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ESSAY
ON THE VALUE OF OWNERSHIP La Revue du Financier, Paris, Octobre 2003 By Daniel Arthur Laprès Member of the Bar in France and in Canada Professor at the Faculté Libre de Droit, de Gestion et d'Economie
(Paris) RESUME Alors que le droit de propriété est reconnu dans presque
toutes les sociétés comme correspondant à une valeur fondamentale, la théorie
financière ne saisit qu'approximativement certains de ses aspects, par exemple
sa signification dans le cadre de projets à long terme. Cet article a pour
objet de démontrer l'incohérence, d'en identifier certaines conséquences, et de
développer dans un cadre pratique des solutions. La recherche de solutions nous
conduit à faire application de la théorie des options pour évaluer l'ensemble
de droits résiduels qui caractérisent le droit de propriété. Une recommandation
pratique tirée de la discussion est que les négociateurs devraient prendre en
compte des options qui surviennent en relation avec leurs contrats notamment
pour déterminer le prix contractuel. Abstract While
ownership is almost universally recognized as a fundamental value, financial
theory has but a loose grasp of certain of its features, for instance its
importance in long-term projects. Our aims are to delineate the inconsistency,
to identify some of its implications, and to highlight practical contexts in
which solutions to the contradiction have been offered. Our search for a
resolution of the inconsistency leads to the application of option theory to
the valuation of the bundle of residual rights characteristic of ownership. A
practical recommendation arising from the discussion is that negotiators should
take account of options arising in relation with their contracts in particular
for determining the price. 1. -
On the meaning of ownership Every year on the benches of
law schools around the globe, entry-level students learn that what
characterizes an "owner" of any asset[1]
is his enjoyment of a bundle of rights including in particular the right for as
long as the asset exists to use it and to exclude others from its use, as well
the right to dispose of it at his discretion, including by sale, hypothecation,
lease, license, gift, and destruction. Ownership rights in any asset arise in a
variety of ways: by gaining effective possession (such as in the case of
hunters' ownership of game), by
discovery (of abandoned treasure), by creation of the object of the rights
(physical goods), by invention (patents), by authorship (copyrights). Owners
bear risks and liabilities associated with their assets, which can be
significant in relation with dangerous objects or animals. And an owner's
exercise of his rights is subject to constraints intended to prevent or correct
abuses of the advantages of ownership (such as predatory monopolies, negative externalities, and criminal or tortious conduct,
breaches of contract relating to the asset). But none of these lines of
thought reveals a method of valuation of ownership. For present purposes, owners of
any asset are defined as those holding the residual claims thereto. In the
corporate context, owners are those who may claim the cash flows of the
business after settlement of all other claims. Shareholders own what is left
after debt holders are paid off. Owners of equity, unless they contract
otherwise, also control how the business is operated.[2]
According
to the famed Proposition I of Modigliani and Miller and subject to the authors'
assumed constraints, the "market value of any firm is independent of its
capital structure and is given by capitalizing its expected return at the rate
appropriate to its class".[3]
The Proposition remains a shining citadel in the maze of contemporary finance
even if the tax savings arising from debt have been recognized as providing an
advantage to debt financing within the limits of the consequent increased risk
of bankruptcy. Also account needs to be taken of information asymmetries such
as exist between shareholders and debtholders and which give rise to greater
costs of governance for debt holders.[4] A
major difference between the owners' situation and that of the lenders concerns
their relations to the residual claims to the business. Since V = E + D where V = value
of the business E =
owners' equity D = long and
short term debt Then, E = A -
D Where A = Assets The value
of owners' interests corresponds to the value of the cash flows remaining after
settlement of all other claims.
