I
,^
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'FEB 5 1988
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
TAKEOVER DF.FENSES AND SHAREHO LDFR VOTING
David Austen- Smith
University of Rochester
and
Patricia C. O'Brien
Massachusetts Institute of Technology
WP# 1823-86
Revised: November 1987
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE. MASSACHUSETTS 02139
TAKEOVER DEFENSES AND SHAREHOLDER VOTING
*
David Austen- Smith
University of Rochester
and
Patricia C. O'Brien
Massachusetts Institute of Technology
WP# 1823-86
Revised: November 1987
* The authors gratefully acknowledge helpful comments from Jeff Banks,
Harry DeAngelo, Linda deAngelo, John Parsons and Rick Ruback, and
from seminar participants at MIT, Stanford and the University of
Rochester.
Remaining errors are soley the authors' responsibility.
M
1.7.
FEB
Ll^'RAR'!^*^
5 1988
RECEIVED
Takeover Defenses and Shareholder Voting*
David Austen-Smith
Department of Political Science
University of Rochester
Rochester NY 14627
and
Patricia C.O'Brien
Sloan School of Management
M.I.T.
Cambridge
MA 02139
October 1986
Revised:
November 1987
*The authors gratefully acknowledge helpful comments from Jeff Banks, Harry DeAngelo, Linda
DeAngelo, John Parsons, Scott Richard, Rick Ruback, David Scharfstein, and from seminar
piu-ticipants at MIT, Stanford and the University of Rochester. Remaining errors are solely the
authors' responsibility.
Abstract
Why do shareholders vote for anti-takeover devices which apparently lower the value of their
firm?
We address this question by constructing an agenda- setting model in which rational,
informed, and value-maximizing shareholders vote on requests for such devices
self-interested
management with employment
opportunities outside the furo.
made by
a
We find sufficient
conditions for the value of the firm to decline as a result of a request, although
it is
approved by
shareholders. In our model, the apparently paradoxical voting behavior occurs because the
expected takeover premium would be reduced more by rejection of the request than by approval, so
shareholders rationally choose approval.
Takeover Defenses and Shareholder Voting
L Introduction
Why do shareholders vote for anti-takeover devices which apparently lower the value of their
firm?
We address this question by constructing a model in which rational, informed, and
value-maximizing shareholders vote on requests for such devices made by a self-interested
management with employment
opportunities outside the firm.
We describe conditions under which
the value of the firm declines as a result of the request, although
it
is
approved by shareholders. In
our model, the apparendy paradoxical voting behavior occurs because the expected takeover
premium
is
reduced more by rejection of the request than by approval.
A large and increasing number of amendments to corporate charters are specifically designed to
increase the cost of transferring control.
amendments
in
1974 through 1979. Linn and McConnell (1983) find generally increasing
incidence of such proposals
among NYSE
Responsibility Research Center
amendments
is
DeAngelo and Rice (1983) repon over 250 proposed
lists
firms over the period ft-om 1960 to 1980.
The
Investor
over 200 in 1985 alone. While the use of anti-takeover charter
increasing, there is considerable disagreement over their effects on shareholders and
on the market for corporate
control.
Two major hypotheses describing the motives for instituting anti-takeover chaner amendments
are
commonly described as "management entrenchment" and
to the
from
management entrenchment view, incumbents
"shareholder interests." ^ According
are interested in job security and seek protection
the takeover market, to the detriment of shareholders.
However, a manager cannot change
corporation's charter without winning voted approval ftom shareholders.
the
Two suggested
explanations for shareholder approval of entrenching antitakeover devices are: (1) for a majority of
shareholders, the costs of becoming informed about the effects of defensive charter
exceed any potential benefits, and uninformed shareholders consistently give
amendments
their proxies to
management; and
(2) large shareholders
wish to maintain friendly relations with management to
ensure the benefits of future business, and large shareholders control sufficient shares to be pivotal
in the vote.
Shareholder irrationality
is
sometimes offered as a
third alternative.
explanation for the observed voting behavior must describe individuals
shares to be pivotal, that
is,
sufficient shares to determine the
The stockholder interests hypothesis recognizes a
who control
outcome of the
free-rider
Note
problem
sufficient
vote.
premia from takeover bidders, particularly
dilution of minority interests are imperfect. Anti-takeover devices
may benefit
if
may have
remedies to limit
shareholders by
enforcing a level of collusion in takeover negotiations, to extract a higher premium. If this
case, there is
little
no inconsistency
in rational shareholders voting for these devices.
evidence that shareholders benefit from such amendments.
statistically insignificant
by
in collective action
shareholders (Grossman and Hart (1980), Jarrell and Bradley (1980)). Shareholders
difficulty colluding to extract larger
any
that
However,
is
the
there is
DeAngelo and Rice (1983)
find
negative abnormal returns around the public announcement of proposed
antitakeover amendments. Linn and McConnell (1983) find positive returns around the board
meeting date
at
proxy mailing
which amendments
date. Jarrell,
announcement of "shark
are proposed, and insignificant negative returns around the
Poulsen and Davidson (1985) find negative returns accompanying the
repellents", viz. supermajority, classified board
and authorized preferred
amendments.
In the context of our model, the
management entrenchment and shareholder interests
hypotheses do not necessarily lead to different predictions about shareholder value. Anticipatory
takeover defenses raise the costs of acquiring control of the firm, thereby entrenching management,
but lead to a higher
potential
premium
for shareholders if a bid succeeds.
managers contribute
different value to a given firm,
We presume that different
by virtue of
skill
or experience. Only
managers capable of producing higher value than the incumbent can mount successful takeover
bids.
Whether shareholders gain or
quality of the
lose as a result of the incumbent's defenses depends
incumbent management
relative to potential bidders,
and the incumbent's
upon the
employment outside
opportunities for
rationally vote for anti-takeover
it
was before
the
shareholders are
better off
The paper is organized
formal model
is
chaner amendments, although
amendments were proposed.
made
developed
We describe circumstances in which
the firm.
their
wealth
2.
lower afterwards than
We also describe different circumstances in which
by the amendments.
as follows. In section 2
in section 3,
we provide
a brief overview of the model.
and we summarize and discuss the
Section 5 concludes. All proofs are confined to Appendix A. Appendix
that illustrates
is
shareholders
B
The
results in section 4.
consists of an
example
our results.
Overview
We construct a two-period model of a firm with risk-neutral shareholders, with a manager who
has employment opportunities outside the firm, and with the prospect of a management change by
takeover.
change
bid
is
We consider the capital structure and assets of the firm to be fixed, and focus on the
in value associated with a
outstanding. During the
charter
change
first
in
management. At the
period, the incumbent
amendments, on which shareholders
made. Dep>ending upon the outcome of the
employment with
the firm versus
vote.
first
expectations about what
period no takeover
period and the manager's preferences for
the firm, the
and the manager leaves the firm for
may occur in
first
During the second period, a takeover bid may be
employment outside
shareholders and the incumbent manager
of the
manager may propose anti-takeover
additional defenses in response to the bid. If the takeover bid
their shares to the bidder
start
make decisions
is
manager may choose
to erect
successful, the shareholders sell
alternative
employment Both
in the first period
based upon rational
the second period.
A major implication of the results developed in sections 3 and 4 is that observations of a firm's
value before and after the implementation of takeover defenses are not observations of the
alternatives shareholders face
when
voting on these defenses. In our model, shareholders
approve defenses face an unobserved, inferior alternative
if
who
they choose rejection, and so rationally
choose approval.
Two central features of the model drive
the results. First, the
manager
agenda on takeover defenses monopolistically, and shareholders may choose only
They
reject the managerial proposal.
are unable to
amend the proposal
sets the
to accept or to
or counter-propose before
the vote.-^ Second, the manager's request changes the subsequent decision-making environment.
The two
critical features,
generate the voting
monopolistic agenda- setting and the real effect of the request
conundrum discussed
power of the manager ensures
in the Introduction.
itself,
The monopwlistic agenda-setting
properly-chosen request, the shareholders can do no better
that, for a
than to approve. In certain circumstances, the value of the firm following approval of a managerial
request for takeover defenses will be lower than the pre-proposal value. Nevertheless, the value
would be no
greater,
and may be lower,
value and the post-rejection value
if the
request
is
rejected.
