots of potential sellers willing to sell you shares for the same price (or
maybe just a tiny bit more). A “perfect market” is a stricter requirement than a “competitive
market” assumption. If a market is perfect, then it is also competitive, but not vice-versa. (For
example, a competitive market can exist even in the presence of opinions and taxes.) For our
discussion, we hope you can further assume that taxes are not distorting rates of return in
a way that makes the PepsiCo shares™ rates of return to a seller any higher or lower than the
equivalent rates of return to a buyer, so that taxes are not distorting holding decisions. (This
assumption may be a little, but probably not too far o¬ from reality.) Moreover, few active
traders in the market have inside information, so objective information di¬erences should not
be too bad either. Everyone should roughly agree to what shares can be sold for tomorrow”
which de¬nes value today. Finally, the transaction costs of trading shares on the New York
Stock Exchange (NYSE) are very low. There are no costs of having to ¬nd out the proper price
of PepsiCo shares (it is posted by the NYSE), and there are no costs to searching for a buyer or
seller. So, the market for PepsiCo shares may indeed be reasonably close to perfect.



Important: For many ¬nancial securities, such as publicly traded stocks, the
assumption that the market is competitive and that the security is worth what it is
trading for is pretty accurate.



Such perfect markets reduce buyers™ and sellers™ concerns that one deal is better than another”
Buyers get what they
pay for in a competitive that buying is better than selling, or vice-versa. For a more concrete example, consider gasoline
low-friction market.
and imagine that you do not yet know when and where on your road trip you will need to pump
more gas. Unlike shares of stock, gas is not the same good everywhere: gas in one location
can be more valuable than gas in another location (as anyone who has ever run out of gas can
con¬rm). But, in populated areas, the market for gasoline is pretty competitive and close to
perfect”there are many buyers (drivers) and sellers (gas stations). This makes it very likely that
the ¬rst gas station you see will have a reasonable, fair price. If you drive by the ¬rst gas station
and it advertises a price of $1.50 per gallon, it is unlikely that you will ¬nd another gas station
o¬ering the same gas for $1 per gallon or $2 per gallon within a couple of miles. Chances are
that “the price is fair,” or this particular gas station would probably have disappeared by now.
(The same applies of course in many ¬nancial markets, such as large company stocks, Treasury
bonds, or certain types of mortgages.) As long as the market is very competitive, or better yet
perfect, most deals are likely to be fair deals. Some shopping around may help a tiny bit, but
an extreme amount of shopping would likely cost more in time and e¬ort than what it could
save.
But there is an important conceptual twist here: Paying what something is worth does not nec-
Competitive markets
leave surplus for average essarily mean that you are paying what you personally value the good for. Even in competitive
buyers and sellers.
perfect markets, there can be many di¬erent types of buyers and sellers. It is only the marginal
buyer and the marginal seller who end up trading at their “reservation values,” where they are
exactly indi¬erent between participating and not participating”but if you are not marginal, a
market will allow you to make yourself better o¬. For example, if you are running out of gas
and you are bad at pushing two-ton vehicles, you might very well be willing to pay a lot more
for gas than even $10 per gallon”and fortunately all you need to pay is the market price of
$1.50 per gallon! The di¬erence between what you personally value a good for and what you
pay for it is called your “surplus.” So, even though everyone may be paying what the good is
worth in a perfect market, most buyers and sellers can come away being better o¬.
¬le=frictions.tex: RP
115
Section 6·1. Causes and Consequences of Imperfect Markets.

Unfortunately, not every good is traded in a perfect market. Let us consider selling a house. A house™s value depends
on idiosyncratic factors.
What is the value of the house? What if the house is in a very remote part of the country, if
There is no single value.
potential buyers are sporadic, if alternative houses with the same characteristics are rare, and
if the government imposes a 50% transfer fee? Now the value of the house depends on the luck
of the draw (how many potential buyers are in the vicinity and see the ad, whether a potential
buyer wants to live in exactly this kind of house, and so on), the urgency of the seller (perhaps
whether the seller has the luxury to turn down a lowball ¬rst o¬er), and the identity of the
seller (the current owner does not need to pay the government transfer fee, so he may value
the house more than a potential buyer). So, it is only easy to determine the value of a good
if the market is perfect. Because the market for many houses is not even close to perfect, the
values of such houses are not unique.
Similarly, not all ¬nancial markets are close to perfect. Transaction costs, information di¬er- Buyers may not get
what they pay for in a
ences, special taxes, or the unique power of the seller or market can play a role even in some
non-competitive
¬nancial markets. For example, many corporate bonds are traded primarily over-the-counter, high-friction market.
meaning that you must call some individual at the brokerage house, who may play the role of
the only easy clearinghouse for these particular bonds and who will try to gauge your expertise
while negotiating a price with you. You could easily end up paying a lot more for this bond
than what you could then sell it for one minute later.
Of course, you should not kid yourself: no market, ¬nancial or otherwise, is ever “perfectly Learn from the perfect
markets concepts, but
perfect.” The usefulness of the perfect market concept is not that you should believe that it
don™t believe it holds.
actually exists in the real world. Instead, it is to get you to think about how close to perfect
a given market actually is. The range in which possible values lie depends on the degree to
which you believe the market is not perfect. For example, if you know that taxes or transaction
costs can represent at most 2“3% of the value of a project, then you know that even if value
is not absolutely unique, it is pretty close to unique”possible values sit in a fairly tight range.
On the other hand, if you believe that there are few potential buyers for your house, but that
some will purchase the house at much higher prices than others, then it will depend on your
¬nancial situation whether you will accept or decline a buyer™s low-ball o¬er.
In sum, when someone claims that a stock or ¬rm is really worth more than he or she is selling A “salesman” may
distort the truth and
it for, there are only a small number of explanations: First, there may be pure kindheartedness
claim great deals.
toward any buyer or a desire by a seller to lose wealth; this happens so rarely that we just
ignore this. Second, the seller may not have access to a perfect market to sell the goods. This
may make the seller accept a low amount of money for the good, so depending on how you
look at this, the good may be sold for more or less than you think it is worth. Third, the seller
may be committing a conceptual mistake. The good is worth neither more nor less than what
it is being sold for, but exactly how much it is being sold for. Fourth, the seller may be lying
and is using this claim as a sales tactic.


Preview: E¬cient Markets
There is an important corollary to a perfect market. A market (or a price) is called “e¬cient” Ef¬cient Market: Use of
all information.
if this market has set the price using all available information. If a market is perfect, it will
inevitably also be e¬cient. If it were ine¬cient, you could become rich too easily. For example,
say the market wanted to o¬er you an expected rate of return of 15% on a particular stock (for
whatever reason), and the expected value of the stock is $115. Then the price of the stock today
would have to be $100 for this market to be e¬cient. This market would not be e¬cient if it
set the price for this stock at $99 or $101, because the stock would then o¬er other than the
15% expected rate of return. Similarly, you should not be able to locate information that tells
you today when/if/that the true expected value tomorrow is really $120 for the $100 stock. If
you could ¬nd this information, you could on average earn more than 15%. If the market has
overlooked this information, it is not e¬cient.
¬le=frictions.tex: LP
116 Chapter 6. Dealing With Imperfect Markets.