Also, where E < 0
(that is A < D) the
original equity holders abandon their residual claims in favor of the debt
holders who then become the effective owners (since they become holders of the
residual claims) arising from the business. But
this "book value" of the owners' residual claims will not reflect
what buyers would pay for them if the present value of the future net cash
flows from the project correspond to a different number. The translation of
future into present values lies at the heart of contemporary financial theory. 2. -
The time value of money Were the reader to be
approached by a friend wanting a loan, the least that the lender would likely
expect would be to be refunded at the term of the loan funds with purchasing
power equivalent to what was loaned in the first place. Now suppose that between the
time the loan is made and the time it is repaid there has been an increase in
the price level, the lender will need to receive a payment larger in nominal
terms than the amount of the original loan. In this sense the lender's
"real purchasing power" would have been maintained. 1 + Rn =
(1 + i) where: Rn =
nominal rate of interest i = rate
of inflation Where the lender obtains an
increase in his purchasing power over the course of loan, the nominal rate of
interest becomes 1 + Rn =
(1 + Rr) (1 + i) where Rn = the
nominal rate of interest Rr = the
real rate of interest i =
inflation One is indifferent between
consuming today and consuming later provided F = P * (1
+ Rn) F = future
value P =
present value R = the
nominal interest rate The proposition
holds true for assets of comparable risk in a free and competitive market where
there are insignificant transactions costs and informational asymmetries. Price
anomalies are eliminated by traders standing ready to buy whichever side of the
equation is under priced and sell the other for profit. For instance, were
there an offer to pay $ 105 in one year against delivery at that time of a
hypothetical risk-free financial instrument asset worth $ 100 today when the
interest rate is 3% per year, traders would borrow $ 100 to buy the instrument
today at $100 (they have bought the right side of the equation) and sell the
asset forward one year at $ 105 (they have sold the left side of the equation).
In so doing they would make a profit of $ 2: Profit =
price of sale of the instrument - the cost of the instrument + interest on the
loan, that is: 2 = 105 -
(100 + 3) The
process launched when all traders see the opportunity causes its disappearance.
Thus the buying activity will push up the current price of the asset and the
sales for future delivery will push that price down. The process will continue
until the price difference disappears. 3. -
How investments should be chosen Investors seek to maximize the
net present value of the free cash flows discharged by their investments. For
any given amount of cash outflows to finance a project and inflows from its
operation, that stream reaching the investor earlier at the same risk level
will yield a higher net present value and will therefore be preferred by the
investor. NPV
= -Io + Sum CF (1 + r) where NPV = net present value Io = the
outflow of cash associated with the initial investment CF = cash
flows discharged by the investment during its expected term r = the
rate of return on the next-best comparable risk opportunity for the invested
capital The value of r
used to discount the cash flows will usually be higher for longer terms. Were r
over the long term lower than its short term comparable risk alternative, then
traders would borrow for the long term, invest in the short term at the higher
rate and pay off the longer term loan at expiration with a profit. Ultimately
the trading activity would cause the anomaly to disappear as demand for long
term credit would push up its price and the increased supply of short-term
credit would cause its price to go down. Consequently long term rates will be
less than short-term rates only in exceptional circumstances such as where a
very high rate of current inflation is expected to be reduced in the medium
term causing to this extent a fall in nominal rates. The
present value of future cash flows will almost always fall as they are
stretched out over time. Indeed even at low discount rates, their present value
will approach zero as can be seen from the table in the appendix. To the extent that distant
cash flows have little present value, the right or claim to such flows is of no
concern to financial theory. In other words, in such cases, it would make little
difference in a net present value based decision whether the long term project
were a concession expiring when its cash flows reach negligible levels in terms
of present value or whether it were owned by the operator who would then
continue to enjoy the benefit of the distant cash flows, however meager their
present value. It
is in this sense that we argue that financial theory undervalues ownership. 4. -
Is ownership valuable? That
ownership has perceived value seems hardly debatable. The
right to own is guaranteed in national constitutions of such disparate
political regimes as the United States,[5]
France[6]
and China,[7]
not to mention its consecration in the United Nations Covenant for the
Protection of Human Rights.[8]
The conditions in which a citizen may be deprived of his ownership rights are
often strictly defined in national constitutions. His possibilities to protect
his ownership rights from intrusion and deterioration are also the subject of
legal guarantees. Owners more often seek to extend the terms of their rights
than to reduce them, as can be observed in the behavior of interest groups such
as copyrightholders who have obtained that the limit of their rights be
extended from 50 years beyond the life of the author to 70 years beyond his
life. Given a choice between the
right to exploit an asset for a limited term and the right to own it and by
virtue of that right of ownership exploit it forever, would anyone choose the
first alternative? Except in such cases as where the project might have
dissuasive high costs of unwinding (such as a strip mining project if, upon
depletion of the mine, there were an obligation to restore the site to its
original condition) or lasting risks (such as might arise from dangerous and
hard to destroy industrial wastes or from errant satellites), there would be no
reason not to prefer ownership to any otherwise identical alternative without
the residual claims inherent in ownership. And yet when the law does
face the issue, specialists tend to fall back on financial methods of analysis.