The wedge between
pre-proposal
induced by the real effect of the request, described below.
is
Previous research on the effects of the implementation of takeover defenses has compared the
pre-proposal value of the firm with
its
post-proposal or post-vote value. In our model, the
comparison for inferences about shareholder rationahty
in voting
is,
instead, the value under
approval of the request versus the value under rejection.
Our model
describes the
potential acquirers.
manager as a
The model
rests
self-interested intermediary
between shareholders and
on a reduced form specification of an outside managerial labor
market, our characterization of the mechanism that produces the real effect of the request for
takeover defenses. Other mechanisms
change
in the
may exist with
decision-making environment
introduce this real effect, since
it
the
same general property of inducing a
We find the outside labor market a natural way to
defines the manager's opportunities in the event of a successful
takeover. In the model, the manager's value added to the firm and utility schedule are
knowledge
at the
time of the vote.
The common knowledge assumption
obtain even
when
common
is
used here to emphasize
shareholders are fully informed
when
recognize the impUcations of their vote: they do not
that the voting
conundrum can
they vote. In our model, shareholders
make mistakes
or have regrets with respect to
their decision. Note,
for
it
to result in a
however,
change
of the vote. This
is
the time of the vote
them worse
would not result
off.
by the proposal
employment, but they leam from the proposal.
we expect that retaining some
known
We
precisely at the time
information asymmetry at
the incidence of shareholders' approving measures which, ex
We return to this point in the fourth section.
change
in a
to shareholders
that manager's utility schedule is
clearly extreme, but
would increase
must by conveyed
the stan of the first period, shareholders are not perfectly
utility for
leam everything, so
that they
post, leave
At
in value.
informed about the manager's
assume
that information
in firm value if
it
were possible
Similarly, the proposal
to eliminate incentive
problems entirely
using contingent claims contracts. Agenda control issues would not arise: shareholders would
hedge themselves ex ante against the
possibility of voting
empirical observation of the phenomenon,
it
on value-reducing amendments. Given
does not appear unrealistic to assume the
non-existence of complete contigent claims maricets.
We assume that contracts to hedge against
value-reducing behavior by management are impossible or too costly to write.
considered further in section
One
final aspect
is
worth noting
at the
outset In
the firm will rise as a result of a request for takeover defenses.
some circumstances,
The empirical
measures arc mixed, admitting the possibility
measures increase shareholder wealth.
the value of
results to date
that
on the
some such
We describe circumstances in which the takeover defenses
arc value-increasing.
However, the focus of this paper is
value of the firm will
fall,
3.
is
5.
of the model
effects of voted anti-takeover
This issue
to provide a rational choice
to describe circumstances in
which the
answer to our opening question.
Model
We assume that, by virtue of skill, experience or effort, different managers can contribute
different value
continuum
added to the fixed
M, which may
be
capital structure
infinite,
possible managers.^ Denote by ra €
and investments of the
finn.
There
is
a
of possible firm values based on the value added by different
M the value of the firm under incumbent management
at the
start
of the
period of the two-period model, absent the possibility of a takeover.^
first
the value of the firm to shareholders will depend on both
m and the expected premium to be
received in the event of a successful takeover, as discussed below.
The
firm values under different managers, with density function f(),
assumed
knowledge. For technical reasons,
we assume
Of course,
is
distribution F(-)
that lim.j^oo[l-F(01/f(t)
be
to
< <»:
on
M of
common
this is not a strong
restriction.^
The firm
is
owned by
a set of risk-neutral shareholders, interested only in maximizing the
expected value of their shares.
the
first
We presume that there is a corporate charter in place at the start of
period, and that this charter does not prohibit dilution of shareholders' claims by potential
acquirers."
The corporate
charter in place at the stan of our
optimally to the current manager. This can be true because
shareholders to write contracts completely exhausting
all
model
it is
is
not presumed to be tailored
prohibitively costly for the initial
possible eventualities. Further, in a
diffuse-ownership corporation each current shareholder has
little
incentive to incur the costs of
revising the charter.
Heuristically, the
model of takeovers we have
in
mind
In the second period, Nature draws a potential alternative
whether or not to make a takeover bid for the firm.
new manager buys
bid, the
the firm
incumbent remains
the firm in this last period
Given
is
the
in control.
is
in the
it
manager from
If a bid is
thereafter. If there is
Since the Ufe of the firm
in the
second period, the
is
no bid or
is
can choose
successful, then the
if
there
is
an unsucessful
only two periods, the value of
first
period expected value of the firm
all
shareholders.
let
discount factors be equal to one for
The expected premium depends on
the probability of a
successful bidder appearing in the second period, and the expected size of the
bidder. In
M, who
value of the net assets under the incumbent management, m, and the expected
second period. Without loss of generality,
manager and
made and
the set
determined by the value added by the second period manager.
model of takeovers
sum of the
premium
the
this
and controls
for the second period is the following.
what follows, we
first
premium paid by
describe the role of takeover defenses, next explain
more
that
fully
the incumbent manager's utility for
work backwards
3.1
employment and
to consider the incumbent's
the second period takeover process, and then
and shareholders' decisions
in the first
period7
Takeover Defenses
The manager
is
endowed with two
potential bidder's perspective, x
minimum price
control variables, x and y, both takeover defenses.
and y are indistinguishable, and are simply increments
From
a
in the
necessary to acquire the finn. Thus, x and y arc measured in the same units as m,
reduce the probability of a successful bid appearing, and increase the expected premium,
conditional
on a successful
bid.
From
the perspective of the incumbent
manager and
the
shareholders, however, x and y are quite distinct.
Defense x
is
anticipatory
bidder appearing.
X.
it
The manager
Majority voting
granted.
:
among
Amendments
can be put in place only in the
is
period, prior to the potential
obliged to ask the shareholders to approve anticipatory defense
the shareholders determines whether or not the manager's request is
to the proposal are not permitted, so the shareholders can only accept or
reject the manager's proposal.
Examples of voted,
anticipatory defenses include staggered board
elections, super-majority voting provisions, "fair price"
form of amendments
first
to the corporate charter,
amendments, "poison
pills" that take the
and establishment of classes of stock with
differential
voting rights.
For convenience,
direct costs to the
However, the manager bears an
whether the request
is
manager of implementing x are normalized
to zero.
indirect cost for requesting anticipatory defense, re gardless of
granted. This cost is in tenns of his outside value
~
the utility payoff he can
expect to receive in the second period, conditional on being ousted from the firm. Our presumption
is that efforts
on the part of incumbent managers
explicit offer indicate that the
manager is,
to erect takeover defenses in the
for instance,
more
interested in personal security than the
welfare of the shareholders; and this lowers his outside market value. Let
level of anticipatory defense x. If
absence of an
X denote a requested
X is approved by shareholder vote, then the implemented level of
8
this
defense
however
> 0]
is
x = X; and
that the
if
it is
not approved then x
above discussion impUes
=
0.
Evidently,
that the states of the
world
X=
[x
implies x = 0. Note
=
I
X = 0]
and
[x
=
I
X
are distinct: this is crucial to our model.
The second type of takeover defense
available to the manager, y, is responsive
.
Responsive
defenses are implemented only to fight an expUcit takeover bid in the second period, conditional on
a bid materializing. Unlike anticipatory defenses, the manager implements responsive defenses
without obtaining shareholder approval. Examples of non-voted, responsive defenses include
anti-trust lawsuits, targeted repurchases, "poison pills"
private placements of stock with parties friendly to
implemented by the board of directors,
incumbent management, and counter-offers
to
acquire the would-be acquirer.
The incumbent
defenses.
These
As
bears direct costs, measured in units of his utiUty, for implementing responsive
described below, the manager receives
direct costs of
firom diverting time
engaging
and
effort
in a takeover battle
from
his usual
utility
may be
managing
from the
activity of
managing
the firm.
thought of as the disutiUty he receives
activities into the less-preferred activity of
fighting a takeover.
The
distinction
we make between
anticipatory and responsive takeover defenses, that the
former are voted by shareholders while the
latter are not, is
purposes, and does not do violence to empirical reality.
an abstraction.
From 1968
It is
a useful one for our
to 1979, the
Williams Act
required that a takeover bid be outstanding for at least ten business days. Currently, SEC's Rule
14e-l, adopted in 1979, sets this
minimum
However, voting decisions by shareholders
time for a takeover bid
arc governed
by
at
twenty business days.
state corporation
law requirements
regarding disclosure and maiUng of formal proxies. Delaware General Corporation
that notice
be mailed to shareholders of record ehgible to vote
at least
Law requires
twenty days prior to the
meeting. While these requirements do not preclude the use of voted defenses as responsive tactics
(the Martin Marietta
-
Bendix case
most voted defenses are put
is
in place
a counterexample), they surely
when no
make
it
more
explicit takeover threat exists."
difficult.