The application and use of the “e¬cient markets” concept faces a number of issues. First,
What is the model? What
is the information set? where does the 15% come from? It will have to come from some model that tells you what rate
of return a stock should have to o¬er (given its characteristics, such as risk). Possible models
will be discussed at length in Part III of this book. Without such a model, talking about market
e¬ciency is meaningless. Second, what information exactly are we talking about? Insiders
often have more information than the public. For example, a drug company executive may
know before ordinary investors whether a drug is likely to work. Thus, the market may be
e¬cient with respect to publicly available information, but not e¬cient with respect to insider
information.
So, to be more accurate, when a market is perfect, we usually believe that it is also e¬cient
Competition and
Ef¬ciency with respect to public information. After all, if other buyers and sellers were to ignore a useful
piece of information, you could likely earn a lot of money trading on it. For example, what
would you do if you learned that the market always goes down on rainy days and up on sunny
days? It is unlikely that the average investor requires extra return to hold stocks on sunny
days”and, even if the average investor does, you would probably not! You would never buy
stocks when the weather forecast predicts that rain is coming, and you would only buy stocks
when the weather forecast predicts that the sun will be shining. Investors like yourself”and
there are of course many such investors in perfect markets”would rapidly bid up the prices
before the sun was shining, so that the prices would no longer systematically go up on sunny
days. If markets are e¬cient, then you should not be able to earn abnormally good sunny-day
returns”at least not this easily. To earn higher expected rates of return, you must be willing
to take on something that other investors are reluctant to take on”such as higher risk (also
the subject of Part III).
A belief in e¬cient markets is what de¬nes classical ¬nance. In contrast, behavioral ¬nance
Classical vs. Behavioral
Finance. believes that markets sometimes do not use all information. Depending on how strong a be-
liever in classical ¬nance vs. behavioral ¬nance you are, you may believe that there are no such
opportunities, that there are few such opportunities, or that there are plenty of such opportu-
nities. Both camps agree, however, that market perfection (and especially competitiveness and
transaction costs) play crucial roles in determining whether a market is e¬cient or not. We will
dedicate an entire chapter to market e¬ciency and its consequences, which will also talk in
See Chapter 19
greater length about classical vs. behavioral ¬nance.
Solve Now!
Q 6.4 Can buyers and sellers be better o¬ if a market is perfect? Or does this mean that everyone
just pays what it is worth, and thus is no better o¬.


Q 6.5 What is the use of perfect markets, given that there is obviously not a single market in the
world that is perfect?


Q 6.6 How does an e¬cient market di¬er from a perfect market?


Q 6.7 Your borrowing rate is 10%/year. Your lending rate is 4%/year. The project costs $1,000
and returns a rate of return of 8%. If you have $900 to invest, should you take the project?


Q 6.8 (Cont™d). You can think of the $900 as the amount of money that you are not consuming.
Say, your wealth is $2,000, but in the previous question, you wanted to consume, e.g., $1,100.
Could you still consume this much and take the project? How much could you consume and still
want to take the project?
¬le=frictions.tex: RP
117
Section 6·2. The E¬ect of Disagreements.

6·2. The Effect of Disagreements

As you already learned, no market is truly perfect. Perfect market assumptions are just approx- A broad perspective.
imations. They work well in some situations, and poorly in others. They typically work quite
well in many (but not all) large ¬nancial markets for large and liquid ¬nancial securities. You
now need to learn how to judge the degree to which markets are imperfect”and how to deal
with imperfections as real-world investors and managers.
Our perfect markets assumptions included one that markets are very deep, consisting of many The assumption “no
market power” is
buyers and sellers. If there is only one investor”say, a capital provider or bank”from which
straightforward.
you can obtain funding, this investor will have market power over you. Of course, this investor
will exploit it by charging you a higher borrowing rate and o¬ering you a lower deposit interest
rate. There is not much more to say about this particular perfect market assumption, so we
now turn to the more interesting discussions.
The remainder of our chapter explores how big typical market imperfections can be, what can Our agenda.
mitigate them, and how you should work with them. This section begins by discussing the role
of opinions. Then we continue to transaction costs. Next, we will take a look at income taxes.
Finally, we will consider hybrid problems”like the role of taxes in the presence of in¬‚ation.


6·2.A. Expected Return Di¬erences vs. Promised Return Di¬erences

The most obvious cause for di¬erent borrowing and lending rates are di¬erences in opinion Under uncertainty,
different opinions can
between the lender and borrower. To think about this particular assumption violation, we must
lead to disagreements.
work in a world of uncertainty”it would be absurd to believe that such di¬erences in opinion
could exist if there is no uncertainty. So, what happens if the lender and borrower have di¬erent
information or di¬erent judgment about the same information? Most prominently, they could
disagree about the default risk! For example, if you have no credit history, then a lender who
does not know you might be especially afraid of not receiving promised repayments from you”
from the perspective of such a lender, you would be extremely high-risk. Your lender might
estimate your appropriate default probability to be 20% and thus may demand an appropriate
default premium from you of, say, 8% above the risk-free yield. On the other hand, you may
know that you will indeed return the lender™s money, because you know you will work hard and
that you will have the money for sure. In your opinion, a fair and appropriate default premium
should therefore be only 0-1%.
When your potential lenders and you have di¬erent opinions, you then face di¬erent expected Expected rates of return
for borrowing and
savings interest rates and borrowing costs of capital. That is, if you know that you are a low risk,
lending now become
then your borrowing cost of capital (the expected interest rate) would not only be much higher different.
than the lender perceives it to be, but it would also be the case that your borrowing expected
cost of capital is much higher than your savings expected rate of return that you would earn
if you deposited your money in the bank. You might be able to borrow at a cost of capital
(expected rate of return) of 12%, but save only at an expected rate of return of 5%.
This issue is very di¬erent from the di¬erence between promised and expected returns that Do not confuse different
promised
was discussed in Chapter 5. It is not just that you must o¬er a higher promised rate of return
borrowing/lending rates
than what you expect to repay. Instead, you must now o¬er a higher expected rate of return (not discussed here)
when you want to borrow, compared with the expected rate of return that you could earn if with different expected
borrowing/lending rates
you deposited money in the bank. (The bank is unlikely to go bankrupt, and your deposit is
(discussed here).
probably insured by the government, which means that the bank may pay not more interest than
the equivalent short-term Treasury. The bank™s promised rate of return is almost the same as
the expected rate of return.) The di¬erence in stated borrowing interest rates and stated saving
interest rates at your local bank could just as well be the default premium”the di¬erence in
the returns you promise and which you expect to pay, although in a di¬erent guise. The bank
quoting you a lower savings deposit interest rate than borrowing loan interest rate would just
compare promised interest rates, not expected interest rates. Instead, the novel issue discussed
in our chapter is that disagreements and information di¬erences are now causing di¬erences in
expected returns. The borrowing and lending expected rates of return are no longer the same.
¬le=frictions.tex: LP
118 Chapter 6. Dealing With Imperfect Markets.



Important: The fact that credit spreads re¬‚ect a default premium”a di¬erence
between the promised rate of return and the expected rate of return”is not a
market imperfection.
The fact that credit spreads re¬‚ect di¬erences in opinion between borrower and
lender”a di¬erence about the two assessed expected rates of return seen”is a
market imperfection.



For example, assume the prevailing interest rate is 10% and you want to borrow $1,000.
Here is an example.


Perfect Market Default Spread Assume you have a 5% objective probability of total default. In
this case, a risk-neutral bank would ask you for a return of

(6.1)
5% · 0 + 95% · x = (1 + 10%) · $1, 000 ’ x ≈ $1, 158 .

This 15.8% interest rate is not a market imperfection. It is merely compensation for your
probability of defaulting. Both you and and the bank would realize that you are paying a
10% cost of capital.

Imperfect Market Credit Spread Now assume that you believe you have a 3% objective proba-
bility of total default, and the bank believes you have a 9% objective probability of default.
In this case, the bank would quote you an interest rate of 20.9%. You, in turn, would
consider this $1,209 in payment to be equivalent not to the 10% expected rate of return
that the bank believes it is, but equivalent to a 97% · $1, 209/$1, 000 ≈ 17.3% interest rate.
You would consider the 7.3% to be the extra spread due to friction”but, of course, who
says you are right and the bank is wrong?



6·2.B. Corporate Finance vs. Entrepreneurial or Personal Finance?

