Reputation Turnaround, Negotiated Block Trade, And Endogenous Cost Of Corporate Control

Description
During this brief paper in regard to reputation turnaround, negotiated block trade, and endogenous cost of corporate control.

Reputation Turnaround, Negotiated Block Trade, and
Endogenous Cost of Corporate Control
?
Pak Hung Au Yuk-fai Fong
Division of Economics
School of Humanities and Social Sciences
Nanyang Technological University
[email protected]
Department of Economics
Hong Kong University of Science & Technology
[email protected]
Jin Li
Kellogg School of Management
Northwestern University
[email protected]
June 2015
Abstract
Reputation is a valuable asset to ?rms, yet the impact of corporate governance of reputation-
reliant ?rms is underexplored. This paper investigates how a ?rm’s reputation in the product
market responds to a change in its controlling shareholder, and derives the optimal ?rm owner-
ship and control structure. We consider a dynamic model of an experience-goods ?rm, in which
a controlling shareholder actively engages in management, and the controlling share block can
be traded through private negotiation. In the optimal equilibrium, the ?rm’s reputation in the
product market is linked to its behavior in the market for corporate control to provide proper
incentive for the controlling shareholder to maintain a good ?rm reputation. Our analysis also
identi?es an endogenous cost of corporate control, and provides a rationale for the separation
of ownership and control. We derive the optimal ownership structure and draw implications on
the dynamics of control premium.
JEL Classi?cations: L14, L15, D86
Keywords: Reputation, Turnaround, Block Trade, Endogenous Cost of Corporate Control,
Optimal Ownership Structure, Experience Goods
?
We thank Ohad Kadan, Simon Loertscher, Glenn MacDonald, Marco Ottaviani, Asher Wolinsky, and seminar
participants at City University of Hong Kong, Chinese University of Hong Kong, University of Hong Kong, the
CRES Foundations of Business Strategy Conference, the Econometric Society World Congress, the International
Industrial Organization Conference, the SAET Conference, and the Summer Workshop in Industrial Organization
and Management Strategy for useful comments and suggestions. All remaining errors are ours.
1 Introduction
Reputation is a valuable asset to a ?rm, because consumer’s purchasing decisions are often based
on their perception of the ?rm’s reputation. Consumer’s faith in the ?rm is particularly important
if some dimensions of the ?rm’s products or services are di?cult to monitor and contract upon.
A ?rm with good reputation can make more sales, charge a price premium, thus enjoy a higher
pro?t. When its reputation turns bad, it loses customers and pro?t. To build and maintain a good
reputation, the ?rm’s top executives must devote personal e?ort and spend the company’s valuable
resources into establishing a history of o?ering high-quality products. In this paper, we consider
?rms that rely on their reputation in the product market, and study how turnover of ownership and
the design of corporate governance structure can facilitate the ?rm’s management of its reputation
in the product market and through which enhances its pro?t. To the best of our knowledge, this is
the ?rst study of implications of reputation concern in the product market on the ?rm’s corporate
governance structure.
It is standard in the literature to capture reputation concern in the product market by con-
sidering a ?rm as a producer of experience goods. A product is an experience good if consumers
cannot observe its product quality at the time of purchase, but their consumption experience pro-
vides public signals about the product’s quality.
1
High-quality production is costly to the ?rm
and therefore, without proper incentive, the ?rm will shirk on its quality and rational consumers
correctly anticipated this. Klein and Le?er (1981) proposed a reputation mechanism according to
which if a ?rm continues to produce at high quality, it carries a good reputation and customers will
pay a price premium for its products; once the ?rm produces bad quality, its reputation turns bad,
and, believing that the ?rm will produce at low quality, customers punish the ?rm by either asking
for a large discount on its product or not purchasing from the ?rm at least for some time. One
implicit assumption of the reputation mechanism is that the ?rm is owned by a single shareholder
throughout the lifetime of the ?rm. When the ?rm does not have perfect control of its quality,
such punishment necessarily occurs with a positive probability on the equilibrium path, leading to
destruction of shareholder value.
In this paper, we revisit the reputation mechanism in a setting which recognizes two commonly
observed features of corporate governance: (i) in many companies there are two types of sharehold-
ers: controlling shareholders who make managerial decisions, and noncontrolling shareholders who
do not; and (ii) the controlling-share block can be traded in the market for corporate control. By
simultaneously studying the ?rm’s strategy for reputation management in the product market and
the design of its dynamic ownership structure, we obtain the following main ?ndings: (i) voluntary
turnover of controlling-share block can help turnaround a ?rm’s damaged reputation and enhance
1
Some examples of experience goods are: movies, red wines newly interoduced to the market, some consumer
durables such as a new generation of smartphone.