For instance, in public international law, nationalization of foreign property
is expected to give rise to prompt, effective and adequate compensation which
in practice generates a debate over whether this corresponds to book value or
going concern value.[9]
In French civil law, very long term leases ("bail emphythéotique"
typically for 99 years) on real property may be concluded and then give rise to
the question of their valuation for the calculation of taxes. The solution in
French law is to establish value for tax purposes as the equivalent of 20 years
of rental income. 5. -
Can the existence of a value of ownership as such be justified theoretically? We
look first at the research involving the concept of public goods and in
particular those that engender intergenerational
externalities. Then we turn
our attention to the corporate context and in particular the premium paid for
golden shares in take-over bids as evidence of the value of one of the
essential features of ownership: the ultimate ability to decide the course of
action to be adopted by the corporation. Finally we consider the opportunities
of options analysis to apply price tags to bundles of ownership rights. 5.1. -
Ownership and public goods analysis In
economic analysis, public goods are characterized by two phenomena. First,
their consumption is non-rivalrous
in that any person's consumption of the good does not deprive anyone else of
its enjoyment. Secondly, once the good is put into circulation, it is impossible,
short of legal protections, to prevent its consumption by others. Ideas and
national defense are frequently cited examples of public goods. Economists
devote considerable attention to the distortions and social costs associated
with public goods. The
point in the present context is that ownership affords a solution to the
so-called tragedy of the commons[10]
which posits that a public good such as grazing land held in common by sheep
owners would in the absence of the institution of ownership necessarily be
overused and therefore ultimately depleted. In such situations, each grazer has
an interest in feeding his sheep more than his competitors feed theirs and/or
putting more sheep on the land. Were the commons to be allocated to an owner,
he would have an interest in managing the resource to ensure its regeneration. Ownership
also provides an incentive to care for those assets the expected life of which
exceeds the normal term of human life. Commentators frequently cite natural
resources such as air quality or water quality as examples of intergenerational
public goods. The harm any single generation does to the environment might only
have negative effects after accumulating over terms exceeding the life span of
any generation. In
this sense, ownership as an institution encourages individuals to improve the
value of their assets because as such they can be transmitted to future
generations. In
a word, ownership clearly has social value.
And while economists have been torturing their minds for at least twenty years
to quantify this value (for instance in the case of long-term public projects),
the results of this research remain largely couched in economists' confidential
language. Still, Columbia Business School economics Professor Geoffrey Heal has
exposed the problem in the these eloquent terms: Valuing the future is
critical to sustainability. Environmental assets provide flows of services over
long periods of time. New York's Catskills watershed has purified water and controlled
stream flow for hundreds if not thousands of years, and if left intact will
continue to do so for at least as long again. Insects have pollinated flowers
for much, much longer, and could continue as long again if not driven extinct
by pesticides. No human systems have such life spans. . . . Because of the
totally different time scales of the capital assets that humans and nature
produce, the techniques that we use for valuing capital assets really cannot be
applied to natural capital. . . .
When we apply this kind of calculation to environmental assets, we are
cutting out most of the contributions that they will make to human societies:
we are taking account of twenty years of the contributions of assets that could
contribute, at no extra cost, for twenty decades or perhaps twenty centuries.
Clearly we are undervaluing them grossly. We have to find ways of doing better.[11] Economists have sought to
resolve the difficulty by adapting the discount rate on very long-term projects.
