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’17.96 ’19.51
DNA Genentech Xolair 1.55
7/9/01-7/11/01
’3.79 ’4.96
FRX Forest Labs Synapton 1.17
11/17/98-11/19/98
Gilead
’21.08 ’21.09
GILD Adefovir 0.01
Sciences 11/01/99-11/3/99
’46.11 ’46.89
GNLB Genelabs Aslera 0.78
6/26/01-6/28/01
Glaxo-Smith-
’0.15 ’1.92
GSK Augmentin 1.77
Kline 12/14/01-12/18/01
12/27/01-12/31/01 ’20.31 ’20.39
IMCL imClone Erbitux 0.08
Johnson& Risperdal
’1.24 ’5.44
JNJ 4.20
Johnson Consta 6/28/02-7/2/02
12/12/00-12/14/00 ’44.78 ’46.98
MAXM Maxim Maxamine 2.20
’0.70 +1.05
NVS Novartis Zelnorm 0.35
6/22/01-6/26/01
’2.51 ’2.80
PFE P¬zer Zeldox 0.29
6/18/98-6/22/98
’7.32 ’7.79
PHA Pharmacia Parecoxib 0.47
7/12/01-7/16/01
’31.74 ’32.76
PRCS Praecis Plenaxis 1.02
6/11/01-6/13/01
’57.67 ’59.14
SCIO Scios Natrecor 1.47
4/27/99-4/29/99
’58.73 ’58.86
SEPR Sepracor Soltara 0.13
3/6/02-3/8/02
’28.94 ’29.08
VPHM ViroPharma Picovir 0.14
5/9/02-5/13/02
Estradiol/
’5.52 ’7.13
WPI Watson 1.61
Progestin 10/30/00-11/1/00
’24.96%
Average
±22.31%
Standard Deviation




We already know that individual stocks do move around day by day. So four ¬rms may not To eliminate noise,
average many events
be representative enough, given typical stock return noise. Instead, we should average the
from many ¬rms.
event returns for many FDA rejections, hoping that the noise averages away and the signal
becomes more apparent. (Having more ¬rms is like tuning a radio station with a more powerful
antenna.) Table 19.1 presents the same event study”to estimate the value consequences of
FDA rejections”for 20 pharmaceutical ¬rms. It is usually a good idea to reduce the in¬‚uence
of overall market returns, so we subtract the overall stock market return on the same day from
each ¬rm™s stock return. After all, we do not want to attribute the fact that the stock market
declined by, e.g., 1% on the announcement day, to the drug announcement. (You also have to
hope that there are no other major corporate events that always occur on the same day as the
FDA drug application rejection.) The larger sample event study in Table 19.1 suggests that
when ¬rms announce that their drug applications are rejected by the FDA, they lose on average
about 25%, plus or minus 22%.
Whereas Table 19.1 gives only the average rate of return on the three days of the announcement Event Study
Graphs”perhaps we can
at the bottom of the table, Figure 19.4 gives the average rate of return on each event day.
make money?!
Graph A indicates that we most likely misidenti¬ed the timing of the announcement day: if
the announcement happened after market closing, then we only see a market reaction on day
+1. On days +2 and +3, however, there appears to be a slight market imperfection: the stocks
seem to go down further, by a total of about 5%”if this pattern is systematic, it is not only a
violation of market e¬ciency, but it would be enough to earn us a lot of money! Graph B plots
the cumulative return”it adds the return to a running sum. It shows that not much happens
¬le=e¬mkts.tex: LP
498 Chapter 19. E¬cient Markets, Classical Finance, and Behavioral Finance.



Figure 19.4. Average Returns and Cumulative Average Returns in Event Time for 20 FDA
Rejections




0.0
0.00




Cumulative Average Rate of Return
Daily Average Rate of Return




’0.1
’0.05




’0.2
’0.10




’0.3
’0.15




’0.4
’0.20




’10 ’5 0 5 10 ’10 ’5 0 5 10

Event Date Event Date

(A) (B)




before the announcement, so there is no evidence of widespread news leakage or insider trading
prior to our event, but there is some negative trend post announcement. It appears as if the
market “underreacted.” This would be worth further investigation, e.g., to see if it holds up
in bigger samples and if it is more pronounced for certain, identi¬able ¬rms”except that this
chapter has now told you (and the investing public) about a possible slow reaction here and a
possible money-making opportunity now. If the slow market reaction with its pro¬t opportunity
was a real e¬ect, it is likely that it will now disappear as traders will try to exploit it.
Event studies are not without drawbacks. There are three signi¬cant issues to deal with.
Event study are not a
panacea.

Event Importance Event studies work well only if the event is signi¬cant enough to in¬‚uence
Big problem 1 is that we
need to have enough the overall stock market valuation: if a $1 billion stock ¬‚uctuates on average by $10
event occurences.
million a day, it is practically impossible to use an event study to determine the value
of a project worth $100,000. To use our physics analogy, the noise would drown out
the signal. A reasonable rule of thumb is to take the ratio of the typical daily stock
market value ¬‚uctuation (here, $10 million) divided by the order of magnitude of the
value consequence (here, $100,000, so the ratio is $10, 000, 000/$100, 000 = 100), and
then require 50 times as many event observations as this ratio. For the example, this
would require 5,000 event observations”which is likely too many to make such a study
feasible for all but the most frequent events.

Event Anticipation Event studies rely on the fact that stock markets react only to news, i.e.,
Problem 2 is that we
need to know exactly the unanticipated component of an information release. There must be a clear event
when news comes
date. But many events are anticipated, announced over a period of time, or never formally
out”we want only the
announced. For example, if a company was expected with 80% probability to win a contract
unanticipated
information.
worth $1,000,000, the stock price would have already re¬‚ected $800,000. The news that
the company actually won the contract would raise the stock price only by $200,000, not
by $1,000,000. The news that the company would not have won the contract would drop
the stock price by $800,000, however. Isolating market expectations can be very di¬cult.
More than likely, the analyst would not know after the fact how expected the event was
by the market at the time. (And, worse: insider trading before the event may have already
moved the stock price to the $1,000,000 before the public announcement.) Therefore, in
many cases, the event study technique is better at helping to determine whether an event
is good or bad for a company (e.g., the announcement of a new law), than it is in helping
to compute an exact value gain.
¬le=e¬mkts.tex: RP
499
Section 19·3. E¬cient Market Consequences.