Where do such market imperfections apply? In the world of large corporations, the interest
For large companies, a
perfect market rate spread between similarly risky borrowing and lending rates is often mild, so they can
assumption with
pretend they live in a “perfect” market in which they can separate the project choice from their
reasonably equal
¬nancial situation. Their promised borrowing interest rates would still be higher than what
borrowing and lending
rates is reasonable.
they can receive investing their money in Treasury bonds”but, given that these large ¬rms
still have some possibility of going bankrupt, their expected borrowing cost of capital would
probably be fairly similar to the expected rate of return that they could earn if they invested
money into bonds with characteristics similar to those that they themselves issued.
In the world of individuals, entrepreneurs, and small companies, however, expected borrowing
For entrepreneurs, a
perfect market interest rates are often higher than expected saving interest rates. In fact, this issue of an
assumption is
extraordinarily high di¬erential between expected borrowing and lending rates”and with it the
problematic.
role of cash-on-hand”is one important di¬erence between “ordinary corporate ¬nance” and
“entrepreneurial ¬nance.” Entrepreneurs ¬nd it very di¬cult to convey credibly their intent and
ability to pay back their loans. As a consequence, many entrepreneurs even resort to ¬nancing
projects with credit cards, which may charge a thousand basis points above Treasury bonds.
These high borrowing costs can thus prevent rational entrepreneurs from taking many projects
that they would undertake if they had the money on hand. It also means that more established
¬rms or richer entrepreneurs should optimally take more projects than poorer entrepreneurs.
But be careful in the real world before you conclude this to be the case: Entrepreneurs tend to
Don™t believe
entrepreneurial claims! have notoriously over-optimistic views of their prospects. (Even venture capitalists, the ¬nanc-
ing vehicle for many high-tech entrepreneurial ventures, which advertise returns of 30%/year
or more seem to have managed to return only a couple of percentage points above the risk-
free rate over the last thirty years.) This may actually mean that entrepreneurs face only high
promised borrowing costs, not high expected borrowing costs. Thus, the quoted spread be-
tween their borrowing and lending rates, which is really all that you can easily observe, likely
¬le=frictions.tex: RP
119
Section 6·2. The E¬ect of Disagreements.

has a large component that is due not to information disagreements but simply due to credit
risk.
Side Note: Valuation services are an important revenue business for many ¬nance professors and consulting
¬rms. When asked to value small, non-public businesses”for example, for purposes of assessing the inheritance
tax or in disputes among former business partners”it is customary and legally acceptable to ¬rst compute the
value of an equivalent publicly traded business or company, and then to apply a “private discount” of around
10% to 30% in order to re¬‚ect the limited access to capital (because lenders tend not to believe in high default
rates for young companies).

Solve Now!
Q 6.9 Can there be a di¬erence in the borrowing and lending rates quoted by the bank in perfect
markets?


Q 6.10 What are the possible reasons why entrepreneurs often have to ¬nance their projects
with credit cards, which can charge interest rates as high as 1500 basis points above Treasury?



6·2.C. Covenants, Collateral, and Credit Rating Agencies

So, if you are an entrepreneur who wants to start a company, what can you do to reduce the You would love to reduce
such disagreements”but
expected cost of capital? The answer is that it is in your interest to disclose to the lender all the
you may not be able to.
information you can, provided you are the type of entrepreneur who is likely to pay back the
loan. You want to reduce the lender™s doubt about future repayment. Unfortunately, this can
be very di¬cult. The lender can neither peer into your brain, nor give you a good lie detector
test. Attempts to convey information credibly in the real world are many, but there will always
be residual information di¬erences”they are just a fact of life. Still, if you can reduce the
information di¬erences, your ¬rm will be able to enjoy lower costs of capital. Also, if you
as borrower fail to give your best try to convince the lender of your quality, then the lender
should not only assume that you are an average company, but instead assume you are the very
worst”or else you would have tried to communicate as much as possible.
There are at least three important mechanisms that have evolved to alleviate such information Good borrowers want to
credibly tell the lender
di¬erences. The ¬rst mechanism is covenants, which specify upfront what a debtor must do
that they are good.
to maintain credit. This can include such requirements as the maintenance of insurance or a
minimum corporate value. The second mechanism is collateral”something that the creditor
can repossess if payments are not made. But anything that in¬‚icts pain on the debtor will do.
For example, if defaulting debtors were thrown into debtor™s prison (as they often were until
the 19th century), the promise to repay would be more credible and lenders would be more
inclined to provide funding at lower rates. Of course, for the unlucky few who just happened
to su¬er incredibly bad luck ex-post, debtors™ prison has some de¬nite drawbacks.
The third mechanism to alleviate repayment uncertainty are credit rating agencies, which keep Bond rating agencies
indicate probability of
a history of past payments to help assess the probability of future default. This is why you need
default.
to give your social security number if you want to take out a substantial personal loan”the
lender will check up on you. The same is true for large corporations. It may be easier to judge
corporate default risk for large companies than personal default risk, but it is still not easy and
it costs both time and money. The two biggest bond credit rating agencies for corporations
are Moody™s and Standard&Poors. (The other two are Du¬ and Phelps and Fitch.) For a fee
that the corporate borrower pays, they will rate the bond™s quality, which re¬‚ects the issuer™s
probability that the bonds will default. This fee depends on a number of factors, such as the
identity of the issuer, the desired detail in the agencies™ investigations and descriptions, and

Anecdote: Sumerian Debt Contracts
Among the earliest known collateralized debt contracts is a tablet from Sumeria (Mesopotamia), which
promises delivery of silver and gives as security the son of the borrower. (The tablet can be viewed at
www.museumofmoney.org/babylon/index.html.) Such contracts are illegal today, but de-facto “debt slavery”
for debts not repaid is common in many countries, according to the September 2003 issue of National Geo-
graphic Magazine.
¬le=frictions.tex: LP
120 Chapter 6. Dealing With Imperfect Markets.

the features of the bond (e.g., a bond that will pay o¬ within one year is usually less likely to
default before maturity than a bond that will pay o¬ in thirty years; thus, the former is easier to
grade). The credit rating agencies ultimately do not provide a whole set of default probabilities
(e.g., 1% chance of 100% loss, 1.2% chance of 99% loss, etc.), but just an overall rating grade. It
is up to the ratings™ reader to translate the rating into an appropriate compensation for default
risk. The top rating grades are called investment grade, while the bottom grade are called
speculative grade (or junk).


Investment Grade: Moody™s Standard & Poors
Exceptional Aaa, Aaa1, Aaa2, Aaa3 AAA, AAA-, AA+
Excellent Aa, Aa1, Aa2, Aa3 AA, AA-, A+
Good A, A1, A2, A3 A, A-, BBB+
Adequate Baa, Baa1, Baa2, Baa3 BBB, BBB-, BB+

Speculative Grade: Moody™s Standard & Poors
Questionable Ba, Ba1, Ba2, Ba3 BB, BB-, B+
Poor B, B1, B2, B3 B, B-, CCC+
Very Poor Caa, Caa1, Caa2, Caa3 CCC, CCC-, CC+
Extremely Poor Ca, Ca1, Ca2, Ca3 CC,CC-, C+
Lowest C C


There is often a sharp di¬erence in quoted interest rates between the worst investment grade
bond and the best speculative grade bond, partly also because many investing institutions are
allowed to hold only investment grade bonds.
So, is there a di¬erence between bonds of di¬erent rating quality? Yes! Altman studied cor-
Here is what ratings
mean. porate bonds from 1971 to 2003 and reported default and recovery rates. Figure 6.1 gives a
sketch of how likely default was for a given credit rating. Very few investment grade bonds
default”and especially right after issue when they would have still carried the original credit
rating. However, many speculative bonds will eventually miss at least one coupon payment
(which is considered default). Upon default, an AAA or AA bond price was worth about 75
cents on the dollar; an A bond price was worth about 50 cents on the dollar; and lower rated
bonds were worth about 30 cents on the dollar. (The previous chapter already told you that
the net e¬ect is that junk bonds that promised a rate of return of about 5% above the 10-Year
Treasury bond delivered only 2.2% above the Treasury on average.)
Unfortunately, although bond rating agencies will update their rating if the condition of the
Ratings are useless for
making money. ¬rm changes, the empirical evidence suggests that these bond ratings are not very good in
helping an investor earn superior rates of returns. In fact, the ratings seem to respond more
to drops in the value of the underlying bonds than vice-versa. The bond rating agencies seem
to be more reactive than proactive. A longer discussion of bond ratings appears on Page 684f.
How do bond ratings translate into di¬erences in promised (quoted) bond yields? Table 6.1
Sample Rates of Returns
lists the borrowing rates of various issuers in May 2002. (Many other current interest rates can
be found at www.bloomberg.com/markets/rates/index.html and bonds.yahoo.com/rates.html.)
Most of the di¬erences between these borrowers™ promised interest rates and Treasury interest
rates are due to default risk, which compensates lenders for di¬erential default probabilities.
Solve Now!
Q 6.11 Using information from a current newspaper or the WWW, what is the annualized yield
on corporate bonds (high-quality, medium-quality, high-yield) today?
¬le=frictions.tex: RP
121
Section 6·2. The E¬ect of Disagreements.