For instance, where the "decisions will affect the entire growth path of
an economy or a region", a "general equilibrium model" is said
to be involved and the discount factor should be based on "utility",
presented as a broader concept than the "consumption" discount factor
which instead should be used for "partial equilibrium" models suited to
problems in which the economy is taken as given and the changes under
consideration are "marginal". Where decisions have
intergenerational effects and the value of a certain state is constant over
time, a discount factor of zero may be appropriate in recognition that the
asset is as important to the well being of future generations as it is to
today's. Typical of such decisions in industrial countries would be those with
respect to greenhouse emission reductions, or in a developing country a major
dam.[12]
That this line of thinking
is having some effect is indicated by the results of a survey conducted among
1,720 professional economists inquiring of their opinions on the appropriate
discount rate for long-term environmental projects such as those addressing
global warming; the modal rate was 2%, the median 3% and the mean 4%, a
fraction of what most corporate decision-makers would consider appropriate in practice.[13] Still
in none of this analysis would ownership as such seem to be a subject of
valuation. At most, it appears as a solution to the problem of internalizing
all the decision-making criteria. In a typical partial equilibrium, an owner
would be better suited to making decisions with intergenerational consequences
than would a tenant. For general equilibrium problems, such as ecosystem
sustainability, governments as "agents" for the "owners"
(the States they represent) are better decision-makers than corporations or
individuals. 5.2. -
Ownership and the golden share in takeovers Now
let us consider whether ownership has any demonstrable value in the financial
context. Let it be observed that control over an asset, such as is associated
with ownership, has value in itself. In general, the greater the degree of
control over an asset, the greater the value of the holding. Ownership of an
asset then would have value at the very least as a vehicle for obtaining and
exercising control over the asset. For
instance, in the corporate take-over context, the value of 51% of the shares of
a company where all shareholders have equal rights, in particular voting
rights, is greater by more than 2% than the value of the remaining 49%.[14]
Vm = ((P * Nma) + Pp) + ((P * Nmi) - Pd)
Pma = (P * Nma) + Pp Nma
Pmi = (P * Nmi) - Pd Nmi
Vm = (Pma * Nma) + (Pmi * Nmi) where Vm = market value of the company P = market
price of any share absent the effects of distribution of control Nma =
number of shares controlled
by the majority Pp = premium
on the value of shares of the majority because of their control of the golden
shares Nmi =
number of shares controlled
by the minority Pd = discount on the value of
shares of the minority because of their lack of control Pmi = price of each share of the
minority If a
company had a value of 100 and the premium for having the majority were 10 and
let us further assume that the discount for not having the majority were also
10, then 100 = ((49 x 1) - 10) + ((51 x 1) + 10) = 39 + 61 Pma = $ 1.20 and Pmi = $
0.80 Generally
the law allows majority owners to reap the benefits of their golden shares, while
excluding the minority from any of the bounty.[15]
The rule is said to encourage transfers of corporate assets to the bidders with
the highest valuation based on their prospects of exploitation. But it also
puts shareholders of the target company in a dilemma because those who might
otherwise hold out for a higher price are led to sell at the offered price lest
the price of their shares plummet after completion of the acquisition of the
majority's shares. On
the other hand, the potential for abuse of the differential value of majority
and minority shares by instigators of takeovers of publicly held companies has
given rise to legal rules to protect the minority.[16]
In the United States, Section 13 of the Securities and Exchange Act requires
that any person acquiring more than 5% of the shares of a company covered by
the Williams Act make public disclosure of his holding; over-tendered shares be
purchased pro rata from all shareholders who tendered during the allowed
period, thus decreasing the pressure to tender. The Delaware Corporations Act
(Section 203) prohibits the acquirer of a 15% stake in any covered corporation
from merging with the target for 3 years from the date of reaching the 15%
threshold. Some States in the United States[17]
require that a purchaser of a specified portion of another corporation's shares
stand ready to buy out the remaining shareholders at the latter's request and
at a "fair" price as determined by the courts in the event of
disagreement. Almost all States as well as the District of Columbia allow
dissenters to a negotiated merger or a consolidation to petition the courts for
determination of "fair" values for their shares and most states even
allow the remedy where the corporation is publicly traded.[18]
When
called upon to determine the price of the dissenters' shares, the Courts
typically are expected to look to "their value immediately before the
effectuation of the corporate action to which the dissenter objects, excluding
any appreciation or depreciation in anticipation of such corporate action
unless such exclusion would be inequitable".[19]
Such a formula of course allows that the dissenters will receive less than the
cooperating shareholders. But it avoids them the aggravation of the loss which
a predatory majority might seek to impose on them. In
carrying out their appraisals, the courts refer to at least three methods of
valuation: (i) the sum of the values of the target's assets will be especially
relevant where the target has undeveloped assets such as land and its future
cash flows are difficult to estimate, (ii) the market value of the shares at
the occurrence of the event giving rise to the request for appraisal unless