Simultaneous Events (Contamination) The event study technique relies on the fact that the Problem 3 is that there
are often simultaneous
event can be precisely isolated from other events. If other events occur in the same time
events.
window, any value consequence may stem from these other events, not from the event
that is examined. Unfortunately, many events occur at the same time. For example, at the
annual meetings, we may get simultaneous announcements of dividend changes, corpo-
rate charter changes, institutional votes, information about successions, tough questions
from shareholders, etc. So there is always the danger that what our study may attribute
to dividend changes really is due to simultaneous announcements of corporate charter
changes, instead. We can only hope that the content in these other simultaneous value
events is non-systematic, so that it only adds noise that will average out over many di¬er-
ent ¬rms.

Nevertheless, event studies are a very powerful tool to measure the value e¬ects of many Event studies work even
if the CAPM does not.
changes. Our usual problem of not trusting the CAPM matters little when it comes to a one- to
three-day event, because the average CAPM return is only around ¬ve basis points for a stock
per day. Whether the true expected rate of return is closer four or six basis points is really
irrelevant. Such small di¬erences in mean expected returns are hopefully small compared with
the signal that we expect from our event.


Short Preview: Other Event Study Results
There have been event studies on all sorts of events, ranging from new legislation, to corpo- Event studies have been
used on many different
rate name changes, to analysts™ opinions, to corporate earnings, to stock splits, to corporate
events. We will rely on
dividends, to corporate debt and equity issuance and retirement, to deaths of the founder, etc. event studies in later
Here are some of the ¬ndings. On the day of the announcement, ¬rm values increase on average chapters.


• when ¬rms announce increases in dividends, share repurchases, or stock splits (by about
0.1% to 1%);

• when ¬rms are taken over by other ¬rms (and by about 10% to 30%!)

• when the founding CEO dies (by about 3 to 4%).

Conversely, ¬rm values decrease on average

• when ¬rms announce new stock sales (by about 1 to 3%);

• when they overpay for other ¬rms in acquisitions;

• when they announce lower-than-expected earnings;

• when they fend o¬ an acquirer who has made a bid.

Also, we know that certain legislation can systematically have a positive or negative impact on
¬rms, and this value impact can be measured. For example, it is possible to determine which
¬rms were helped and which ¬rms were hurt when telecommunication and airline markets were
deregulated. For another example, we know that when the U.S. Congress imposed banking and
tax-related sanctions on ¬rms doing business with South Africa™s Apartheid regime, there was
again little e¬ect on these ¬rms. Despite the boycott™s positive moral e¬ect, it was largely not
e¬ective in economic terms.
Side Note: We may wish sanctions on South Africa™s Apartheid regime had been e¬ective, but the evidence
is clear that they were not”possibly because there were too many loopholes to evade the boycott. Of course,
sanctions may still be appropriate on moral grounds regardless of their economic e¬ectiveness. Whether to
boycott socially objectionable behavior is a decision that policy makers should make, not economists. The role
of the ¬nancial economist is only to inform policy makers of the ultimate e¬ectiveness of their actions.
¬le=e¬mkts.tex: LP
500 Chapter 19. E¬cient Markets, Classical Finance, and Behavioral Finance.

Solve Now!
Q 19.9 Which of the following are good candidates for ascertaining the value e¬ects with an
event study, and why:

(a) An acquirer wants to buy the ¬rm.

(b) The CEO dies.

(c) The CEO ages.

(d) Positive earnings surprise at the annual meetings.

(e) Purchase of a new machine.

(f) A law is passed to force the company to reduce its emissions.

(g) An ad campaign.


Q 19.10 What kind of response (“unusual” stock price change and “unusual” rate of return)
would you expect when the company announces that it has struck oil and plans to pay it out next
month? What reaction do you expect over this month? What reaction do you expect on the day
when it pays the dividends?


Q 19.11 What are the factors that make an event study more likely to be more or less informa-
tive?
¬le=e¬mkts.tex: RP
501
Section 19·4. Summary.

19·4. Summary

The chapter covered the following major points:

• Arbitrage is a riskless bet with no negative out¬‚ows under any circumstances. Anyone
would like to take an arbitrage opportunity. When and if they appear, they are likely to
be very small.

• A great bet can be risky”although it can be very pro¬table. If not too risk-averse, an
individual may prefer a large, great bet to a tiny arbitrage opportunity. Like arbitrage
opportunities, great bets are very rare.

• Market e¬ciency simply means that the market uses all available information in setting
prices to o¬er “appropriate rates of return.”

• In the short run, the appropriate expected rate of return on stocks must be small. There-
fore, market e¬ciency prescribes that stocks roughly follow random walks.

• In the long run, it is rarely clear what this “appropriate rate of return” should be. Because
noise makes it di¬cult to measure the average rate of return, it is very di¬cult to either
test models like the CAPM or to test long-run market e¬ciency.

• Beliefs in e¬cient markets come in di¬erent forms.
A more current E-M classi¬cation emphasizes the rationality of the stock market: true be-
liever (stock prices always re¬‚ect underlying project NPVs), ¬rm believer (small deviations,
but di¬cult to take advantage of), mild believer (small deviations, and somewhat possible
to take advantage of), or non believer (arbitrage opportunities and great bets abound).
The standard E-M classi¬cation emphasizes what information it would take to beat the
market: weak form (just past stock price patterns), semi-strong form (other historical
information), and strong form (inside information).

• The overall evidence suggests that it is not easy to become rich”a belief shared by most
¬nance professors. The relative strength of their beliefs in market e¬ciency”the extent
to which professors believe that market prices always re¬‚ect underlying value”separates
¬nance professors into “rationalists” (or “classical” economists) and “behavioralists.”

• Given the millions of investors, many will beat the stock market by chance, and some
investors will beat the stock market many years in a row. Market e¬ciency does not
mean that there are not some investors who will beat the stock market ten years in a row
ex-post, only that any one particular investor is unlikely to beat the stock market ex-ante
ten years in a row.

• Managers can learn valuable information from market prices, both from their own share
price and from other prices. To improve corporate ¬rm value, managers must create
fundamental value”they must undertake positive NPV projects. Simple activities such as
purchasing a random ¬rm to lower risk or splitting shares will not add value.

• Event studies allow us to ascertain the corporate value impact of sharp events, such as
legislative action (FDA rulings) or corporate events (dividend increases).
¬le=e¬mkts.tex: LP
502 Chapter 19. E¬cient Markets, Classical Finance, and Behavioral Finance.

