HD28
MAR
fP. 1CQ7
L, SftAjvli--
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
''takh3\^r defenses and shareholder voting*
David Austen -Smith
University of Rochester
/^
and
Patricia C. O'Brien
Massachusetts Institute of Technolog)'
WP# 1823-86
Revised: Januar>' 1987
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
^
TAKBO\^R DEFENSES AND SHAREHOLDER VOTING*
David Austen-Smith
University of Rochester
"
and
Patricia C. O'Brien
Massachusetts Institute of Technology'
WP# 1823-86
*
,
Revised: Januar>' 1987
The authors gratefully acknowledge helpful comments from
Jeff Banks, Harry DeAngelo, Linda DeAngelo Johm Parsons
and Rick Ruback, and from seminar participants at MIT,
Stanford and the University of Rochester. Remaining
errors are soley the authors' responsibility.
,
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: January 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 solely the authors' responsibility.
M.I.T.
LP
MAR
1 o K
Abstract
Why
firm?
do shareholders vote
for anti-takeover devices
which apparently lower the value of their
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 firm.
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
is
reduced more by rejection of the request than by approval.
1.
Introduction
Why
firm?
do shareholders vote for anti-takeover devices which apparently lower the
value of their
We address this question by constructing a model in which rational, fuUy 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
premium
is
tiie
expected takeover
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
DeAngelo and Rice (1983)
report over
250 proposed
1974 through 1979. Linn and McConneU (1983) find generally increasing
incidence of such proposals
among
ResponsibiHty Research Center
NYSE firms over the period from
lists
1960
The Investor
to 1980.
over 200 in 1985 alone. The two major hypotheses describing
the motives for instituting anti-takeover charter
amendments
are
commonly
"management entrenchment" and "shareholder interests." ^ According
entrenchment view, incumbents are interested
in
described as
to the
management
job security and seek protection from
market, to the detriment of shareholders.
Two
entrenching antitakeover devices are:
for a majority of shareholders, the costs of
(1
)
tiie
takeover
suggested explanations for shareholder approval of
becoming
informed about the effects of defensive charter amendments exceed any
potential benefits, and
uninformed shareholders consistentiy give
v^sh
to maintain friendly relations with
their proxies to
management
management; and
to ensure the benefits
(2) large shareholders
of future business, and
large shareholders control sufficient shares to be pivotal in the vote.
Shareholder irrationality
sometimes offered as a
The stockholder
is
third alternative.
interests hypothesis recognizes a free-rider
problem
in collective action
by
shareholders (Grossman and Hart (1980), Jarrell and Bradley (1980)). Shareholders have
premia from takeover bidders, so anti-takeover devices benefit
difficulty colluding to extract larger
shareholders by enforcing a level of collusion in takeover negotiations. Since defensive charter
amendments
benefit shareholders, there
them. Hovt'ever, there
is Uttle
is
no inconsistency
in rational shareholders voting for
evidence that shareholders benefit from such amendments.
DeAngelo and Rice (1983) fmd
statistically insignificant
negative abnormal returns around the
public announcement of proposed antitakeover amendments. Linn and
positive returns around the board meeting date at
McConnell (1983) fmd
which amendments are proposed, and
insignificant negative returns around the proxy mailing date. Jarrell, Poulsen
find negative returns
classified
accompanying
the
announcement of "shark
and Davidson (1985)
repellents", viz. supermajority,
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
managers contribute
for shareholders
if
a bid succeeds.
We presume that different
different value to a given firm, 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
incumbent management
opportunities for
The paper
formal model
is
is
employment outside
relative to potential bidders,
and the incumbent's
the firm.
organized as follows. In section 2
developed
in section 3,
and
we
provide a brief overview of the model. The
we summarize and discuss
the results in section 4.
Section 5 concludes. All proofs are confined to Appendix A. Appendix
that illustrates
our results.
depends upon the
B
consists of an
example
2.
Overview
The main implication of the
firm's value before
and
results
in sections
when
is
that observations of a
voting on these defenses. In our model, shareholders
approve defenses face an unobserved, inferior alternative
choose approval.
3 and 4
implementation of takeover defenses are not observations of the
after the
alternatives shareholders face
developed
Two central features
if
who
they choose rejection, and so rationally
of the model drive the results.
First, the
manager
sets the
agenda on takeover defenses monopolistically, and shareholders have only veto power over the
managerial proposal. In particular, they are unable to amend the proposal 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
that, for a
in the Introduction.
itself,
The monopolistic agenda-setting
properly-chosen request, the shareholders can do no better
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
is
if
the request
is
The wedge between pre-proposal
rejected.
induced by the real effect of the request, described below.
Previous research on the effects of the implementation of takeover defenses has compared the
pre-proposal value of
liie
firm v»iih
iio
posi-proposal or post-vote value. In our model, the
comparison for inferences about shareholder
rationality in voting
is,
instead, the value under
approval of the request versus the value under rejection.
In the next section,
we offer
a particular
model
to illustrate this central idea.
on a reduced form specification of an outside managerial labor market. This
is
Our model
rests
our characterization
of the mechanism that produces the real effect of the request for takeover defenses. Other
mechanisms may
exist with the
same general property of inducing
a change in the decision-making
environmenL
We find the outside labor market a natural way to introduce this real effect, since
it
defines the manager's opportunities in the event of a successful takeover.
Two further aspects of the model
are worth noting at the outset First, in our model,
shareholders recognize the implications of their vote: they do not
make mistakes
or have regrets
with respect to their decision. Second, in some circumstances, the value of the firm will rise as a
result of a request for takeover defenses.
However, the focus of this paper
circumstances in which the value of the firm will
fall,
is
to describe
to provide a rational choice
answer to our
opening question.
3.
Model
We are interested in managerial control of a firm with assets and financial structure fixed.
There
is
a continuum
M of different managerial types capable of running the firm, different types
contributing differently to the value of the firm.
A manager's type is the common expectation of
owners and the outside market of the value added
the
incumbent manager's type, and assume
M
types on
is
common knowledge
question. Because
we
the
whole
real line.^
The
let F(-)
also describe the distribution over
is
We additionally assume that lim.j_^oo[l-F(0]''f(t)
<
<»: this is
is
distribution F(-) of
we
that the support of
owned by
F
is
in
can,
managers of possible firm
F
The firm
m e M denote
and induces a distribution over possible values of the firm
connected, and that
Assume
function.
is
by that manager. Let
take the value of the assets and the financial structure to be fixed,
without loss of generality,
values.
M
to the firm
smooth. Let
f(-)
be the
densit>'
not a strong restriction.'^
a set of shareholders holding fully diversified portfolios. Being fully
diversified, each shareholder
is
interested only in
maximizing the expected value of the
firm. This
expected value depends both on the incumbent manager's type and on the expected premium paid to
the owners, conditional
Heuristically, the
on the firm being taken over by an
model of takeovers we have
in
mind
alternative
is
management
the following.
