Università degli Studi di Parma
Dipartimento di Economia
Via Kenney 6, Parma (I)
A Theory of Hostile Takeovers
Augusto Schianchi1
Andrea Mantovi2
Abstract
In this paper, a consistent picture of the multifaceted mechanism of a hostile
leveraged takeover is provided. The analysis points out two basic issues. The first is the financial
problem caused by the leveraged acquisition, which calls for detailed strategic planning in order to
ascertain the feasibility of the operation with respect to the capital structure of the target company.
The second issue is the agency problem caused by the delegation of the acquisition to a raider, who
possesses the unique skills needed for such a task. A coherent framework has thus been developed,
which enables the raider to evaluate different potential targets and the lender to guarantee the
optimal behaviour of the agent.
JEL No. G32, G34.
Keywords: Takeover, Debt/Equity ratio, Principal-Agent model.
May, 2006.
1
2
augusto.schianchi@unipr.it
mantovi@fis.unipr.it
1
In the corporate world, a raider is a special type of economic agent. He is a financial investor who
buys a company (the target) on the stock exchange, using cash retained by the targeted company
itself and/or exploiting its borrowing capability. The technical mechanism for conquering such a
target is relatively simple and well established in financial markets. The raider creates a new legal
entity, usually called the new-co, with a small amount a of equity capital (the seed capital), and a
large amount of debt obtained by the financial allies for the takeover. The new-co, with the financial
resources in its hands, buys enough shares in the stock market to take control of the target company.
Immediately after successfully attaining his goal, the raider begins the process of merging the newco with the acquired firm. The new company will show more or less the same amount of equity
capital and an increased level of debt, quite close to the amount of money required to take control of
the company itself. This process may be called a hostile leveraged takeover, to be distinguished
from a friendly one, which can be viewed as much more similar to an agreed merger.
It goes without saying that there is ‘a market’ for takeovers, or, to put it better, for corporate control.
If a company’s balance sheet reveals a high profile of expected cash flow and/or a low level of debt,
it can be attractive to likely predators, therefore its price (i.e. its stock price) rises and a takeover
becomes increasingly more expensive, inducing a competitive bid. Eventually the market clears.
The probability of the new merged company surviving is related to the dimension of the cash
flows in the following years: the cash flow should be high enough to pay for the dividends to the
stockholders and, more important, to pay for interest on the new debt. The ability of the raider to
appoint a new management able to restructure the company and extract new levels of cash flows
will eventually decide the success of the takeover in the long run. At the beginning of the
restructuring activity, selling off non-core activities and pruning unprofitable branches of the
company may be particularly useful for a policy of debt containment. Management buyouts (MBO)
follow exactly the same procedure; the role of raider is played by the managers of the target
company, who decide to take control of the company into their own hands.
Over the last 25 years, we have seen dozens of takeover examples1, some of them very relevant
because of the amount of money involved. Some corporate raiders have become well known in
financial communities around the world because of their activities.
However, takeovers are ‘more easily said than done’; several problems may arise, and this is the
reason why several takeovers have failed in the end. In many cases, the company continues to be a
target and there may be another takeover after the first one.
There are several problems to be faced in a takeover.
2
Firstly, the raider needs some initial capital to start the process of acquisition; of course he may
borrow this capital, but that would increase the financial cost of the whole process and the relative
risk may reach an unbearable level. Moreover, there is a reputation problem: a raider who takes on
himself a significant part of the risk for the whole operation, is much more credible to his potential
financial allies.
Secondly, to get control of the target company without owning enough money to buy the shares
that guarantee such control, a pyramid of legal entities in cascade form is normally required to be
set up with different partners, not always easy to involve in a complex project like a takeover,
particularly if the target company is large and split into diverse activities. The usual law pertains:
the higher the pyramid, the higher the associated risk, the higher the interest rate to be paid. The
whole construction may become very difficult to support financially. The different levels of the
legal pyramid must face different risks in case of bankruptcy, therefore different legal arrangements
are required for the different financial allies. Normally a new set of covenants is required; to sum
up: the pyramids are extremely useful, but the raider’s legal advisers must find a shape to the
pyramid, which is fair to all parties. But even with the best of intentions, a real risk of cross default
may arise.
Thirdly, some of the original shareholders of the target company, not involved in the takeover
itself, if they retain their stake, may expect, quite rightly, a higher level of dividends to be paid for
the higher risk associated with the new level of the debt/equity ratio. An increased risk warrants an
increased dividend, otherwise the price/earnings ratio may rapidly become unacceptable to fund
managers and therefore the new dividend policy may become too costly for the company to sustain.
If, by any chance, the debt is downgraded, for instance to junk bond status, default may follow.
Fourthly, for the same reason, the former creditors of the company and the lenders associated in
the takeover may take a sanguine view on the financial structure of the company and request more
risk premium for their loans.
Fifthly: clearly a takeover structure remains intact if, and only if, the incoming cash flows during
the following years are high enough to cover interest and dividend payments. A correct evaluation
of prospective cash flows is vitally important in a takeover.
Sixthly – last but not least – the takeover architecture requires a set of contracts to be signed
between the raider and those who provide the financial resources, to secure an acceptable solution
to problems of the Principal-Agent type, namely moral hazard and adverse selection. Limited
liability to protect the raider is assumed, a standard condition for these types of contracts. It follows
that an agreed set of guarantees on future behaviour is a crucial issue to be resolved in advance.
3
It must be added that the board of directors of the company under threat of takeover usually tries to
protect their company (and their jobs!) in several ways using different legal tools, such as the well
known so called poison pills, or they may look for a white knight if they are scared of the incoming
stockholders. Only the current directors see the takeover as possibly hostile; from a welfare point of
view, takeovers should be considered as beneficial. Moreover, it must be stressed that national laws
regulate takeover procedures in different ways. At the moment, national governments are trying to
take reciprocal action to regulate trans-national business operations, but the general opinion is that
an acceptable compromise is still a long way away. In this paper, the strictly legal aspects of a
takeover are not faced: only the main economic mechanism comes under analysis.
To sum up: for a takeover, the three critical issues are:
-
to evaluate correctly future cash flows;
-
to manage the new debt/equity ratio;
-
to arrange a related set of contracts to find a satisfactory compromise between information
sets and incentive patterns for the various agents involved.
In this paper, a simplified analytical model is set up to solve most of these problems. Specifically
we would like to try to answer two basic questions:
1) by which criteria can the raider determine the optimal target company?
2) which kind of contract should be devised for the Principal-Agent game between the raider
and the lender?
1 Literature review and plan of the paper.
Our work is about options to invest, in quite a generalized sense. The option paradigm establishes
a consistent body of techniques, which enables the economic agent to assess the value of options,
whether real or financial. Such a paradigm is at the basis of modern investment theory. In this
respect one can define the value and equity of a firm: the value of a firm is basically the value of a
set of options, and the equity value of a firm is equal to the value of the owner’s option.
The option ‘revolution’ started in the realm of capital budgeting with the celebrated seminal
papers by Black and Scholes (1973) and by Merton (1973). Then in his Determinants of Corporate
Borrowing Myers (1977) introduced the expression real options, which is now used to denote the
whole conceptual framework for both real and financial options. McDonald and Siegel (1986)
represented a turning point in investment theory, by exploring the core nature of options, namely
4
“comparing the value of investing today with the (present) value of investing at all possible times in
the future.”
The option approach has been thoroughly examined in economic literature, the fundamental
reference being: Dixit and Pindyck (1994), which outlines the basic framework and provides the
essential analytical tools. We also refer the reader to the foundational monograph by Trigeorgis
(2002) and to the advanced view by Smit and Trigeorgis (2004), which explores options related to
game theory. In fact, our utilization of the option framework somehow crosses the border of
canonical interpretations, and can be used to choose the target firm in a large stock market, see
section 2.B.