1
the ?rm’s long-run shareholder value, and (ii) the optimal ownership structure is the outcome
of the tradeo? between managing the controlling shareholder’s moral hazard and mitigating the
punishment from the product market.
Formally, our model is a repeated game with imperfect public monitoring augmented with
voluntary player turnover, and we solve for the perfect Bayesian equilibrium that maximizes the
total shareholder value. In the optimal equilibrium, following a bad outcome, the controlling
shareholder voluntarily sells her block of shares to a new entrepreneur through negotiation. As long
as the endogenously determined negotiated price for the shares is su?ciently low, the controlling
shareholder is su?ciently punished and the fear of punishment provide him enough incentive to
exert personal e?ort and spend company’s valuable resources to improve the product’s quality. The
low negotiated price can be sustained in equilibrium because if the controlling shareholder fails to
sell her shares, consumers would believe that the ?rm engages in high-quality production only if a
huge discount is o?ered. Since the new entrepreneur and the noncontrolling shareholders are not
responsible for the bad outcome, once the control block changes hands, customers no longer have
to punish the ?rm severely and will continue to pay a premium for the ?rm’s product. Consumers’
preferential treatment of the new controlling shareholder allows the ?rm’s damaged reputation
to be repaired through the turnover of control block. It is interesting to note that in the optimal
equilibrium, the gain from trade of the control block arises endogenously from the product market’s
di?erential treatments of the incumbent and new controlling shareholders. Another noteworthy
feature is that the incumbent controlling shareholder exits the ?rm voluntarily and she receives a
price for the share block in excess of what she could get would she stay in control of the company.
In our setting, the controlling shareholder enjoys a positive private bene?t in excess of the ef-
fort cost of managing the company and there is no other exogenous cost of corporate control. This
means that the control premium, de?ned as the di?erence in values between controlling shares and
noncontrolling shares, is positive as long as the controlling shareholder and minority shareholders
receive the same stream of income per share. However, in equilibria with turnover of controlling
share block, the control premium is not necessarily positive. The reason is that in the optimal
equilibrium with turnover of control rights, the controlling shareholder has to bear an endogenous
cost of corporate control : they have to be punished for bad outcomes on the equilibrium path while
minority shareholders do not. More speci?cally, following a bad outcome, the controlling share-
holder has to voluntarily sell her shares at a low price while the ?rm’s high pro?t is preserved. The
noncontrolling shareholders are entitled to the entire stream of high pro?ts, while the controlling
shareholder is not. This creates a wedge between the income streams o?ered by each controlling
share and noncontrolling share. When this wedge exceeds the net private bene?t of control, the
control premium becomes negative. This theoretical possibility of negative control premium is con-
trary to the conventional wisdom that shares with more control rights are valued weakly higher
than shares with less or no control rights. Our ?nding is also empirically relevant because there are
2
well documented examples of negative control premiums.
2
Moreover, our model predicts that the
control premium is lower and more likely to be negative when a ?rm is performing poorly. This
prediction is also consistent with empirical ?ndings.
3
Our model provides a rationale for partial separation of ownership and control, and sheds
light on the optimal ?rm ownership structure. In the optimal equilibrium, controlling shares are
subject to punishment in the product market when the product quality fails, but noncontrolling
shares are not. This implies that the total shareholder value can be raised by converting some
of the controlling shares into noncontrolling shares. In other words, the founder of the company
can bene?t by issuing noncontrolling shares after setting up the company. Note that despite this
bene?t of issuing noncontrolling shares, the total shareholder value does not monotonically increase
in the fraction of noncontrolling shares. As more shares are converted into noncontrolling shares,
the controlling shareholder’s incentive to exert e?ort weakens because she now receives a smaller
share of the pro?t but is required to put forth the same amount of managerial e?ort to maintain
high-quality production. In our framework, the optimal share structure is the outcome of a tradeo?
between managing the controlling shareholder’s moral hazard problem and preserving ?rm value
from product market’s punishment.
The structure of the paper is as follows. Below, we discuss the literature in economics and
corporate ?nance pertinent to our study. In Section 2, we set up our model. Section 3 analyzes
the benchmark case in which the market for corporate control is shut down. In Section 4, we study
the e?ect of negotiated block trade on the ?rm’s reputation and pro?t, and show how the product
market and the market for corporate control interact with each other in equilibrium. Section 5
discusses how our theory accounts for an endogenous cost of corporate control and implications on
control premium. In Section 6, we solve for the optimal ownership structure. Section 7 discusses
some modelling issues and generalizations. The ?nal section concludes.