The
lifetime of the
firm
two periods.
is
A manager of type m controls the firm in the first period.
period. Nature draws a potential alternative
not to
make a takeover bid
for the firm.
controls the firm for the remainder of
incumbent remains
in control.^ Since
maximum value of the
in control,
Given
is
i.e.
firm in
this last
the
If a bid is
its life.
made and is
M, who
this
model of takeovers
in the
if
arc possible
in the
second period, the
all
first
is
an unsucessful bid, the
beyond the second period,
the
period expected value of the firm
sum of the incumbent manager's
let
value added, m, and the expected
discount factors be equal to one for
The expected premium depends on
shareholders.
successful bidder appearing in the second period, and the size of the
from
there
new manager
determined by the value added by the manager then
is
second period. Without loss of generality,
manager and
extracted
can choose whether or
successful, then the
no bid or
If there is
no takeover bids
period
the set
the second period manager's type.
completely determined by the
premium
manager from
In the second
the probability of a
premium which can be
that bidder.
We suppose that there is no utility value to making a bid per se, so that, given the incumbent
manager's type m, only managers of types n >
there
is
any cost
to bidding, then
no type n <
m find
it
worthwhile to make a takeover
m wUl make an offer.
Hereafter,
m. Hence, given the
distribution F, the probability that a
a successful takeover bid arrives
The
is
qualification "minimally"
above
refers to the possibility that the
used, the potential bidder's type n must exceed
firm.
is
to be implicit
manager minimally capable of making
incumbent
will contest a
We denominate takeover defenses in terms
of the increment in price, above m, necessary to acquire the firm. Thus,
m
it
[l-F(m)].^
bid by erecting takeover defenses, as described below.
Being a manager of t>'pe n >
If
we assume there is
such a cost, but, to avoid cluttering the notation, supf)ose the cost constant and take
in
bid.
if
takeover defenses are
m by at least the amount of takeover defenses.
necessary but not sufficient for making a successful bid for the
The manager
is
we view defenses
endowed with two
control variables, x and y, both takeover defenses. Since
as an increment in price, as described above, both x
e R^^, and are measured
variables: (x, y)
managerial types n >
in the
same
units as
and y are nonnegative
real
m. In the absence of any defense,
m will successfully bid for the firm: if there
is
any defense, a successful
bidder must be capable of overcoming the defenses in addition to improving on m. Therefore,
given defenses x and y, a takeover bid must be
there
at least
equal to [m+x+y] in order to win.
As
yet
nothing to distinguish the two types of defense and, indeed, from any potential bidder's
is
perspective the two sorts are indistinguishable.
They
are,
however, quite different from the
incumbent manager's perspective.
Defense x
is
anticipatory
:
can be put
it
in place
only in the
first
period, prior to any potential
bidder appearing. For convenience, direct costs of implementing x are normalized to zero.
However, the manager
among
is
obliged to ask the shareholders explicitly for a level of
the shareholders determines whether or not the manager's request
is
Majority voting
x.
granted.
Amendments
are not permitted, so the shareholders can only accept or reject the manager's proposal. There
indirect cost borne by the
request
manager
granted. This cost
is
is
in
for requesting anticipatory defense, re gardless of whether this
terms of his outside value
— the
utility
receive in the second period, conditional on being ousted from the firm.
efforts
offer
is
on
the part of
an
is
incumbent managers
an indication that the manager
is,
payoff he can expect to
Our presumption
to erect takeover defenses in the
for instance,
more
is
that
absence of an explicit
interested in personal security than the
welfare of the shareholders; and this lowers his outside market value. Let x? denote a request for a
level of anticipatory defense. If
this
defense
however
is
x = x?; and
that the
X? > 0] are
if
x?
it is
is
approved by shareholder vote, then the implemented level of
not approved then x =
above discussion implies
distinct: this is crucial to
0.
implies x = 0. Note
Evidently, x? =
that the states of the
world
[x
=
|
x? = 0] and
[x
=
our model.
The second type of takeover defense
available to the manager, y,
is
responsive
.
Responsive
|
defense
implemented only
is
to fight an explicit takeover bid in the
second period, conditional on a
bid materializing. Unlike anticipatory defenses, the manager implements responsive
defense,
without obtaining shareholder approval.^ There
are,
however, direct costs to engaging
takeover fight Let c(y) be the direct costs, measured in units of
implementing a responsive defense of y. Assume c(0) =
For technical reasons,
depend on
utility,
0, c'(y)
>
in a
borne by the incumbent in
and c"(y) >
for all y > 0.
convenient to assume lini.y_^o c'(y) = 0: none of our principal results
it is
this.°
In the heuristic discussion of the takeover process above, given defenses x and
y,
that a successful bidder
must pay
at least
Because shareholders are interested only
[m+x+y]
in
to acquire the firm.
maximizing wealth,
than [m+x+y] to persuade them to remove the incumbent.
it is
we
argued
Will any more be paid?
sufficient to
pay £ >
No acquirer wishes to pay
more
any more
than necessary to take over the firm. Therefore, in the limit, epsilon will be zero. Hence,
the
premium
incumbent secures for the shareholders
that the
dsSEile defenses x and y
-- is
manager of type n > [m+x+y]
is
- conditional on
losing a takeover battle
precisely [x+y]. Moreover, again taking x and y as fixed, only a
will
make an
offer,
and any such offer will succeed. Recalling
the distribution over managers, the probability of takeover in the second period
by
[1
is
that
F
therefore given
-F(m+x+y)].
To derive
the expected
premium, consider
surely in control of the firm in the
enterprise
is
taken as given,
it is
first
first
the incumbent's objective function. Since he
is
period and the investment and financial structure of the
necessary only to examine his second period payoff.
It is
necessary to describe this second period payoff under two employment alternatives: within the
firm, or, if a bid succeeds, outside the firm. If there
incumbent stays
in control
and receives
utility
co(x,
y
I
X?) =
W(x+y, X? m)
I
-
no takeover bid
in the
second period, the
V(m). Conditional on losing control of the firm, and
given X and y, the manager's net second p)eriod
(1)
is
c(y),
utility is:
8
where WC-)
lim.jj<)^oo
is
Assume
the manager's gross outside value given x, y and x?.
^2 = **'' ^1
losing his current position
and
<
1
W^2 - 0-
— ultimately, at
the acquirer; decreasing
anticipatory defenses in the
first
j
an ever-increasing rate
premium he
~
in
any
is
possibility that
we
W
is
(x
=
suppose V(m) > W(0,
|
We argued above that,
m).
if
approved requests.
in
on the former are
^^
To make
is
particular managerial type
n drawn by Nature
made
V, and
c,
are
Therefore, the potential acquirer
A
bidder's best offer (that
makes no
acquirer
response
Though
the
is, if
offer at
(m+x+y <
n),
is
is
problem
nontrivial,
is
indeed given.
second period. The incumbent's
knowledge, as
is his
utility
and
type m. Likewise, once Nature has
is
common knowledge.
capable of calculating the incumbent manager's credible
is
credible
if,
when n
is bid,
y.^ If this utUity-maximizing response
m+x+y
all.