The options framework has been applied to any type of investment. One such type is the planning
of a takeover. Lambrecht and Myers (2005) use the real options approach to pinpoint the optimal
disinvestment timing for a declining firm (a sort of ‘inverse problem’ of ours), in which upon
closure the company releases its capital stock. Takeovers have been the subject of much research
because of their unique characteristics; according to Henry (2005) “if the market for corporate
control functions correctly […], then all takeovers should be valuable and value enhancing
corporate transactions for shareholders”. Weston et al. (1999) address various governance issues
entailed in the restructuring which follows a takeover. In recent times, Italian capitalism has started
to face the financial takeover mechanism: Kruse (2004) addresses various aspects of the 1999
takeover bid of Telecom Italia by Olivetti’s CEO Mr. Colaninno and his allies. Incidentally, a few
years later, Mr. Colaninno was himself ousted (but with a large capital gain) by a new takeover led
by Pirelli’s CEO Mr. Tronchetti Provera. Today Telecom Italia is perhaps, in absolute value, the
most indebted company in the world. Martynova and Runneboog (2006) give a comprehensive
account of the empirical experience of takeovers in Europe.
Corporate finance is the basic setting of our model. Debt is a key variable in our model; Jensen
(1986) shed new light on the significance of debt, and related free cash flows to general agency
conflicts; it has now become clear how debt is a basic mechanism for enhancing management
efficiency: it plays a key role in the governance policy of a company. A thorough exposition of the
general theory of corporate finance is to be found in Tirole (2006), which moves from the Berle and
Means (1932) paradigm of ownership and control separation up to the forefront of modern research;
the basic theme underlying the whole work is that, far beyond Modigliani-Miller’s ‘irrelevance’
theorem, the financial structure of the firm does indeed matter. Notice that the whole analysis by
Tirole is given in terms of the NPV valuation criterion, and no option formula is used: such an
approach enables to perceive the exact extent of the financial analysis, and therefore disentangle
these propositions from investment evaluations which pertain to a different paradigm.
5
From the corporate finance perspective, our focus is merely the relation between the raider and
the lender, and therefore our analysis does not touch upon the issues explored by Tirole in the
chapter on takeovers; we do not come to grips with the many issues related to managerial turnover
or entrenchment.
Corporate governance is the general framework; a classic survey is given in Tirole (1999). Our
focus is only on the phase of acquisition, and we do not enter into the issues raised in the
subsequent phase of governance restructuring, involving entrenchment issues, which lie beyond our
aim; for a thorough account of such problems, see Morck et al. (2005).
One of the key issues of corporate governance is the agency problem raised by the asymmetries
inherent in any delegation of tasks. Contract theory is a source of active research (for a survey, see
Bolton and Dewatripoint 2006); one of the main goals of incentive theory is to establish the size of
the departure from first best (FB) optimal values, which characterize the problem in the absence of
delegation. Such a departure is needed in order to incentivize the agent; the resulting second best
(SB) outcomes solve the constrained optimization problem. Needless to say, such a perspective
plays a key role in the real world applications of contract theory, and yet its relevance is mainly
theoretical, since the amount of available information is one of the basic issues in most economic
disciplines, and the related revelation principle is a quite general issue.
The basic paradigms of incentive theory are moral hazard (MH) and adverse selection (AS),
which shape the basic asymmetries generated by the delegation of tasks. It is fair to say that the
theory of incentives lies at the foundation of economics. In fact the Principal-Agent model has been
developed in depth in the last decades and its structure is thoroughly explored in the monographs by
Selanié (1997), Laffont and Martimort (2002), and Bolton and Dewatripoint (2006), which recall
that the notions of ‘incentive compatibility’ and incentive for ‘truth telling’ provided the basic
underpinnings for the theory of incentives and the economics of information. They also provided
the first formal tools for a theory of the firm, corporate finance, and, more generally, a theory of
economic institutions. The first chapter of Laffont and Martimort (2002) fashions a brief and
intriguing history of incentives within economic thought; this monograph is built around the
deconstruction of the theory into its paradigms, i.e. the nature of the asymmetry in the agency
relationship, the fundamental paradigms being MH and AS, whereas Bolton and Dewatripoint
(2006) is designed in a somewhat ‘game oriented’ shape in which the topic is developed from static
to dynamic contracting. Myerson (1999) is a brief account of the relevance of game theory and
incentive approaches.
Among the many areas of its application, the theory of incentives can be merged with the
investment perspective. Our model is quite close to the one in Grenadier and Wang (2003), which
6
stylizes the basic elements of a theoretical delegation of exercising an American call option, by a
clever choice of interplay between hidden information and hidden action issues.
Finally, let us remark on the relevance of the dynamic programming approach in the present work
and in general for the whole body of modern microeconomics. The last decades have witnessed a
growing interest in quantitative predictions, which can be exploited in terms of optimization in
continuous time, we refer the reader to Chang (2004). Such quantitative approach embodies the
uncertainty paradigm as well as the optimization perspective, and is now perceived as a very
promising approach to the elaboration of legal recipes related to governance problems. One such
problem is the well known investor protection: see Albuquerque and Wang (2005)
From now on the paper continues as follows. In section 2, the model is developed in terms of the
fundamental variables. Section 2.A introduces the fundamental equations; section 2.B discusses the
basic mechanism at work; section 2.C is devoted to the evaluation of various quantities related to
re-establishing the minimum debt/equity ratio value to guarantee the survival of the company.
Section 2D gives an overall perspective of corporate finance and governance. In section 3 the
agency issue is addressed and section 4 tailors a possible deterministic (and chaotic) dynamics for
the debt/equity variable. Finally, section 5 contains the conclusions and perspectives of our analysis.
Notes are collected at the end of the work.
In what follows E will be employed for conditional expectations of stochastic processes; Ξ will
stand for enterprise value, E for equity, η for the debt/equity ratio and ε for the ‘instantaneous’
investment opportunity value.
ρ denotes the exogenously given discount factor and r the interest rate to which the leveraged
firm is subjected (with respect to the owners of the liability), which in turn depends on the
debt/equity ratio.
2 The model
In this section the model is defined in terms of the problems faced by the raider and the lender. In
section 2.A, the variables and their dynamics are defined. In section 2.B the financial issues raised
by the leveraged acquisition are discussed. In section 2.C the analytical treatment of the postacquisition debt/equity is examined. In section 2.D a concise review is provided of the financial and
governance perspective in which the model fits.
7
The timing of the process develops in two phases, in the first of which the acquisition is planned,
and eventually carried out; in the second of which the company is governed financially, in such a
way as to guarantee the survival of the company itself.
2.A Assessment of variables dynamics
The key assessment in the first phase is the recognition of the dynamics of the cash flow F, the
income once costs and interest (and dividend payments) have been subtracted. It is therefore the
proper variable to be considered for evaluating the robustness of the company with reference to the
leverage perspective. Cash flow is related to the Ebitda, which measures the quality of the business,
but which is ‘unaware’ of the financial structure of the company; for the relation between cash flow
and Ebitda, see Moody’s (2000), according to whom “a company may have a strong reported
consolidated EBITDA but not the cash to pay interests.” F is a stochastic function of (continuous)
time; it is a standard hypothesis to take it as a geometric Brownian motion (GBM),
dF = µ F Fdt + σ F Fdz
(1)
whose drift µF and volatility σF characterize the firm under consideration; z represents a standard
Wiener process.