Solutions and Exercises




1. If the arbitrage opportunity can only be done once and gains $10, it is probably worse than a good bet that
loses 1 cent one percent of the time, and gains $1,000,000 ninety-nice percent of the time.


2. The market uses all available information in the setting of its price.
3. More likely.


4. See Formula 19.2.
5. The price can de¬nitely and most likely will be di¬erent. Only the expected price is the same as the price
today.
6. The typical movement (variation) is around plus or minus 1% to 3% a day. The average rate of return is much
lower.
7. If a stock has an expected rate of return of 20% per year”which is de¬nitely on the high side for most
¬rms”the daily rate of return would be
(1 + 20%)1/365 ’ 1 ≈ 0.05%.

8. If each of them has a chance of 50-50 in any given year, then the answer is 10, 000/210 ≈ 10.
9.
(a) An acquirer wants to buy the ¬rm: Super. Usually unannounced and big event.
(b) The CEO dies: Maybe. Depends on suddenness (anticipation) and replace-ability of CEO.
(c) The CEO ages: Bad. No sudden information release. Value e¬ect not big enough.
(d) Positive earnings surprise at the annual meetings: Maybe. Problem is many other things may happen at
the same time.
(e) Purchase of a new machine: Probably Bad. Problem is that one machine is usually too small to make a
big value di¬erence.
(f) A law is passed to force the company to reduce its emissions: Maybe. The value consequences could be
large enough, but by the time the law passes, it has long since been anticipated.
(g) An ad campaign: Bad. First, there is no unique date on which to pin down the information release, and
the value e¬ects are often not too overwhelming, either.

10. The share price response would immediately be positive. Over the following month, you would not expect
any unusual upward or downward drift: it should be about zero. Finally, when the ¬rm pays out the special
dividend, the rate of return should be zero on average, too, although its share price will have to drop by the
amount of dividend paid to keep the return around zero.
11. The e¬ect should be big, unanticipated, and there should be many other companies that have already expe-
rienced similar events in the past.



(All answers should be treated as suspect. They have only been sketched, and not been checked.)
Part IV

Financing Choices and Capital Structure




(A part of all versions of the book.)




503
505


Transition
We are still plagued by one problem: Although we know how ¬rms should value
projects, and although we know the determinants of our cost of capital, we do
not yet know how we can best get new investors to part with their cash. We
just assumed that if our ¬rm had the right project (with a positive NPV), then
the funds would come by themselves.

In the real world, this may not be the case, but our ¬rm does have many venues
for raising funds. We now discuss both the types of securities that our ¬rm
can sell to potential investors and the selling process itself.
506


What You Want to Accomplish in this Part
The goal of this part of the book is to learn how ¬rms should ¬nance projects with debt and
equity, and how this in¬‚uences the ¬rm™s cost of capital.

• Chapter 20 explains how you should think of securities that ¬rms sell (issue), and how
these securities are sold into the ¬nancial markets.

Typical questions: What rights do stock investors have, e.g., if the underlying
¬rm goes bankrupt? What is preferred stock?

• Chapter 21 shows that if everything is perfect, then the value of the ¬rm is the value of
its underlying assets and not dependent on whether it is ¬nanced with debt or equity.

Typical questions: How does the value and expected rate of return of the ¬rm™s
equities change if the ¬rm issues a large bond in order to buy back stock?

• Chapter 22 shows how ¬rms should make capital structure and capital budgeting deci-
sions if they have to pay corporate income taxes.

Typical questions: What is the ¬rm™s cost of capital and value if it ¬nances itself
with 50% debt and 50% owner™s equity, instead of with 100% owner™s equity.

• Chapter 23 explains other considerations that can have important in¬‚uences on capital
structure.

Typical questions: Should a fast growing ¬rm ¬nance itself with more or less
debt than a pro¬table value ¬rm? If investors are concerned that managers like
to raise funds primarily when they know that their current projects are not very
good, then what can managers do to calm investor fears in order to be able to
raise more money?

• Chapter ?? describes the capital structure landscape in the United States. Primarily, it
shows in some detail how IBM™s capital structure evolved from 2001 to 2003. Secondarily,
it describes how companies generally are ¬nanced.

Typical questions: How should we de¬ne debt/equity ratios? How do debt/equity
ratios really come about?

• Chapter 25 describes how managers should be thinking about changes in capital structure.

Typical questions: What mechanisms can managers use to change capital struc-
ture and ¬rm size.

• Chapter 26 tries to understand the relative importance of di¬erent mechanisms and
causes of capital structure change.

Typical questions: How important are equity issues in determining the debt-
equity ratio of the typical company?

• Chapter 27 describes the role of investment banks.

Typical questions: What do investment bankers really do? Who are the top
investment bankers? How much do they charge?

• Chapter 28 focuses on corporate governance in more detail.

Typical questions: If investors are concerned that managers like to steal or waste
money, what can managers do (and what do they do) to calm investor fears?
CHAPTER 20
Corporate Financial Claims

Who owns What?
last ¬le change: Feb 23, 2006 (14:59h)

last major edit: Apr 2005




After the ¬rm has determined what projects to take, the question is how they should be ¬nanced.
This is called the capital structure of the ¬rm. You have already encountered the two basic
¬nancing choices that ¬rms have: Current ¬rm owners can accept new partners, which they
can accomplish by issuing equity (stock). Or they can borrow money, which they can accomplish
by issuing debt (bonds). There are also many other ¬nancial claims, most of which are hybrids
of these two basic choices.
This chapter describes some of the choices that corporations have, and how to think of them.
The next chapters will explain how to choose among them.




507
¬le=corpclaims.tex: LP
508 Chapter 20. Corporate Financial Claims.

20·1. The Basic Building Blocks

The capital structure of a ¬rm consists of the ¬nancial claims on its future payo¬s. Claims
Bonds and Stocks are
the basic building blocks. have two aspects to them:
Homes and Corporations
are really the same.
Cash Flow Rights, which describe how future project payo¬s will be allocated; and

Control Rights, which allow the claim owners to in¬‚uence corporate decisions, often necessary
to enforce their cash ¬‚ow rights.