>
n),
then
If the potential
-
is
the manager's
sufficient to beat the
because of the bidding cost
acquirer
is
-
the potential
capable of topping the incumbent's best
then she makes the smallest offer necessary to win control of the firm.
incumbent loses
fighting, c(y),
It
common
in the
resix)nse y to a bid n
utility-maximizing response
the
responsive, the incumbent's selection of y depends, inter alia, on the
her draw, the type n of the potential bidder in the second period
response y to any bid.
is,
x and y are fixed and known, only bids which can succeed will be
However, since defense y
W,
employment
-
made. At the beginning of the second period, the anticipatory defense x
cost schedules,
with
This does not exclude the
x?), strictly decreasing in x.
everywhere decreasing
'W2 <
efforts to secure
period; and the cross-effects of this latter
enough approved requests
0,
able to extract from
non-increasing. These assumptions imply that the manager's utility for alternate
for large
>
Thus the incumbent's outside value conditional on
increasing concave in the takeover
is
W
surely,
by definition of credibihty he prefers to bear the costs of
and the winner pays the premium [x+y]. Hence the
remains to determine the set of credible responsive defenses.
Let X? and x be given, x € {0, x?}, and define:
earlier
argument goes through.
y*(x
(2)
From
we
(1),
(3)
a(o%
(4)
d2a)/dy2 =
j^^ (o(x,
y
x?).
|
= Wi-c';
=
W
<
c"
J 1
0,
Vy.
impUcitly defines y*(x
and lim.y_^o
>
^
obtain:
Setting aco/9y
Wj
X?) = argmax.y
I
c'(y)
=
By
x?).
|
by assumption,
(4), y*(i-) is
>
y*(-|-)
unique for
all
x?,
x>
Since
0.
0.
We now defme, Vn > x+m:
v(n, X
(5)
The schedule
I
m) = V(m)
-
c(n-x-m).
v(-) describes the
maximum second period
given he fights and defeats a bidder of type
n(x
(6)
I
x?) = [inf n
[inf n
As described below, n
that,
|
I
v(n, x
(6) reveals that, for bids n
co(x,
Defme, for x? >
y*(x
V(m) = W(n-m, x?
minimum
defines the
because V(m) > W(0,
=
|-)
n.
|
|
|
x?),
other hand, any potential acquirer
see
how premia paid by
n*(x
(7)
I
where y*
is
X?) = X + y*(x
defined as in
employment outside
only
if
(2), to
it
is
|
x?),
|
and x e
x?)], if
V(m) > W(x+y*(x
x?) +
x?),
|
x? m);
|
m)], otherwise.
|
m+x
x?) >
for
bid n > n(x
|
x? ^
all x,
0.
Inspection of
x?) will be successful, and the
On
premium
>
and x e
{0, x?}:
m,
be the responsive defense that maximizes the incumbent's
x?
under the assumption that x = x? >
]),
the
utility function.
successful bidders vary, define, for x?
|
(0, x?}:
credible that the incumbent will fight and win.
who can
the firm. There are
V(m) < W(x+y*(x
x?)
incumbent manager can obtain,
bid which can succeed against the incumbent. Notice
she will pay depends on n and on the incumbent's
To
i
m) by assumption, n(x
< nCx
utility the
two
and
cases: (a) n*(x
(b)
n*(x
|
x?)
|
x?) > n(x
< n(x
|
x?).
|
x?),
Figure
which occurs
1
utility in
if
and
illustrates these
0.
[HGURE 1 ABOUT HERE]
Consider Figure
1(a)
and
first let
n € (n(x
|
x?),
n*(x
|
x?)].
The incumbent's
best response
is
to
Figure 1(a)
V, CO
V(m)
W(x,x?lm)
n(x
I
x?)-m-x
n*(x x?)-m-x
1
Figme
1(b)
V, 0)
V(m)
W(x,x?lm)
n*(x x?)-m-x
I
n(x x?)-m-x
I
10
and then to leave the firm
fight to extract (virtually) all the bidder's willingness-to-pay for the firm,
to collect his net outside value, co(x,
exceed n*(x
equal to [n*(x
x?)-m-x
I
x?)
|
-
Now let the bidder-tyjje n
x?): this is clearly credible.
to extract a
premium,
m], and then leaving the firm and obtaining his outside value,
in this case
co(x,
n*(x
|
X?).
Notice in
this last
case that bidders do not pay
may
although the firm
this event,
only two periods,
is
pay a premium of [n*(x
|
x?)
second period by virtue of the new
owners of the acquiring
in the firm until
incumbent, observing a bidder of type n > n(x
|
-
Since the
n*(-|-).
life
of
firm.
n(x x?), where the fight
|
make takeover bids.
m], however, regardless of type. This
-
n
the surplus,
one thinks of the new manager as another firm,
x?) will
|
they are willing to pay for the firm. In
consume
employment
Thus, only types n > n(x
costly.
all that
in the
If
as a gain to the
In Figure 1(b), the incumbent prefers
becomes too
to
this is reasonable.
may be viewed
then this surplus
n
attain a value
new manager is assumed
manager's type, the
the firm
|
Again the incumbent optimizes by fighting
x?).
|
n-m-x
is
Ail successful bidders
true because the
x?), recognizes defeat, but fights to
n* to maximize
his outside value.
For future reference, for
For any successful
7t(n,
x
I
bid, the
premium
x?) = min.[n
We are now in a position
from the
(9)
first
-
firm under
n,
>
0, let 7t(n,
above the value
x
|
x?) denote the
premium
m contributed by the incumbent.
m, n*(x
|
x?)
to specify the
-
m].
incumbent's expected second period payoff, viewed
period, as a function of anticipatory defenses x:
U(x
6=1
x?) and for any x
7i is:
I
x?) = F(n(x
1
x?))-V(m) + 6-[F(n*(x
+ {5-[l-F(n*(x
where
|
by the successful bidder of t>'pe
actually paid
(8)
n > n(x
all
iff
n(x
|
x?) < n*(x
management
m
is
|
x?),
X?))]
I
and 5 =
given by:
|
x?))
-
F(n(x
+ [l-5]-[l-F(n(x
otherwise.
|
The
|
x?))]-J^{o(x,
x?))]}-co(x,
first
n-m-x x?)-f(n)dn
n*(x
|
|
x?)-m-x
|
x?),
period expected value of the
11
S(x
(10)
I
X?) =
m + 5-[F(n*(x
|
x?))
+ {5[1-F(n*(x
-
F(n(x
x?))]J[n-m]-f(n)dn
+ [l-5]-[l-F(ii(x
x?))]
I
|
|
x?))]}-[n*(x
|
x?)
-
m]
with 6 defined as above.
The responsive defense y
is
chosen optimally by the management, independent of shareholder
approval and given the bidder type that appears in the second period. Anticipatory defenses x
require shareholder approval and have to be set in the
optimization problem
therefore to choose a request, x?