We are interested in describing a situation in which the company has a stable share of the market,
which more or less guarantees the cash flow (1). We suppose the leveraged acquisition has no effect
on the business and the equation (1) still represents the net income; on the other hand the leveraged
situation, after the acquisition, calls for the payment of the interest I, therefore the cash flow
becomes F – I. The two variables, which characterize the financial structure of a firm, are well
known. The first one is its debt D, a deterministic function of time, decided by the financial policy
of the company. The debt D of the firm is in its ‘regular form’, i.e. a decreasing function of time
with jumps upwards corresponding to periodic investments, and an asymptotic value which may
represent a structural permanent debt inherent in the company, whose level is chosen with particular
care; recall Jensen (1986) and the role of debt in corporate finance. As an effective parametrization
we take
8
D(t ) = D0 + D1e − Ωt ;
(2)
we suppose this equation as a single function representing the various ‘forms’ of claims upon the
firm. It is a basic problem of corporate finance to figure out the optimal (beyond M-M’s
irrelevance) policy for designing various forms of debt; we suppose (2) is an efficient
parametrization.
The other cornerstone of corporate finance is equity capital. It is a fundamental variable for our
model since it is the value of the firm, which must be evaluated by the raider in order to decide
which company should be bid for. We define the equity variable starting from the enterprise value,
as a general parameter, which assesses the value of the firm. Given the cash flow (1) and the interest
I = rD, which must be ‘extracted’ from it, the standard expression for enterprise value Ξ is given
by the conditional expectation of the projected cash flow,
Ξ ≡ E(F − I ) ,
(3)
and for the cash flow resulting from (1) and the interest I proportional to debt, such a variable
results in,
Ξ ( F (t ), F0 , I , ρ ) =
F (t )
I
F (t )
r
r
− =
− D0 −
D ,
ρ − µF ρ ρ − µF ρ
ρ −Ω 1
(4)
I is the constant yearly ‘price’, which guarantees the continuance of such borrowing, and which
must be subtracted from F. Such an expression represents the NPV determination, well known in
standard capital budgeting. Ito’s lemma tells us that (4) is GBM with the same drift and volatility of
(1), despite the differences between the two quantities: (1) represents a cash flow, (3) represents a
present value and has a deterministic contribution given by (2).
Out of (4) we define equity as the difference between the enterprise value and debt,
E (t ) = Ξ( F ) − D(t )
(5)
Once we move towards the options approach we must turn to the consideration that “the value of
a firm is largely the value of a set of options” (Dixit and Pindyck 1994, p. 211). Then the general
expression for the ‘investment value’ is given by the familiar expression,
9
⎧⎛ F ⎞ β *
⎪
ε ( F ) = ⎨⎜⎝ F * ⎟⎠ F − I
⎪ F −I
⎩
(
)
F < F*
else
(6)
.
It could be called an instantaneous investment value with respect to the options paradigm. It is not
the aim of this paper to account for theoretical aspects of the option approach. We refer the reader
β
⎛F ⎞
to the broad literature (see: section 1). The term ⎜⎜ 0 ⎟⎟ is a sort of ‘discount function’ in that it
⎝ F1 ⎠
establishes the value of a unit investment at the time of exercising it; thus it is a discount function
which has relevance to the problem in hand: it is partially determined by the overall
market/economy and partially by the parameters which characterize the process in hand.
In such a framework the well-established expression for the investment trigger value is given by
F* =
β
β −1
I
,
(7)
I being again the yearly cost of interest which guarantees control of the company, as discussed in
the introduction. In standard real options terminology, such a value is termed sunk cost since it
represents the cost of acquisition of an option for an irreversible investment. From the raider’s
standpoint it is a cost to be paid to the lender, from the lender’s standpoint it is the income, which
justifies the initial loan.
The most interesting region is the one in which the stochastic variable is below the investment
trigger; in such a region ε is the stochastic process defined by the equation
1
⎞
⎛
dε = ⎜ βµ F + β ( β − 1)σ F2 ⎟ε dt + βσ F ε dz ;
2
⎠
⎝
(8)
taking advantage of such an expression, the properties of such a GBM can be exploited. Such a
stochastic variable is used to define the utility function of the principal for solving the agency
problem, see section 4.
Finally, from the financial standpoint, we point out that D and E uniquely characterize the
corporate finance problem and policy, whose general agenda is establishing and/or planning the
dynamics of the capital structure of the firm. The debt to equity ratio
D
≡ η is a stochastic process
E
10
whose equation we are in a position to compute, again by Ito’s lemma (this time for time dependent
functions),
2
⎛ ∂D ⎛ 1 D ⎞ D dE
1 2 2 2 D ⎛ dE ⎞ ⎞⎟
⎜
dη =
µ F + σ F F 3 ⎜ ⎟ dt + σ Fηdz .
−
+
⎜ ∂t ⎜⎝ E E 2 ⎟⎠ E 2 dF F
2
E ⎝ dF ⎠ ⎟⎠
⎝
(9)
As expected, it is a stochastic process (not a GBM as a consequence of the explicit time dependence
of D) with negative drift. The first term in the drift accounts for the explicit time dependence of
equity (in the peculiar form of our model), the second and third terms are the familiar ones. Notice
that in a more general model a term could appear which accounts for the second derivative of equity
with respect to cash flow.
At the time of acquisition η experiences a sudden upward jump corresponding to the leveraged
buyout of the company; the evaluation of the sustainability of such a jump is the key issue of this
paper. The leveraged takeover entails the raider becoming the new controlling shareholder and
charging the firm with the debt L+a by which he has taken control of the firm. It is the sustainability
of the new debt to equity ratio, which decides the feasibility or not of the takeover. Therefore the
choice of the firm to be targeted is a delicate question, which the raider must address with great
care, and such a variable can be considered as the ‘handle’ of the analysis.
The leveraged acquisition is performed by means of a huge sum of money, partly provided by the
raider, and mostly by the lender. The seed capital a is provided by the raider, the loan capital L
provided by the lender. Such amounts are charged on the balance sheet of the company and
represent a debt which remains, and which can be somehow reduced via suitable restructuring after
the acquisition.
As outlined in the introduction, the requirement of the lender is that he receives every year the
sum I, the interest, which the raider must guarantee to pay him. Such a sum is the main factor in the
determination of the choice of the target company. The interest is a function of the debt; the exact
relation is established by the interest rate
r ( D) = r + ρ (η ) ,
which is the sum of a fixed component (in Europe, the so called Euribor), plus a spread ρ(η)
determined by the financial status of the firm under consideration. It is such a parameter, which
enters the real option formula. r is a function of η, and is a stochastic variable (which can change at
discrete times and we can consider constant over a period, typically a year). A reasonable functional
form for r is
11
r ( D) = r + ρ1η + ραη α ,
α > 1,
a convex function with positive derivative on vanishing, and positive second derivative all through
the range of η . The nonconstant terms on the rhs represent a possible expression for the sum of the
spread and of the risk premium (and of the deduction of taxes).
In fact, in spite of such general dependence on debt, in our analysis r will remain constant, for
several reasons. Firstly, we are interested in describing the lending effects due to the huge increase
in debt; secondly, taking into account the dependence r (η) does not involve dramatic changes. We
want to disentangle the effect of such a dependence from the main analysis, since our focus is to
assess the basic mechanism outlined in the introduction, and which we are going to discuss in depth
in the following sections.
2.B First phase: the choice of the firm
In this section the leverage mechanisms involved in the acquisition are discussed. We will not
concern ourselves with legal mechanisms (see Hopt 2002), nor actual examples of takeovers
(Martynova and Runneboog, 2005); rather, our focus is theoretical, namely: on the consequences of
the leveraged acquisition with reference to the sustainability of the company’s new capital structure,
and to the relative evaluation of the feasibility of the operation.