When claims are issued by a publicly traded company, they are called securities, because they
are registered with the Securities and Exchange Commission (SEC). However, the term is now
used much more liberally, e.g., for foreign securities and privately placed securities, which
really are not securities in the original sense of the term.
The two basic building blocks of capital structure are also the most common ¬nancial claims:
Debt and Equity.
Owning the ¬rm really bonds (leverage) and stocks (equity). Just as our buyer from Chapter 5 ¬nanced a house
requires owning all
purchase with a mortgage and kept the rest as levered equity, so do ¬rms issue bonds and
claims without further
stocks. By de¬nition, you own the ¬rm only if you own all claims that the ¬rm has issued. It
obligations.
is not enough for you to own only all stock. If you are the levered equity homeowner, you can
make a lot of decisions about the house, but you really do not fully own the house, because
you cannot dispose of the house and keep the money without repaying the mortgage. It is you
plus the mortgage company that together own the house. Similarly, the levered equity holders
in a corporation make almost all decisions, but they do not fully own it. The value of the ¬rm
is by de¬nition the sum-total value of all its outstanding claims.


20·1.A. Bonds

In Part I, we have already worked extensively with bonds, though not necessarily corporate
Bonds are Loans, with
speci¬ed obligations by bonds. Bonds are just loans that promise speci¬c payo¬s at speci¬c times in the future. The
the company to its
borrower (or issuer) receives cash upfront and contractually promises to pay cash in the future.
creditors.
This returned cash can be classi¬ed into tax-deductible interest payments and repayment of
principal. Most bonds promise payments every 3 or 6 months. At maturity, corporate bonds
usually pay back the principal. Under the most common arrangement, the absolute prior-
ity rule (APR), bondholders ¬rst receive what they have been promised, before more junior
claimants (such as equity) can receive anything.
Control Rights: Unless the ¬rm is near ¬nancial distress, bondholders typically do not have the
Bondholders have no
control rights, unless right to participate in the decisions of the ¬rm or the selection of its management. But if the
the ¬rm goes bust.
¬rm misses a payment, the bondholders have the right to force the ¬rm into bankruptcy. In the
United States, bankruptcy means either corporate reorganization under Chapter 11 or corpo-
rate liquidation under Chapter 7, named for their respective chapters in the Federal Bankruptcy
Code. In theory, bankruptcy allows bondholders to take over and thereby own the company to
recover what they were contractually promised. In practice, this is not as easy as it is in many
European countries, but it does happen frequently enough. In any case, few managers survive
even Chapter 11 bankruptcy, so they generally try to avoid missing bond payments. In addi-
tion to the universal right of repayment through control in default, many lenders contract for
additional control rights in the original lending agreement. These are called bond covenants.
For example, a loan agreement may specify that the ¬rm must maintain a certain liquidity, or
its loan can be declared to be in default.
¬le=corpclaims.tex: RP
509
Section 20·1. The Basic Building Blocks.

20·1.B. Ordinary Equity (Common Stock)

Stock, a common abbreviation for ordinary equity or common equity, is like ownership: stock Stock ownership is
ownership post-debt,
shareholder (or just stockholders) receive whatever is left over after the promises to bond-
earning dividends and
holders have been honored. The bad news is that equity typically has the lowest priority in capital gains, and having
bankruptcy. The good news is that shareholders enjoy unlimited upside. If they are lucky, control rights.
they receive dividend payments and capital appreciation. Unlike coupon interest payments,
dividend payments not only can be omitted at the corporation™s discretion, but also have to
be paid from after-tax earnings. Then, even though the corporation has already paid corpo-
rate income tax on its earnings, individuals have to pay personal income tax on their dividend
receipts. This is sometimes called the double taxation of dividends. The Bush Tax Cuts of
2003 have greatly reduced the double taxation, which has also been the norm in many other
countries (such as in the United Kingdom). In sum, you can think of equity holders as corporate
owners that are protected by limited liability (see also Chapter 5).
Control Rights: In situations outside ¬nancial distress, shareholders own the control rights
to make almost all decisions for the company. In publicly traded companies, shareholders
usually elect (and thereby hire and ¬re) the corporate board, to whom they thereby delegate
their control rights. (The legal details to accomplish this vary by corporate charter and country.)
The corporate board in turn appoints the managers, to whom they delegate many if not most
day-to-day control rights. There is considerable disagreement about whether these control
rights also function well in large, di¬usely held, older corporations function. (The managerial
control rights are the focus of Chapter 28 on corporate governance.)
Solve Now!
Q 20.1 What is a control right?


Q 20.2 What is limited liability?




Anecdote: Judge Li¬‚and and Eastern Airlines™ Creditors
Absolute Priority is the theory. In practice, bankruptcy courts can and sometimes do violate the pre-agreed
priority rules in the bankruptcy process. In turn, because corporate managers can choose where to ¬le for
bankruptcy, they usually do so in the court where they expect to fare best.
The Southern District of New York Bankruptcy Judge Burton Li¬‚and was so notorious for violating creditors™
rights, that he attracted not only Eastern Airlines™ bankruptcy, but also those of Manville, Orion Pictures, and
LTV. But it was Eastern Airlines that was Judge Li¬‚and™s crowning achievement: When it went bankrupt in
March 1989, it was fully solvent. Unsecured creditors would have likely been satis¬ed in full. Instead, Judge
Li¬‚and allowed Eastern to continue operating for two more years, partially on the basis that closing it would
have disrupted Christmas travel. Eastern™s ongoing operation evaporated about $1.5 billion through operating
losses and another $100 million through legal fees. In the end, unsecured creditors received practically nothing
of their $2.3 billion claim.
Despite frequent modest APR violations and despite such occasional spectacular examples of drastic APR viola-
tions, APR violations are usually mild. (They may even be necessary. After all, society would not want to see our
lawyers starve!) These days, creditors are aware of expected violations and legal fees, and therefore take them
into account when they purchase bonds and stocks in the ¬rst place. Thus, the presence of lawyers increases
corporations™ costs of ¬nancing.
¬le=corpclaims.tex: LP
510 Chapter 20. Corporate Financial Claims.