^
subject
if
the
to:
S(x
x?)
|
> S(0
manager asks x? =
be no less than
0,
|
period
x?).
then the constraint trivially binds. However,
its
value
the request
if
is
if it is
not granted
we have
--
in
rejected, given x? > 0.
general that S(0
|
0)
if
x? >
Because the incumbent manager's
on
^ S(0
his request, x?, in the first period
|
x?) for any x?
>
0.
words, the alternative that rational shareholders compare against the manager's request
0), their situation prior to
any request, but
is
S(0
i
then the
on the request being approved must
decision environment in the second period depends, inter alia,
even
first
0, to:
constraint says that the expected value of the firm conditional
-
The manager's
period.
max.U(x|x?)
(11)
Clearly,
is
first
x?), the result if they reject the
In other
is
n^I S(0
request This
|
is
the central idea of the model.
If the constraint
binds at
rejecting the request. Since
some x? >
0, then
managers are not
shareholders are indifferent between accepting and
indifferent, they
circumstances by slightly perturbing the request, x?, to induce
shareholders: as
Appendix
A
shows, such a perturbation
constraint binds, then the manager's request
is
is
can insure acceptance
strict
in
such
preference on the part of
always available.
approved. Alternatively,
We assume that if the
we can
adopt the
convention that in cases of shareholder indifference, shareholders always "vote with the
management". ^^
We
turn
now
to
some
results.
12
4.
Results
There are three possible conditions
beginning of the second period:
at the
requested no anticipatory defenses, (2) the manager
shareholders, and (3) the manager's request
second period response
on the
first-period
Proposition
Corollary
1:
1:
to a takeover bid
Let x = x? >
was approved. Proposition
if
than
if
is
0.
Then y*(0
|
0)
the request
is
|
^ y*(0
i
x?) > y*(x
x?) > y*(0
|
|
x?) > 0.
x?).
by shareholders, the second-period maximizing response
approved. However, from Corollary
is
premium
in a successful bid, this implies that
feature evident
from Proposition
never larger after a request, even
we show
if
1, total
is
defenses
rejected. Since total defenses determine
shareholders can expect a smaller
if
1
is
that the second-period
the request is denied, than if
Thus, the request carries no implicit threat of "scorched earth" responses
Rather, as
puts an ordering on the
they reject the manager's request and a successful bidder emerges.
An interesting
response
1
which maximizes the manager's outside value, conditional
Letx = x?>0. Then x + y*(x
premium received
premium
manager
made a request which was voted down by
(anticipatory plus responsive) are smaller if the request
the
the
outcome.
If a first-period request is rejected
strictly larger
( 1 )
below, the request
alters the
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
first
minimum
bid
Generally, the higher the level of anticipatory defense approved by
period, the lower will be the manager's choice of responsive defenses.
13
Comparative
(a7))
show
statics
that this
on y*(x
response
how
In evaluating
x?), the
|
maximizing second-period response (Appendix A, (a3)
-
non-increasing in the size of the first-period request.
is
value-maximizing shareholders consider both the size of the
to vote,
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:
ii(x
(b)
Vx =
x?)
(a)
I
is strictly
X? >
0, ii(x
Proposition 2 states that the
increases with the
1
increasing in x?, x e {0, x?};
X?)
>
11(0
I
X?) > n(0
1
0).
minimum bid which can succeed
against incumbent
amount of anticipatory defense requested. Since
bid will emerge falls as the
minimum
management
the probability that a successful
successful bid rises, part (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
anticipatory defenses are requested, declines
request
state
is
from
approved. Notice that part (b)
[x
= x? x? >
|
0] to [x
=
|
is
if
there
is
a request, and
may
takeover
decline
not an immediate consequence of part
x? > 0]
is
is
largest if no
more
(a):
not incremental because of the "take
it
if
the
the change in
or leave
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
unambiguously worse off
they were before the request.
if
level of anticipatory defense,
which generally decreases. Proposition 3 shows
if
a
and on the
that shareholders
they reject management's request for anticipatory defenses than
14
For x? >
Proposition 3:
The voting
0,
S(0
0) > S(0
1
|
x?).
(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
latter
circumstance, no request,
To complete
leave
would have been
they reject the request than they
is
if
no request had been made. (Note
not available to shareholders deciding
how
to vote
on a
that this
request.)
our description of the apparent paradox that shareholders vote for defenses which
them worse
we require
off,
shareholder value
if
no request
is
a comparison of shareholder value
made: S(x x?) versus S(0
|
1
0).
the request
if
approved with
is
Proposition 4 gives a sufficient
condition for the apparent paradox to occur.
Proposition 4:
V(m) < W(y*(0
|
0),0
=> 3x? G
According to Proposition
his
maximum gross
which shareholders
m)
(0, oo):
4, if the
S(0
manager's
I
0) > S(x
utility
|
x?)
^ S(0
|
x?),
x = x?.
from employment with the firm
will approve, but
this
which leave them worse off than they were before.
maximum gross
period. Nature draws a bidder of type n
in the
outside utility
> n*(0
1
firm was larger than his
0).
is
available only
Recall that
initial
we assumed
gross outside
utility:
if,
utility:
Figure
1(a),
that
than
is,
considering his optimal choice of y at x? =
by setting x = x? =
With Proposition
4,
0.
The
in the
It is
second
the incumbent's utility
that
before defenses x or y are considered. Proposition 4 concerns the incumbent's
outside
is less
outside utility before any request for anticipatory defenses, then requests exist
important to observe that
from employment
|
is,
his utility
maximum
situation
is
gross
pictured in
0.
we have shown
the existence of requested levels of anticipatory defense
15
which
result in the voting behavior
we hoped
That
to describe.
is,
rational, fully informed,
value-maximizing shareholders will approve the defenses, but are made worse off by them. The
sufficient condition for the result
depends on the manager's
utility in
current and alternative
employment.
We have not yet demonstrated, however, that these levels of anticipatory defense
would
be requested by managers with
in fact
no inconsistency between
utilities satisfying
utilities satisfying this
the sufficient condition. There
condition and utihties generating the level of
anticipatory defense, identified in the Proposition, as a best choice. In
example of a manager with
utility satisfying the
is
Appendix B, we provide an
condition of Proposition 4,
whose optimizing
choice of anticipatory defense will be approved by shareholders, and will leave them worse off than
if
no request had been made. The example
It is
is in
no sense
pathological.
worth noting that under some circumstances, shareholders can be made better off by
implementing some anticipatory defense. By Proposition
is
that the
It is
not,
some
manager's request, x?, be
a necessary condition for
3,
strictly interior to the constraint set; i.e.
however, a sufficient condition. In our example
anticipatory defense x, but the
manager
prefers
in
S(x
|
this to
x?) > S(0
|
occur
x?).
Appendix B, shareholders would Uke
more and,
despite the constraint not binding,
the request results in a decline in shareholder wealth.
Tlie primar}' implication of our
is
model
for interpreting the empirical
that inferences about whetiier shareholders vote rationally
shareholder wealth before and after the vote.
management
as an
unambiguous drop
We
rationalin,'.
in shareholder value,
a comparison of
is
Oar model suggests
n^I as a return to the pre-proposal
skill relative to potential bidders.