this price has been tainted by improper behavior or other factors, (iii)
projections of future earnings based on observation of past earnings, rather
than corporate or expert projections.[20] Generally
the value of residual claims varies directly with the extent of control over
the asset. In the corporate valuation context and in the absence of legislation
such as the Williams Act, Vo = f(E, W) Where Vo = value
of ownership E = equity
provided A > D W = % of
shares controlled To the
extent that the value of holdings of shares of equal standing increases with
the number of shares held within the limit of the number of shares issued,
ownership of the shares then has value. Were
it to be objected that not all shares in fact have voting rights, it should be
borne in mind that the issue of such shares is for instance discouraged by the European
Directive and the Model Business Corporations Act. And in any case, such
non-voting shares will trade for less than voting shares, which observation
establishes that ownership such as of voting rights has value. 5.3. -
Applications of options theory in valuing ownership Especially in its "real
options" variant, options theory proves very useful in the valuation of
the premium for owning long term investments as distinguished from the
enjoyment of the rights to exploit them subject to constraints, such as in
terms of time or scope of disposition, and where the life of any project were
to exceed the term of the right of to dispose thereof. For instance, in forms
of contracting infrastructure projects such as "concessions" or
"build-own-transfer" (BOT) projects, the owner of the residual rights
to the project, generally the State, would include in its valuation of the
project the benefit associated with the call option on continuing the project
beyond the term of the concession or BOT contract. The
right of ownership corresponding to the residual rights to the asset might be
valued as a call option entitling the owner of the investment to continue its
operation subject to: -
an exercise price equivalent to the expected
costs of maintaining or re-launching the asset (Ps), for example refurbishing
of equipment, repositioning of product lines, renewals of patents and trademark registrations, -
a valuation of its pay off equivalent to the
present value free net cash flows from the continued exploitation of the asset
after reversion of the project to the owner (Pm), -
a measure of the risk exposure on the
project's free net cash flows relating to the residual rights as measured by
their standard deviation (s), -
the number of terms until recovery of the residual
rights equivalent to the term on a European option (t), -
an estimate of the risk free interest rate
(r), -
an estimate of the probability that a normally
distributed random variable will be less than or equal to a reference (Nd). With such
information, the value of the option on the residual rights to an asset
inherent in ownership could be estimated using the Black and Scholes formula:[21] C = (Nd1 x Pm) - (Nd2 x Ps x e-rt) Where: C = value
of the European call option Nd1 = log(Pm/Ps
x e-rt) + st0.5 st0.5
2 Nd2 = d1
- st
0.5 By
way of illustration, let us suppose the government of a State were to conclude
a BOT project with a foreign enterprise. The foreign investor agrees to invest
in planning, developing, commissioning, financing and operating the project for
a term of 30 years. During the term of the agreement, the profits and losses
from the project belong to the foreign investor. At the end of 30 year term,
the residual rights of the State entitle it to take over the project without
indemnifying the operator and to continue operating the project or negotiate a
fresh concession. It could also choose not to exercise this option and abandon
the site altogether. In any case, at expiration of the concession, continued
operation will require a revision of the plant costing $10 million at that
future date, that is some $ 4.12 million in present value. The
present value of the free cash flows after expiration of the concession
discounted to their present value is assumed to correspond to $ 5 million, such
that the net present value of the continuation of the project is greater than
zero (NPV = $ 0.88 million). Let
us then suppose that -
Ps = $ 10
million -
Pm = $ 5
million -
t = 30
years -
s = 0.30 -
r = 0.03 Then Nd1 = Nlog(5/10xe-0.03x30)
+ 0,30 x 300.5 0,30 x 300.5
2 = 0.93 Nd2 = 0.93
- (0.30 x 300.5) = - 0.70 The
value of the call option associated with the residual rights in the project,
i.e. ownership thereof, would be determined as follows: C = (Nd1
x Pm) - (Nd2 x Ps x e-rt) = (0,82
x 5) - (0.24 x 4,12) = $ 4.10 - 0,98 = $ 3.12 million The
value of owning the project as estimated by
applying option theory is substantially greater than the project's net present
value ($ 3.12 million compared with $ 0.88 million). Sole
reliance on the net present value to evaluate the project would have failed to
provide an accurate or reliable method for negotiating its financial aspects. By
virtue of the necessity of call/put parity, the value of the put (P), entitling
its holder to pass off onto the seller of the put the residual rights (and
obligations) of the project, would be calculated as follows: P = Pse-rtN(-d2)
- PmN(-d1) For
instance, for an operator with the anticipation quantified in the example
above, it would be worth P = (4.12 x 0.75) - (4 x 0.17) = 3,09
- 0.68 = $
2.25 million to have the right, but not the obligation, to vest the residual
rights in his counter-party and the latter would expect to be indemnified to
the extent of at least $ 2.25 million for standing ready to assume the residual
rights of the project. 5.4. -
Applications of options theory to attributing ownership of long-term contracts Depending
on a party's assessment of and adversity to the risk that ownership entails, it
might be prepared to pay the other to enjoy the option, depending on its
anticipation of future events, to claim the residual rights or on the contrary
to pass them off onto the other party.