20·1.C. Debt and Equity as Contingent Claims

In Chapter 5, you learned about the main tool for the analysis of promised payments: payo¬
Payoff diagrams, again.
tables and payo¬ diagrams. For example, consider a ¬rm with a capital structure that consists
of equity and a single bond that promises to pay $200 next year. The value of the corporation
will be the total value promised to bondholders and shareholders. How much each claims
holder will receive will depend on the value of the ¬rm. Figure 20.1 shows that if the ¬rm is
worth $100, bondholders will receive $100 and shareholders will receive nothing. If the ¬rm is
worth $200, bondholders will receive $200 and shareholders will receive nothing. If the ¬rm
is worth $300, bondholders will receive $200 and shareholders will receive $100. If the ¬rm
is worth $400, bondholders will receive $200 and shareholders will receive $200. And so on.
This is the best way to think of the contractual payment obligations of bonds, stocks, and most
other ¬nancial claims. (There are other important considerations, though, which are covered
in subsequent chapters.) Because you can call the future value of the ¬rm (the base asset) the
underlying state, debt and equity are often called state-contingent claims: their value depends
on the future state of the ¬rm.
Note that if the market is perfect, it is not important to our analysis whether the ¬rm continues
Timing does not matter
to the usefulness of to exist after the bond comes due. You could imagine that the ¬rm is then sold to new owners
these diagrams.
for its fair value ¬rst. The proceeds are then distributed to stockholders and bondholders
according to their claims. Of course, stockholders and bondholders could use these proceeds
to repurchase the remaining ¬rm if they so desire. (On Page 93, in our tornado/sunshine
example, we explained that it does not matter whether the house is sold at the end of time 1.)
However, although payo¬ diagrams are very useful as conceptual aids for a contract that is
Payoff diagrams cannot
tell the part of the story on one payment at a given point in time, they are not as good at illustrating features that are
that is time-varying,
themselves a function of time or a function of many di¬erent points in time. Our example
rather than ¬rm-value
really made it easy to see the value of a zero bond. It would be more di¬cult to use the payo¬
varying.
diagram to fully describe a coupon bond, because these have multiple payment dates, which
can cause quite a set of interesting complications that we would rather avoid. (Similarly, payo¬
diagrams are less useful to illustrate the value of a claim that consists of randomly timed future
payo¬s.) Nevertheless, even in such cases, there is usually a link between the value of the ¬rm
and the value of the ¬nancial claim”so thinking of ¬nancial claims as contingent claims often
remains a useful conceptual, if not entirely accurate, tool.
Solve Now!
Q 20.3 To gain some practice with payo¬ diagrams, assume your medical insurance pays 90% of
your medical expenses, subject to a $500 deductible, and subject to an annuaal limit of $10,000
payout. Write down your insurance payo¬ table and graph an insurance payo¬ diagram, as a
function of your medical expenses. What is the slope of the line at each segment?
¬le=corpclaims.tex: RP
511
Section 20·1. The Basic Building Blocks.




Figure 20.1. Sample Bond and Stock Payo¬ Table (at Time 1)

Firm Value Bond Value Stock Value
$0 $0 $0
$50 $50 $0
$100 $100 $0
$150 $150 $0
$200 $200 $0
$250 $200 $50
$300 $200 $100
$350 $200 $150
¦ ¦ ¦




Sample Bond and Stock Payo¬ Diagram (at Time 1)
Financial Claim
Value, Time 1




T




 
 
 
 
$200




   
   
   
   
y)
t)




   
it
eb




qu
(D




   
(E
nd




k




   
oc
Bo




St




   
he




he
T




   
T




   
   
   
   
   
    E
Firm Value,
$200
Time 1
¬le=corpclaims.tex: LP
512 Chapter 20. Corporate Financial Claims.

20·2. More About Bonds

Over time, many variations and hybrids of the two basic claims have developed. The features
Firms can choose any
claim features they wish. of ¬nancial claims are not written in stone. Firms can and do experiment. Naturally, if a claim
o¬ers more features or protections that are of value to investors, then these investors will be
willing to pay more for the claim upfront. In a perfect market, both companies receive and
investors pay the appropriate fair share (price), regardless of the features chosen by corpo-
rations o¬ering claims for sale. The features described in this chapter are among those that
have survived, evolved, and thrived over the years”those that increase value. Of course, cor-
porations could issue claims that do not maximize value, even if they are fairly priced. For
example, a claim might o¬er its owner the right (or obligation!) to become CEO if it were to
rain in Los Angeles next April 21. This claim would fetch an appropriate price, but it would
probably signi¬cantly lower the value of the ¬rm.


20·2.A. Bond Features

Corporate bonds come in many forms. The issuer can choose what speci¬c rights to o¬er to
Bonds come in a
thousand varieties”and buyers and what rights to reserve for the ¬rm. Naturally, the more rights a bond buyer receives,
then some.
the higher the value of the bond when the issuer sells them, and therefore the lower the cost of
capital (the expected interest rate) on the bond. Some bond features are unique to corporations,
while others are common. Among the more common are the following:

Bond covenants promise that the ¬rm will keep certain promises, or else it will be forced
to repurchase (redeem) the bond. Among the more common covenants are restrictions
on what the ¬rm can do with its assets, how much in dividends it may pay, how many
and what kind of other ¬nancial claims it may issue, what kind of ¬nancial ratios (e.g.,
debt/equity ratio) it needs to maintain, who the auditor is, what happens if the corporation
defaults on any other bond, and how much of its own bonds it will repurchase each year.
This last feature is called a sinking fund commitment and is very common.

Bond seniority speci¬es which bond receives ¬rst dip in case of bankruptcy and liquidation. A
senior bond will have to be satis¬ed in full before a subordinated bond (or junior bond)
may receive any money. In turn, equity receives its funds only after even the most junior
bonds have been fully satis¬ed.

Collateral or security are speci¬c corporate assets pledged to a speci¬c bond in case of default.
For example, mortgage bonds are collateralized by the value of the underlying real estate.
If the issuer fails to pay, the bondholders may repossess the underlying real estate, and
use it to satisfy their claim. If the real estate is not enough to satisfy the claim of the
secured bond, the remaining claim becomes an ordinary bond, waiting in line with other
creditors for payment.

Convertability allows the bond holder to exchange the bond for shares. This is explained in
greater detail in the next section.

Puttability allows bondholders to return the bonds to the issuer, in exchange for pre-agreed-
upon payment. This is like convertibility, only that the conversion is into cash, not into
equity.