1.1 Related Literature
The insight that pro?ts from future sales incentivize sellers to engage in good behavior dates back
to Klein and Le?er (1981). In their model of repeated game with perfect monitoring, when the
seller su?ciently cares about the future, there exists a (subgame perfect) equilibrium in which
buyers pay a premium to purchase from the seller if and only if the seller has always provided
high-quality goods in the past. The fear of losing the future pro?ts deters the seller from cheating
2
While many empirical studies have found that shares with voting rights are traded at a positive premium (see
Zingales (1994) for a notable example), there are plenty of examples of negative control premium. See, for example,
Chen (2004), Dyck and Zingales (2004), Kruse, Kyono, and Suzuki (2006), Lease, McConnell, and Mikkelson (1983),
Pinegar and Ravichandran (2003), and Valero, Gomez, and Reyes (2008). These studies are further discussed in
Section 5.
3
See, for example, Barclay and Holderness (1989) and Kruse, Kyono, and Suzuki (2006).
3
(by o?ering low-quality goods). If the seller does not have perfect control of quality, as it is the
case in reality, when she fails to provide high-quality goods, the reputation is sullied and she loses
the pro?ts associated with good reputation.
The notion of ?rm instead of its owner as a reputation-bearer is ?rst proposed by Kreps (1990).
He points out that even though a ?rm owner has a ?nite lifetime, she is motivated to maintain
a good ?rm reputation because when she retires and has to sell the ?rm, the buyer is willing to
pay a higher price if the ?rm has a good reputation. The theory of ?rm ownership turnover has
later been further developed by Tadelis (1999, 2002, 2003) and Mailath and Samuelson (2001) who
study secret ownership transfers of ?rms with good reputation. Contrary to Tadelis (1999, 2002,
2003) and Mailath and Samuelson (2001), our complementary theory is about publicly observable
ownership turnover of ?rms with damaged reputation.
4
Our theory also di?ers from the theories of
?rm ownership turnover mentioned above in that our model allows us to endogenize the timing of
turnover, demonstrate how ownership turnover can help turnaround a ?rm’s bad reputation, derive
the optimal ownership structure, and draw implications on the dynamics of control premium. For
a comprehensive survey of the literature on seller reputation, see Bar-Isaac and Tadelis (2008).
Our theory considers ?rms in which a dominant shareholder holds a signi?cant fraction of
total shares and the rest of shares are widely held by small investors. Empirical research on
corporate ownership concentration shows that the existence of controlling shareholders in modern
corporations, even in large and publicly-listed ones, is prevalent (see, La Porta, Lopez-de-Silane, and
Shleifer (1999) for an international study, and Gadhoum, Lang, and Young (2005) and Anderson
and Reeb (2003) for studies on U.S. ?rms). It is common for these controlling shareholders to have
control rights in excess of their cash ?ow rights and to actively participate in management. Closely
related are empirical studies on insider ownership. Holderness, Kroszner, and Sheehan (1999) ?nd
that insiders (?rm’s main o?cers and directors) on average owned 21 percent of the common stock
of a typical ?rm.
5
A motivation for large block ownership is that it is e?ective in overcoming
a free-rider problem: while overseeing ?rm operations and improving ?rm performance bene?t
all shareholders, these activities involve high personal cost. By assigning substantial cash-?ow
right to one or a few large shareholders, they have strong incentives to engage in value-improving
activities. This is the view put forth by Shleifer and Vishny (1986), and Demsetz and Lehn (1985).
6
Building on the notion that share ownership mitigates the controlling shareholder’s moral hazard,
4
There are other notable di?erences between their theories and ours. In terms of modelling, these theories rely
heavily on adverse selection, i.e., ?rm owners abilities are hidden information. Also, the owners’ exit decisions are
exogenous, and ?rm’s performance does not improve following ownership transfer. In sharp contrast, our model is a
purely one of moral hazard. Moreover, in our model, a controlling shareholder exits following bad performance and
the ?rm’s performance is expected to improve under the new controlling shareholder.
5
See also Mikkelson and Partch (1989) for related ?ndings.
6
In this paper, we abstract away from the strategic interaction among multiple blockholders by assuming there is
a single controlling shareholder. This allows us to simplify the analysis and focus on the relationship between ?rm
reputation and turnover of the control block.
4
we introduce a novel bene?t of separation of ownership and control and derive the optimal ownership
structure in our setting.
In his seminal article, Manne (1965) suggests that the market for corporate control can incen-
tivize incumbent managers by threatening them with the prospect of losing their job in case the
?rm is acquired following poor performance. Jensen and Ruback (1983) argue that control trans-
actions such as tender o?ers, and proxy contests are best viewed as relatively passive shareholders
choosing among competing managerial teams. In their framework, poorly performing managers are
involuntarily forced out of the ?rm, and deprived of the rent and/or private bene?t associated with
their job. Barclay and Holderness (1991) identify negotiated block trade as an important class of
corporate control transactions by presenting empirical evidence that negotiated block trade is very
often associated with extensive post-trade managerial and board turnover. They point out that
negotiated block trade is best viewed as corporate control events in which “activist stockholders....
buy control of a company and hire and ?re management to achieve a better resource utilization”.