Figure 6.1. Cumulative Probability of Default by Original Rating
50




CCC
40
Cumulative Default Rate

30




B
20




BB
10




BBB
A
AA
0




AAA

2 4 6 8 10

Years After Issue

This ¬gure shows the probability of default within x years after issue. For example, at some point during the ¬rst
seven years of their issue, 25% of all bonds originally issued as B (poor) had not delivered on at least one promised
bond payment.
Source: Edward Altman and Gonzalo Fanjul, New York University, February 2004. Moody™s also o¬ers similar reports,
and publishes an interesting monthly report on credit risk, including corporate bond default forecasts (which change
with the business cycle). Older Moody™s reports can be found at riskcalc.moodysrms.com/us/research/mdr.asp. For
example, in August 2002, the report described that no bonds rated Aaa“A2 bonds had defaulted, 0.3“0.6% of bonds
rated A3“Ba3 had defaulted, and 1.8%, 7.6%, 9.9%, and 21.0% of bonds rated B1, B2, B3, and Caa“C had defaulted.
¬le=frictions.tex: LP
122 Chapter 6. Dealing With Imperfect Markets.




Table 6.1. Promised Interest Rates For Some Loans in May 2002.

Annual Similar
Security (Bond) Yield U.S. Treasury
FNMA May 2003 2.36% 2.22%
FNMA March 2031 6.29% 5.60%
Boston Celtics 6s38 9.40% 5.60%
United Airlines 11.21s14 14.40% 4.82%
≈ 3%“4%
Corporate High-Quality 1“10 years 4.89%
≈ 3%“4%
Corporate Medium-Quality 1“10 years 6.24%
≈ 4%“5%
Corporate High-Quality 10+ years 6.76%
≈ 4%“5%
Corporate Medium-Quality 10+ years 7.65%
High-Yield (Junk Bond) Corporates 11.36% ?

Source: Wall Street Journal, Page C13. FNMA is a quasi-governmental agency that underwrites home mortgages. See
also Page 798.

Warning, I am cheating a little: not all of the differences in promised rates of return
in Table 6.1 are due to default risk. Some of the interest rate differentials can be due
to transaction costs, liquidity premia, bond duration mismatches, risk premia (to be
discussed in Part III [Investments]), or extra bond features (such as embedded bond
options, to be discussed in Part IV [Financing]). For all these reasons, the quoted yields
in Table 6.1 are not exactly comparable to treasuries. Nevertheless, the differences are
mostly due to default risk.
¬le=frictions.tex: RP
123
Section 6·3. Market Depth and Transaction Costs.

6·3. Market Depth and Transaction Costs

The next market imperfections that can drive a wedge between borrowing and lending rates are There can be other
causes of different
transaction costs. If it is very di¬cult and costly to administer loans, an investor must charge
expected rates of return,
you a higher borrowing rate than deposit rate just to break even. This is the subject of this too.
section, in which you will see how corporations and individuals should account for transaction
costs.


6·3.A. Typical Costs When Trading Real Goods”Houses

When you engage in transactions, i.e., a purchase or sale, you face costs to facilitate the trans- Real Estate is an
important market in
actions. Real estate is a perfect example to illustrate transaction costs. The personal residence
itself, and a great
is the most signi¬cant asset that most people own, real estate is a very large part of the total comparison for us.
value of the economy, and real estate transaction costs are so high that they will register with
anyone who has ever had to sell a house. The real estate example also will allow you to contrast
the real-estate transaction costs later with ¬nancial securities transaction costs.
So, what does selling or buying a house really cost?
Brokerage Commissions, a direct cost: In the United States, if a house is sold, the seller™s Direct transaction costs
require a money
broker typically receives six percent of the value of the house as commission (and splits this
transfer.
commission with the buyer™s agent). Thus, if a real estate agent manages to sell a house for
$300,000, the commission is $18,000. Put di¬erently, without an agent, the buyer and seller
could have split the $18,000 between them. (Of course, brokers do many useful things, such
as matching buyers and sellers, shepherding the selling process, etc., so the $18,000 may just
be the intrinsic transaction cost to selling a house. However, inconsistent with this view, real
estate commissions are much lower in other countries, and it is di¬cult to see why the cost of
selling houses would be exactly 6% in practically all markets in the United States.)
Although only the seller pays the broker™s cost, it makes sense to think of transaction costs Thinking of transactions
in “round-trip” form.
in terms of round-trip costs”how much worse you are o¬ if you buy and then immediately
sell an asset. You would mislead yourself if you thought that when you buy a house, you have
not incurred any transaction costs because the seller had to pay them”you have incurred an
implicit transaction cost in the future when you need to resell your investment. Of course, you
usually do not immediately sell assets, so you should not forget about the timing of your future
selling transaction costs in your NPV calculations.
Housing transaction costs are so high and so important that they are worth a digression. If you Transaction costs are on
the whole investment, so
borrow to ¬nance the investment, transaction may be higher than you think. The real estate
if you borrow to ¬nance
agent earns 6% of the value of the house, not of the amount of money you put into the house. the investment, your
On a house purchase of $500,000, the typical loan is 80% of the purchase price, or $400,000, part of the transaction
costs may be much
leaving you to put in $100,000 in equity. Selling the house the day after the purchase reduces
higher than you think!
the owner™s wealth of $100,000 by the commission of $30,000”for an investment rate of return
of “30%. This is not a risk component; it is a pure and certain transaction cost.
Let us brie¬‚y consider what happens if the house price decreases or increases by 10%. If house Let™s add some price
volatility.
prices decline by 10%, or the buyer overpays by 10%, the house can only be resold for $450,000,
which leaves $423,000 after agent commissions. The house owner is left with $23,000 on a
$100,000 investment. A 10% decline in real estate values has reduced the home owner™s net
worth by 77%! In comparison, a 10% increase in real estate values increases the value of the
house to $550,000, which means that $517,000 is left after real estate commissions. The house
owner™s rate of return for the same up movement is thus only 17%.
With the tools you already know, you can even estimate how the value of a typical house might This is how one
estimates the value
change if the Internet could instantly and perfectly replace real estate agents. You cannot
effects of commissions.
be too accurate”you can only obtain a back-of-the-envelope estimate. A typical house in the
United States sells every seven years or so. Work with a $1,000,000 house, and assume that
the expected house capital-gain appreciation is 0%”you consume all gains as rental enjoyment.
In this case, the house will stay at $1,000,000 in value, the commission will stay constant at
¬le=frictions.tex: LP
124 Chapter 6. Dealing With Imperfect Markets.