Callability allows the issuer (the ¬rm) to “call in” the outstanding bond at a prespeci¬ed price.
For example, a callable bond contract may state that the ¬rm can redeem the bond by
paying back principal plus 10% rate of interest in May 2020. Usually, callable bonds do
not allow a call for the ¬rst ¬ve years in the life of the bond. Callability also often comes
in connection with convertibility, so the call can be used to force bond holders to convert:
The corporation calls the bonds, and the holder of the bond ¬nds that it is in her interest
to convert the bond into equity, rather than to accept repayment.
While a convertible bond gives bondholders extra rights, callable bonds give the ¬rm extra
rights. Therefore, when a bond contains a call feature, it is less valuable than an otherwise
¬le=corpclaims.tex: RP
513
Section 20·2. More About Bonds.

identical bond, which means that issuers of bonds with call features receive less money
when they include the call feature. Put di¬erently, they must pay a higher interest rate
upfront. In e¬ect, every mortgage is a callable bond, because the seller of the bond (the
homeowner, that is you) can just pay back the remaining loan balance (the principal) and
be absolved of all further obligations.
The call feature is a good example of where payo¬ diagrams do not capture the whole Actual calling may
depend not just on the
situation. The value of the callable bond is often more a function of the prevailing in-
value of the ¬rm, but on
terest rate than it is a function of the ¬rm value. Corporations tend to call bonds when such things as interest
the economy-wide interest rate has dropped so replacement bonds have become much rate.
cheaper. (Similarly, homeowners tend to repay their mortgages and re¬nance when the
mortgage interest rate has dropped.) But, because the interest rate is not a one-to-one
function of the ¬rm value in the future, the payo¬ diagram against the ¬rm value at a
¬xed point in time would not tell the whole story.

CFOs must also make decisions on the following corporate bond features. Because these fea-
tures are shared by non-corporate bonds, we have already described them in Part I.

Bond maturity is the time to ¬nal payback. Indeed, borrowing may be very short-term (as
little as overnight!), or very long-term (as long as forever). Bonds of di¬erent maturities
may have di¬erent names. For example, commercial paper is short-term debt, often
guaranteed by a bank™s credit line (see below), and therefore is almost risk-free to the
lender. On the corporate balance sheet, funded debt is the term for debt that has a
maturity of less than 1 year. Unfunded debt has a maturity of more than 1 year.
Again, our payo¬ diagrams do not do bond maturity full justice. The reason is that matu-
rity can sometimes be like “super-seniority.” That is, a subordinated bond may be repaid
before the more senior bond comes due, and, once paid, the money paid to the subor-
dinated bond can often not be reclaimed to satisfy the senior creditor™s higher-priority
claim.

Bond duration is a measure of how soon payments are made. It was described on Page 74.

Coupon bonds vs. zero bonds: We have already talked extensively about this distinction in
Part I of our book. Zero bonds pay a ¬xed amount of money only at a ¬nal date. Coupon
bonds make (interest) payments on a regular schedule, typically (but not always) twice a
year, and the principal is repaid as a balloon payment at the end.
In a practice called bond stripping, investment banks sometimes separate the coupon
Side Note:
obligations from the ¬nal balloon payment. That is, they purchase bonds, put them into an escrow
account, and o¬er two types of new ¬nancial claims collateralized by the escrowed bonds: one pays all
the coupon, the other pays all the principal. The reason for doing this is to exploit tax loopholes in Japan
and other countries.
You can think of a coupon bond as a special kind of unit, consisting only of similar payment obligations.
More generally, a unit is simply a bundle of multiple types of ¬nancial claims that are sold together,
usually involving a warrant and another claim (like a stock or a bond). The purchaser can keep both types
of claims, or similarly unbundle them and sell them separately.


Fixed interest-rate debt vs. ¬‚oating interest-rate debt: Bonds can promise to pay a predeter-
mined interest rate over the life, or a spread relative to some other interest rate. Floating
debt is often issued at a spread relative to the prime rate (an average interest rate that
banks usually o¬er their best customers) or relative to LIBOR (London Interbank O¬er
Rate). The interest rate on ¬‚oating rate debt is often capped or collared; that is, the
interest rate will never exceed a predetermined ceiling. (Highly reputable companies can
typically borrow at interest rates that are about LIBOR. More risky companies typically
pay interest rates that are about 100-300 basis points (or 1-3%) above LIBOR.)
¬le=corpclaims.tex: LP
514 Chapter 20. Corporate Financial Claims.

There is no limit to the imagination as far as bond features are concerned. For example, the
There is an endless array
of possible bond Russian car maker Avtovaz issued Lada bonds in 1994, which allowed the holders to convert
features.
their bonds into Lada cars. Other bonds™ payo¬s have been linked to commodities, such as the
price of oil, to other ¬nancial claims, or to exchange rates.
Another important dimension along which loans di¬er is whether there is a relationship be-
Bank Loans may be
Credit Lines. tween the lender and the issuer. Firms can raise funds with a public debt issue, in which there
is typically no relationship between borrower and multiple lenders, or with a bank loan, in
which there is only one lender. The advantage of borrowing from the bank is that it may know
the ¬rm better, and thereby grant better terms. The disadvantage is that there is less compe-
tition among banks for extending loans than there is among public bondholders. Bank loans
can also take the form of a credit line. Credit lines are like instant debt, permitting borrowers
to draw down money (and pay higher interest) only upon need. (Borrowers typically agree to
pay a low interest rate even on the unused part of the credit line.) The opposite of a credit
line is negotiated debt, in which both the bank and the ¬rm commit to a ¬xed loan. Just as
the lines between debt and equity are often blurry, so are the lines between bank and public
debt. There is now a large market (more than $135 billion in 2003) for bank loans extended by
syndicates of banks, in which multiple banks can share the risk of a loan, and many individual
banks routinely resell loans that they have made. And there are vulture investors who purchase
public debt and then seek to monitor the actions of the company, behaving much like a bank.
Solve Now!
Q 20.4 Write down all bond features (variations) that you remember.


Q 20.5 A ¬rm is ¬nanced with a senior bond that promises to pay $100, a junior bond that
promises to pay $200 (of lower seniority but of equal maturity to the senior bond), and equity.
Write down the payo¬ table and then draw the payo¬ diagrams when the two bonds are due.