In these studies, turnover of ownership and control improves the ?rm’s performance by making
punishment for bad outcome more severe and/or replacing poor managers with more capable ones.
While we also show that negotiated block trade can improve ?rm pro?t, turnover enhances ?rm
pro?t through very di?erent forces in our setting. In our model, the incumbent controlling share-
holder exits the ?rm voluntarily following bad performance, and the entrepreneur replacing her
is no more capable at running the business. Barclay and Holderness (1989, 1991) are the ?rst
systematic empirical studies of negotiated block trades. We discuss the connection between their
empirical ?ndings and our model’s predictions in Section 5. For a comprehensive survey of block
ownership and transaction, see Holderness (2003).
The most frequently cited bene?ts of separation of ownership and control include management
specialization, risk-sharing, and liquidity constraint (Fama and Jensen (1983) and Shleifer and
Vishny (1997)). By taking into account the management of reputation in the product market, we
identify an underexplored bene?t in separating ownership and control. The bene?t arises because
turnover of control allows punishment to be targeted on the controlling shareholder and the ?rm’s
damaged reputation to recover in a less costly way. As a result, noncontrolling shares can enjoy a
higher pro?t stream, and the total shareholder value can be higher if a ?rm has a larger fraction of
outstanding noncontrolling shares. Finally, our analysis of optimal ownership structure is related
to Zingales (1995), which investigates how the original ?rm owner can maximize proceeds from the
sale of the ?rm by ?rst selling a fraction of cash-?ow rights in a competitive IPO market, and then
directly bargaining with a new owner. While his model and ours share some common features, the
objectives of the analyses are markedly di?erent. His model studies how the original owner can best
utilize the di?erence in his bargaining powers in the IPO market and the corporate control market
in order to extract the increase in ?rm pro?t and/or private bene?t of control by the new owner.
In contrast, our model’s objective is to analyze the ownership structure that minimizes the impact
5
of product market punishment on ?rm value while providing proper incentive for the controlling
shareholder in maintaining a good ?rm reputation.
2 Model
Players Time is discrete and in?nite, t = 1, 2, .... There are three kinds of players in the game:
entrepreneurs, customers, and investors. All players share the same discount factor, ? ? (0, 1),
across periods. There is a continuum of anonymous customers of measure one. The market is
served by a monopoly ?rm possessing a technology of producing an experience goods, i.e., goods
of which the quality cannot be observed at the time of purchase. The monopoly ?rm is owned by
one entrepreneur who has full control rights over the ?rm’s business decisions, and a continuum
of anonymous investors who own the company’s shares but have no control rights. We call the
entrepreneur with control rights the controlling shareholder and the other investors the noncon-
trolling shareholders. Denote the fraction of shares owned by the controlling shareholder by ?, and
the remaining fraction, 1 ??, is owned by the non-controlling shareholders. For now, ? is assumed
to be ?xed and exogenous, but in Section 6, we will endogenize ? by considering it as optimally
chosen by the founder of the company. The share structure ? and the identity of the controlling
shareholder are perfectly observable to all players.
Production Technology In every period, t, the production technology may yield two possible
outcomes, y
t
? {0, 1}, with each outcome representing the utility received by customers upon
consumption. The realization of the outcome is publicly observable and perfectly correlated among
customers consuming the goods in period t. The probability of each outcome depends on both the
monetary production cost the ?rm incurs, c
t
? {c
H
, c
L
}, and the controlling shareholder’s e?ort
choice in monitoring and managing, e
t
?
_
e
H
, e
L
_
, and we assume
7
1 > Pr
_
y
t
= 1|e
t
= e
H
? c
t
= c
H
_
? p > q ? Pr
_
y
t
= 1|e
t
= e
H
? c
t
= c
H
_
> 0.
While c
t
is born by all shareholders, both c
t
and e
t
are chosen by the controlling shareholder.
Both c
t
and e
t
are unobservable by consumers. Since p < 1 and q > 0, this is a game of imperfect
public monitoring. E?ort and monetary costs are perfect complements in the sense that both have
to be high to result in a high likelihood of a good outcome; neither e
H
nor c
H
alone will result in
high likelihood of good outcome. When e
t
= e
H
and c
t
= c
H
, we say the ?rm engage in high-quality
production, even though doing so does not guarantee high quality; otherwise, we say it engages in
low-quality production. We assume that quality improvement is socially e?cient:
e
H
+ c
H
?
_
e
L
+ c
L
_
< p ?q.