Indeed,
3.2
The Second
Period:
The Incumbent's
Utility for
Employment
We suppose that there is no utility yalue to making a bid per se, so that, giyen the value m of
the finn under the incumbent manager, only managers with values n
make takeover bids.
If there is
any administrative cost
of the firm's shares), then no manager n <
to bidding
m will make an offer.
>
m find
(i.e.,
it
worthwhile to
a cost other than the price
Hereafter,
we assume
such a cost, but, to avoid cluttering the notation, suppose the cost constant and take
in
m. Hence, n >
m
is
The condition n >
that the
m
is
not sufficient for a successful takeover bid because of the possibility
the potential bidder's value n
y,
to be implicit
a necessary, but not sufficient, condition for a successful takeover bid.
incumbent will erect takeover defenses, as described above.
defenses x and
it
there is
must exceed
If
takeover defenses are used,
m by at least the amount of takeover defenses.
Given
a takeover bid must be at least equal to [m+x+y] in order to win. Will any more
be paid? Because shareholders are interested only in maximizing wealth, and given that dilution
available to the acquirer,
the
it is
sufficient to
incumbent No acquirer wishes
limit epsilon will
shareholders
[x+y]. Hereafter, denote the
incumbent
is
more than [m+x+y]
pay any more than necessary
be zero. Hence, the premium above
— conditional on
To derive
to
pay e >
the expected
to persuade
to take
to
remove
over the furo, so in the
m that the incumbent secures for the
losing a takeover battle despite defenses x and y
premium by
them
is
—
is
precisely
n.
premium, consider
first
surely in control of the firm in the
first
the incumbent's objective function.
period, and the investment
structure of the enterprise are taken as given. Therefore,
it is
The
and financial
necessary only to examine his second
period payoff under two possible employment alternatives: within the firm, or,
if
a bid succeeds,
outside the firm.
If there is
utility
V(m)
no takeover bid
fi-om
in the second period, the
managing the
responsive defense
y, as
firm. If there
is
incumbent stays
a takeover bid, the
in control
and receives
manager may choose
to erect
described above. Let c(y) be the direct costs of implementing responsive
10
defense
is
assumed increasing convex
y,
convenient to assume lim.y_^o ^'(y) =
Because of these
is
in y, c'
costs, the incumbent's
ultimately unsuccessful
is
v=
V
-
^'
>
0, c"
>
0,
with c(0) =
"°"^ °^ °"^ principal
second period
0.
results
For technical reasons,
depend on
it
this.^
he must fight a takeover bid which
utility if
c.
In the event of a successful takeover bid, the manager's second period utility is the utility he
receives from his
takeover
is
(o(x,
y X) = W(7:, X)
I
is
takeover
premium he
diminishing marginal
is
We assume the
is
able to extract
rate.
As
from the
acquirer,
Wj
>
0,
is
increasing concave in the
Wj j < 0,
he
is
rewarded
at a
described above, the manager suffers a decline in outside value,
when no explicit takeover threat exists.
W2
We assume
^2 = -«>, so that requests for guaranteed job security result in extreme loss of outside
We further assume the cross-effects of the decline due to the request on the increase due to
value.
extracting the
if
employment
ousted from the firm. His outside value
for requesting anticipatory defenses
lim.^-^oo
premium
are non-increasing,
Wj2 ^ 0.
That
is,
they are not then they dampen, not amplify, each other.
supj)Ose that at the stan of the
employment
in the firm to his outside alternative,
enough approved requests
W
is
period, before any request
first
The above assumptions imply
that
c(y).
rewarded by the outside labor market for extracting a higher premium for
shareholders, given he
but
-
the manager's gross outside value, or utihty for alternative
incumbent
< 0,
alternative outside the firm, net of the costs borne in engaging in the
battle:
(1)
W
employment
(x
manager of requesting
two
effects
To make
is
V(m) > W(0,
the
in
strictly
decreasing in
x.
may be
problem
separable,
nontrivial,
we
made, the manager prefers
0).
that the manager's utility for alternate
= X),
everywhere decreasing
the
employment
is,
for large
This does not exclude the possibility
approved requests. This decrease
is
the indirect cost to the
anticipatory defenses, mentioned above.
Conditional on anticipatory defenses x, the manager can raise his outside value in the event of a
successful bid by using responsive defenses y to increase the
premium received by
shareholders.
11
Given the anticipatory defenses
in place after the first pericxl,
X
>
and x e
{0,
X
}
,
and observing
a bidder with value n, the incumbent chooses responsive defense y in the second period to
his utility. Define y* as the response
maximize
bid
is
successful and the
y*(x X) = argmax.y ^ r^
(2)
From
I
we obtain
(1),
doi/dy
(4)
82(o/9y2
da/dy =
first-
Wj
=
(3)
Setting
manager leaves
which maximizes the incumbent's net
utility if the
the firm:
0)(x,
y X).
I
and second-order conditions:
- c';
= Wii-c"<0,Vy.
implicidy defines y*.
By
(4),
y*
is
unique for
all
X, x >
0.
We now define the incumbent's net utility from fighting and retaining his job, that
bid which
Observing a bidder with value n ^
fails.
is
incumbent's net
utility
v(n, x)
The manager
will fight to
co.
so increases his outside
The Second
-
Once
utility;
CO
his net utility
is
he chooses y >
y = n-m-x. Thus v, the
as a function of n and x:
that
doing
co.
Period: Takeover Bids
if
any bidding
x and y are fixed and known, only a potential bidder with value n >
offer.
cost,
Moreover, only bids which can succeed will be made, as
and no
utility
value to making unsuccessful bids. At the
is
indeed known. However, since
responsive, the incumbent's selection of y depends on the particular n drawn by
Nature in the second period.
schedules,
if
dominates v, however, he will fight only to the extent
beginning of the second period, the anticipatory defense x
defense y
win
from employment with the firm v exceeds
then he will leave to collect
[m+x+y] can make a successful
is
will
fighting a
c(n-x-m).
win as long as
We argued above that,
long as there
is
from fighting an unsuccessful bid can be written
= V(m)
his net outside utility
3.3
incumbent
cosUy, the incumbent's best winning response
n-m-x. Since y
(5)
m-i-x, the
is,
W,
V, and
c,
are
By
the second pericxl,
common
we suppose
the incumbent's utility and cost
knowledge, along wiUi his contribution to firm value m.
12
made her draw,
Likewise, once Nature has
the value n of the potential acquirer is
knowledge. Therefore, the potential acquirer
bidder's best offer (that
acquirer
makes no
offer at
response (m-f-x+y <
Though
the
fighting, c,
n),
m+x-Hy >
n), then
then she
makes
by
surely,
employment
is sufficient to
because of the bidding cost
~
beat the
the potential
capable of topping the incumbent's best
against the incumbent
inside the firm, V, or
it is
utility,
not. In
in
W*
=
win control of the
firm.
I
defined by examining the
scenarios prior to the takeover
W(x-t-y*, X),
is
either less than his utility
what follows, we discuss the process which
each of these two cases in turn. Formally, denoting the
bid which can succeed by n, and defining CO*
[inf.n
is
The manager faces one of two
(O.
determines bids and responsive defenses
(6)
the manager's
definition of credibility he prefers to bear the costs of
His highest attainable gross outside
minimum
is bid,
and the winner pays the premium n = x+y.
manager's choice between v and
for
when n
the smallest offer necessary to
The minimum bid which can succeed
battle.
-
If the potential acquirer is
all.
incumbent loses
if,
y.^^ If this utility-maximizing response
is
is, if
capable of calculating the incumbent manager's
A response y to a bid n is credible
credible response y to any bid.
utility-maximizing response
is
common
=
W*
-
c(y*):
ifW*>V;
V =
CD],
V =
CO*], otherwise.
n(xlX) ={
[inf n
In the first case,
that allows the
where
manager to
I
W* > V, the minimum bid which can succeed will be below the one
attain his
maximum outside utility. To see
this,
note that at the
beginning of the second period, absent a takeover bid, the incumbent prefers his job inside the firm
to outside
for
employment, or
V > W(x-K), X). ^
some y between zero and
prefers outside
employment
to
Thus, a bidder whose value n
illustrated in
Figure
y*,
Since by hypothesis
^
V = W or equivalently v = co.
employment with
is
slightly
Above
it
must be
this point, the
that,
incumbent
the firm, and so prefers to surrender control.
above the point where v =
1(a).