The raider’s task is to choose the target company wisely, a company that can sustain (at least for
some time) a high level of debt, thanks to its high level of cash flow. From the raider’s standpoint
the problem is finding a target which more or less guarantees such a huge cash flow (beyond the
unavoidable uncertainty inherent in any market), and therefore guarantees the payment of the
interest I which the lender aims to receive every year. Notice that the takeover we are studying is ‘in
primis’ a financial investment, and as such the target company is chosen with reference to the
criterion of best expected return, almost irrespective of the industry in which the company operates.
As stated in the introduction, the leveraged acquisition is carried out using loan capital to acquire
the company; and then, through suitable mergers, the related debt is transferred to the target. The
financial details of such an operation are discussed in section 2.B.
The evaluation of the suitability of the target company necessitates three well-established
paradigms for the enterprise value, which can be read off the balance sheet. The first parameter to
be considered is cash flow, which must be high and stable enough: such a criterion informs us about
the market share which the target has acquired over time, and the degree of its stability. The second
12
parameter is the relationship between Ebitda and debt, which tells us about the quality of the
business. The third aspect concerns the assets of the firm, and such a static criterion guarantees a
stable enterprise value in the face of potential shocks and instabilities in the economy. In principle
all these aspects should be considered to some extent, in order to value the firm correctly and
therefore to be able to choose which firm is in a position to be charged with the high level of debt
necessary for the leverage mechanism. From such evaluations comes the judgement about the
target, and also the enterprise value (4). Take note that in principle, a more general indicator of the
value of the target could be defined by adopting a suitably weighted average, or even a more
general function Φ of the three indicators, and then arriving at the enterprise value in terms of Φ via
the same functional form in (3).
Then, once the choice has been made and the acquisition operation has been successfully
completed, the new-co is merged with the target company, which faces a sudden huge increase in its
debt. It is therefore crucial that, after the acquisition, the debt-equity ratio does not exceed a ‘safety’
level, or if it does exceed this level, it does not last for too long. A key issue is that the interest paid
to the lender depends on the level of debt/equity according to (11) and therefore the interplay
between equity and debt is, in principle, fundamental. The relationship may be represented by a
simple scheme, in which the independent variables F (as discussed) and D both determine the value
of equity capital.
Equity ≈ enterprise value - D
‘Cash flow’
→
←
Debt
Interests I = r (η) D
Cash flow is positively related to equity and out of it the payment of interest must be guaranteed.
On the other hand, debt has a negative effect on the level of equity as well as on the level of interest
since the interest rate r is an increasing and convex function of η as we have pointed out in the
preceding section. It is precisely the interplay between these ‘forces’, which must be taken into
account in the choice of target company. The new high level of debt, caused by the leveraged
acquisition, can only be sustained by a strongly performing firm, or the overall operation will
eventually fail. Thus from an analytical standpoint, a precise assessment of the time it takes to
recover from the excessive debt burden, is a key feature in establishing the feasibility of the
operation. The next section is devoted to such a problem. As already stated, the dependence of the
interest rate on η can be neglected, in that such an effect can be disentangled from the basic
mechanism addressed in this paper.
13
Another point should be mentioned. It is well known that flexibility is crucial to the options
approach: “both operating flexibility and strategic flexibility (that is, the option to alter a planned
course of action in the future, given then-available information) are important elements in valuation
and planning decision.” (Mason, S. P., Forward to Trigeorgis 2002). We feel the options framework
is ‘flexible’ enough to admit a definite interpretation: the option to ‘wait’ can be interpreted as an
option to choose from different firms, representing potential targets.
In fact, the task which the raider is meant to perform is to collect information about the possible
targets and choose from these on the basis of the criteria already discussed. Therefore he must
collect information from the balance sheets about the cash flows and equity debt of the potential
targets. We suppose the (in principle, continuum) set of companies studied by the raider contains a
company with cash flow (1) and debt given as in formula (2). Out of such information the following
recipe can be constructed for every firm with a cash flow as given in (1).
The raider, facing the problem of searching through the stock market for a good target, must
collect information from all firms about the dynamics of their cash flows and debt. For modelling
purposes let us consider a market in which the following holds:
The raider has a ‘continuum’ of targets at his disposal, that is, he can choose at will a firm with
respect to the parameters in (1) cash flow and (2) debt.
Notice that such an assumption comes without any loss of generality, since at varying drift and
volatility, a wide range of behaviour can be accounted for. In any case, our analysis is theoretical
and is concerned with methods for a correct evaluation of the target. And in this respect, our idea of
an option to ‘choose’ can be an alternative to the former idea of an option to ‘wait’. One could
debate the consistency of such an interpretation, which implicitly assumes the market is composed
of a continuum of firms with respect to cash flows, and therefore waiting for new information may
be equivalent to finding a better target.
After the data has been examined, the equity and equity/debt ratio can be evaluated and after that
an estimate of the seed and loan capital needed for the acquisition can be made.
It is not difficult to convince oneself that a high level of debt/equity ratio cannot be sustained for a
long time. In the ‘takeover wave’ of the eighties it was fairly common to find astonishing levels of
such a dangerous ratio (see: Tirole 2006); these days, such levels are never reached.
We do not assign a specific number to the critical debt/equity ratio, beyond which sustainability is
highly problematic; such a number is exogenously estimated in our model and it depends on the
financial climate. In fact, often it is a number not very far from one. We will come back to this
point in section 4.
14
In the next section, an analytical treatment of some basic assessments about the expected time of a
return to a sustainable financial structure is provided.
2.C Second phase: approach to equilibrium
In this section a number of relationships are derived between the variables and parameters of the
model. As pointed out in the introduction, the phase which follows the acquisition is the delicate
one since the variables, by which the firm has been valuated, face a sudden change at the
acquisition, due to the leverage mechanism. The dynamics of such variables must be studied with
care in order to know how they will behave in the critical phase.
The goal is to assess the expected time taken for Ξ , E and η to approach a financial ‘equilibrium’,
and the associated sensitivities on the parameters of our model. By the term equilibrium we denote
a situation in which the capital structure of the company is under (relative) control and in no danger
of bankruptcy. Such an equilibrium we define in terms of critical values Ξ*, E* and η*; beyond these
critical values the survival itself of the company is questionable. We take such critical values as
exogenously given; they are meant to be estimated by the raider with respect to a number of criteria,
related to his personal expertise as well as general valuations of the overall market. We do not go
into the argument about what the numbers might be; let us simply point out that η* cannot exceed 1
without serious danger of default: the debt equity ratio should be controlled so as to avoid
exceeding such a critical value, at least for a short time. It is therefore fundamental for the planning
of the strategy to recognize how much time it would take to regain equilibrium.
In the following computations we suppose (see section 2.A) that the interest rate r is constant in
the range spanned by the variables of interest and in the phase we are studying; as already argued,
this is not dramatic an assumption since the range of variation of r is limited and the aim is to
disentangle such an effect from the mechanisms at work in our analysis. Let us take advantage of
the properties of the stochastic processes Ξ , E and η and compute the expected times to reach the
respective critical values; let us start with the enterprise value (3). Such a GBM can be handled with
standard techniques (Karatzas and Schreve 1991, Chang 2004), which provide the estimate of the
expected time of reaching a definite level Ξ*, i.e.
tΞ* = ta +
1
µΞ −
σ Ξ2
ln
Ξ*
,
Ξ(ta )
(10)
2
15
being ta the time of the leveraged acquisition, which corresponds to the sharp rise in the debt. As
expected, such a time interval depends on the drift and volatility of Ξ , and therefore on the drift and
volatility of the cash flow process. Then, in principle, one could reduce such an expected time by
pushing on the drift and/or by increasing the volatility of the cash flow. As is well known, in the
takeover perspective it is quite usual to devise a comprehensive restructuring policy after the
acquisition of a group. Such transformations can ‘push’ the firm through technological innovation
and therefore augment the drift µF of the cash flow process. At the same time, a new corporate
finance policy of reducing debt (which, in principle, can be accomplished in ‘infinite’ ways) can be
parametrized by an increase in Ω. One could compute the dependence of (10) on Ξ * – Ξ (t), since
one can devise mechanisms like pyramids which reduce the loan capital needed to get control of the
company and therefore reduce the size of the upward jump in debt, but we are not going to embark
on such an analysis which lies beyond the goals of this work.