7
We do not include both e?ort cost and monetary cost purely for realism. Corollary 3 and the discussion preceding
that make it clear that c
H
?c
L
and e
H
?e
L
a?ect the ?rm’s optimal ownership structure di?erently.
6
The interpretation of the production technology is that quality improvement requires purchasing
expensive production inputs and providing incentives for workers (who are not explicitly modelled
here). To implement high-quality production, it is also necessary for the controlling shareholder
to engage in e?ortful management and monitoring. The assumption of perfect complementarity is
made for simplicity.
Payo?s Denote the price the ?rm charges by P
t
. Denote the (normalized) values of each unit
of controlling shares and noncontrolling shares in period t by V
t
and U
t
, respectively. A customer
buying from the ?rm receives an instantaneous payo? of
Pr (y
t
= 1) ?P
t
.
The controlling shareholder receives fraction ? of the ?rm’s pro?t and incurs e?ort cost e
t
. We
assume she also receives an exogenous private bene?t of control, B.
8
Our assumption that the
private bene?t is independent of ? is in line with the model in Zingales (1995). When all customers
buy from the ?rm, her total payo? in period t is
?V
t
= B ?e
t
+ ? (P
t
?c
t
) .
Noncontrolling shareholders simply receive fraction (1 ??) of the ?rm’s pro?t:
(1 ??) U
t
= (1 ??) (P
t
?c
t
) .
We assume that B?e
L
> B?e
H
> 0 so that when the controlling shareholder and noncontrolling
shareholders receive the same stream of income per share, the net bene?t of controlling the company
is positive regardless of the controlling shareholder’s e?ort.
9
Furthermore, we assume p ? c
H
>
q ? c
L
? 0. This assumption ensures that even if customers hold the most pessimistic belief that
the ?rm engages in low-quality production forever, the ?rm can still earn a nonnegative pro?t, thus
the values of both kinds of shares remain nonnegative.
10
Turnover of Controlling Shareholder We model negotiated trading of the controlling share
8
If the private bene?t is partly derived from appropriating shareholders’ pro?t, then we have
?Vt = B ?et + ?(Pt ?ct ?b); Ut = Pt ?ct ?b
for some b ? B. The analysis will not be qualitatively a?ected in this alternative setup. To see this, de?ne
ˆ ct ? ct + b. Then we can express the payo?s in the form as in our model:
?V
t
= B ?e
t
+ ?(P
t
? ˆ c
t
); U
t
= P
t
?c
t
.
9
It will be clear that in the context of our model, these two types of shareholders will receive the same stream of
income when ownership turnover is not allowed or when consumers treat the incumbent controlling shareholder and
new controlling shareholder symmetrically. However, when ownership turnover is allowed, they may not receive the
same stream of income.
10
This assumption simpli?es the analysis without a?ecting the main message.
7
block in the following way: every period an entrepreneur arrives and may purchase the entire block
of shares from the incumbent controlling shareholder. After the purchase, the entrepreneur becomes
the new controlling shareholder of the ?rm. If acquisition does not take place in a period, the
potential acquirer exits forever. When acquisition takes place, it is publicly observable. However,
the actual transfer price can neither be publicly observed nor credibly disclosed by the transacting
parties.
11
We assume that the transaction price is determined by Nash bargaining, and we denote
the incumbent’s bargaining power by ? ? (0, 1).
12
Timeline The following ?gure illustrates the timeline within each period:
Finally, we assume that if there are transfers between the controlling shareholder and noncon-
trolling shareholders, such transfers can neither be publicly observed nor credibly disclosed by the
transacting parties. If any transfer between the controlling shareholder and any noncontrolling
shareholder is creating any value, we assume that the value will be fully captured by the control-
ling shareholder. In other words, the controlling shareholder has 100% bargaining power over the
noncontrolling shareholders.
13
The main objective of our analysis is to characterize the optimal equilibrium of the game. We
de?ne the optimal equilibrium as the perfect public equilibrium (PPE) that maximizes the total
11
If the transaction price of the controlling share block is observable, then a low equilibrium price can be easily
enforced by consumers’ belief that the new owner will engage in high quality production if and only if the transaction
price is su?ciently low.
12
It is quite natural to assume that the incument’s bargaining power is less than 1. Zingales (1995) also makes a
similar assumption.
13
The role of this assumption is to rule out the use of transfer between controlling and noncontrolling shareholders
as a punishment device for bad outcome.
8
(normalized) shareholder value:
S = ?V + (1 ??) U.
It will become clear in Section 6 that S is also the value of the company to the founder if she
can sell noncontrolling shares to perfectly competitive investors. Note that the total shareholder
value is bounded from above by S := B +p ?
_
e
H
+ c
H
_
, which is achieved when the ?rm engages
in high-quality production every period and consumers pay p every period. The lower bound of
the total shareholder value is S := B + q ?