20·2.B. Convertible Bonds

Convertibility is a common and important corporate bond feature, because it can be thought of
Convertible bonds allow
the bondholder to as creating a claim that is somewhere between bonds and stocks. A convertible bond permits
exchange the bond into
holders to convert their bonds into equity at a predetermined price at predetermined dates.
something else, usually
Here is a simple example, in which a bond can only be converted at one point in time: a ¬rm
equity. An example.
with 400 outstanding shares of equity also has 200 outstanding convertible bonds that promise
$10,000 each in January 2050. Each such bond can be converted, at the bondholder™s discretion,
into three new shares of stock. If the bond holders convert, the original shareholders will own
a lower share of the company. The cost to them would no longer be the money that the ¬rm
has to pay to creditors, but a loss in ownership. This is called dilution.
If you own these bonds, what would you do if the value of the ¬rm™s assets in January 2050 were
Understanding the
speci¬c example: at the $2 million or less? Your 200 bonds would own everything that is in the ¬rm. It would not be in
time the bond comes
your interest to exchange their bonds for shares. But what would you do if the value were $1
due.
billion? You would make the following calculation: If you take advantage of the convertibility
feature and exchange your 200 bonds for 600 shares, there will be 1,000 shares in total. Your
shares will therefore own 60% of the ¬rm or $60 million”a whole lot more than the $2 million
that you would receive if you did not request conversion. Therefore, you will exercise your
right to convert.


Anecdote: Are Convertibles Debt or Equity?
In a 2002 survey in which CFOs were asked to describe why they issue convertible debt, the most frequent
answers alluded to the fact that convertibles are “equity in disguise.” 58% of the managers answered that it is
an inexpensive way to issue “delayed” common stock. 50% answered that they did so because they considered
their own stock currently undervalued, which again could be interpreted as managers thinking of convertibles
as stock in disguise.
(Source: Graham and Harvey, Duke, 2002.)
¬le=corpclaims.tex: RP
515
Section 20·2. More About Bonds.

Can you determine at what ¬rm value you would be indi¬erent between converting and not Determining the cutoff
at which convertible
converting? It is where 60% of the ¬rm would be equal to $2 million. This occurs when the ¬rm
bondholders will prefer
value is equal to $3.3 million. To summarize: converting.


• Below $2 million, you get everything.

• Between $2,000 and $3,333, you get $2 million and the shareholders get the residual
above $2 million.

• And above $3.3 million, the shareholders and bondholders both bene¬t from higher val-
ues, with you receiving 60% of the ¬rm™s value and shareholders receiving 40% of the
¬rm™s value.

The payo¬ diagram in Figure 20.2 shows this claim.
One ¬nal question: Why would shareholders be willing to give bondholders this right, which in Owners are willing to
give the convertible
e¬ect deprives them of much upside? The answer must be that by doing so, bondholders are
right, because it
willing to pay more for the bond upfront. And, indeed, we know that if ¬nancial markets are increases the cash they
competitive, bondholders will get what they pay for. receive upfront.

Solve Now!
Q 20.6 A convertible zero bond that promises $10,000 can be converted into 50 shares of equity
at its maturity date. If there are 2,000 such bonds and 300,000 shares outstanding, how would
the payo¬ table (and diagram) for both bond holders and equity holders look like?
¬le=corpclaims.tex: LP
516 Chapter 20. Corporate Financial Claims.




Figure 20.2. Sample Convertible Bond and Stock Payo¬ Diagram at Time 1

Convertible Common
Firm Value Bond Value Equity Value
$0 $0 $0
$1,000 $1,000 $0
$1,500 $1,500 $0
$2,000 $2,000 $0
$2,500 $2,000 $500
$3,000 $2,000 $1,000
$3,333 $2,000 $1,333
$3,500 $2,100 $1,400
$4,000 $2,400 $1,600
$4,500 $2,700 $1,800
¦ ¦ ¦



Convertible Bond and Stock Payo¬ Diagrams
Financial Claim
Value, Time 1




T

¨
¨¨
¨¨
¨
¨
¨¨
$2,000




¨
  ¨
¨¨
 
nd




¨¨
Bo




  ¨
le




¨¨
 
ib
rt




¨¨
 
ve
on




   
C




   
he
T




   
   
ty
ui




   
Eq




   
he
T




   
   
   
   
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Firm Value,
$2,000 $3,333
Time 1
¬le=corpclaims.tex: RP
517
Section 20·3. More About Stock.

20·3. More About Stock

There are fewer variations of equity securities than debt securities, but two should be brie¬‚y
mentioned.


20·3.A. Preferred Equity (Stock)

Many companies also issue preferred equity. Preferred equity is an instrument somewhere be- Preferred Equity gets
better dividend
tween debt and equity. Preferred equity holders usually receive higher dividends than ordinary
treatment by the
equity holders”hence the description “preferred.” Unlike ordinary equity, where dividends corporation.
are declared annually at the discretion of management, preferred equity dividends are usually
speci¬ed at issuance (for example, $2.25 per calender quarter per share). Unlike bondholders
who fail to receive their promised coupon payment, preferred equity holders cannot force the
¬rm into bankruptcy if dividends are not paid”but their contract usually states that they have
priority over common equity holders: the preferred equity holders receive dividends before
ordinary equity holders.
But the real advantage of preferred equity over ordinary equity is that, although not tax- Preferred Dividends
receive better tax
deductible to the issuing corporation, the preferred dividend payments are not fully taxable
treatment when held by
when received by other ¬rms. The IRS considers only 15“30% of preferred dividends taxable for other corporations.
the recipient. Preferred equity is therefore usually not held by individuals, but by corporations
investing in other corporations. (Individuals can earn higher post-tax yields in other claims.)
Preferred equity is junior to the company™s bonds, which means that in case of bankruptcy, More preferred equity
features.
preferred equity holders will be paid only after bondholders are paid. Preferred equity is often
retired on a ¬xed schedule”even though many preferred equities have no formal maturity. Like
common stock, some preferred stock is traded on public stock exchanges. Though preferred
equity usually enjoys covenant restrictions (speci¬cally promised dividend payments before
common equity), it has neither precedence to bonds, nor control rights, nor unlimited upside
(rights to the residual value of the ¬rm). Naturally, any such features can be explicitly added
by contract. For example, in many small ¬rms, it is not uncommon for preferred equity to be
convertible into common equity (“convertible preferred stock”) and to explicitly provide for
voting rights. The holders of such claims are usually themselves corporations, often venture
capitalists, who can write o¬ the claims if the ¬rm fails and convert them into common equity
if the ¬rm succeeds.
Solve Now!
Q 20.7 In what sense is preferred equity like bonds? In what sense is preferred equity like stocks?