The sensitivity of tΞ* on the parameters can now be established: tΞ* decreases with µΞ and
increases with σΞ at the opposite rates
∂tΞ*
∂µΞ
=−
1
⎛
σ ⎞
⎜ µΞ − 2 ⎟
⎝
⎠
2
Ξ
ln
2
∂tΞ
Ξ*
=− *
Ξ(ta )
∂σ Ξ
(11)
Such effects can in principle be taken into account in the planning of the acquisition and of the
subsequent phase. In practice, though, acting on the volatility of cash flow looks quite problematic ,
both on the contingent level (the uncertainty of the market is exogenously given) and on the
theoretical level, since questions as to how such a change can be ascertained in the short run are
difficult to answer.
Analogous steps lead one to assess the corresponding results for the equity variable E. As already
stated, such a process is no GBM and we cannot rely any longer on expression (10); yet we can
isolate the GBM and write the expression
t E* = ta +
1
µΞ −
σ Ξ2
ln
E* + D (t E* )
E (ta ) + D (ta )
(12)
2
which implicitly defines t E* as the solution to the equation
16
H (tE* , µΞ ,σ Ξ , Ω) = 0 ,
(13)
H being the function defined as the rhs of (12) minus the lhs; t E* can be determined numerically;
the sensitivity of (12) on the parameters of the system can be established by means of the approach
tailored by the implicit function theorem, according to which
∂H
= ∂Ω
∂H
∂Ω
∂t E*
−
∂t E*
.
(14)
Then, the differential dependence on the parameter Ω of debt reduction policy reads
(
D1 exp −Ωt E*
∂t E*
∂Ω
=
(
)
E* + D0 + D1 exp −Ωt E*
(
−ΩD1 exp −Ωt E*
E* + D0 + D1
)−µ
Ξ
+
)
σ
2
Ξ
t E* .
(15)
2
The sensitivities on the drift and volatilities of the cash flow can be established in the same way.
Finally, let us turn to the expected time taken for the debt/equity ratio to reach the critical value
η*. As already stated, it is this variable which represents the most significant indicator in order to
establish the feasibility of the leveraged acquisition. It is important to have an estimate of how long
such a variable is supposed to lie beyond the safety margin, as well as an estimate of the sensitivity
of such a time on the parameters of the model. The stochastic behaviour of η is inherited from the
equity process E, since in our model debt is a deterministic function of time, planned by the
corporate finance teams. Yet, evidently, debt plays a role in the estimates which follow. As already
pointed out, η is not a GBM, and the relationship
tη* = ta +
1
µΞ −
σ Ξ2
ln
D(tη* )η (ta ) (1 − η* )
D(ta )η* (1 − η (ta ) )
(16)
2
17
can be used, which implicitly defines tη* as the solution of
K (tη* , µΞ ,σ Ξ , Ω) = 0 ,
(17)
out of which the sensitivities on the parameters can be derived. The sensitivity on Ω can be
established, again by means of the implicit theorem approach,
(
D1 exp −Ωtη*
∂tη*
∂Ω
=
(
)
E* + D0 + D1 exp −Ωtη*
(
ΩD1 exp −Ωtη*
(
)
D0 + D1 exp −Ωtη*
)
)
− µΞ +
σ Ξ2
tη*
(18)
2
Once again, the corresponding sensitivities on the other parameters can be established in the same
way. Thus, it is possible to establish such a differential behaviour without the need of a closed form
solution for the expected time. Such relation should be considered in order to establish a policy of
debt reduction which guarantees the survival of the acquired target company.
2.D Corporate Finance and Corporate Governance.
In this section the basic perspectives into which our model fits are described. A financial takeover
is a typical problem of corporate finance, to the extent that such an acquisition is entangled with the
given financial structure of the group and its robustness in the face of sudden changes. On the other
hand, the delegation of management tasks from the lender to the raider is a typical corporate
governance issue; it is not the aim of this paper to provide a general overview of corporate
governance, let us simply point out that in the process of an actual leverage acquisition several
governance issues must be addressed, like board resistance (Henry 2005) and managerial
entrenchment (Morck et al., 2005), to name but a few.
2.D.1 Corporate finance: the leverage mechanism
In the previous sections, we have dealt with the strategy planned by the raider in order to perform
a successful leveraged takeover. Once the raider has taken control of the firm he finds himself in the
18
position of controlling shareholder and therefore can decide on the future financial policy of the
company, firstly to guarantee the correct handling of the debt/equity ratio and then to ensure the
survival of the company. As has already been stated, the key problem of corporate finance is the
planning of the capital structure, i.e. the allocation of equity and debt, which has been dramatically
changed by the leveraged acquisition. Thus, quite contrary to Modigliani’s ‘irrelevance’, the capital
structure of the firm really does matter, and in fact is the key issue to be addressed by the new
management, whether they are the same managers with new directives or the managers brought in
by the raider (now the controlling shareholder).
Concerning the relationship between the raider and the lender, another perspective arises: the
general agency problem in which a Principal-Agent relationship must be dealt with by means of a
proper contract which is intended to elicit the informational asymmetries inherent in such a
problem.
As stated in the introduction, a new set of collateral problems arises, if the takeover is legally
supported by a pyramidal structure of financial entities (on pyramids, see Morck et al., 2005).
In this section, the major financial and governance issues, which emerge from the acquisition, are
explored.
2.D.2 Corporate governance
The other perspective, which must be considered, is the governance perspective into which the
agency relationship between the lender and the raider fits.
Corporate governance is a major theme in modern theory of the firm and particularly after the
bankruptcies of the last few years (Enron, Parmalat, and many more), it has been the subject of a lot
of attention from scholars (see Melis 2004 and references therein). In this paper, attention is
concentrated only on the analytical viewpoint of Principal-Agent type.
Existing literature on corporate governance offers a broad spectrum of analysis of the various
conflicts between entrepreneurs, boards, stockholders, managers and anything else which plays a
role in the ‘governance’ of a microeconomics. Our aim is to conceive the relevance of analytic
methods which can define consistent models for such conflicts, define clear questions and assess the
possibility of answering such questions. Tirole (1999) can be considered as a landmark in this
perspective: his notion of pledgeable income2
⎛
B
ph ⎜⎜ R −
ph − pl
⎝
⎞
⎟⎟
⎠
(19)
19
defines a handle through which to carry out quantitative analyses of models. In such a paper
corporate governance is defined as the issue of solving both an MH and an AS problem; in fact,
broader perspectives can be considered, which call for powerful analytical tools in order to deal
with the growing complexity of the problems.
Thus at the core of the governance issue lies contract theory, in terms of which one can address
the problem of devising the optimal contract between the lender and the raider. Such an agency
issue is raised by the information asymmetry inherent in any delegation of tasks: the lender is not in
a position to ascertain either the effort exerted by the agent or the true state of nature of his stolen
benefits. The properties of the contract do not alter the conclusions we have reached and will be the
subject of section 3.
So much for the general perspective. Yet, many governance issues are specific to the takeover
perspective. Hopt (2002) points out the relevance of the secrecy issue in the takeover plan with
respect to the different legal systems of European countries.