_
e
L
+ c
L
_
, which is achieved when the ?rm engages
in low-quality production every period and consumers pay q every period. We are particularly
interested in the condition under which the ?rm can achieve the highest possible total shareholder
value. Before proceeding with our characterization, we consider the benchmark in which the market
for corporate control is shut down, i.e., transfer of the controlling share block is not feasible.
3 Benchmark Case: No Transfer of Controlling Share Block
In this section, we consider the case in which there is only one player who can be the controlling
shareholder, i.e., the ?rm’s control rights cannot be transferred. The purpose of this section is to
show that any equilibrium in which the ?rm engages in high-quality production necessarily entails
the destruction of the ?rm’s pro?t. We show that when ownership turnover is not allowed, the
optimal equilibrium yields a total shareholder value strictly less than the theoretical upper bound,
i.e. S < S, the ?rm pro?t (which is also the value per noncontrolling share) is strictly less than
p ?c
H
, and the value of each controlling share is strictly less than p ?c
H
+
_
B ?e
H
_
/?.
First note that the controlling shareholder has the option of perpetually engaging in low-quality
production and selling the product at P
t
= q. When the controlling shareholder exercises this
option, each noncontrolling share receives a ?ow payo? of q ?c
L
and each controlling share receives
_
B ?e
L
_
/? +
_
q ?c
L
_
> 0. Also note that our assumption that each individual consumer has zero
measure and is anonymous implies that the ?rm may not charge higher than the expected value of
the product, i.e., P
t
? p. We do not impose a lower bound on P
t
in the formal analysis.
Recall that V and U are the per-unit market values of the controlling and noncontrolling shares,
respectively. When the controlling shares cannot be traded, both the controlling and noncontrolling
shareholders receive the present discounted value of the ?rm’s pro?t stream and the values of the
two classes of shares di?er only due to the private bene?ts and e?ort costs:
V = U +
B ?e
H
?
> U.
In other words, there is a positive control premium of
_
B ?e
H
_
/?.
Let W be the (normalized) market value per controlling share following a bad outcome. If
9
W is strictly less than V , it is attained by the ?rm giving a su?ciently deep discount for one
period.
14
To ensure that the controlling shareholder is willing to o?er the required discount, any
deviation will trigger the o?-the-equilibrium-path on which consumers believe the ?rm perpetually
engages in low-quality production. Notice that every time the controlling shareholder is punished,
the noncontrolling shareholders are punished to the same extent on a per-share basis.
The value of each controlling share, V , is given by
?V = (1 ??)
_
B ?e
H
+ ?
_
P ?c
H
_¸
+ ? (p?V + (1 ?p) ?W) .
Since U and V di?er only by a constant, both U and V increase in W. To induce e?ort, the
following incentive constraint is needed:
?V ? (1 ??)
_
B ?e
L
+ ?
_
P ?c
L
_¸
+? (q?V + (1 ?q) ?W) . (1)
Combining the two to eliminate V , we obtain
(1 ??)
_
B ?e
H
+ ?
_
P ?c
H
_¸
+ ? (1 ?p) ?W
? (1 ??p)
?
(1 ??)
_
B ?e
L
+ ?
_
P ?c
L
_¸
+ ? (1 ?q) ?W
? (1 ??q)
.
(2)
One immediate observation is that since 1/ (1 ??p) > 1/ (1 ??q), for any given W, the incentive
constraint is easier to be satis?ed with a higher P. Setting a higher P also raises both U and V .
Therefore, in the optimal equilibrium, P = p.
For the analysis to be nontrivial, it is necessary that the moral hazard problem is not too severe.
Speci?cally, we need
e
H
?e
L
+ c
H
?c
L
?
(p ?q)
2
1 ?q
. (3)
We will adopt this assumption throughout the paper. Since (p ?q)
2
/ (1 ?q) < p ? q, (3)
implies our earlier assumption that quality improvement is socially e?cient. In fact, it means that
the e?ciency gain from quality improvement must be large enough for high-quality production to
be sustainable.
The proposition below states the result of this section formally.
Proposition 1 Let
¯
V
0
(?) be the maximum equilibrium value per controlling share,
¯
U
0
(?) be the
maximum equilibrium value per noncontrolling share, and
¯
S
0
(?) be the maximum equilibrium total
14
An alternative punishment is that with a certain probability consumers coordinate to believe that the ?rm forever
engage in low-quality production in the future.
10
shareholder value. Suppose (3) holds and
? > ? ?
(1 ?q)
_
e
H
?e
L
_
(p ?q)
2
?(1 ?q) (c
H
?c
L
)
.
(i) If
? ?
ˆ
? (?) ?
e
H
?e
L
+ ?