^
not the conrect benchmark for
that empirical investigation of shareholder
voting and takeo\'er defenses should consider the manager's outside
and the manager's
made from
it
describe the alternative to voting with
status quo. Therefore, pre-proposal shareholder wealth
determining shareholder
cannot be
work which has preceded
employment oppormnities,
16
5.
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
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
he had made no request Shareholders recognize
if
In the model, the manager's typ>e
and
utility
question of why any manager would be hired
which decrease the value of the firm
have
in
mind
a signalling
we
In other words, our
signalling
who
will
to shareholders.
game which precedes
perhaps the hiring stage, the manager's type
as a signal, and
schedule are
the
not
is
this in
common
is
different if the request
evaluating
how
is
to vote.
knowledge. This raises the
wish to implement anticipatory defenses
To this
extent, our
model
two periods we study. At
known with
certainty.
The
is
incomplete.
We
this earlier stage,
request x? functions
are implicitly assuming the signal fully reveals the manager's type (and utility).
model
is
predicated on the existence of a separating equilibrium to this earlier
game.
Finally,
we
offer
two remarks.
First,
it is
frequently asserted
(cf.
Easterbrook and Fischel
(1983)) that the alienability of ownership claims protects shareholders from detrimental
management entrenchment
tactics.
However, unless shareholders
takeover defenses by management, they cannot
SEC proxy
mailing requirements
proposal date.
any drop
in
Once
demand
the proposal
is
sell a
anticipate the proposal of
voting claim in response to the proposal.
that the record date for shareholder voting
announced, the constituency
is
fixed.
precede the
Our model suggests
share value should occur with the announcement of the proposal, not with the vote.
Second, our model implies that changes
takeover defenses
may
in
shareholder wealth associated with voting on
be positive or negative, depending on the manager's type and utihty
that
17
schedule. In cases where shareholders' wealth
the manager's request If there
is
is
reduced, the reduction should occur at the date of
any detectable change
at the date
positive. This follows
from Proposition 3 and the voting
shareholders' wealth
unambiguously reduced
is
shareholders' wealth under rejection
interpretation, empirical results
is
no
if
of the vote,
it
should be
constraint: the first states that
they reject a request; the second ensures that
larger than their wealth under approval.
On
this
which fmd shareholders' wealth declines following implementation
of anticipatory defenses are not evidence of shareholder
informed choice of the lesser of two declines in value.
irrationality or ignorance, but reflect
an
18
Appendix A: Proofs
Proposition
Let x = x? >
1:
Then: y*(0 0) ^ y*(0 x?) > y*(x x?) >
0.
|
0.
|
|
Proof:
(i)
follows from assuming
y*(x X?) >
I
(ii)
y*(0
)
I
> y*(0
|
Use
(iii)
0),
Wi(y*(0
c"
c'(y)
=
0.
I-)
-
Then, by
x?).
|
Wi(y*(0
|
x?
x?),
Wj
j
<
>
0.
x?
|-)
|-)
0,
W12 <
=
c'(y*(0
and x? >
0:
1
|
|
Then
WjCx +
c"
1:
I
x?),
x?
0, so that
Wj
2
|
1:
I
x?)]
|
> y*(0
Let x = x? >
|
I
0))
-
Comparative
-
|-)
V,\(y*{0 x?), x?
|
>
first
c'(y*(0
|
x?)).
order condition (3) to get:
|-)
= c'(y*(x x?))
|
0.
implies LHS(a.2) < 0: contradiction.
iff
Then:
1
W12 = 0.
Hence, x = x? >
and
[x
with
+ y*(x x?)] > y*(0
|
Wj
j
<
and
c" > 0.
|
x?).
||
Statics:
X = X? => dy*(x
|
-
c'(y*(0
|
x?)).
0.
0).
Proof: Use (3) and Proposition
(a.3)
x?),
and again use the
<
y*(0 0) = y*(0 x?)
+ y*(x
Corollary
y*(x
x?),
|
implies RHS(a.2)
>
But X = X? >
Remark
|
x?)
Suppose y*(0 x?) < y*(x
(a.2)
Wi(y*(0
|-) -
0),
I
implies the RHS(a.l) < 0: contradiction,
>
y*(0 x?) > y*(x
[x
everywhere, and lim.y_^ g
(3) to obtain:
(a.l)
But
I
>
x?)
|
Suppose y*(0 0) < y*(0
Wi(y*(0
Wj
x?)/dx? = -[Wj
i+Wj2VrWll-c"] <
0-
||
W12 =
imply:
19
(a.4)
dy*(0 x?)/dx? = -Wj2''rWn-c"] ^0. with the inequality
(a.5)
X = X?
(a.6)
dco(0, y
|
Note
1
|
x?)/dx? =
|
W
x?)/dx? =
+ W2, which a
^
<
x?)
= x + y*(x x?) + m, and y*(x x?)
|
(a.5)
1
|
(a.6)
|
|
0, then
an*(0 x?)/ax?
|
is
is
an*(x x?)/ax > (<)
(a.7)
Lemma
as c"(y*(x
|
given by
(a.4).
Let x? >
0, x
g
{0, x?}. Then: ii(x
|
If
1
x?)
is
x = x?, then an*(x
|
x?)/ax?
we obtain:
x?))
^
(<)
x?)
is
differentiable in x?;
I
1:
0.
sign.
differentiable in x?, n*(x
dy*(x|x?)/3x?. Substituting from (a.3) and collecting terms,
+
ambiguous
<
|.
|
=
priori has
Wj2
W2 < 0.
y,
differentiable in x?. If x
=
y
any
that at
Since n*(x
da)(x,
=i>
strict iff
-Wi2(x+y*(x
1
x?),
x?
|-).
and 9n(x
I
x?)/ax? > 0.
Proof:
(i)
n(x
I
X?)
is
differentiable.
from section 3
First, recall
A* =
[v(n*(x
I
X?), X
A* with
Differentiating
]•) -
that n(x
|
x?) >
y*(x
|
x?)
CD(x,
respect to x? at x
aA*/ax? = -W2(x+y*(x|x?), x?
Therefore,
A* can change
Suppose there
V(m) <
So by
case
a
exists an
:
By
n(x
In this case, n(x
(a.8)
and,
x?)
I
<
Consider x <
(6),
=
W(x+y*(x
(>)
(6): ii(x
21
sign at
x?)
|
|
8n(x
x?)
|
(>)
2L?
|
>
|
|-)
iff
x?) iff x
Let x = x? >
0,
and define:
and using
(3) gives:
0.
most once
x?
0.
x?)].
x?,
as x increases,
such that A* =
x?),
n*(x
|-)
=
|
x+m, Vx, x? >
0.
x < (>)
<
Then i
is
and only from negative
to positive.
unique and:
x.