In
the context of the negotiation of a long-term project, and starting from a
value of the project negotiated without taking account of its ownership, a
party bullish as to future events might consider that, if it could be vested in the residual rights to the project, its other
benefits from the project could be decreased (through a change in the concession
tax for instance) without any change in its overall position.[22]
A party bearish on the ultimate outcome of the project might pay the other to
enjoy the option to pass off onto it the residual rights (and
responsibilities). Pursuing
the example of the negotiation of a BOT project between a State and an
investor/operator, the value of the project from the State's viewpoint would be
the value of private and public benefits minus private and public costs. Its
value from the viewpoint of the investor/operator would be the net present
value of its free cash flows. Starting
from any negotiated equilibrium excluding the vesting of the residual rights,
the unfolding of the negotiation thereafter would depend on the parties'
expectations with respect to the incidence of the residual rights. A
BULLISH A
BEARISH B
BULLISH I Co = Ca
+ Cb
2 II Co = Ca
+ Cb
2 or Po = Pa
+ Pb
2 B
BEARISH III Co = Ca
+ Cb
2 or Po = Pa
+ Pb
2 IV Po = Pa
+ Pb
2 In
quadrants I and IV, each of the parties would be indifferent whether it
obtained the residual rights or a payment of an amount equal to its valuation thereof.
An optimal price of C or P would be reached when no improvement of one party's
position could be implemented without the other suffering greater detriment. If
the parties agree on the price of C or P, then they might reasonably be
expected to reach an agreement whereby one pays the other C or P, as the case
may be, for the residual rights (and obligations). If they had different
valuations, the optimal price would correspond to Co = Ca
+ Cb 2 where Co = optimal
price of C And Po = Pa
+ Pb 2 where Po = optimal
price of P. Using
the numbers imagined in the example above, if both parties had exactly the same
anticipation, that is Ca = Cb = $ 3.12 million either
party should be willing to pay the other $ 3.12 million to secure the residual
rights, and the other party would consider itself indemnified for the foregone
opportunity. This would be an optimal solution in that it could not be improved
for either party without causing the
other to suffer proportionately greater detriment to its position. From
the investor/operator's viewpoint in our hypothetical BOT project, it would be
worth an additional $ 3.12 million to have an option on the residual rights in
the project. If
the parties had different anticipates of the value of C or P, then we might
imagine Ca < Co
< Cb $ 3 <
3.12 < 3.24 Co = Ca
+ Cb 2 = $ 3.12 An
attractive solution, that is attractive in practical terms, would consist in
one of the parties paying the other $ 3.12 to enjoy the residual rights corresponding
to ownership.[23] The rights
would have been attributed to the highest bidder and the parties would have
shared the gain from the agreement. In
quadrants II and III, the parties have opposite outlooks on the probable
relation at expiration of the exercise price and the market price over the
underlying asset. Abstracting from the different risk profiles of the
instruments and the risk sensitivities of the parties, as well as from the
incidence of the directions of the flows of cash, and assuming put/call parity
conditions, a bullish party would pay to hold a call or would indifferently
sell a put; and a bearish party would pay to hold a put or would indifferently
sell a call. The parties should then be able to reach an agreement. Selling
a call would be considered as entailing the obligation, at expiration, of
obtaining an asset equivalent of value equivalent to that of the asset over
which the residual rights would have been foregone. In a long-term competitive
context, the assumption is realistic. The
seller of a put expects that the project's market value at expiration will be
greater than its strike price. In a negotiating context, the seller of a put
may be a frustrated call buyer In
the numerical example developed above, a party would be willing to buy the call
on the project's residual rights for $ 3.12 million, or by virtue of put/call
parity, it would be willing to sell a put for $ 2.25 million. A
BULLISH A
BEARISH B
BULLISH I Co = $
3.12 II Co = $
3.12 Po = $ 2.25 B
BEARISH III Co = $
3.12 Po = $ 2.25 IV Po = $ 2.25 In
quadrant II, A wants to buy a put and B would be willing to sell a put at $
2.25. Where their valuations of P were different, then a negotiation would ensue
to divide the difference such that, at the price finally agreed, neither
party's position could be improved except at greater expense to the other
party. Alternatively, but for the fact that the (opportunity) cost would be
unlimited, A should be willing to sell the call to B for $ 3.12 (abstracting
also from the incidence of the direction of the cash flow). In
quadrant III, B wants to buy a put and A would be willing to sell a put at $
2.25. Or A should be willing to sell the call to B for $ 3.12 (abstracting from
the risk of exposure to opportunity costs and from the incidence of the
direction of the cash flow). 6. -
Conclusion Our