_
c
H
?c
L
_
q (e
H
?e
L
+ ? (c
H
?c
L
)) + ? (p ?q)
2
,
then the equilibrium share values are given by:
¯
V
0
(?) =
B ?e
H
?
+ p ?c
H
?
1 ?p
p ?q
_
e
H
?e
L
?
+ c
H
?c
L
_
,
¯
U
0
(?) = p ?c
H
?
1 ?p
p ?q
_
e
H
?e
L
?
+ c
H
?c
L
_
,
¯
S
0
(?) = B ?e
H
+ p ?c
H
?
1 ?p
p ?q
_
e
H
?e
L
?
+ c
H
?c
L
_
.
(ii) If ? <
ˆ
? (?), then
¯
V
0
(?) =
B ?e
L
?
+ q ?c
L
,
¯
U
0
(?) = q ?c
L
,
¯
S
0
(?) = B ?e
L
+ q ?c
L
.
Clearly, when the discount factor is too low, i.e., when ? <
ˆ
?(?), high-quality production will
not be sustainable. Proposition 1 points out that even when the discount factor is high enough, i.e.,
when ? ?
ˆ
?(?), the monopolist is still unable to charge consumers the expected value of its product
every period. This is due to the fact that the ?rm can only charge consumers their reservation value
p during the normal phase; whenever the ?rm has produced at the low quality, which happens with
a positive probability, it has to o?er consumers a discount even if they continue to produce at high
quality. This loss in pro?t is similar in nature to the loss in pro?ts of collusive oligopolies under
imperfect public monitoring identi?ed by Green and Porter (1984).
Focusing on the case of ? ?
ˆ
? (?), the ?rst term
_
p ?c
H
_
in
¯
U
0
(?), is the expected accounting
pro?t of the ?rm if the ?rm always operates in the absence of an agency problem. Similarly, the
?rst term in
¯
V
0
(?) is the sum of the same expected accounting pro?t and the net private bene?t
per share. The second terms in
¯
U
0
(?) and
¯
V
0
(?) are the pro?ts that must be destroyed to provide
incentives for the controlling shareholder to improve output quality. Notice that the noncontrolling
shareholders su?er the same loss in pro?ts as does the controlling shareholder. Following a bad
outcome, the controlling shareholder must be punished or she will have no incentive to exert
11
high e?ort and incur high monetary costs to increase the chance of producing high-quality goods.
However, the punishment imposes a negative externality on the noncontrolling shareholders, who
are also punished despite the fact that they are not responsible for the bad outcome. Perhaps
more importantly, noncontrolling shareholders do not su?er from a moral hazard so it is wasteful
in terms of shareholder value to punish them for a bad outcome.
Another point worth noting is that the severity of the agency problem is related to the share
structure of the ?rm. It can be veri?ed that the cuto? discount factor
ˆ
? is decreasing in the fraction
of controlling shares, ?. Figure 2 depicts how
ˆ
? changes in ?.
When the controlling shareholder owns too few shares, i.e., when ? ? ?, there is no discount
factor at which high-quality production is sustainable. De?ne ? (?) as the solution to ? =
ˆ
? (?) for
? ? [
ˆ
? (1) , 1).
15
It is easy to see from Proposition 1 that
¯
S
0
(?) = ?
¯
V
0
(?) + (1 ??)
¯
U
0
(?) is the
lowest for ? < ? (?) and increases in ? for ? ? ? (?). The analysis so far implies that the optimal
share structure is to set ? = 1. In other words, all the shares should be owned by the controlling
shareholder. Doing so maximizes
¯
S
0
(?) and minimizes
ˆ
? (?). Note that in the optimal equilibrium,
U and V are also maximized respectively.
4 The E?ect of Negotiated Block Trade
In this section, we investigate the interplay between the product market and the market for corpo-
rate control in providing incentives for reputation maintenance. Our focus is on negotiated block
trade, and in our model, the market for corporate control works as follows: in each period, an
entrepreneur arrives and engage in private negotiation with the incumbent controlling shareholder
15
? (?) is well-de?ned on the domain [
ˆ
? (1) , 1) as
ˆ
? (?) is strictly decreasing in ? for ? ? [?, 1].
12
in acquiring the entire block of controlling shares. If negotiation yields trade, the entrepreneur
becomes the new controlling shareholder; otherwise, she exits the game forever.
Consider the following equilibrium, which consists of four phases: a normal phase, an on-the-
equilibrium-path punishment phase, and two o?-the-equilibrium-path punishment phases.
• The game begins in the normal phase. In the normal phase, the controlling shareholder
sets the price at p and engages in high-quality production, i.e., exerts e?ort e
H
and incurs
monetary cost c
H
on the ?rm’s behalf. If the outcome is good, there will be no turnover of
controlling shareholder and the game stays in the normal phase.