Henry (2005) provides a thorough account of the consequences of the behaviour of the target
company faced with to a takeover bid. Among the checks which the raider must perform, is the
feasibility of the takeover from the point of view of the current shareholders, i.e. to establish if the
present board structure of the company can accomplish the takeover; or if they are against the
takeover, to establish if a hostile move can be successful. If this is not the case, the takeover bid
would be pointless, even if the state of the firm’s finances is excellent and so is its debt/equity ratio.
There exists a conflict between the raider and the lender: the latter is interested in receiving the
interest I = rL and therefore aims at maximizing r and consequently η. The former on the other
hand, aims at minimizing r. Does an equilibrium exist for such a ‘conflict’?
Furthermore the contract between the lender and the raider is meant to address the agency issues
raised by the information asymmetry: the lender is in a position to ascertain neither the effort
exerted by the agent nor the true nature of his benefits. The properties of the contract do not alter
the conclusions reached and will be the subject of section 4.
We refer the reader to the literature (section 1) for a general perspective on the governance issue
raised by a takeover plan; let us turn to the theoretical analysis of the agency relationship.
3 Agency issues: optimal contract between the raider and the lender
20
In this section, the agency problem between the raider and the lender is solved analytically. The
delegation of management tasks causes subtle problems, generated by asymmetry in the relationship
between the principal and the agent. These can be addressed in terms of a suitable incentive
strategy, which enables the principal to devise the optimal contract in terms of the SB solution of
the model employed. It is not the aim of this section to provide a general introduction to the
Principal Agent model. This section is meant to be reasonably self-contained with respect to the
formulation and solution of the constrained optimization problem. For the variables, principal agent
type notations are maintained to fit in with current literature; details of the solution are provided,
given the theoretical nature of this analysis.
In our model, the task of performing the takeover is assigned to the raider (the agent), which,
upon acquisition of the target firm, becomes the controlling shareholder (entrepreneur), free from
any monitoring, and allowed to have access to unique information. The lender (the principal) must
therefore rely on a signed contract in order to protect himself from any misbehaviour of the raider, a
contract which must be devised so as to elicit the information asymmetries which plague the agency
relationship. Both the basic agency issues, namely MH and AS, and a definite interplay between
such general problems are considered; then the SB quantities are solved. Let us describe the model
employed, in which the two basic ‘themes’ of contract theory are at work.
In the first instance, asymmetry in the relationship between the lender and the raider stems from
the absence of efficient monitoring of shareholder behaviour, an issue, which is at the core of
corporate governance (Tirole 1999). Absence of monitoring may induce the agent not to exert
maximum effort, therefore reducing the probability of a successful outcome of the task he has been
given. Such a hidden action issue is the core of the MH problem, and calls for proper incentive
constraints, which guarantee that a rational agent exerts effort, in spite of the cost he incurs by
behaving in such a correct way. The standard notation for effort variable e is employed, which is
taken as binary for the sake of simplicity, and let it range in the set {0,1} ; let ψ denote the cost of
exerting effort. In this basic setting such cost reduces to a single parameter.
The other side of the agency relationship is concerned with the advantage of the raider in
possessing private information about the quality of the project in which he is engaged; in this model
such private information coincides with a component of the investment cost, which has a publicly
known component I and a hidden component –θ, which the contract is meant to reveal. The range of
θ coincides with the amount of private benefits, which the raider is in a position to steal from the
balance sheet of the company. We let the random variable θ (the state of nature or quality of the
project as the standard literature used to call it) embody such an information asymmetry, which
guarantees the agent a dominant position. In the first instance, such a random variable is taken as
21
binary and let us denote its values by θ1, θ2, with θ1 > θ2 , and therefore b ≡ ∆θ ≡ θ1 − θ 2 > 0 is the
amount of private benefits which the raider is in a position to steal without being discovered;
extensions of the range of θ do not alter the conclusions of the analysis. The framework will now be
briefly sketched. The probability p(θ) function represents an ‘effective’ approach to the information
asymmetry to which the principal is forced by the dominant position of the agent, and which the
contract is meant to elicit.
The two agency issues have a well defined nature of their own; and several forms of interplay
may be conceived (Laffont and Martimort 2002). Let us define the model in terms of an agency
problem between the lender and the raider.
For any value of the effort variable, el = 0, eh =1, the (exogenously given) probabilities pl(θ),
ph(θ) for the random variable θ are given: the utility functions of the subjects will be averages over
such random variables, for any given effort level. Clearly, we let exertion of effort increase the
probability of the good state of nature from pl to ph .
Recall from section 3.1, the (FB) utility functions for the raider and the lender in the absence of
private information or asymmetry due to delegation. Now, let us turn to the true agency issue and
suppose the relationship is plagued by the problems we have discussed. The utility function for the
risk neutral principal, and for a binary θ, is the expected value of the well established option
valuation formula
⎧⎛ F ⎞ β *
⎪
V ( F ) = ⎨⎜⎝ F * ⎟⎠ ( F − I + θ − w)
⎪
F − I +θ − w
⎩
F < F*
else
(20)
.
with the star quantity defined in analogy with the standard option trigger, i.e.
F * (θ ) ≡
β
β −1
(I − θ )
(21)
defined by the (FB) option trigger which corresponds to common knowledge of the parameter θ . It
is the aim of the Principal Agent model to devise methods to compare FB and SB quantities and
establish exactly the extent of their differences, thus providing all the information needed to design
the contract.
The risk neutral agent maximizes the expected value of his utility
22
β
⎛F⎞
⎜⎜ ⎟⎟ w
⎝ F1 ⎠
(22)
i.e. its contracted wage, appropriately discounted in the option framework which has been employed
in the evaluation of the investment perspective.
In general the wage for the agent should be scheduled by taking into account all of the (possibly
hidden) information and (possibly hidden) actions available; therefore it must be a function of all
the parameters which are included in the constrained problem defined by the incentive strategy..
Notice that the private benefits θ are not included in the utility function of the raider, which we
want to maximize in the constraints structure: it is a general feature of the principal agent model, in
which the (constrained) optimization is based on the utility function; such private benefits are not
the subject of a rational problem.
For the choice of the maximization procedure, let us make an assumption reasonable from an
investment perspective.
We look for a solution of the maximization problem in which all triggers (for varying θ ) are
above the starting point F of cash flow.
After such an hypothesis the principal’s problem reads
β
max w1 , w2 , F1 , F2
β
⎛F⎞
⎛F ⎞
p⎜⎜ ⎟⎟ ( F1 − I + θ 1 − w1 ) + (1 − p )⎜⎜ ⎟⎟ ( F2 − I + θ 2 − w2 ) ;
⎝ F1 ⎠
⎝ F2 ⎠
(23)
correspondingly the raider’s problem reads
β
max w1 ,w2 ,F1 ,F2
β
⎛F⎞
⎛F⎞
p⎜⎜ ⎟⎟ w1 + (1 − p)⎜⎜ ⎟⎟ w2 .
⎝ F2 ⎠
⎝ F1 ⎠
(24)
The optimization of such functions is determined by a set of constraints, which determine a
suitable incentive strategy, i.e. the one which solves the problems raised by the specific
asymmetries of the relationship in hand.
First of all, the agent is induced to sign the contract by the participation constraint,
23
β
β
⎛F⎞
⎛F⎞
ph ⎜⎜ ⎟⎟ w1 + (1 − ph )⎜⎜ ⎟⎟ w2 ≥ ψ
⎝ F2 ⎠
⎝ F1 ⎠
(25)
which gives an assurance that, entering the project and signing the contract, implies a non negative
expected return. Notice that such a participation constraint is written in terms of the probability
associated with the high level of effort, which is not an occurrence guaranteed ‘a priori’.