[HGURE ABOUT HERE]
1
V < W*, then
(O
can win. This case
is
13
premium paid by
In this case, the
the successful bidder
may depend on
the bidder's value n.
Define n* to be the bid correspx)nding to the incumbent's highest attainable outside utiUty:
n*(x X)
(7)
I
where y*
first let
is
n €
=m+X+
y*,
defined as above. Note that n*
(n, n*].
The incumbent's
>n
co: this is
and only
best response
willingness-to-pay for the firm by choosing y
outside value,
if
is to
y = y* and then leaving the firm
Consider Figure
and
1(a)
fight to extract all the bidder's
= n-m-x, and then
to leave the firm to collect his net
Observing
is,
the bidder does not
the firm. Although the firm
may attain
manager's value added, the
new manager is assumed
that the anticipatory defenses
in the
this, the
incumbent optimizes by choosing
to obtain his outside value, (O*.
pays only n* to acquire the firm. That
chosen by the manager
W* > V.
clearly credible.
Now let the bidder's value n exceed n*.
presume
if
Any
pay
bidder with value n > n*
all that
the value n in the second period
x put in place
second period,
set the
to
consume
by
is
willing to pay for
virtue of the
the surplus, n
in the first period,
minimum
she
-
new
n*. That
we
is,
along with the responses
acquisition price but
do not prevent
acquirers from capturing benefits above this price.
Now consider the other case,
where
W* < V.
Here the manager
is
willing to undertake costly
responsive defenses y until the cost of doing so drives his net utiUty from continued employment
with the firm below his
the incumbent prefers
alternative
fight
maximum
employment
which nets him
co.
attainable outside utility. In Figure 1(b), observing any n
in the firm, for
Thus, for any n
< n,
which he receives
is
a, will
n,
outside
the manager's utility-maximizing action
and defeat the bidder. Any successful bidder, with n >
value added. This
utility v, to his
<
is
to
pay n* regardless of individual
true because the incumbent, observing a bidder
who can contribute
a firm
value of n > n, recognizes defeat, but chooses y = y* to maximize his personal outside value.
From
value
the
above discussion, the premium n paid by the successful bidder of value
m contributed by the incumbent, can be defined:
(8)
7t(n,
X
I
X) = min.[n
-
m, n*
-
m].
n,
above the
14
Inspection of (6) and Figure
and win.
On
1
reveal that, for bids n
the other hand, any potential acquirer
<
n,
credible that the incumbent will fight
it is
who can
bid n
>n
will be successful.
Therefore, the probability of a successful bid appearing in the second period
premium she
will pay, described
by
depends on n and on the incumbent's
(8),
[1-F(n)].
is
The
utility function.
Together, these two pieces of information determine the expected second-period premium,
evaluated by shareholders and the manager in making their
3.4
The
first
period choices.
Shareholder Voting on the Incumbent's Proposal
First Period:
We now specify the actions of the incumbent and the shareholders in the first period, which are
based on their expectations about the second period. Viewed from the
expected second period payoff is a function of anticipatory defenses
utility
fhjm retaining
firom alternative
his job times the probability
employment times
x.
period, the incumbent's
This expected payoff
no bidder exceeding n appears, plus
is his
his utility
the associated probability of a successful bidder appearing:
U(x X) = F(n)V + 8[F(n*)
(9)
first
I
-
F(n)]-! (o(x,
n-m-x X)-f(n)dn
I
Q
+ {5[1-F(n*)] + [l-5][l-F(n)]}cD(x,n*-m-x
where 5 =
1
iff
n
< n*
(equivalently, iff
incumbent's best response
The
first
V < W*), and 5 =
may depend on
otherwise.
the bidder's value n if
period expected value of the firm under
IX),
As
described above, the
V < W*.
management
m is the sum of m and the
expected premium:
(10)
S(xlX) =
m + 6[F(n*)-F(n)]|[n-m]-f(n)dn
+ {5[1-F(n*)] + [l-5][l-F(n)]}-[n*
-
m]
with 6 defined as above.
Since anticipatory defenses x require shareholder approval, the manager's
optimization problem
is
to
choose a request,
constraint of shareholder approval:
first
period
X ^ 0, to maximize his expected utility, subject to a
1
15
max. U(xlX)
(11)
subject to:
The
S(X X) ^ S(0
I
I
X).
constraint says simply that shareholders will vote rationally
if the
manager asks
However,
if
X>
for
no anticipatory defense,
is
no
it is
X = 0, then the constraint trivially binds.
less than its value if the request is rejected.
manager's outside value in the second period
if
request. Clearly,
then the constraint says that approval of the request must result in an expected
value of the firm that
even
on the manager's
not granted
- we have in
is
Because the incumbent
reduced by his request, X, in the
general that S(0
I
0)
t^
S(0 X) for any
I
first
X > 0.
period
In other
words, the alternative that rational shareholders compare against the manager's request
0), their situation prior to
notion
is
any request, but
central to the results
If the constraint
binds at
rejecting the request. Since
on
is
the voting
some
S(0 X), the result
I
Appendix
is
not S(0
they reject the request. This
conundrum.
X > 0, then shareholders are indifferent between accepting and
managers are not
indifferent, they
circumstances by slighdy perturbing the request, X, to induce
shareholders: as
if
-
A shows,
such a perturbation
is
can insure acceptance
strict
in
such
preference on the part of
always available. From a
game-theoretic perspective, this induces a unique subgame perfect voting rule for the shareholders
(Banks and Gasmi (1987)): vote for the management's proposal with probability one
S(X X) > S(0 X), and vote
I
I
against the proposal with probability one otherwise
S(0 X)). Therefore, without loss of generality,
I
we can
if
(i.e.
and only
S(X X) <
I
adopt the convention that in cases of
shareholder indifference, shareholders always "vote with the management".
We turn now to some results. ^^
4.
Results
We now analyze the voting conundrum discussed in the Introduction in the context of the
model described
in section 3.
The manager requests
shareholders vote on the request
anticipatory defenses in the first period, and
The outcome of the vote can
if
affect both the probability of a
16
takeover bid appearing in the second period, and the premium shareholders receive
if
a takeover bid
succeeds. In pan, these effects are driven by the fact that the manager has responsive defenses
available to counter a particular takeover bid, and his utility maximizing use of responses will be
affected
by the outcome of the
second period
all
cases, the probability of a bid appearing in the
a result of a request for anticipatory defenses, and in
falls as
firm to shareholders
period. In
first
is
lower
if
they reject the proposal than
been requested. The value of the firm to shareholders
less than than
if the
it
would have been
value under acceptance
is
if
if
it
all
cases the value of the
would have been
if
they accept the proposal
no defenses had
may
be greater or
no defenses had been requested. The voting conundrum occurs
larger than the value under rejection, so rational voting implies
acceptance; but the value under acceptance
lower than
is
it
would have been
if
no defenses had been
We provide a sufficient condition for this to occur.
requested.
There are three possible conditions
beginning of the second period: (1) the manager
at the
requested no anticipatory defenses, (2) the manager
made
a request
which was voted down by
shareholders, and (3) the manager's request
was approved. Proposition
the second period response to a takeover bid
which maximizes the manager's outside value,
puts an ordering on y*,
1
conditional on the first-period outcome.
Proposition
Corollary
1:
1:
y*(0 0) > y*(0 X) > y*(X X) >
I
I
X + y*(X
I
than
if
0.
X) > y*(0 X).
I
If a first-period request is rejected
strictiy larger
I
the request
is
by shareholders, the second-period maximizing response
approved. However, from Corollary
1
,
total
is
defenses
(anticipatory plus responsive) are smaller if the request is rejected. Since total defenses determine
the
premium received
premium
if
in a successful bid, this implies that shareholders
can expect a smaller
they reject the manager's request and a successful bidder emerges.