(>) i-
i-
is
is
impUcitly defined by:
differentiable because
V(m) - W(ii(x x?)-m, x?
|
W
is
!•)
=
0.
differentiable. In particular,
x?)/9x? = -W2(ii(x|x?)-m, x? |-)AVi(n(xlx?)-m, x?
|-);
Vx
<
x,
20
Um-x^
(a.9)
case P
Consider x >
:
By
(6),
n(x
I
X?)
[^ndO/Bx?] = -Wjdi^Cx
X-
x?)-m, i? |-)/Wi(n*(2c
V(m)
implicidy defined by:
is
|
-
c(ii(x
|
x?)-x-m)
-
I
where Wj*(x) = Wi(n*(x|x?)-m, x?
=1,
|-), i
Wj*(x)
-
-
W.
x?) follows from differentiability of c and
dn(x x?)/9x? = [c'(iilx|x?)-x-m)
i?
co(x,
y*(x x?)
|
the second equality follows
dii(x
(ii)
case
a
-
Wi*(i)
-
W2*(2c)]/c'(n*(2Ll2L?)-i-m)
case
is
immediate from
(a.
11) complete
x?.
Il(x|x?).
this
By
(3),
Wi*(x) =
Therefore, c" >
V
y impUes,
(a.l2)
Moreover,
(a.lO).
c'(n(x
W2+W2 < W
suppose X =
9ti(0
Remark
2:
Lemma
2:
and
(a.9).
|
j.
= c'(n*(xlx?)-x-m). Since A* >
Therefore, the numerator of
and
Lemma
and x? >
x?)/9x? >
(a.7)
c'(y*(x|x?))
0, n*(x|x?)
|x?)-x-m)>Wj*(x)>0.
completes the proof of the
Now
(a. 8)
x?>2t
Consider
and
Together, (a.9) and
(3).
lO;
x = x? <2C
:
Casg P: x =
X?,
differentiable
0.
W2*(x)]/c'(ii(x|x?)-x-m),
everywhere when x =
is
x?) =
x?)/ax? >
i
The proof of
this
from another application of
x?)
|
|
In particular, using (3):
= -W2(n*(i|x?)-m, i? |-)AVj(n*(i|x?)-m, i?
the argument that n(x
|-).
Hence,
2.
lim.j^^ ^^ [an(t)/ax?] = [c'(n*(ili?)-i-m)
(a.ll)
2c?)-m,
1
x.
Differentiability of ii(x
(a.lO)
|
=
10)
is strictly
positive. Since
0.
1
Similar reasoning as before gives n(0
imply that U(x
Then:
ii(x
I
x?)
c'
>
0,
x?.
|
x?) differentiable in
follows on implicit differentiation of (6) for x? < x and for x? >
Lemma
Let x = x? >
0.
for x
(a.
|
x?) and S(x
> n(0
|
x?);
|
x?) are differentiable in x?.
x.
||
<
21
Proof:
case
a V(m) < W(x+y*(x
:
By
(a.l)
(6)
x?),
|
m, x?
-
|
V(m) < W(n*(0
x?)
|
-
m, x?
-
m, x?
I
=> W(n(x
I
x?)
=>n(x|x?) =
By
|-)
and the premise, V(m) = W(n(x x?)
=> V(m) = W(n(0 X?)
(a.2)
x?
-
m, X?
(6)
m, x?
-
|
|
x?)
m, x?
-
=* V(m) =
[co(0,
y*(0 x?)
=> W(ii(x
X?)
m, X?
-
|
definition of y*(0
Therefore,W(n(x
by
|-),
!•)
ii(0|x?).
V(m) > W(n*(0
I
possibilities:
|-)
= W(ii(0 x?)
|-)
There are then two
|-).
|
|
x?)
x?) + c(n(0
|
c(n(0
-
I-)
m, x?
x?)
|
y*(0 x?)
x?), 0(0,
-
|-)
|
|-) -
c(n(0
|
x?)
|
m) =
-
|
-
m)], by (6)
co(0,
y*(0
x?) > W(ii(0
x?)
-
|
|
x?)
x?)
m) > W(ii(0
|
x?).
|
m, x?
-
x?)
-
|-) -
m, x?
c(n(0
|-) -
|
x?)
c(n(0
|
-
m).
x?)
-
m)
=>ii(x|x?)>n(0|x?).
This proves the proposition for case (a),
gasg P:
V(m) > W(x+y*(x
=> V(m) =
By
Corollzry
1
co(x,
y*(x
and x? >
|
x?),
|
x?)
0,
x?
x?) + c(n£x
|
W(x+y*(x
Hence, V(m) > W(n*(0|x?)-m, x?
(a.l3)
V(m) =
co(0,
|-)
y*(0
|
!•)•
x?)
|
1
|
x?),
So by
x?)-x-m), by
x?
(6).
> W(y*(0
|-)
|
x?),
x?
|-).
(6),
x?) + c(ii(0
x?)
|
m).
-
Therefore,
(a.l4)
By
(o(x,
Proposition
y*(x
|
x?)
|
x?)
and Corollary
1
-
1,
co(0,
15)
11(0
Now implicitly
I
x?) > ii(x
I
X?)
differentiating
-
1
LHS(a.l4)
likewise be strictly positive. Since
(a.
y*(0 x?)
c'
>
|
x?)
= c(n(0
is strictly
and x = x? >
we obtain Vx? >
x?)-
m)
-
c(ii(x
positive; hence, the
0, this implies,
X.
(a. 13),
|
0:
|
x?)-x-m).
RHS(a.l4) must
22
ail(0
Using
I
we have Vx? >
10),
(a.
(a.
x?)/3x? = -W2(y*(01x?), X? |-)/c'(n(0|x?)-m) >
16)
[aii(x
x?)/ax?
I
0:
dnCO x?)/9x?] =
-
I
+ {[W2(y*(0|x?),
By
(a. 12),
1,
By
(a.
15)
and c" >
(a.
18)
<
Together,
When
X? =
0,
[W2(x+y*(x|x?), x?
nonnegative
Vx? >
0.
|-)/c'(ii(x|x?)-x-m)]}.
Consider the second term
in {•}.
I
t) ^ W2(x+y*(x
X?),
I
x?), t).
0,
c'(n(x
17)
(a.
-
W2 < 0, and W12 ^ 0,
> W2(y*(0
(a.l7)
is
[Wi(x+y*(x|x?), x? |-)/c'(ii(x|x?)-x-m)]}
{ 1 -
x?|-)/c'(ii(0|x?)-m)]
the first term of (a. 16) in {•}
By CoroUaiy
0.
and
I
x?)-x-m) < c'(n(0
x?)-m).
|
18) imply that the second term of
(a.
(a.
Vx? ^
0:
an(0 r)/ar]dr >
0,
both terms in {•} vanish. Therefore,
16) in {•}
is
also positive
Vx? >
0.
X?
[n(x
I
X?)
-
ii(0
I
X?)]
-
[an(r
j
|
as required (with equality iff x?
=
0).