$60,000 and will be paid every 7 years. If the appropriate 7-year interest rate were 40% (around
5% per annum), then the value of the brokerage fees would be a perpetuity of $60, 000/40% =
$150, 000. The capitalized transaction cost would therefore have lowered the value of the
$1,000,000 house by $150,000. If you could eliminate all commissions, e.g., by selling equally
e¬ciently over the Internet, such a house would increase in value by about 15%. However, if
you believed that the brokerage commission were to go up by the in¬‚ation rate (2% per annum,
or 15% per 7-years), the friction would not be $150,000 but $240,000”more like 25% of the
value of the house, not just 15%.
Other direct costs: In addition to direct agent commissions, there are also many other direct
Other direct expenses.
transaction costs. These can range from advertising, to insurance company payments, to house
inspectors, to the local land registry, to postage”all of which cost the parties money.
Indirect and opportunity costs: Then there is the seller™s own time required to learn as much
Indirect transaction
costs are the loss of about the value of the house as possible, and the e¬ort involved to help the agent sell the
other opportunities.
house. These may be signi¬cant costs, even if they involve no cash outlay. After all, the seller
could spend this time working or playing instead. Furthermore, not every house is suitable
for every house buyer, and the seller has to ¬nd the right buyer. If the house cannot be sold
immediately but stays empty for a while, the foregone rent is part of the transaction cost. The
implicit cost of not having the house be put to its best alternative use is called an opportunity
cost. Opportunity costs are just as real as direct cash costs.
Solve Now!
Q 6.12 If you presumed that the appropriate interest rate was 8%/year rather than 5%/year for
the rental ¬‚ow on a house, what would you presume the value e¬ect of the 6% commission be?



6·3.B. Typical Costs When Trading Financial Goods”Stocks

Similarly, ¬nancial markets transactions also incur transaction costs. If an investor wants to buy
Transaction Costs for
Stocks are also either or sell shares of a stock, the broker charges a fee, as does the stock exchange that facilitates
direct or indirect.
the transaction. In addition, investors have to consider their time to communicate with the
broker to initiate the purchase or sale of a stock as an (opportunity) cost.
Brokerage and Market-Maker Commissions, direct costs: Still, the transaction costs for selling
The typical Transaction
Costs for Stocks are ¬nancial instruments are much lower than they are for most other goods. Let™s look at a few
relatively low.
reasons why. First, even if you want to buy (or sell) $1 million worth of stock, some Internet
brokers now charge as little as $10 per transaction. Your round-trip transaction, which is a
buy and a sale, costs only $20 in broker™s commission. In addition, you have to pay the spread
(the di¬erence between the bid and the ask price) to the stock exchange. For example, a large
company stock like PepsiCo (ticker symbol PEP) may have a publicly posted price of $50 per
share. But you can neither buy nor sell at $50. Instead, the $50 is really just the average of
two prices: the bid price of $49.92, at which another investor or the exchange™s market-maker
is currently willing to buy shares; and the ask price of $50.08, at which another investor or
the exchange™s market-maker is currently willing to sell shares. Therefore, you can (probably)
purchase shares at $50.08 and sell them at $49.92, a loss of “only” 16 cents which amounts
to round-trip transaction costs of ($49.92 ’ $50.08)/$50.08 ≈ ’0.32%. You can compute the
total costs of buying and selling 20,000 shares ($1,000,000 worth) of PepsiCo stock as

Anecdote: Real Estate Agents: Who works for whom?
Real estate agents are con¬‚icted. If they sell sooner, they can spend their time focusing on other properties.
Thus, the typical seller™s agent will try to get the seller to reduce the price in order to make a quicker sale.
Similarly, the buyer™s agent will try to get the buyer to increase the o¬er. In a ¬nancial sense, the buyer™s agent
is working on behalf of the seller, and the seller™s agent is working on behalf of the buyer. Interestingly, Steve
Levitt found that when agents sell their own houses, their homes tend to stay on the market for about 10 days
longer and sell for about 2 percent more. Source: Steve Levitt, University of Chicago.
¬le=frictions.tex: RP
125
Section 6·3. Market Depth and Transaction Costs.

Financial Round-trip Transaction
Pay $50.08 · 20, 000 = $1, 001, 600
Purchase 20,000 Shares
+$10 = $1, 001, 610
Add Broker Commission
Receive $49.92 · 20, 000 = $998, 400
Sell 20,000 Shares
’$10
Subtract Broker Commission = $998, 390
Net Round-trip Transaction Costs “$3,220


This is not exactly correct, though, because the bid and ask prices that the exchange posts (e.g.,
on Yahoo!Finance or the Wall Street Journal) are only valid for 100 shares. Moreover, some
transactions can occur inside the bid-ask spread, but for most large round-trip orders, chances
are that you may have to pay more than $50.08 or receive less than $49.92. So 0.32% is probably
a bit too small. (In fact, if your trade is large enough, you may even move the publicly posted
exchange price away from $50!) Your buy order may have to pay $50.20, and your sell may
only get you $49.85. In real life, the true round-trip transaction cost on a $1 million position
in PEP is on the order of magnitude of 50 basis points.
The above applies primarily to a market order, in which you ask your broker to buy or sell at An even lower cost
alternative: limit orders.
the prevailing market price. A limit order can specify that you only wish to buy or sell at $50.00,
but you are patient and willing to take the chance that your order may not get executed at all.
There is a common belief that limit orders are “cheaper” in terms of transaction costs, but also
“riskier.” For example, if you have a standing limit order to buy at $50, and the company reveals
that it has managed earnings, so its value drops from $51 to $20, your limit order could still
easily execute at $50.
Indirect and Opportunity Costs: Investors do not need to spend a lot of time to ¬nd out the Opportunity costs are
low, too.
latest price of the stock: it is instantly available from many sources (e.g., from the Internet
such as Yahoo!Finance). So, the information research costs are very low: unlike a house, the
value of a stock is immediately known. Finally, upon demand, a buyer can be found practically
instantaneously, so search and waiting costs are also very low. Recall the often multi-month
waiting periods if you want to sell your house.
Compare the ¬nancial securities transaction costs to the transaction costs in selling a house. Compared to other
economic assets, ...
Broker fees alone are typically 6%: for the $100,000 equity investment in the $500,000 house,
this comes to $30,000 for a round-trip transaction. Add the other fees and waiting time to this
cost and you are in for other transaction costs, say, another $10,000. And houses are just one
example: Many transactions of physical goods or labor services (but not all) can incur similarly
high transaction costs.


Table 6.2. Comparison of Transaction Costs on Stocks and Real Estate

Financial Security
Real Estate
Cost Type Explanation (House) (Stock)
≥6%
Direct Typical Round-trip Commission etc. 0“1%
Search/Research Time to Determine Fair Price high zero
Search/Liquidity Time Waiting to Find Buyer variable zero




Anecdote: Payment for Order Flow
The next ¬nancial scandal may well be payment for order ¬‚ow. Although well known among ¬nance pro-
fessionals, and disclosed to customers, most individual investors do not know that especially (but not only)
discount brokers, such as Charles Schwab, Ameritrade, and e-Trade, can route their investors™ orders rou-
tinely to market makers who charge relatively high bid-ask spreads, and then pay the discount broker a re-
bate kickback (typically 1 to 4 cents per share). Some brokerage houses can even ¬ll customer orders with
other customer orders in-house, at execution prices that are not the best prices. In any case, from the point
of view of transaction costs, very wealthy investors may not necessarily be better o¬ using discount bro-
kers, but this is di¬cult for individual investors to determine conclusively. More information can be found
at invest-faq.com/articles/trade-order-routing.html. The SEC also publishes “What every Investor should know”
at www.sec.gov/investor/pubs/tradexec.htm.
¬le=frictions.tex: LP
126 Chapter 6. Dealing With Imperfect Markets.

In contrast, if you want to buy or sell 100 shares in, say, Microsoft stocks, your transaction
...¬nancial securities
have such low costs are relatively tiny. Because there are many buyers and many sellers, ¬nancial transaction
transaction costs that
costs are comparably tiny. Even for a $100,000 equity investment in a medium-sized ¬rm™s
they can almost be
stock, the transaction costs are typically only about $300“$500. To oversimplify, this book
assumed to be zero.
will make the incorrect, but convenient assumption that ¬nancial transaction costs are zero
(unless otherwise described). For individuals buying and selling ordinary stocks only rarely (a
buy-and-hold investor), a zero transaction cost assumption is often quite reasonable. But if
you are a day trader”someone who buys and sells stocks daily”you better read another book!
(And if you are a company that wants to issue new shares, wait until Section 27.)
Solve Now!
Q 6.13 What would you guess the order of magnitude to be for a round-trip transaction in
$10,000 worth of shares of DELL Computer be? Describe in percent and in absolute terms.