17
An interesting
response
is
feature evident
from Proposition
never larger after a request, even
if the
1
is
that the second-period
request
is
denied, than
Thus, the request carries no implicit threat of "scorched earth" responses
Rather, as
premium
we show
if
below, the request
alters the
if
if
maximizing
no request
is
made.
shareholders deny it
manager's incentives to fight for a higher
a successful bidder appears.
Anticipatory and responsive defenses are substitutes in their effects on n, the
required to acquire the firm.
shareholders in the
Comparative
first
minimum
Generally, the higher the level of anticipatory defense approved by
period, the lower will be the manager's choice of responsive defenses.
on y*, the maximizing second-period response (Appendix A,
statics
bid
(a3)
-
show
(a7))
that this response is non-increasing in the size of the first-period request.
how
In evaluating
to vote, value-maximizing shareholders consider both the size of the
premium they can expect from a
successful bid, and the probability that such a bid will emerge.
Proposition 2 describes the probability of a successful takeover bid, as a function of requested
anticipatory defenses and shareholder approval of the defenses.
Proposition 2:
X)
increasing in X, x e {0, X};
(a)
n(x
(b)
VX>0,n(XIX)>n(OIX)>n(OIO).
I
is strictly
Proposition 2 states that the
minimum bid which can
succeed against incumbent management
increases with the level of anticipatory defense requested. Since the probability that a successful
bid will emerge,
[1
-
F(ii)],
falls as the
minimum
successful bid rises,
pan
(a)
of Proposition 2
implies that the probability of takeover declines with increases in the level of requested anticipatory
defenses, whether or not these are approved. Part (b) implies that the probability of takeover
largest if
if the
no anticipatory defenses
request
is
approved Notice
are requested, declines if there
that part (b) is not an
is
a request, and
may
immediate consequence of part
is
decline
(a):
the
more
18
change
leave
from
in state
it"
[x
=
X X > 0]
I
=
X > 0] is not incremental because of the "take
1
or
it
nature of the shareholders' decision.
The value
successful bid
to shareholders
is
from anticipatory takeover defense depends on both the premium
made, which generally increases with the
probability of a successful bid,
are
to [x
level of anticipatory defense,
which generally decreases. Proposition 3 shows
unambiguously worse off if they
reject
if
a
and on the
that shareholders
management's request for anticipatory defenses than
they were before the request
ForX>0,
Proposition 3:
S(0 0) > S(0 X).
1
I
Proposition 3 follows directly from part (b) of Proposition
Proposition
1.
The
will be
is
result
manager's proposal, because the
now higher. Moreover,
no higher than
effects are driven
along with the
first
inequality of
probability that a successful bid will appear in the second period
after rejection of the
incumbent
2,
it
for any successful bid the
would have been
by the manager's
minimum
if
is
lowered
bid which can succeed against the
premium received by
shareholders
no request had been made, and may be lower. These
utility for
employment outside
the firm,
which declines
as a
of the request for anticipatory defenses.
The voting
(incentive compatibility) constraint in the
model requires
that approval
of a request
leave shareholders at least as well off as rejection. Proposition 3 states that shareholders are worse
off if they reject the request than they
latter
circumstance, no request,
To complete our description
leave them worse off,
shareholder value
if
is
would have been
if
no request had been made. (Note
not available to shareholders deciding
how
to vote
that this
on a request.)
of the apparent paradox that shareholders vote for defenses which
we require a comparison of shareholder value if the request is approved
no request
is
made: S(X X) versus S(0
condition for the apparent paradox to occur.
I
1
0).
with
Proposition 4 gives a sufficient
19
Proposition 4:
V(m) < W(y*(0
3X
=>
According to Proposition
his
maximum
1
0), 0)
e
(0, oo):
4, if the
S(0 0) > S(X
I
manager's
I
X) > S(0 X).
I
utility fix)m
employment with
the firm is less than
gross outside utility before any request for anticipatory defenses, then requests exist
which shareholders
will approve, but
important to observe that this
which leave them worse off than they were before.
maximum gross outside utility is available only if, in the
period, Nature draws a bidder with value n
was
> n*(0
I
0).
Recall that
we assumed
from employment
utility
before defenses x or y are considered, ftoposition 4 concerns the incumbent's
gross outside utiUty: that
in Figure 1(a),
by
setting x
With Proposition
which
is,
4,
we have shown
who are fully
worse off by them. An
X = 0.
is,
maximum
The simation
is
we hoped
informed
artifact
at the
to describe.
That
is,
rational,
value-maximizing
time of the vote, will approve the defenses but are
of our assumption of identical, risk-neutral shareholders
and holders of large blocks may
well-diversified portfolios.
pictured
the existence of requested levels of anticipatory defense
The
differ
made
is that all
votes will be unanimous. Empirically, shareholders will differ: for example, managers
shares,
his
X = 0.
result in the voting behavior
shareholders
larger than his initial gross outside utility: that
considering his optimal choice of y at
=
second
the incumbent's
utiUty
in the firm
It is
who own
from holders of small positions who have
results will apply to non-identical shareholders as long as the
pivotal voter is risk-neutral and value-maximizing.
The
sufficient condition for the result in Proposition
current and alternative
employment
In
4 depends on the manager's utihty
Appendix B, we construct an example of a manager with
utility satisfying this condition,
whose optimizing choice of anticipatory defense
by shareholders, and
them worse off than
in
will leave
no sense pathological, and demonstrates
requested by managers with
in
if
be approved
no request had been made. The example
that these levels
utilities satisfying the
will
of anticipatory defense could be
antecedent of Proposition
4.
is
20
It is
worth noting that under some circumstances, shareholders can be made better off by
implementing some anticipatory defense.
By
Proposition
3,
a necessary condition for this to occur
S(X X) > S(0
is that
the manager's request, X, be strictly interior to the constraint set;
is not,
however, sufficient In our example in Appendix B, shareholders would like some
anticipatory defense, but the
manager prefers more and, despite
i.e.
I
1
X).
It
the constraint not binding, the
request results in a decline in shareholder wealth.
We remarked in section 2 that, in order for the stock price to fall as a result of a request, some
information must be conveyed by the request. The information conveyed concerns the manager's
from employment outside the
utility
firm. In the circumstances described
clear that any probability weighting of S(0
revision
place
when
some
0) with
prior probability on the
X>
outcome
it
is
S(X X) or S(0 X) implies a downward
I
I
that the
manager will prefer no
which are associated with a drop
The primary implication of our model
for inteipreting the empirical
shareholder wealth before and after the vote.
as an
unambiguous drop
anticipatory defense,
in the value of the firm.
inferences about whether shareholders vote rationally cannot be
management
4,
the first possibility is eliminated. In these circumstances, as long as shareholders
there exist requests
is that
1
by Proposition
work which has preceded
made from
it
a comparison of
We describe the alternative to voting with
in shareholder value, n^t as a return to the pre-proposal
status quo. Therefore, pre-proposal shareholder wealth
is
not the correct
benchmark
for
determining shareholder rationality. Our model suggests that empirical investigation of shareholder
voting and takeover defenses should consider the manager's outside employment opportunities,
and the manager's
5.
skill relative to potential bidders.
Conclusion
We have provided a rational choice model of shareholder voting on anticipatory takeover
defenses. In our model,
it is
feasible for informed, value-maximizing shareholders to approve
measures which leave them worse off than they were before the measures were requested. What
21
drives this result
is that
a manager, in requesting such measures, lowers his outside market value.
Consequently, the manager's optimal response to an actual takeover bid
rejected than
An open
he had made no request Shareholders recognize
if
question
devices, and allow
is
him
why
is
different if the request
this in evaluating
shareholders allow the manager to act
first
how
is
to vote.
to request anti-takeover
discretion over the level of responsive defenses. Shareholders will not
generally want to prohibit the use of responsive defenses as
we have
characterized them. This
is
true because, although their existence reduces the probability of a successful bid appearing,
responsive defenses allow shareholders to receive higher premia from some bidders. In
fact, if a
bidder appears with sufficiently high value added (n > n*), shareholders would like the incumbent
to use
more responsive defense than he
shareholders cannot
will
know ex ante which
choose to maximize his
own utility.
bidder will appear in the future, and
Since
may have
difficulty
discerning the utility schedules of current and future managers, prohibiting takeover defenses
The
preclude value-increasing actions as well as value-reducing ones.
empirical fact that managers
are given control over voting agendas, and are not prohibited by shareholders
from engaging in
responsive tactics suggests that complete contingent contracts are costly to write. However,
offer as an observation that recent charter
targeted repurchases,
which,
if
may
implemented,
Finally,
we
offer
is
amendments which
may
we
prohibit the use of "greenmail," or
be viewed as shareholders' prohibiting a particular responsive defense
unlikely to result in a higher
two remarks.