point has been to highlight how loose is financial theory's grasp of the value
of ownership despite a perceived value so great as to propel it in the legal
systems around the world to the status of fundamental human right. Ownership
may be understood as corresponding to control over the residual rights with
respect to any asset. We
have sought to demonstrate that ownership as an institution has demonstrable
social value in particular as a solution to the tragedy of the commons. Ownership
sometimes can be attributed a price; for instance, the residual rights to very
long term projects which can usefully be treated using options theory. From
the point of view of the host State in a hypothetical BOT project, the value of
the option to take over a project after its term of concession might be added
to the project's benefits against which would be weighed its costs. The
investor/operator in a BOT arrangement may be considered to have assumed an
opportunity cost, in having foregone an opportunity to hold the residual rights
arising from ownership. Depending
on the parties' anticipation of the probable relationship of the market value
of the project and the price of its continuation after expiration of the BOT
contract, the parties may adopt negotiating strategies and pricing methods
exploiting options valuations models. The
special attraction of options theory in the valuation of ownership is that it
tends to compensate for underestimation biases of the net present value theory,
namely the length of time and the variance of the projections. PRESENT VALUES
OF $ 100 INTEREST RATE NUMBER OF YEARS 5 10 25 50 100 0,01 485,34 947,13 2 202,32 3 919,61 6 302,89 0,02 471,35 898,26 1 952,35 3 142,36 4 309,84 0,05 432,95 772,17 1 409,39 1 825,59 1 984,79 0,10 379,08 614,46 907,70 991,48 999,93 0,15 335,22 501,88 646,41 666,05 666,67 0,20 299,06 419,25 494,76 499,95 500,00 INCREASES IN
PRESENT VALUES OVER TIME OF $ 100 INTEREST RATE YEARS 0-5 FROM YEARS 5 -10 FROM YEAR 10-25 FROM YEARS 25-50 FROM YEARS 50 -100 0,01 485,33 461,79 1 255,19 1 717,30 2 383,28 0,02 471,33 426,91 1 054,09 1 190,01 1 167,47 0,05 432,90 339,23 637,22 416,20 159,20 0,10 378,98 235,38 293,25 83,78 8,45 0,15 335,07 166,66 144,54 19,64 0,61 0,20 298,86 120,19 75,51 5,19 0,05 __________________________ Cabinet d'avocats
Pma = price of
each share of the majority
The result inherent
in the Black and Scholes formula is sensitive to those very variables the
influence of which is underestimated by the present value method. In
particular, it is apparent that the option value increases with increases of
the time remaining on the term of the option, as well as with increases of the
standard deviation of the project's cash flows accruing to the residual rights
holders, i.e. the owners.
[1] In truth, law school discussions would be conducted
in terms of rights in "property" not "assets". However,
this may give rise to thorny debates about is meant by "property";
for instance while to some it may seem obvious that "intellectual
property" is "property", there is in fact serious debate about
whether intellectual property is not indeed a misnomer. Precisely to avoid this
debate, and especially considering that it is not germane to our object, we
will refer to owners' rights in assets.
[2] Let this not be understood to mean that shareholders manage the business, a function that is generally attributed
by law exclusively to a board of
directors elected by the shareholders. While the debate over the balance
between management, outside directors, employees, and other stakeholders is as
important as it is topical, but it is not the subject of this discussion.
[3] Franco Modigliani and Merton H. Miller, The Cost of
Capital, Corporation Finance and the Theory of Investment, The American
Economic review, Vol XLVIII, June 1958, 3, at 10.
[4] Richard A. Brealey and Stewart C. Myers, Principles
of Corporate Finance, Irwin Mcgraw-Hill, 2000 in particular at pages 499 and
following. Frank H. Easterbrook and Merton H. Miller, The Modigliani-Miller
Propositions after Thirty Years, 2 J. Of Economic Perspectives, Fall 1998, 99.
[5] The Fifth Amendment of the United Sates Consitution
provides in part that "No person shall be deprived of life, liberty, or
property, without due process of law; nor shall private property be taken for
public use, without just compensation" The Fourteenth Amendment provides that
"No State shall deprive any person of life, liberty, or property, without due
process of law; nor deny to any person within its jurisdiction the equal
protection of the laws". At
http://supreme.lp.findlaw.com/constitution/amendments.html
[6] Déclaration des
Droits de l'homme et du citoyen du 26 aot 1789 Art. 17 stipule que "La propriété étant un droit inviolable et sacré, nul ne
peut en tre privé, si ce n'est lorsque la nécessité publique, légalement
constatée, l'exige évidemment, et sous la condition d'une juste et préalable
indemnité"
[7] Since 1982, the Chinese Constitution has provided in
its article 13 that the State "protects the right of citizens to own lawfully
earned income, savings, houses and other lawful property. The State protects
according to law the right of citizens to inherit property". The Laws of the
People's Republic of China, 1979-1982, Foreign Languages Press, Beijing, 1987),
p.8.