Q 6.14 List important transaction cost components, both direct and indirect.



6·3.C. Transaction Costs in Returns and Net Present Values

As an investor, you usually care about rates of return after all transaction costs have been
Commissions need to be
taken out of meaningful taken into account, not about quoted rates of returns from quoted prices. Let™s see how you
rates of return.
should take these transaction costs on both sides (buy and sell) into account.
Return to our housing example. If you purchase a house for $1,000,000 and you sell it to the
next buyer at $1,100,000 through a broker, your rate of return is not 10%. At selling time, the
brokers charge you a 6% commission. There are also some other costs that reduce the amount
of money you receive, not to mention the many opportunity costs. Say these costs amount
to $70,000 in total. In addition, even when you purchased the house, you most likely had to
pay some extra costs (such as an escrow transfer fee) above and beyond the $1,000,000”say,
$5,000. Your rate of return would not be $1, 100, 000/$1, 000, 000 ’ 1 = 10%, but only

($1, 100, 000 ’ $70, 000) ’ ($1, 000, 000 + $5, 000)
= ≈ 2.5% .
r
($1, 000, 000 + $5, 000)
(6.2)
Dollars Returned, Dollars Invested,

after Transaction costs after Transaction costs
Rate of Return = .
Dollars Invested, after Transaction costs

Note how the $5,000 must be added to, not subtracted from the price you paid. The price
you paid was ultimately higher than $1,000,000. The $5,000 works against you. (Incidentally,
in order to make their returns look more appealing, many professional fund managers quote
their investors™ rates of return before taking their own fees (transaction costs) into account.
Usually, a footnote at the bottom satis¬es the lawyers that the investors can not sue for being
misled”they are supposed to know how to adjust returns for transaction costs themselves,
which you now do.)
How do you take care of transaction costs in present value calculations? This is relatively
In NPV, work with
after-transaction-cost straightforward. In the example, you put in $1,005,000 and receive $1,030,000”say, after one
cash ¬‚ows”and
year. So,
after-transaction costs
$1, 030, 000
of capital.
NPV = ’$1, 005, 000 + (6.3)
.
1 + Opportunity Cost of Capital
The only thing you must still take care of is to quote your opportunity cost of capital also in
after-transaction cost terms. You may not be able to get a 10% rate of return in comparable
investments, because you may also be required to pay a transaction cost there, too. In this case,
presume that an alternative investment with equal characteristics in the ¬nancial markets (not
the housing markets) earns an 8%/year return, but has a 50 basis point cost, so this project
may have an appropriate NPV of

$1, 030, 000
(6.4)
NPV = ’$1, 005, 000 + ≈ ’$141, 860 .
1 + 7.5%
¬le=frictions.tex: RP
127
Section 6·3. Market Depth and Transaction Costs.



Solve Now!
Q 6.15 Compute your after-transaction costs rate of return on purchasing a house for $1,000,000,
if you have to pay 0.5% transaction fees upfront and pay 6% broker™s commission (plus 2% in
waiting costs). Assume a $4,000/month e¬ective dividend of enjoying living in the house. At
what rate of capital appreciation would the NPV be zero if you resold after one year? Assume
that your opportunity cost of capital is 7% per year.



6·3.D. Liquidity

Things get even more interesting when transaction costs in¬‚uence your upfront willingness to More illiquid
investments often have
purchase assets. You might not want to purchase a house even if you expect to recoup your
to offer a higher rate of
transaction cost, because you dislike the fact that you do not know whether it will be easy return.
or hard to resell. After all, if you purchase a stock or bond instead, you know you can resell
without much transaction cost whenever you want.
So, why would you want to take the risk of sitting on a house for months without being able to Physics in Finance? The
Liquidity Analogy.
sell it? To get you to purchase a house would require the seller to compensate you. The seller
would have to o¬er you a liquidity premium”an extra expected rate of return”to induce you to
purchase the house. (We have already brie¬‚y mentioned this premium in the previous chapter.)
The liquidity analogy comes from physics. The same way that physical movement is impeded by
physical friction, economic transactions are impeded by transaction costs. Financial markets
are often considered low-friction, or even close to frictionless. And when the amount of trading
activity subsides, pros would even say that “the market has dried up.”
Housing may be an extreme example, but liquidity e¬ects seem to be everywhere and important” This is true even for
and even in ¬nancial markets with their low transaction costs. A well-known and startling ex- Treasury Bonds:
on-the-run vs.
ample is Treasury bonds. One bond is designated to be on-the-run, which means that everyone off-the-run bonds.
who wants to trade a bond with roughly this maturity (and the ¬nancial press) focuses on this
particular bond. This makes it easier to buy and sell the on-the-run bond than a similar but not
identical o¬-the-run bond. For example, in November 2000, the 10-year on-the-run Treasury
bond traded for a yield-to-maturity of 5.6% per annum, while a bond that was just a couple
of days o¬ in terms of its maturity (and thus practically identical) traded at 5.75% per annum.
In other words, you would have been able to purchase the o¬-the-run bond at a much lower
price than the on-the-run bond. The reason why you might want to purchase the on-the-run
bond, even though it had a higher price, would be that you could resell it much more quickly
and easily than the equivalent o¬-the-run bond. Of course, as the date approaches when this
10-year bond is about to lose its on-the-run designation and another bond is about to become
the on-the-run 10-year bond, the old on-the-run bond drops in value and the new on-the-run
bond increases in value.
The provision of liquidity in markets of any kind is a common business. For example, you Liquidity provision is a
common business.
can think of antique stores or second-hand car dealerships as liquidity providers that try to
buy cheap (being a standby buyer), and try to sell expensive (being a standby seller). Being a
liquidity provider can require big risks and capital outlays. If it was easy, everyone could do
it“and then there would be no more money in liquidity provision!
Solve Now!
Q 6.16 What is the di¬erence between a liquidity premium and transaction costs?
¬le=frictions.tex: LP
128 Chapter 6. Dealing With Imperfect Markets.

6·4. An Introduction to The Tax Code

Our next violation of market perfection is taxes. They are pervasive and usually not small
potatoes”they play such an important role that it is worthwhile to make a digression and
explain the overall U.S. tax code once, at least in broad strokes. The actual tax code itself is
very complex, and its details change every year, but the basics have remained in place for a
long time and are similar in most countries. So, let us summarize in this section most of what
you shall need in this book. It is an unusual section, in that it covers a subject matter to which
we will refer again many times later”and like the tax code itself, it is somewhat tedious. I will
try to liven it up with some anecdotes of how crazy the tax code really is, but you will just have
to bear with it.


6·4.A. The Basics of (Federal) Income Taxes

With the exception of tax-exempt institutions, such as charitable institutions and pension
The Tax Code basics are
simple, the details are funds (which su¬er no taxes), individuals and corporations in the United States are taxed in
complex.
a similar fashion, so we can combine our discussion of the two. The name of the Internal
Revenue Service (IRS) tax form that individuals have to ¬le is feared by every U.S. tax payer:
it is the infamous Form 1040.
Earned income or ordinary income is subject to both federal income taxes and state income
Step 1: Compute your
Taxable Income. taxes. There are, however, some deductions that taxpayers can take to result in lower taxable in-
come. Most prominently, in the United States, individuals who itemize their deductions can re-
duce their taxable income through mortgage interest payments. (This does not extend to other
kind of interest payments, so mortgage borrowing”rather than, say, car loan borrowing”is
often the best choice in terms of after-tax e¬ective interest costs for many individuals.) Fur-
ther, with some restrictions, individuals may deduct other expenses, such as some educational
expenses and certain retirement savings (speci¬cally, through contribution to an individual
retirement account, such as an ordinary I.R.A. or a 401-K). (These are only tax-advantaged, not
tax-exempt. Most contributions are income-tax exempt, but the IRS will collect taxes when the
money is withdrawn in the future.) Individuals can also carry forward losses or deductions that
they could not legally deduct in the current year into future years.
Corporations are treated similarly, but often more generously by the tax code: they are gener-
Corporations are similar.
ally allowed to deduct all interest, not just mortgage interest, and many corporations enjoy a
plethora of preferential tax exemptions and loopholes, too numerous to list in just one book
and ever-changing. Unlike individuals, corporations that have losses or extra deductions can
even receive a refund for taxes paid in the most recent three years. This is not necessarily
unfair”after all, corporations are just entities owned by individuals. Just as your car is not
paying the car tax the DMV imposes”you, the owner, are paying the car tax”taxing corpora-
tions is just a di¬erent mechanism of taxing the individuals who own the corporation.
Table 6.3 shows how your taxable income computation might look like. After you have com-
Tax Rates (Brackets) are
“progressive.” puted your taxable income, you must apply the appropriate income tax rates. Income tax rates
for individuals depend on your marital status and are usually progressive”that is, not only do
you have to pay higher taxes when making more money, you have to pay increasingly higher
taxes when making more money. (They are roughly progressive for corporations, but not per-
fectly so.) For example, Table 6.4 shows the U.S. federal income tax rates in 2004 for single
individuals and corporations.