First,
it is
premium
for them.
frequently asserted
(cf.
Easterbrook and Fischel
(1983)) that the alienability of ownership claims protects shareholders firom detrimental
management entrenchment
However, unless shareholders
tactics.
takeover defenses by management, they cannot
SEC proxy mailing requirements demand
proposal date.
any drop
Once
the proposal
in share value
is
sell
anticipate the proposal of
a voting claim in response to the proposal.
that the record date for shareholder voting
announced, the constituency
is fixed.
precede the
Our model suggests
should occur with the announcement of the proposal, not with the vote.
Second, our model implies that changes
in shareholder
wealth associated with voting on
that
22
takeover defenses
may be positive
or negative, depending on the manager's value added and
schedule. In cases where shareholders' wealth
the manager's request If there
positive.
is
is
reduced, the reduction should occur at the date of
any detectable change
at the date
of the vote,
This follows from Proposition 3 and the voting constraint: the
shareholders' wealth
is
unambiguously reduced
shareholders' wealth under rejection
interpretation, empirical results
is
no
utility
if
it
should be
first states that
they reject a request; the second ensures that
larger than their wealth under approval.
On
this
which find shareholders' wealth declines following implementation
of anticipatory defenses are not evidence of shareholder irrationality or ignorance, but reflect an
informed choice of the lesser of two declines in value.
23
Appendix A: Proofs
Proposition
X > 0.
Let
1:
Then: y*(0 0) > y*(0 X) > y*(X X) >
I
1
I
0.
Proof:
(i)
y*(X X) >
follows from assuming
I
(u) y*(0
)
1
Wj
c'(y)
=
0.
I
I
Wi(y*(0
I
I
0), 0)
-
Wj
Wi(y*(0 X), X) >
1
j
<
0,
W ^2 ^
and
X > 0:
0.
(3) to obtain:
Wi(y*(0
(a.l)
-
0), 0)
I
Wi(y*(0 X), X) =
I
c'(y*(0
I
0))
-
c'(y*(0
I
X)).
implies the RHS(a.l) < 0: contradiction,
But c" >
(iii)
everywhere, and lim.y_^
> y*(0 X)
Suppose y*(0 0) < y*(0 X). Then, by
Use
>
y*(0 X) > y*(X X)
I
I
Suppose y*(0 X) < y*(X X), and again use the
I
I
WjPC + y*(X
(a.2)
Then
But
X
Remark
>
c"
>
1:
I
X)
implies RHS(a.2)
0, so that
W
j |
<
I
1
I
1:
Let
X > 0.
I
Wi(y*(0 X), X) = c'(y*(X X))
-
I
I
>
iff
-
c'(y*(0
I
X)).
0.
implies LHS(a.2)
y*(0 0) = y*(0 X)
[X + y*(X X)] > y*(0
Corollary
X),
order condition (3) to get:
first
W12 = 0.
<
0: contradiction.
X>
Hence, x =
and
II
W12 =
imply:
0).
Then: [X + y*(X X)] > y*(0 X).
Proof: Use (3) and Proposition
I
I
1
with
Wj <
and c" >
j
0.
II
Comparative Statics:
(a.3)
dy*(X X)/dX = -[W^ j+Wi2]/[Wi
(a.4)
dy*(0 X)/dX = -Wj2/[Wi
I
I
j-c"]
<
j-c"]
0,
<
0.
with the inequality
strict iff
W12 < 0.
24
(a.5)
dco(X, y
(a.6)
dco(0, y
Note
Since n*(x
X)/dX =
W2 < 0.
y,
I
(a.5)
I
<
^
I
X.
x=
If
(a.6)
0, then
I
from
Let
X)
is
X > 0, x e
{0,
(a.3)
sign.
is differentiable in
given by
is
(a.4).
and collecting terms,
as c"(y*(x
I
ambiguous
I.
an*(0 X)/9X
9n*(x X)/9X ^ (<)
1:
a priori has
I
Substituting
I
(a.7)
+ W2, which
I
+ dy*(X X)/9X.
Lemma
W
X) = x + y*(x X) + m, and y*(x X)
I
differentiable in
1
I
any
that at
X)/dX =
I
I
I
is
I
is
x = X, then 9n*(X
I
X)/3X
we obtain:
X)) ^ (<) -Wi2(x+y*(x
X} Then: n(x X)
.
If
X, n*(x X)
differentiable in
I
X), X).
X; and an(x X)/dX >
I
0.
Proof:
(i)
n(x
I
differentiable.
from section
First, recall
A* = [v(n*(X
I
X), X)
A* with
Differentiating
-
3 that n(x
I
y*(X X)
co(X,
I
respect to
I
A* can change
Suppose there
V(m) <
So by
case
a
(6):
:
By
exists an
(>)
I
X
Consider
(6),
In this case,
X)].
Then
X)
iff
X
n*(X X)
iff
X < (>) X.
I
X),
I
<
X is unique and:
(>) X.
< X-
n(X X)
is
I
n(X X)
I
X > 0, and define:
0.
X such that A* = 0.
(>)
Let x =
sign at most once as x increases, and only from negative to positive.
W(X+y*(X
n(X X) <
I
X ^ 0.
X at x = X, and using (3) gives:
aA*/ax = -W2(X+y*(X X), X) >
Therefore,
X) > x+m, Vx,
impUciUy defined by: V(m)
is
differentiable because
W
-
W(n(X X)-m, X) = 0.
I
differentiable. In particular,
is
(a.8)
dn(X X)/aX = -W2(n(X X)-m, X)AVi(ii(X X)-m, X);
(a.9)
lim.x^ x-
I
I
VX
I
and,
case p
:
Consider
X
[^Il(-'-)/9X]
> X.
= -W2(n*(2L 20-m, 2DAVi(n*(X X)-m.
1
I
X).
< X,
25
By
(6),
n(X X)
t
Differentiability of
is
impliciUy defined by:
n(X X) follows from
I
an(X X)/dX =
(a.lO)
[c'(n£X
I
V(m) - c(n(X X)-X-m)
I
differentiability
X)-X-m)
I
where Wi*(X) = Wi(n*(X X)-ni, X),
I
i
=1,
of c and
W.
y*(X X) X) =
0>(X,
-
I
I
0.
In particular, using (3):
Wi*(X) - W2*(X)]/c"(n(X X)-X-m),
-
I
Hence,
2.
lim.x_^x+[^(')/9^1 =
(a.ll)
[c'(n*(X
1
2D-X-m)
-
Wi*QD
-
W2*(2D]/c'(n*(X
I
X)-X-m)
= -W2(n*(X X)-m, 2DAVi(n*(X X)-m, 2D;
I
the second equaUty follows
differentiable
The proof of this case
is
immediate from
I
Together, (a.9) and
(3).
)
complete
an(x X)/9X >
I
case
case
a
[3
x =
:
:
x=
X<X
(a.lO).
By
>
c"
I
Moreover,
Wi*(X) =
(3),
X) < n(X X). Therefore,
(a.l2)
(a.8)
and
(a.9).
X>X
Consider
c'(y*(X
I
X)) = c'(n*(X X)-X-m). Since A* >
I
Wj+W2 < Wj
and
(a.
10)
is strictly
I
X > 0.
Similar reasoning as before gives n(0
follows on implicit differentiation of (6) for
Remark
Lemma
I
2: (a.7)
and
1
imply
n(X X) > n(0 X);
I
I
Proof:
a V(m) < W(X+y*(X
I
positive. Since
c'
>
0,
Lemma for x = X.
and 9n(0 X)/9X >
:
n*(X
V y implies,
Therefore, the numerator of
.
completes the proof of the
Lemma 2:
0,
c'(n(XIX)-X-m)>Wi*(X)>0.
Now suppose x =
case
(a. 1 1
everywhere when x = X.
is
(ii)
this
from another application of
X)
the argument that n(x
I
X), X)
that
U(x X) and S(x X)
I
I
I
X)
differentiable in X,
X < X and for X > X.
are differentiable in X.