Lemma
2
is
Remark
from
[x
I
Notice that
= x? X? >
Remark
if
3:
0] to [x
I
4: Together,
X = X? and S(x
x?~) > S(0
Lemma 3:
I
|
=
Remark
x?) = S(0
By
uQi implied by
is
Lemma
1
:
this is
because the change in
state
not incremental.
2, footnote 8
and
Lemma 2 justify
the claim
x?), then there exists a perturbation in
x?
-
made
say,
x?~
in section 3 that,
--
such that S(x~
x?~).
For any x? >
0,
Proof: Given x = 0, v(n, x
in n.
|
|
||
X? > 0]
I
-
r)/9r
W2 < 0, W(y, x?
n(0
|
|-)
I
x?) > ii(0
m) = V(m)
< W(y,
-
|-),
|
0).
c(n-m). Since
Vy >
0.
So by
c'
>
0, v(n,
(6), ii(0
|
x
|
m)
is strictly
x?) > nCO
|
0),
decreasing
Vx? >
0.
||
23
Proposition 2:
nix
(a)
x?)
|
is
strictly increasing in x?,
Vx = x? > 0, ii(x
(b)
Proof: The proposition follows firom
Proposition 3: For x? >
By Lemma
Proof:
(a.19)
By
Proposition
casg
n>
ff:
By
case p
<
F
fact that
[1-F(ii(0
|
|
11(0
is
2 and
1,
3.
I
0).
||
x?).
defmed on
a c.d.f.
a continuous variable n:
0))].
I
0),
|
x?) > 11(0
I
with the inequality
strict iff
Wj2 <
at
any y < y*(0
|
0).
X?).
I
(8):
(a.20)
If
x?))]
I
>
Lemmas
0) > S(0
|
n*(0 x?) < n*(0
1,
11(0
and the
3,
[1-F(ii(0
S(0
0,
X?)
I
x e {0, x?}; and,
7C(n,
0)
|
>
i
n*(0 X?) < n*(0
I
n €
:
(ii(0
|
0),
x?).
7t(n,
0), the inequality in (a.20) is strict
I
n(0
Vn > n*(0
|
x?).
x?)).
1
By an argument
in section 3,
only types n > n(i-) will miake takeover bids. Therefore:
(a.21)
0) > 7t(n,
X?)
7t(n,
I
I
H
0.
casgy n<ii(0|0).
By
the
(a.22)
same argument
7t(n,
Together, (10) and
Lemma
4:
|
0)
(a.
=
as case
7i(n,
19)
-
|
(3:
x?)
(a. 22)
h
0.
yield the desired result.
Let x = x?. Then: ]im.^')_^^ S(x
|
x?)
||
= m.
Proof:
By assumption,
Wj
j
> xj?, V(m) > W(x+y*(x
S(x
I
x?) =
m+
<
|
and lim.j^9_^^
x?),
[1-F(n(x
|
x?
|-).
W2
Hence, by
x?))]-[n*(x
|
= -~. Therefore, for
(10),
x?)-m].
Vx? >
xj?,
sufficiently large x?, say
x?
24
By Remark
2, S(-
1
9S(x
(a.23)
I
•)
differentiable in x?. In particular,
is
I
x?))]-an*(x
x?)/ax?
I
We prove the Lemma by first showing 8S(x
By Lemma
is strictly
case
a
:
case p
By
and the assumption
(7)
(a.24)
|
and
for all x?
x?)/ax? <
|
[1-F(ii(x
x?))]/f(n(x
|
I
x?))-aii(x
(a.7), the first
I
x?)/ax?-[n*(x
for all finite x?
V(m) > W(0,
that
>
^
|
>
I
x?)-m]}.
X2?, X2? sufficiently
m), the term in {•} on the RHS(a.23)
term on the RHS(a.23)
is
of ambiguous sign.
X2?.
X2?.
x?)/ax?] =
|
{f(ii(x
X2?.
for all x?
sup.[an*(x
I
^
-
x?)/3x? <
|
for all finite x?
x?)/ax? >
(a.3),
By
all finite x?.
dn*(t)/ax? <
an*(x
:
1
positive for
Then, aS(x
x j?,
x?)/ax? =
[1-F(ii(x
large.
Vx? >
<
x?))
For sufficienUy large x?, aS(x x?)/ax? <
1.
|
aii(x
|
x?)/ax?-[n*(x
|
x?)
-
if:
m].
r,
By
assumption, lim.j_^^
<
lini.jj9_^oo[LHS(a.24)]
(a.
10), therefore,
Vx? ^
an(x
|
<
[[l-F(t)]/f(t)]
<».
Also by assumption,
\l)/dxl >
X2?. Hence, (7) and y
>
1
=
0, the
Lemma follows
Proposition 4: V(m) < W(y*(0
=> 3x? e
Proof:
By
Corollary
V(m) < W(y*(0
I
1,
3
x"
x?"), x?"
|-)
W^ ^
Lemma
<
1
By
from
|
(10).
0),
00.
for all x?
>
|
From
x?)/ax? > 0,
Therefore, there exists a
X2?. Since lim.j_^^
||
:
S(0
|
0) > S(x
|
x?)
> S(0
|
x?), x
=
such that both V(m) < W(x"+y*(x"
= x?" >
W2 = -«>.
m)
|
(0, 00)
obtain.
aS(x x?)/ax? <
x?,
hypothesis, an*(x
imply that lim.j^'>_^^,oCRHS(a.24)] =
|
and x =
and lim.j^9^^
for sufficiently large x?.
sufficiently large value of x?, X2?, such that
[1-F(t)]
Therefore, by
<».
Then by case
(a. 1) of
Lemma
2, ii(x"
x?.
and
x?"), x?"|-),
|
|
x?")
= n(0 x?") =
|
n.
Hence:
(a.25)
By
[1-F(n(x'|x?"))] = [l-F(ii(0ix?"))] = [l-F(n)].
Corollary
1,
n*(x"
|
x?")
> n*(0
|
x?").
From
the premise of the Proposition and the choice
25
of X?", n*(0 X?") >
Using
this
(a.26)
and
Vn < iL
Vn
= {x? >
7:(n,
x?")
|
and (a.26) imply
S(x
px? e C
I
oo
I
[Vx? €
C
:
I
& S(x
=> [S(0 0) > S(x
(ii)
only types n > n will
3,
make
a takeover bid.
|
|
x?")
= 0;
x?")
=
|
>
x?")
that S(x"
X?),
7i(n,
|
X = X?}
7t(n,
1
7t
=n
-
m;
x?").
> S(0
x?")
x?")
|
x?"). Therefore,
|
0.
now two cases:
X? <
:
> S(0
X?)
7i(n,
x"
7t(n,
I
I
=
X?")], 7i(n, x"
I
> n*(0 X?"),
Let X = X?. There are
(i)
x"
n*(0
(n,
(10), (a.25)
C
an argument of section
(8):
Vn €
Given
By
n-
I
X? <
=> px?" €
C
oo
:
,
X?'
I
X?)],
S(x
<
check
this last inequality, recall
0) >
(Proposition
1),
X?)
