Cabinet d'avocats





La Revue du Financier, Paris, Octobre 2003




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)





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.





    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




V = value of the business

E = owners' equity

D = long and short term debt




E = A - D 




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)




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)



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)




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



Pmi =    (P * Nmi) - Pd



Vm  =    (Pma * Nma) + (Pmi * Nmi)




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


Pma =    price of each share of the majority


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




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)




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)




C   =    value of the European call option


Nd1 =    log(Pm/Ps x e-rt) +  st0.5

               st0.5                          2

Nd2 =    d1 - st 0.5


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.


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




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.

















Co = Ca + Cb





Co = Ca + Cb




Po = Pa + Pb











Co = Ca + Cb





Po = Pa + Pb






Po = Pa + Pb




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





Co =    optimal price of C




Po =    Pa + Pb





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



    =    $ 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.













Co = $ 3.12


Co = $ 3.12

Po = $ 2.25






Co = $ 3.12

Po = $ 2.25



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. 






















2 202,32 

3 919,61 

6 302,89 




1 952,35 

3 142,36 

4 309,84 




1 409,39  

1 825,59 

1 984,79 













































FROM YEARS 50 -100




1 255,19 

1 717,30 

2 383,28 




1 054,09 

1 190,01 

1 167,47 




































Cabinet d'avocats




[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 ao×t 1789 Art. 17 stipule que "La propriété étant un droit inviolable et sacré, nul ne peut en Étre 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


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.