II
)
26
By
(6)
and the premise, V(in) =
W(n(X X) - m,
I
V(m) < W(n*(0 X)
-
m, X)
=> V(m) = W(n(0 X)
-
m, X), by
(a.l)
I
I
=>
X). There are then
two
possibilities:
(6)
W(n(X X) - m, X) = W(n(0 X) - m, X)
I
I
=> n(X X) = n(0 X).
I
I
(a.2)
V(m) > W(n*(0 X)
=> V(m) =
m/X)
y*(0 X) X) + c(n(0 X)
[0)(0,
I
-
I
definition of y*(0
I
I
W(n(X X) - m, X)
=>
By
-
I
cCn(0
X)
I
X), co(0, y*(0
I
Therefore,W(n(X X)
-
I
m, X)
I
c(n(0
-
m) =
-
-
m)], by (6)
(o(0,
y*(0 X)
I
X) X) > W(n(0 X)
I
I
X)
I
-
m) > W(n(0 X)
-
I
X).
I
m, X)
-
c(n(0
-
m, X)
-
I
c(n(0
X)
I
-
X)
m).
-
m)
=> n(X X) > n(0 X).
I
I
This proves the proposition for case (a).
case B
:
V(m) > W(X+y*(X X), X)
I
=> V(m) = co(X, y*(X X) X) + c(n{X X)-X-m), by
I
By
Corollary
1
and
X > 0, W(X+y*(X
I
I
13)
V(m) =
(0(0,
y*(0 X)
I
I
W(y*(0 X),
X), X) >
Hence, V(m) > W(n*(0 X)-m, X). So by
(a.
(6).
I
I
I
X).
(6),
X) + c(n(0 X)
I
-
m).
Therefore,
(a.
By
14)
co(X,
Proposition
1
y*(X X) X)
I
and Corollary
co(0,
-
I
1,
c'
>
is strictly
X
and x =
differentiating
(a.
13),
we
obtain
an(0 X)/ax = -W2(y*(0 X), X)/c'(n(0
I
I
(a. 10),
(a.l6)
I
>
-
c(n(X X)-X-m).
I
positive; hence, the
RHS(a.l4) must
0, this implies,
n(OIX)>nCXIX)-X.
Now impUcitly
Using
I
I
LHS(a.l4)
likewise be strictly positive. Since
(a.l5)
y*(0 X) X) = c(n(0 X)- m)
we have
X)-m) >
0.
VX > 0:
[8n(X X)/dX
I
I
VX > 0:
-
dniO X)/dX] =
+ {[W2(y*(0
I
I
{ 1
-
X), X)/c'(n(0
[Wi(X+y*(X
I
X)-m)]
-
I
X), X)/c'(n(X
[W2(X+y*(X
I
I
X)-X-m)]
X), X)/c'(n(X
I
X)-X-m)]).
27
By
the first term of
(a. 12),
By CoroUary
(a.
1,
16) in {)
VX > 0.
nonnegative
is
Consider the second term
in {•}.
W2 < 0, and Wi2 - 0'
> W2(y*(0
17)
(a.
X),
I
X) > W2(X+y*(X X), X).
I
By(a.l5)andc">0.
(a.
< c'(n(X X)-X-m) <
18)
I
and
c'(n(0
I
X)-m).
18) imply that the second term of
Together,
(a.
17)
When X =
0,
both terms in
(a.
{•
vanish. Therefore,
}
(a.
16) in {•} is also positive
VX > 0.
VX > 0:
X
[n(X
X)
I
-
n(0
I
X)] =
j
[an(r
as required (with equality iff
Remark 3:
from
[x
=
Remark
Notice that
I
X = 0).
8n(0 r)/ar]dr > 0,
-
I
II
I
X > 0]
is
I
1
:
this is
because the change
in state
not incremental.
Remark 2 and Lemma 2 justify
S(X X) = S(0 X), then
I
r)/8r
Lemma 2 is not implied by Lemma
X X > 0] to [x =
4: Together,
I
the claim
there exists a penurbation in
made
in section 3 that, if x
X -- say, X' -- such
that S(X'
I
X')
=
X and
> S(0
I
X').
Lemma 3:
For any
Proof: Given x =
X > 0, n(0
0, v(n, x)
I
X) > n(0
= V(m)
-
W2 < 0, W(y, X) < W(y, 0), Vy > 0.
Proposition 2:
(a)
n(x
(b)
I
X)
is strictly
Vx = X >
0,
I
0).
c(n-m). Since
So by
(6),
n(0
c'
I
>
0, v(n, x) is strictly
X) > n(0
0),
VX
increasing in X, x € {0, X); and,
n(X X) > n(0 X) > n(0
Proof: The proposition follows from
I
I
I
Lemmas
1,
2 and
3.
II
I
0).
>
decreasing in
0. H
n.
By
28
X > 0,
Proposition 3: For
By Lemma
Proof:
By Proposition
case
a
:
By
n*(0 X)
1,
By
n*(0
1
n:
0))].
1
0),
on a continuous variable
a c.d.f. defined
with the inequality
strict iff
W12 <
at
any y < y*(0
I
0).
I
(8):
010)^ 7i(n.
7i(n,
I
:
<.
I
n*(0 X) < n*(0
case p
F is
n ^ n(0 X).
(a-20)
If
fact that
< [1-F(n(0
X))]
I
I
1
and the
3,
[1-F(n(0
(a.19)
S(0 0) > S(0 X).
n e (n(0
I
I
X).
Vn >
0), the inequality in (a.20) is strict
I
n*(0 X).
I
n(0 X)).
0),
I
an argument in section
3,
only managers with value n >
n(-l-)
will
make takeover bids.
Therefore:
(a.21)
7:(n,
casey n < n(0
:
By
the
I
0)
I
>
7i(n,
7i(n,
010) =
Together, (10) and
Lemma 4:
X) s
0.
0).
same argtmient
(a.22)
I
(a.
as case
7t(n,
19)
I
{3:
X) =
0.
(a.22) yield the desired result.
-
II
lim.x_>oo S(X X) = m.
I
Proof:
By
assumption,
Wj
^
<
> Xi, V(m) > W(X+y*(X
S(X X) =
I
By Remark
(a.23)
I
and lim.x_^oo
X), X). Hence, by (10),
m + [l-F(n(X
2, S(-
•)
1
is
^2 = -««.
I
X))]-[n*(X
I
Therefore, for sufficiently large X, say
VX > Xj,
X)-m].
differentiable in X. In particular,
VX > Xj,
8S(X X)/ax =
I
[l-F(n(X
I
X))]-dn*(X
I
X)/dX
We prove the Lemma by first showing 3S(X
I
-
{f(n(X
X)/9X <
I
X)ydn(X X)/aX-[n*(X X)-m]).
for all finite
I
I
X > X2, X2 sufficiently
X
29
By Lemma
large.
1
and the assumption
strictly positive for all finite
case
a
dn*(l-)/9X <
:
for
for
I
dn*(X X)/9X >
:
(7)
and
By
I
X))]/f(n(X
<
therefore,
(a. 10),
VX > X2.
(7)
[l-F(t)]
=
0, the
By CoroUary
W(y*(0 X"), X")
obtain.
I
[l-F(n(X"
(a.25)
By
Corollary
1,
of X", n*(0 X") >
I
Vn < n,
Vn e
Vn >
Given
(10), (a.25)
7i(n,
(n,
3X
1
hypothesis,
€
I
(10).
for all
(0, 00)
:
an*(X X)/dX >
I
0,
Therefore, there exists a
Since lim.j_^^
II
S(0 0) > S(X
I
such that both
Then by case
I
X) > S(0 X).
I
V(m) < W(X"+y*(X"
(a.l) of
Lemma 2,
= [1-F(n(0 X"))] =
I
an argument of section
I
X"), X"), and
n(X" X") = n(0 X") =
I
I
the premise of the Proposition
3,
I
I
7i(n,
7t(n,
7i(n,
X") =
I
X" X") =
I
X" X") >
and (a.26) imply
I
that
S(X"
7c(n,
I
n.
Hence:
and the choice
only managers with value n > n will
(8):
X" X") =
V(m) <
[1-F(n)].
I
n*(0 X"),
From
0), 0)
n*(0 X")],
I
By
W2 = -«>.
X > X2.
I
By
and lim.x_^j^
3S(X X)/3X <
n*(X" X") ^ n*(0 X"). From
n.
<
that
takeover bid. Using this and
(a.26)
and x = X,
X, X2, such
X"))]
I
1
00.