[8] Article provides that "(1) Everyone has the right to
own property alone as well as in association with others, and (2) No one shall
be arbitrarily deprived of his property". At
http://www.un.org/Overview/rights.html.
[9] Among an abundance of publications on the subject the
author modestly refers readers to his own article on the subject Principles of
Compensation for Nationalized Property, International and Comparative Law
Quarterly, (January 1977, volume 26, p. 97)
[10] Garrett Hardin, The Tragedy of the Commons, Science
162:1243-48 (1968).
[11] Geoffrey Heal, Markets and Sustainability,
[12] "Partial equilibrium" problems would rather more involve plant level decisions with no
wider than regional implications.
[13] G. M. Heal, Intertemporal Welfare Economics and the
Environment, September 1999, last revised february 2001, at
http://www.gsb.columbia.edu/faculty/gheal/pw-96-03.pdf
[14] Were it to be objected that not all shares in fact
have voting rights, it should be borne in mind that the issue of such shares is
for instance discouraged by the European Directive and the Model Business
Corporations Act. And in any case, such non-voting shares will trade for less
than voting shares, which observation establishes that ownership such as of
voting rights has value.
[15] In American law the leading cases are Treadway Co. v
Care Corp. 638 F 2d 357 (2d Circ. 1981), Zetlin v. Hanson Holdings, 48 N.2d 684
(1979), Tyron v. Smith, 191 Ore. 172 (1951). But for a contrary view where the
majority were considered to have diverted a corporate opportunity see Perlman
v. Feldmann, 219 F2d 173 (2d Cir. 1955).
[16] According to one study, following upon the
implementation of the these rules, the average premium over the pre-offer price
in a cash tender offer rose from 32% to 53%. Jarrell and Bradley, The Economic
Effects of Federal and State regulation of Cash tender offers, 23 J.L. &
Econ. 371 (1980).
[17] William A. Klein and John C. Coffee, Jr., Business
Organization and Finance, Legal and Economic Principles (Foundation Press,
1993), at page 194.
[18] Steven M. Crafton and Margaret F. Brinig,
Quantitative Methods for lawyers, Carolina Academic Press, 1994), page821.
[19] Model Business Corporations Act, Section 13.01 (a).
[20] While in theory, the three approaches would seem to
be three ways of saying the same truth, several studies have been done on the
American case law with respect to the appraisal methods and their results. It
turns out that
AV > MV > EV
Where
AV = asset value
MV = market value
EV = earnings value
Note, 30 Oakla. L. Rev. 629, at 640-641 (1977),
where AV exceeded MV in 9 of 10 cases reviewed by an average off 144% and AV
exceed EV in 11 of 13 cases by an average of 261%. See also Note, 79 Harv. L.
Rev. 1453 (1966) and Note, Dickinson L. Rev. 582 (1974). In Weinberger v. UOP,
Inc., the Delaware Supreme Court took account of earnings projections such as
internally prepared valuation studies and expert testimony about acquisition
premiums in comparable situations. 457 A. 2d 701 (Del. 1993).
[21] The formulas used here are presented in Richard A.
Brealey and Stewart C. Myers, Principles of Corporate Finance, McGraw Hill, New
York,2000, p. 606-8. Other sources present different formulations of the
relation. The result obtained above coincides with valuations by Robert's
Online Option Pricer at
http://www.intrepid.com/~robertl/option-pricer1/option-pricer.cgi and by BloBec AB at
http://www.blobek.com/black-scholes.html.
The analysis of the State's
position does not require that there be counter-party having sold the call. But
such a scenario is certainly imaginable: where an owner occupant concludes a
leaseback with a financial institution and the lease grants the tenant an
option to repurchase the property at the end of the lease, the financial
institution would have sold the call on the ownership or residual rights.
[23] This calculation assumes for the sake of simplicity
that the indifference functions of the parties are linear; were they not, and
most likely they are not, then the calculations would be different but the
principle of seeking the intersection of the indifference curves would
remain.