Anecdote: The Income Tax
The ¬rst federal income tax was introduced during the Civil War. It amounted to two percent per year on income
above about $80,000 in 2002 dollars. Attorney Joseph H. Choate argued against the federal income tax in the
Supreme Court”and won! It took a constitutional amendment to reinstate it. In his argument, Choate warned
that the two percent rate might one day rise to twenty percent. (Source: Don Mathews.)
Between 1945 and 1963, the top income tax rate was around 90%; this was also the period in which the United
States experienced the greatest economic boom in its history. Presumably, this was just coincidence.
¬le=frictions.tex: RP
129
Section 6·4. An Introduction to The Tax Code.




Table 6.3. Sample Taxable Income Computation

Actual Earned Income $100,000
“ Allowed Mortgage Interest $10,000
“ Allowed Retirement Investment
Deduction $5,000
(if investor is a person)

= Taxable Income $85,000

Corporations are taxed similarly, but may be allowed a plethora of possible deductions. Details vary year to year,
state to state, and company to company.




Table 6.4. Federal Income Tax Rate Tables for 2004

Single Individual
Tax Rate Description Minimum Maximum (Cumulative)
10% on the ¬rst $7,150 $0 $7,150 $715
15% on the next $21,900 $7,150 $29,050 $4,000
25% on the next $41,300 $29,050 $70,350 $14,325
28% on the next $76,400 $70,350 $146,750 $35,717
33% on the next $172,350 $146,750 $319,100 $92,592
35% on the remainder $319,100 unlimited



Corporations
Tax Rate Description Minimum Maximum (Cumulative)
15% on the ¬rst $50,000 $0 $50,000 $7,500
25% on the next $25,000 $50,000 $75,000 $13,750
34% on the next $25,000 $75,000 $100,000 $22,250
39% on the next $235,000 $100,000 $335,000 $113,900
34% on the next $9.6 million $335,000 $10.0 million $3,377,900
35% on the next $5.0 million $10.0 million $15.0 million $5,127,900
38% on the next $3.3 million $15.0 million $18.3 million $6,381,900
35% on the remainder $18.3 million unlimited

Source: www.smbiz.com.




Table 6.5. Sample Income Tax Computation

Rate on Amount Tax
10% on $7,150 = $715
15% on $21,900 = $3,285
25% on $41,300 = $10,325
28% on $14,650 = $4,102
Computed Total Income Tax on $85,000 = $18,427
¬le=frictions.tex: LP
130 Chapter 6. Dealing With Imperfect Markets.

Each of the tax rates in Table 6.4 is also called a tax bracket, because each de¬nes a range of
Step 2: Look up Your
Tax Bracket. income. If you are an individual in the 28% tax bracket, it means that you have taxable earn-
ings between $70,350 and $146,750. Again, as with the computation of the taxable income,
be warned that this particular tax rate table also contains many simpli¬cations. (For example,
there is also an Alternative Minimum Tax (A.M.T.) that nowadays applies to many taxpay-
ers.) Table 6.5 shows how you would compute your federal income tax on a taxable income of
$85,000, assuming you are single”it would come to $18,427.


6·4.B. Before-Tax vs. After-Tax Expenses

It is important for you to understand the di¬erence between before-tax expenses and after-tax
Taxpayers prefer
before-tax expenses to expenses. Before-tax expenses reduce the income before taxable income is computed. After-
(equal) after-tax
tax expenses have no e¬ect on tax computations. Everything else being equal, if the IRS allows
expenses.
you to designate a payment to be a before-tax expense, it is more favorable to you, because
it reduces your tax burden. For example, if you earn $100,000 and there were only one 40%
bracket, a $50,000 before-tax expense leaves you

($100, 000 ’ $50, 000) · (1 ’ 40%) = ,
$30, 000
(6.5)
Before-Tax Net Return · (1 ’ Tax Rate) = After-Tax Net Return

while the same $50,000 expense if post-tax leaves you only with

(6.6)
$100, 000 · (1 ’ 40%) ’ $50, 000 = $10, 000 .

We have already discussed the most important tax-shelter: both corporations and individuals
can and often reduce their income tax by paying interest expenses, although individuals can do
so only for mortgages. (Chapter 23 explores income tax reduction schemes for corporations in
great detail.)
However, even the interest tax deduction has an opportunity cost, the oversight of which is
Save yourself some
money by not repeating a common and costly mistake. Many home owners believe that the deductibility of mortgage
this mistake!
interest means that they should keep a mortgage on the house under all circumstances. It is
not rare to ¬nd a home owner with both a 6% per year mortgage and a savings account (or
government bonds) paying 5% per year. Yes, the 6% mortgage payment is tax deductible, and
e¬ectively represents an after-tax interest cost of 4% per year for a tax payer in the 33% marginal
tax bracket. But, the savings bonds pay 5% per year, which are equally taxed at 33%, leaving
only an after-tax interest rate of 3.3% per year. Therefore, for each $100,000 in mortgage and
savings bonds, the house owner throws away $667 in before-tax money (equivalent to $444 in
after-tax money).




Anecdote: The Use of Taxes
Where do all the taxes go?
In 2002, there were 128 million households ¬ling federal income taxes. About $1 trillion (or about $7,800
per household) went to entitlement programs (primarily Social Security and Medicare). About $350 billion (or
$2,700 per household) each went to defense spending and to non-defense spending. In in¬‚ation-adjusted terms,
defense expenditures have remained roughly constant since 1962, non-defense expenditures have doubled,
and entitlements have grown eightfold. Entitlements are projected to continue growing rapidly in the future,
although this growth is likely not to be economically sustainable by the working population. (Source: The
Heritage Foundation.)
State and Local Government expenditures in total are about half as large as federal government expenditures.
In 2002, total government expenditures ran at about $2,855 billion per year, for a Gross Domestic Product of
$10,150 billion, almost 30% of the total. Put di¬erently, for every two dollars spent in the private economy, one
dollar is spent by government somewhere.
¬le=frictions.tex: RP
131
Section 6·4. An Introduction to The Tax Code.