3X" >
1,
Lemma
lim.x_>oorRHS(a.24)] =
Proposition 4: V(m) < W(y*(0
Proof:
m].
Wj j
if:
I
-
Therefore, by
°°.
X, aS(X X)/dX <
that
Lemma follows from
=>
is
of ambiguous sign.
imply
and y >
sufficiently large value of
is
X)/aX-[n*(X X)
for sufficiently large X.
1
I
sufficiently large
I
I
Also by assumption,
«>.
dn(X X)/dX >
Hence,
For
1.
X)) < dn(X
I
assumption, lim.^^oo [[l-F(0]/f(t)] <
lini.x_^oorLHS(a.24)]
on the RHS(a.23)
{•}
X > X2.
I
[l-F(n(X
(a.24)
term in
X ^ X2.
sup.[an*(X X)/3X] =
(a.3),
0), the
term on the RHS(a.23)
(a.7), the first
all finite
for all
I
By
By
V(m) > W(0,
X > X2.
all
Then, 9S(X X)/9X <
case B
X.
that
0;
7c(n,
I
I
X") = n
-
m;
X").
X") ^ S(0 X"). Therefore,
I
make
a
30
C=
Let X
{X >
I
= X. There
S(X X) ^ S(0 X)}
I
I
are
now two
cases:
pX e C X < oo & S(X
(i)
0.
?t
:
I
X) = S(0 X)]
I
=> [S(0 0) > S(X X)], by Proposition
I
I
(ii)
[VX e
C X
:
=> \3X' €
check
>
<
C
oo
:
,
S(X X) > S(0 X)]
1),
X' <
m < n(0
I
I
oo
I
& S(0
1
0)
> S(X'
V(m) < W(y*(0
this last inequality, recall
(Proposition
3;
0)
<
~ and n*(0
I
I
I
X')],
0), 0)
0)
> m.
by
Lemma 4
and S(0 0) > m. To
I
by hypothesis. Hence, by
II
(6)
and y*(0 0)
1
31
Appendix B: Example
We claim in section 4 of the text that there exist managerial utilities satisfying the sufficient
condition of Proposition 4, under which the manager would ask for, and shareholders approve, a
level of anticipatory defense, X, such that S(0
1
0)
> S(X
I
X). In this appendix,
we justify
our
claim with an example.
In the interests of computational simplicity,
violated in the example:
The example
therefore
some
technical assumptions of the
the support of F is not the
viz.
shows
that the
main
whole
real line,
result (Proposition 4)
assumptions. Also, there are choices of the distribution function
do
assumptions of the
satisfy all the
text,
and which are
and
Wj
is
model
are
zero at x = y
=
does not depend on these
F and
the outside utility
arbitrarily closely
W,
that
approximated by the
functional forms exploited in the example.
Let
F be uniform on
manager
the closed interval [-2,2], and
assume the value added by
the incumbent
m = 0.
is
Let
V(m)=1.57,
W(7r,
c(y)
For
X) = 2-[x+y]l/2
=
.
[x2]/2 + m,
(2/3)y(3/2).
this specification, U(-l) is strictly
dU(X X)/9X =
I
incumbent's
utility
specification,
X* =
0, that is, the
we
function
X*
the |X)int
where
incumbent's unconstrained optimizing choice of X. The
U(x X)
I
is
as defined in equation (9) of the text.
obtain the following results, illustrated in Figure B.l.^^
.35
U(OiO) = 1.3623
U(X* IX*) =1.3766
au(x* x*)/ax =
I
concave. Denote by
o.o
Given
this
For the manager:
0.
32
For the shareholders:
S(0 0) = 0.2592
1
S(X* X*) = 0.2582
I
S(0 X*) = 0.2570
I
so the condition S(0
shareholders. That
is,
request than they are
worse than
> S(X* X*) > S(0 X*)
0)
1
1
I
by the second
if
they approve
their starting value
In this example, at x
=
S(0
I
holds, and
S(X* X*)
I
inequality, shareholders are
it,
but by the
is
the
outcome
worse off if they
the final
first inequality,
for
reject the
outcome S(X* X*)
I
is
0).
X = 0:
aU(0 0)/ax = 0.095 >
0,
9S(0 0)/ax = 0.024 >
0,
1
I
and
so both the manager and the shareholders prefer a strictly positive level of
manager's most-preferred x
is strictly
x.
However, the
greater than the shareholders'.
[RGURE B.l ABOUT HERE]
Notice
that, for this
parameterization, the manager's unconstrained optimal choice of
anticipatory defense, X*,
is
the manager's unconstrained
constrained
low enough
that the constraint,
optimum were approximately
optimum X* would be approximately
this alternate result
.39,
by raising V(m), the incumbent's
S(X X) > S(0 X), does
I
I
0.4 or above in this example, then the
where S(X X) = S(0 X). (We can obtain
I
utility for current
I
employment.) In
circumstance, shareholders are indifferent between approving or rejecting.
accepted
we could
management
introduce the convention that,
Alternately, as described at the
Remark 4 of Appendix
when
this
To ensure that X
indifferent, shareholders
X by e >
to
is
always vote with
end of section 3 (and justified more formally
A), the manager can reduce his request
preference by the shareholders.
not bind. If
induce
strict
in
33
Footnotes.
1.
DeAngelo and Rice (1983) provide
2.
SEC disclosure requirements regarding
management mail proxy
determining
a thorough discussion of these hypotheses.
matters put to shareholder vote specify that the
materials to shareholders eligible to vote. Thus, the record date for
who may vote
is
prior to the proxy mailing date.
The proxy
materials include, in the
case of charter amendments, the wording of the proposed change and a proxy form with which
shareholders
Therefore,
may vote in absentia,
at the
proxy mailing
indicating approval, rejection, and sometimes abstention.
date, both the constituency for the vote
This type of voting arrangement, termed "take
studied in a political context by
3.
We consider infinite M
or leave
Romer and Rosenthal
in
it"
agenda control, has been extensively
(1978, 1979).
for this exposition. This
Appendix B, we construct an example
on a
it
and the proposal are fixed.
is
not essential to our arguments. In
which the voting conundrum obtains when
M
is
uniform
finite interval.
4.
We consider the value added by the incumbent to be fixed.
Scharfstein (1987) considers
circumstances in which the threat of takeovers can induce the manager to work harder, and
consequendy, to increase the value of the firm.
5.
For example, the uniform, normal,
gamma
and exponential distributions
all satisfy this
restriction.
6.
Grossman and Hart (1980) have shown
be made. Thus, some dilution
Generally, dilution
is
is
that if dilution is prohibited,
no takeover bids
necessary for the circumstances modelled here to be of
will
interest.
possible unless specifically precluded by provisions of the corporate chaner
or state corporation law. In the Grossman and Hart framework, our model can be interpreted as
describing mechanisms by which shareholders and incumbent managers set the level of allowable
dilution and acquirer- sj^ecific acquisition costs.
7.
game
Although our exposition
in
is
not explicidy game-theoretic, the model
which the manager, the shareholders. Nature, and
is
a sequential
potential bidders are players.
move
It is
34
straightforward to describe the formal model as an extensive-form game.
we employ
subgame
is
perfect
agents' optimal behavior
Nash
(in
pure strategies), and
by working backwards ftx)m the
it
is this
final stage
The equilibrium concept
which motivates solving
of the process to the
for
first
(Selten, 1975).
8.
Sec Gilson (1986) for discussion of these and other aspects of takeover law.
The role of the assumption
9.
level of y will
lim.y_^Q
that
c'(y)
=
0, is to insure that
some
stricdy positive
always be chosen by the manager, whatever the value of x. Consequently,
use the calculus in our analysis. Without the assumption,
we have
to consider the
we can
comer case
explicidy: this adds very litUe and does not substantively alter our main results. Similarly, insisting
on the cost function being
make
strictly
convex
in
y
is
not essential for our results.
It
does, however,
the arguments cleaner.
10.
1 1.
The concept
of credibility
is
simply that of subgame perfection: cf fn.7.
This follows from the assumption that the incumbent prefers employment with the firm to
the outside alternative at the stan of the
12.
Proofs of all results are
in
The
period, and that he rationally chooses X.
Appendix A. These proofs
unique subgame perfect equilibrium
13.
first
in
also establish the existence of a
pure strategies to the model.
derivations of these results are available from the authors
upon
request.
35
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