Second, the standard assumption of limited liability is enforced by the constraint,
wh ,l ≥ 0
(26)
which guarantees that no penalty can ‘hit’ the agent upon revelation of the true state of nature, a
‘shelter’ from monetary punishments in case of a bad outcome to the project.
The MH problem is addressed in terms of a constraint, which induces the agent to exert effort,
β
β
β
β
⎛F⎞
⎛F⎞
⎛F⎞
⎛F⎞
ph ⎜⎜ ⎟⎟ w1 + (1 − ph )⎜⎜ ⎟⎟ w2 ≥ pl ⎜⎜ ⎟⎟ w1 + (1 − pl )⎜⎜ ⎟⎟ w2 + ψ
⎝ F2 ⎠
⎝ F1 ⎠
⎝ F2 ⎠
⎝ F1 ⎠
(27)
since any misbehaviour results in an expected lower return.
Finally the consistency constraints,
β
β
β
β
⎛F⎞
⎛F⎞
⎜⎜ ⎟⎟ w1 ≥ ⎜⎜ ⎟⎟ ( w2 + b)
⎝ F2 ⎠
⎝ F1 ⎠
β
⎛F⎞
⎛F⎞
⎛F⎞
⎜⎜ ⎟⎟ w1 ≤ ⎜⎜ ⎟⎟ w2 + ⎜⎜ ⎟⎟ b
⎝ F1 ⎠
⎝ F2 ⎠
⎝ F1 ⎠
(28)
enforce the revelation principle since they induce the raider to exercise at the trigger corresponding
to the state of nature, therefore revealing his private information and ‘renouncing’ private benefits.
As can be easily seen, one inequality induces the raider to reveal the true cost and to renounce
private benefits; the other inequality guarantees that false statements and private benefits do not
affect the agent’s behaviour.
The result is that the whole set of constraints can be reduced to the pair of essential constraints,
24
β
β
⎛F⎞
⎛F⎞
⎜⎜ ⎟⎟ w1 ≥ ⎜⎜ ⎟⎟ b
⎝ F2 ⎠
⎝ F1 ⎠
(HI)
β
⎛F⎞
ψ
⎜⎜ ⎟⎟ w1 ≥
ph − pl
⎝ F1 ⎠
(HA)
which alone enforce the overall incentive strategy; clearly, at least one of them will be effective.
The first constraint solves the hidden information problem resulting from private knowledge of the
possible benefits, which the raider could extract from the balance sheet. The second constraint
solves the hidden action problem, which stems from the (evidently) private knowledge of the true
effort exerted. The recognition of the feasibility of such a reduction to this pair of essential
constraints goes as follows.
In the first instance, the constraint wh ≥ 0 does not bind, since the compatibility constraints imply
that w1 (as expected) exceeds w2 . This being the case, it is not difficult to convince oneself that the
participation constraint is guaranteed provided the MH incentive is satisfied. Furthermore, the lower
level wage vanishes3, since any positive value would result in a lower value of the principal’s
utility;. Finally, the two consistency constraints can be reduced to (HI), the one which induces the
high level agent to exercise at the high level trigger, therefore preventing ‘stealing’.
Now that the formulation of the problem has been completed and optimized, let us turn to the
solution. It has already been established that a solution to the reduced problem (23, 24, HI, HA)
exists, which guarantees that the agent exerts effort, so that the probability associated with the
participation constraint can consistently be taken as the one associated with fair behaviour on the
part of the raider. Let us point out a key detail, which enables us to solve the problem.
A feature of the Principal Agent model is central to our analysis, namely that the SB higher
trigger F1 equals the FB, (Laffont and Martimort 2002, p. 43). This is a general feature of
information asymmetry in delegated investments, and the reader is referred to the literature on the
subject. Then, the goals of our analysis are the determination of the lower trigger F2 and the higher
wage w1 . The solution depends on the cost to benefit ratio
ψ
ph − pl
of exerting effort and on the
difference between the states of nature; but whatever the values of such parameters, the manager
has a greater option to ‘wait’, as will be seen, due to the fact he is not the owner of the option. Thus,
the major conclusion of the analysis is that the contract must be designed in such a form as to
account for the departure from FB quantities implied by the delegation of tasks. Needless to say, the
departure is in the direction of greater values, since a lower trigger would imply a worse final result.
25
This model follows the one employed by Grenadier and Wang (2003), which carries out a further
detailed analysis of the three parameter regions, which rule the constrained optimization.
Let us discuss the properties of the solution.
A first parameter region is the one in which the constraint which does bind, is (HI) since the cost of
effort is low enough for the MH problem to be ignored. Thus the agency problem is a pure AS
problem, in which the goal of the principal is to induce the agent to act in accordance with the
revelation principle. This being the case, the wage for the agent does not depend on ψ and can
therefore be completely ascribed to an effective reduction of the hidden information parameter θ .
The problem for the principal can thus be written,
β
max w1 ,Feff
⎛ F
⎛F⎞
p⎜⎜ ⎟⎟ ( F1 − I + θ1 ) + (1 − p )⎜
⎜F
⎝ F1 ⎠
⎝ eff
β
⎞
⎟ ( Feff − I + θ eff )
⎟
⎠
in terms of the effective parameter value,
θ eff = θ 2 −
ph
∆θ
1 − ph
which accounts for the enhancement of the investment cost due to the delegation of tasks. Again,
such an effective value is a general issue of the Principal Agent problem (see the related literature)
and maps the constrained optimization problem (in this parameter region) into an effective FB
optimization in the option framework: all we need is to define the effective trigger Feff = F * (θ eff ) ,
formula (21). The solution for the unknowns follows: the SB trigger F2 is given by the effective
FB-like trigger Feff , and the wage for the high level situation is determined by the (HI) constraint,
⎛ F*
w1 = ⎜ 1
⎜F
⎝ eff
⎞
⎟b .
⎟
⎠
(wHI)
which, as expected, grows with the spread of θ , i.e. with the possible benefits which the raider
could extract without being discovered. The argument entails the exact extensions of the parameter
⎛ F
region, i.e. 0 ≤ ψ ≤ b⎜ *
⎜F
⎝ eff
β
⎞
⎟ ( ph − pl ) .
⎟
⎠
26
Correspondingly, there exists a region of the parameters in which AS plays no role, a region
which is exclusively ruled by the hidden action issue: the region defined by the cost of exerting
effort being so high, that we simply need to solve a pure MH problem. The solution does depend on
ψ , and the wage is linear in ψ ,
β
⎛ F* ⎞
ψ
w1 = ⎜⎜ 1 ⎟⎟
⎝ F ⎠ ph − pl
(wHA)
as can be read off (HA). In fact, the SB trigger F2 equals the FB, since the AS problem can be
disregarded and, by definition, MH has no impact on the investment decision. The goal of the
contract is simply to induce the agent to fair behaviour, without interfering with the strategic
evaluation of the investment, which has been delegated. Notice that, in the mathematical setting,
this incentive guarantees a higher probability of a good state of nature, not its departure from FB.
Between these two regions, is located the most interesting area, the one in which the interplay
between MH and AS takes place and reflects the entire nature of the agency problem. Obviously,
from the theoretical standpoint, this aspect is crucial since it is in this region that the theory is
supposed to provide evidence for its robustness.