6·4.C. Average and Marginal Tax Rates

It is also important for you to distinguish between the average tax rate and the marginal tax The Average Tax Rate is
what you pay on your
rate. The average tax rate is the total income tax divided by the income. In our example from
overall income.
Table 6.5, the average tax rate is
$18, 427
Average Tax Rate = ≈ 21.68%
$85, 000
(6.7)
Total Tax Paid
= .
Total Taxable Income

(Some people prefer computing average tax rates relative to Total Income, rather than relative
to Total Taxable Income). In this example, Uncle Sam receives 21.68% of this individual™s taxable
income.
In contrast, the marginal tax rate is the tax rate that applies to the last dollar earned (i.e., The Marginal Tax Rate is
what you paid on your
someone™s tax bracket, as explained above). In our example with an income of $85,000, Table 6.4
last dollar of income,
shows that this rate was and what you would
have to pay on one more
(6.8)
Marginal Tax Rate = 28% .
dollar of income.
The marginal tax rate is important, because it applies to any additional activity you might
undertake. For example, if you want to work one extra hour at a $40 an hour pre-tax pay rate,
you only receive (1’28%)·$40 = $28.80 as spendable extra cash, not (1’21.68%)·$40 = $31.32.
Thus, in the decision whether to work (which is itself a project ) or to play basketball (a sort
of consumption “project” that is not taxed!), it is the marginal tax rate that matters, not the
average tax rate.
Or, take a company facing the same tax situation (income and tax rate) next year, which now has In deciding between
corporate investments,
to decide between investing in a project that costs $100 and will return $110, or investing in a
the marginal tax rate
tax-exempt vehicle that costs $100 and will return $107.50. If it takes the project, its earnings matters!
will increase from $85,000 to $85,010. At the marginal tax rate of 28%, its taxes will increase
to $18, 427 + 0.28 · 10 ≈ 18, 429, slightly raising the average tax rate (still 21.68%, though). So
the extra after-tax income will only be $7.20”less than the $7.50 that the ¬rm can get from
putting its $100 into the tax-exempt vehicle instead. The ¬rm™s average tax rate of 21.89% is
irrelevant”whatever the ¬rm was able to avoid in taxes on its ¬rst dollars of earnings is the
same and thus does not matter to each additional dollar. Economists are almost always more
interested in the marginal tax rate than the average tax rate.


6·4.D. Dividend and Capital Gains Taxes

While ordinary income applies to products and services sold, capital gain applies to income Capital gains are taxed
less than ordinary
that is earned when an investment asset that was purchased is sold for a higher price. Capital
income.
gains are peculiar in three ways:

1. If the asset is held for more than a year, the capital gain is not taxed at the ordinary
income tax rate, but at a lower long-term capital gains tax rate. (In 2002, the long-term
capital gains tax rate is 15 percent for taxpayers that are in the 25% tax bracket or higher.)

2. Capital losses on the sale of one asset can be used to reduce the taxable capital gain on
another sale.

3. The tax obligation occurs only at the time of the realization: if you own a painting that
has appreciated by $100,000 each year, you did not have to pay 20% · $100, 000 each year
in taxes. The painting can increase in value to many times its original value, without you
ever having to pay a dime in taxes, just as long as you do not sell it. In contrast, $100,000
in income per year will generate immediate tax obligations”and you even will have to pay
taxes again if you invest the labor income for further gains.
¬le=frictions.tex: LP
132 Chapter 6. Dealing With Imperfect Markets.

Dividends, that is, payments made by companies to their stock owners, used to be treated as
Dividends”until 2008 ?!
ordinary income. However, the “Bush 2003 tax cuts” (formally, the Jobs&Growth Tax Relief
Reconciliation Act of 2003) reduced the tax rate to between 5% and 15%, the same as long-
term capital gains taxes”provided that the paying company itself has paid su¬cient corporate
income tax. However, this will only be in e¬ect until 2008, when dividends may be taxed at the
More on dividends is in
Chapter 23. ordinary income tax level again. There is no guarantee that this will not change every couple of
years, so you must learn how to think about dividend taxes, not the current details of dividend
taxes.
In the United States, corporations holding shares in other companies are also taxed on dividend
Corporations are
“lonelier” in the U.S., proceeds. This makes it relatively ine¬cient for them to hold cross equity stakes in dividend
because they do not
paying companies. However, in Europe, dividends paid from one corporations to another are
want to be taxed on
often tax-exempted or tax-reduced. This has allowed most European corporations to become
inter-corporate dividend
distributions.
organized as pyramids or networks, with cross-holdings and cross-payments everywhere. (In
e¬ect, such cross-holdings make it very di¬cult for shareholders to in¬‚uence management.)


6·4.E. Other Taxes

In addition to federal income taxes, there are a plethora of other taxes. Most states impose
Other Income Taxes:
state, county, their own income tax. This typically adds another tax rate of between 0% and 10%, depending
international taxes.
on state and income. Worse, each state has its own idea not only of what its tax rate and tax
brackets should be, but even how taxable income should be computed. Thus, you need to learn
not only the federal tax code, but also your state™s tax code. For example, California has the
highest marginal state income tax bracket that is not federal deductible: 9.3%. Montana has
the highest marginal state income tax bracket that is tax deductible on your federal income tax:
11%. Alaska, Florida, Nevada, South Dakota, Texas, Washington, and Wyoming levy no state
income tax, and New Hampshire and Tennessee tax only interest and dividend income.
Many counties pay for school education with property tax rates. In the richer counties of south-
Property Taxes are
state/local. west Connecticut, the tax is about 1% of the value of the house, but it can reach about 4% in the
poorer urban counties. In Maine (the second-highest property tax collector in the nation), resi-
dents pay 5.5% of their income in property tax. Many states also levy a sales tax. Tennessee and
Louisiana have a sales tax of 8.35%; Alaska, Delaware, Montana, New Hampshire, and Oregon
levy no sales tax. (A nice summary can be found at www.retirementliving.com/RLtaxes.html.
It also includes a ranking of the tax burdens by state”Alaska [with 6% of total income], New
Hampshire, Delaware, and Tennessee have the lowest; New York [with 12.9% of total income],
Maine, Ohio, and Hawaii have the highest.)




Anecdote: Taxing the Rich, or Taxing the Wealthy?
The political rhetoric about who wants to “tax the rich” is just false. Neither Democrats nor Republicans ever
debate about taxing the rich. Instead, they debate about taxing high-income individuals. This matters because
there is a big di¬erence between wealth increases and income. The lowest tax rates on wealth increases are
enjoyed by the richest Americans. Most of these are households that earn most of their wealth increases not
in ordinary income, but in capital gains from existing wealth. If not realized, these wealth increases may never
have been taxed, at all! For example, Warren Bu¬ett has probably paid about 0.0% in personal income tax on
his wealth increase of over $30 billion over the last 30 years.
In contrast, most ordinary households receive their annual wealth increases in ordinary income or interest
receipts. These wealth increases are taxed every year, and are taxed at a much higher marginal tax rate than
capital gains wealth increases. Roughly, an ordinary worker™s wealth increases su¬er taxes to the tune of about
25% to 50% per year. (Chapters 22“23 will describe tax sheltering in greater detail.) The primary tax on wealth
today seems to come from property taxes”the value of one™s house. Again, this does not much to tax the
“super-wealthy,” because for them, the residence constitutes only a very small part of their wealth.
Although a tax on all wealth increases would be fairer than the current income tax and provide better incentives
to work, it would also be far more di¬cult to administer. Nevertheless, most European countries have both
annual wealth-based taxes and wealth-based inheritance taxes.
¬le=frictions.tex: RP
133
Section 6·4. An Introduction to The Tax Code.

If you have to ¬le in multiple states or even in multiple countries”although there are rules that Complex Complexity.
try to avoid double taxation”the details can be hair-raisingly complex. If you ¬nd yourself in
such a situation, may the force be with you!
Finally, there are social security and medicare contributions. Although these are supposedly “Social” Taxes: Social
Security and Medicare.
insurance premia, any money taken in today is immediately spent by the government on the
elderly today. Thus, anyone young today is unlikely to receive much in return from the govern-
ment in 20 to 30 years”when there will be fewer young people around to pay their retirement
bene¬ts. Thus, many ¬nancial economists consider social taxes to be as much a form of income
tax as the statutory income tax.
This book also ignores many other non-income taxes. For some taxes, such as the sales tax, it is Non Income Based Taxes:
Sales Tax, Real Estate
not clear how to use expertise in ¬nance to lower them. For other taxes, such as the estate tax,
Taxes, Estate Taxes.
you need extremely specialized ¬nancial vehicles to avoid or reduce them. These are beyond
the scope of this book.


6·4.F. What You Need To Know About Tax Principles In Our Book



Important: You must understand

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