20·3.B. OPTIONAL: Options and Warrants

Firms sometime issue call options (or just calls), or warrants. These are usually more junior There are two more
claims that especially
even than common equity. In publicly traded corporations, they rarely have control rights”
smaller and privately
except for the right of the owner to convert them into equity. If they do, shareholders will held ¬rms are using.
su¬er dilution, although calls or options typically require a payment into the ¬rm by call or
warrant holders that will raise the value of the overall ¬rm.
¬le=corpclaims.tex: LP
518 Chapter 20. Corporate Financial Claims.

Call Options
A call option is a right to purchase (“call in”) the shares from the call seller for a given price at
Call options are rights to
purchase equity at a or by a given point in time. For example, a call might be the right to purchase 300 shares of
predetermined price in
the ¬rm for $50/share on January 15, 2050. If shares will then be worth more than $50/share,
the future.
then the call option will have value. Otherwise, the call will be worthless because it will not
be in the interest of the call holder to exercise it. (See also the Web chapter on options and
derivatives for a longer explanation of call options.)
Let us look at the call option in more detail. In our context, the call seller is the corporation
Working the Example.
having raised money by selling it. Figure 20.3 shows a ¬rm that has 1,000 outstanding equity
shares as well as call options for 300 shares at $50/share each. If call option owners were to
choose to exercise the call option for 300 shares, they would own the equivalent of 30% of the
¬rm. Now, if the stock price will be $40/share (total ¬rm value $40,000) at option expiration,
the call option will be worthless, because owning 30% of $40,000 ($12,000) in exchange for
paying 300 shares times the exercise price of $50 ($15,000) would not be in the call owner™s
interests. However, if the price will be $60/share, call option holders will exercise their option,
and demand 300 shares in exchange for payment of $50/share. The ¬rm will have to repurchase
300 of its own shares at $60/share (for $18,000), but receive only $50/share (or $15,000). This
will cost old shareholders a net $10/share for 300 shares, or $3,000 in total. This net bene¬t
goes to the new shareholders (the original call option owners). Old equity holders will own 70%
of the $60,000 ¬rm which sums to $42,000, plus the $15,000 call payment. In sum, their wealth
will be $57,000. New shareholders will own the remaining $3,000. (An entirely equivalent
transaction”without having to go through the repurchasing and handing over exercise”would
be for the old shareholders to just hand over to the option holders $3, 000/$57, 000 = 5% of
the ¬rm, the equivalent of 50 out of 1,000 equity shares.)


Warrants
Companies rarely issue call options, because it is usually easier for them to just issue new
Companies usually issue
Warrants, not Call shares (to satisfy the option like claim) than it is for them to repurchase existing shares. Such
Options.
call option-like ¬nancial claims are called warrants. They give warrant holders exactly the
same rights that call option holders would have, except that the money that the warrant holder
pays ¬‚ows into the corporation, and the corporation issues new shares to satisfy the warrants.
If the above claim (300 shares at $50/share) is a warrant rather than an option, and if the
¬rm ends up being worth $60,000, then the warrant holders would exercise their rights, the
¬rm would be worth $75,000, and warrant holders would own 300/(1, 000 + 300) ≈ 23% of this
¬rm”the equivalent of $17,307.69 in exchange for their $15,000 payment. Note that this is less
than the $18,000 in stock that a call option holder would have received in exchange for $15,000
payment. Therefore, a warrant is worth less than an equivalent call option. Exhibits 20.4 shows
the warrant payo¬ diagram.


Put Options
A put option gives the owner the right (but not the obligation) to sell (“put”) shares for a given
Put options are rights to
sell equity at a price at or by a given point in time. For example, a put might be the right to sell 300 shares of
predetermined price in
the ¬rm for $50/share on or before January 15, 2050. Say you sell me such a put for $5/put
the future.
today. If shares will then trade for $35/share, I can buy the shares on the open market for
$35/share, and exercise my right to sell them to you for $50/share, i.e., at a pro¬t of $15/share.
If shares will then trade for $70, the put right will be worthless to me, because it would not be
in my interest to exercise it. A put is therefore an instrument to speculate that the shares will
decline in value. (See also the Web chapter on options and derivatives for a longer explanation
of call options.)
¬le=corpclaims.tex: RP
519
Section 20·3. More About Stock.




Figure 20.3. Sample Call Option Payo¬ Diagram at Time 1

Firm Value Option Value Equity Value
$0 $0 $0
$10,000 $0 $10,000
$20,000 $0 $20,000
$30,000 $0 $30,000
$40,000 $0 $40,000
$50,000 $0 $50,000
$60,000 $3,000 $57,000
$70,000 $6,000 $64,000
¦ ¦ ¦

The call option strike price is $50 for 300 shares. With 1,000 shares in total, the option is “payment of $15,000 in
exchange for 30% of the ¬rm.” At a ¬rm value of $60,000, this means $18,000 minus $15,000 payment. At a ¬rm
value of $70,000, this means $21,000 minus $15,000 payment.



Sample Call Option Payo¬ Diagrams
Financial Claim
Value, Time 1




T
$50,000




 
 
 
 
y)




 
it
qu




 
(E
rm




 
Fi




 
he




 
T




 
 
ion
  t
Op
  ll
a
eC
  Th
  E
Firm Value,
$50,000
Time 1
¬le=corpclaims.tex: LP
520 Chapter 20. Corporate Financial Claims.




Figure 20.4. Sample Warrant Payo¬ Diagram at Time 1

Pre-Warrant Post-Warrant Old
Firm Value Firm Value Warrant Value Equity Value
$0 $0 $0 $0
$10,000 $0 $0 $10,000
$20,000 $0 $0 $20,000
$30,000 $0 $0 $30,000
$40,000 $0 $0 $40,000
$50,000 $0 $0 $50,000
$60,000 $75,000 $2,308 $57,692
$70,000 $85,000 $4,615 $65,385
¦ ¦ ¦

The warrant strike price is $50 for 300 shares. With 1,000 shares in total, the option is “payment of $15,000 in
exchange for 300/1, 300 = 23% of the ¬rm.” At a pre-warrant ¬rm value of $60,000, this means 23%·$75, 000 ≈
$17, 308 minus $15,000 payment. At a pre-warrant ¬rm value of $70,000, this means 23%·$85, 000 ≈ $19, 615
minus $15,000 payment. (Old Equity owners now own 77% of a $85,000 ¬rm, which is $65,385.)


Sample Warrant Payo¬ Diagram
Financial Claim
Value, Time 1




t
arran


tion
T
ith W


l Op
Cal
ty) W


ith
)W
(Equi

uity
Firm

(Eq
Firm
The
$50,000




The

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