This region is defined by the equality on the rhs of the constraints (HI, HA),
β
⎛F⎞
ψ
⎜⎜ ⎟⎟ b =
ph − pl
⎝ F2 ⎠
so that both must be taken into account in order to solve for the unknowns, which turn out to
depend on all of the parameters of the model. In searching for the unknowns, let us notice that the
previous relationship establishes the dependence of the lower level trigger on effort cost and on the
size of the distribution of θ ,
F2 = F2 (b,ψ , ph − pl ) = F β
( ph − pl )b
ψ
Therefore, again considering both the essential constraints, the wage results in,
27
β
β
⎛ F* ⎞
⎛ F* ⎞
ψ
w1 = ⎜⎜ 1 ⎟⎟
= ⎜⎜ 1 ⎟⎟ b
⎝ F ⎠ ph − pl ⎝ F2 ⎠
with the caveat that the two expressions relate to different perspectives. The first equality
establishes that the wage, as expected on general grounds, must be proportional to the effort cost in
order to incentivize the agent to behave fairly. The second equality reflects the AS perspective in
which the efficient wage increases with the spread of the values of θ, and also depends on the SB
lower trigger, which, in turn, depends on ψ.
This proposition, i.e. proportionality between compensation and effort, is coherent with the
standard conclusion of the Principal-Agent model, is in accordance with our intuition. Clearly, the
idea of a proportionality between wage and effort is ‘relative’ to the specific context referred to. It is
only through empirical research that we will understand what it does mean in terms of actual wages
(including the well-known issue of stock option assignments), referred to actual efforts related to
the specific company’s performance: Ebitda/Ebit percentages on sales, various ROI, ROE, ROA,
etc4.
We refer the reader to Grenadier and Wang (2003) for technical details, which lie beyond the
scope of our analysis; the extension to a continuous range for θ does not alter the overall picture.
The model for the agency problem has thus been proved to provide the proper solution for devising
an optimal contract between the lender and the raider.
4 A final remark
Before coming to conclusions, let us add a few notes referring back to debt/equity ratio. Let us
suppose that the takeover has been successfully completed, and now the issue is to choose a suitable
financial policy for the new leveraged company. Let us also assume that, before the takeover, the
debt/equity ratio was very low, but because of and after the takeover, an aggressive financial policy
has been chosen by the new management.
Since the takeover the debt/equity ration may show rather unpredictable behaviour; one model
which can be considered is the dynamics defined by the logistic equation
η (t + 1) = αη (t )(1 − η (t ) )
(L)
28
(where α is the so called control parameter); such an equation may well describe a process of debt
accumulation. Such a discrete time equation has been introduced in the realm of population
dynamics (May 1976) and the factor 1–η accounts for the ‘back reaction’ to an excess of population
growth, which the equation is meant to describe.
The original debt/equity ratio is very low in the beginning, then the rise after the acquisition is
sudden. Notice that when the debt/equity ratio reaches the value of 1, the equation ‘collapses’: the
dynamical system defined by (L) is a map of the interval [0,1].
The logistic equation possesses various interesting properties, among which the bifurcation of
equilibrium points defines the well known structures represented in Figure 1.
Figure 1 Equilibria of the logistic system as a function of the control parameter
Such a property can be recognized in the following plots (Figures 2,3,4): the debt/equity ratio
stabilizes only if the multiplier factor is below a definite level, otherwise, in the first case it
29
oscillates wildly. Even worse, in the second case it reveals chaotic behaviour. In fact, the logistic
equation is one of the fundamental systems which exhibit deterministic chaos: (for the use of
chaotic function see, among others, Shone 2002). The extreme sensitivity of the solution on the
initial condition implies that no one can say what the actual solution is going to be.
0.8
0.6
0.4
0.2
0
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
0
5
10
15
20
25
30
35
40
45
50
1
0.5
0
1
0.5
0
Figure 2
The dynamics of debt/equity according to the logistic map for different values of the
multiplier factor: from top to bottom α = 2.4, 3.4, 3.99. Initial condition = .01
30
Figure 3 Logistic map for different values of the multiplier factor: from top to bottom α = 2.2,
3.2, 3.8. Initial condition = .01
31
Figure 4 Logistic map for different values of the multiplier factor: from top to bottom α = 2.2,
3.2, 3.8. Initial condition = .02
To stress again: managing the debt/equity ratio after the takeover, is the most committing task for
the raider.
5 Conclusions and perspectives
In this paper we have provided a consistent picture of the multifaceted mechanism of a hostile
leveraged takeover. The analysis has pointed out the two basic issues, which must be addressed in
order to manage the two phases of the process. The first is the financial problem caused by the
leveraged acquisition, which calls for detailed strategic planning in order to ascertain the feasibility
of the operation with respect to the capital structure of the target company. The second issue is the
32
agency problem caused by the delegation of the acquisition to the raider, who possesses the unique
skills and expertise needed for such a task.
In the first phase, before the acquisition, the balance sheet of the target company must be studied
in order to judge if its business is strong enough to withstand a possible hard leverage profile in the
future. The financial structure of the firm is under scrutiny and the basic variables of such an
analysis are the corporate liabilities of the firm, i.e. debt and equity, whose ratio η cannot exceed a
safety level. It is such debt, which experiences a sudden jump following the acquisition: the firm is
charged with the leverage used to acquire it, and therefore it is fundamental to have control over the
evolution of η after the acquisition itself. The next phase must be planned with great care in order to
reduce η to a safe level within a reasonable time. We have computed, as an example, the expected
time needed to regain the safety level and the increment in the drift of cash flow and in the damping
of debt in order to reduce such an expected time by a factor of 2. Such an analysis is the raider’s
point of view, the agent in the agency relationship.
On the other hand, the principal, the lender, faces the problem of devising a contract, which
prevents the rational raider from misbehaving. We have utilized the analytical treatment of the
incentive constraints, which rule the optimal contract. Such a contract guarantees that the raider
exerts effort and reveals the true amount of the private benefits he ‘steals’ from the cash flow; it is
devised after the recognition that the agent is led to an investment ‘lag’ (in the various meanings
discussed), which raises the exercise trigger, and depends on the parameters which characterize the
agent, namely, the spread ∆θ in the private benefits and the cost ψ of exerting effort. In the analysis
of the agency relationship, we have come to grips with general features of incentive theory, such as
the fact that under limited liability the lower wage vanishes and that the SB first trigger equals the
FB.
A coherent framework has thus been developed, which enables the raider to evaluate different
potential targets and the lender to guarantee the optimal behaviour of the agent, to whom the task of
acquisition has been delegated. Such an ‘ideal’ case study should be relevant on an empirical basis
as well as on theoretical grounds. In fact, the relevance of the devised picture lies in its usefulness
for assessing the feasibility of the operation. Because of the enormous costs involved, as little as
possible must be left to chance (except for stochastic behaviour). We feel that the major spinoff
from our analysis is a contribution to the revamping of a consistent legal and economic framework
for corporate governance In fact, our analysis has pointed out how different perspectives should
converge into a single view in order to master the problem: investment theory and the real options
framework, stochastic calculus in the valuation of functions of stochastic variables, the Principal
Agent model in order to address the agency issues. Not to speak of the corporate finance issue,
33
which underlies the whole analysis. What emerges is a coherent picture in which both analytical
tools and general principles tailor a well-defined model for devising the strategy of both players.
We perceive corporate governance heading towards a more precise characterization of those
problems, which can be satisfactorily solved on the basis of consistent mathematical models, under
the assumption of rational behaviour. In our view, the model presented here should be considered
paradigmatic for corporate governance in its fundamental perspective.
Acknowledgments
We thank the Dipartimento di Fisica of Parma for the computational resources for numerical simulations.
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Notes
1
See The Economist, April 8th 2006, page 73.
2
The p’s denote the probability of success of a project for different values of effort exerted, R is the
yield income of such a project in case of success, and B is the amount of private benefits which the
manager can steal.
3
The vanishing of the lower level wage under limited liability is a general feature of the PrincipalAgent model, see: Laffont and Martimort (2002), p. 156.
4
For a survey on this problem see, among others, Bebchuk and Fried (2003).
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36