I
m < ii(0
I
oo
= S(0
!
x?)]
by Proposition
X?) > S(0
& S(0
1
0)
|
x?)]
> S(x'
V(m) < W(y*(0
i
0)
<
oo
3;
|
I
0),
X?')],
|-)
Lemma 4
and S(0 0) > m.
|
by hypotiiesis. Hence, by
and n*(0 0) > m.
|
by
||
(6)
To
and y*(0
26
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
|
x?). In this appendix,
we justify
our
claim with an example.
In the interests of computational simpUcity,
violated in the example:
The example
therefore
viz.
the support of F
shows
that the
main
is
some
not the whole real Une, and
satisfy all the
assumptions of the
text,
and which are
W^
is
are
zero at x = y =
F and
the outside utility
arbitrarily closely
W,
F
be uniform on the closed interval [-2,2], and assume the manager's type
is
m = 0.
Let
V(m)=1.57,
W(x+y, X? m) = 2-[x+y]1^2
.
I
c(y)
For
=
[x?2]/2
3U(x
I
x?)/3x?|j^_j^'7
incumbent's
utility
specification,
we
=
0, that is, the
function
U(x
|
I
0)
= 1.3623
U(x x?*)= 1.3766
I
aU(x
I
concave. Denote by x?* the point where
incumbent's unconstrained optimizing choice of x?. The
x?)
is
as defined in equation (9)
of the
Given
text.
obtain the following results, illustrated in Figure B.l.^^ For*'
X?* = .35
U(0
+ m,
(2/3)y(3/2).
this specification, U(-|-) is strictly
x?)/ax?|j^^x?* = 0-0
that
approximated by the
functional forms exploited in the example.
Let
0.
does not depend on these
result (Proposition 4)
assumptions. Also, there are choices of the distribution function
do
model
technical assumptions of the
•
;
this
"ger:
27
For the shareholders:
S(0 0) = 0.2592
I
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
0)
1
> S(x x?*) > S(0 x?*) holds, and S(x x?*)
1
|
|
is
outcome
the
by the second inequality, shareholders are worse off if they
if
they approve
their starting value
In this example, at
S(0
x = x? =
|
it,
but by the
first inequality,
reject the
outcome S(x x?*)
|
is
0).
0:
aU(x x?)/9x?|x=x?=0 = 0-^^^ >
°'
dS(x x?)/ax?|x=x?=0 = 0024 >
0,
I
I
^<^
so both the manager and the shareholders prefer a
manager's most-preferred x
the final
for
is strictly
strictly positive
x to x =
However, the
0.
greater than the shareholders'.
[HGURE B.l ABOUT HERE]
Notice
that, for this
parameterization, the manager's unconstrained optimal choice of
anticipatory de'^-nse, x?*,
is
the manager's unconstrained
constrained
low enough
that the constraint,
|
x?)
> S(0
optimum were approximately 0.4 or above
optimum x?* would be approximately
this alternate result
S(x
.39,
by raising V(m), the incumbent's
where S(x x?) = S(0
|
utility for
we
management
-'ould introduce the
fi.
convention
Uemately, as described
Remark 4 of Appendix
that,
at the
when
|
does not bind.
If
example, then the
x?).
(We can
obtain
current employment.) In this
To ensure
indifferent, shareholders
that
x?
is
always vote with
end of section 3 (and justified more formally
A), the manager can reduce his request x? by e >
preference by the shareholders.
x?),
in this
circumstance, shareholders are indifferent between approving or rejecting.
accepted
|
to induce strict
in
Figxire B.l
U, S
U(x
X?*
I
X?)
X,
X?
28
Footnotes.
1.
DeAngelo and Rice (1983) provide
2.
This type of "take
context by
3.
it
or leave
Romer and Rosenthal
The use of the term
it"
agenda control has been extensively studied
somewhat from
impounded
only a technical convenience; a claim
we justify
For example, the uniform, normal,
the usual game-theoretic concept Here,
of the firm. In contrast
into the value
useage, managers of the same "type" can have different
4.
in a political
(1978, 1979).
"type" differs
"type" indicates a skill level, as
a thorough discussion of these hypotheses.
via the
utilities.
to conventional
Further, allowing infinite
m is
worked example of Appendix B.
gamma and exponential distributions
all satisfy this
restriction.
5.
This structure
6.
To make
7.
The
is
similar to that used in
the bidding-cost explicit,
distinction
we make between
Grossman and Hart (1980).
we would have
anticipatory
former are voted by shareholders while the
to write [l-F(m+e)]: this
adds nothing.
and responsive takeover defenses,
latter are not, is
an abstraction.
It is
that the
a useful one for our
purposes, and does not do violence to empirical reality.
8.
The
level of
role of the assumption that lim.y_^Q c'(y)
=
0, is to insure that
y will always be chosen by the manager, whatever the value of
use the calculus in our analysis. Without the assumption,
explicitiy: this
adds very
little
on the cost function being
make
9.
and does not substantively
strictly
convex
in
y
is
we have
alter
x.
some
strictly positive
Consequently,
to consider the
our main
results.
not essential for our results.
It
we can
comer case
Similarly, insisting
does, however,
the arguments cleaner.
Although the model
is
not explicitiy game-theoretic,
it
can be reformulated as an
extensive-form
game
of credibility
simply that of (subgame) perfection (Selten, 1975).
is
in
which the manager. Nature and the shareholders are players. The concept
10. In the explicit game-theoretic formulation (see fn.9), in equilibrium shareholders
29
necessarily accept a take-it-or-leave-it offer
Note
that both managerial proposals
1 1.
The
when
indifferent (see, e.g.,
and acquirers' bids are such
derivations of these results are available
Banks
& Gasmi,
offers.
from the authors upon request.
1987).
30
References
Banks,!, and GasmiJF., Endogenous agenda formation in three-person committees, Forthcoming
in Social
Choice and Welfare (1987).
DeAngelo,H. and RiceJE., Antitakeover charter amendments and stockholder wealth, J.Financial
Economics
11
(1983)329-360.
Easterbrook.F. and FischelJ)., Voting in corporate law,
J.Law and Economics 26 (1983)
395-427.
Grossman, S. and Hart,0., Takeover
bids, the free-rider problem,
and the theory of the
corporation. Bell J.Economics, Spring (1980) 42-64.
Jarrell,G.
and Bradley >!., The economic
and
state regulations
of cash tender
J.Law and Economics 23 (1980) 371-407.
offers,
Jarrell.G.,
effects of fec.ral
Poulsen,A. and Davidson,L., Shark repellents and stock prices: the effects of
antitakeover
amendments
since 1980,
mimeo, Ofilce of the Chief Economist,
SEC
(1985).
Linn,S. and McConnell,!.,
on common stock
An
empirical investigation of the impact of 'antitakeover'
prices, J.Financial
Romer.T. and Rosenthal Jl.,
Economics
amendments
11 (1983) 361-399.
Political resource allocation, controlled
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by direct democracy. Quarterly J.Economics 93 (1979) 563-587.
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in extensive
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4953 045
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