16
If the outcome is bad, the
game switches to the on-the-equilibrium-path punishment phase.
• In the on-the-equilibrium-path punishment phase, the controlling shareholder sells the entire
block of controlling shares to a new entrepreneur at the transaction price T through Nash
bargaining. The ?rm under the new controlling shareholder may or may not have to o?er
the good at a discounted price. The new controlling shareholder engages in high-quality pro-
duction in the on-the-equilibrium-path punishment phase and receives a continuation payo?
ˆ
W. The game switches back to the normal phase if the outcome is good but stays in the
on-the-equilibrium-path punishment phase if the outcome is bad.
• If the Nash bargaining breaks down, then the game switches to the ?rst o?-the-equilibrium-
path punishment phase in which the incumbent controlling shareholder continues to engage
in high-quality production and o?ers a one-period discount to customers for the experience
good, receiving a continuation payo? W.
• Any other publicly observable deviations, including a deviation from the above-mentioned
punishment phases, will trigger the second o?-the-equilibrium-path punishment phase in
which the controlling shareholder forever engages in low-quality production and sets price
equal to q.
In the search of the optimal equilibrium, it is without loss of generality to focus on the class of
equilibria outlined above. In our model, there are only two feasible ways of imposing punishment
on the controlling shareholder for bad outcomes: (i) a cut in its product price(or equivalently
coordinating on a certain probability of forever reverting to the low-quality-low-price equilibrium);
and (ii) an outright sale of controlling shares to the newly arrived entrepreneur at a discounted
16
In Section 5, when we analyze the company’s control premium, we will discuss a payo? equivalent equilibrium in
which turnover also takes place following a good outcome.
13
price.
17,18
In the benchmark analysis in the section above, we focus only on the product market
punishment (i). In what follows, we shall show that as long as high-quality production can be
supported, the total shareholder value can be improved relative to the benchmark case when both
the product market and the market for corporate control (i.e., punishment (ii) above) are involved.
We ?rst explain how the transaction price of the control block is determined. Recall that
W is the value of a controlling share in the ?rst o?-the-equilibrium-path punishment phase, i.e.,
when the control block is retained by the incumbent controlling shareholder, and that
ˆ
W is the
corresponding value when ownership is transferred to the new entrepreneur. The incumbent and
the new entrepreneur engages in Nash bargaining in which the bargaining power of the incumbent
is ?. Thus, the transaction price per share, T, is given by
T = W + ?(
ˆ
W ?W). (4)
To account for the value of a controlling share V , a shortcut is to imagine hypothetically
that every time a bad outcome arises, the controlling shareholder, instead of realizing the loss of
? (V ?T) by selling her block of shares, realized the loss of ? (V ?T) but then continued to hold on
to the controlling shares. With this interpretation, the value per controlling share can be expressed
as
V =
B ?e
H
?
+
_
p ?c
H
_
?? (1 ?p)
V ?T
1 ??
. (5)
To account for the value of a noncontrolling share U, notice that the company’s pro?t per share
loses the amount V ?
ˆ
W every time a bad outcome is realized and the control block subsequently
changes hands. Both the new controlling shareholder and the noncontrolling shareholders su?er
the same loss. Therefore,
U =
_
p ?c
H
_
?? (1 ?p)
V ?
ˆ
W
1 ??
. (6)
We show in the following proposition that by allowing the turnover of the controlling shares,
the value of the noncontrolling shares can be increased and the highest possible value of the non-
controlling shares, p ? c
H
, can be attained if the discount factor is large enough. Recall we fo-
cus on the optimal equilibrium, i.e., the equilibrium that maximizes the total shareholder value,
S = ?V +(1 ??) U. Let
¯
U and
¯
V be the values of noncontrolling shares and the controlling shares
in the optimal equilibrium, respectively.
17
Here, the sale of controlling shares must be outright simply because ? is assumed to be ?xed. If we do not assume
? is ?xed, the optimal relational contract may require only a partial sale of controlling shares to the newly arrived
entrepreneur while the remaining controlling shares are sold as non-controlling shares to outside investors. However,
the optimal relational contract always requires an outright sale of controlling shares when ? is chosen optimally by
the founder of the company, the case we analyze in Section 6.
18
Transfers between controlling shareholder and noncontrolling shareholders cannot be used to punish the incum-
bent controlling shareholder for bad outcome because it is assumed that the amount of transfer cannot be credibly
disclosed publicly and that the incumbent controlling shareholder has full bargaining power over the noncontrolling
shareholders.
14
Proposition 2 Suppose (3) holds, ? > ?, and ? ? (0, 1). For each ?, there exists
˜
? (?, ?) ?
_
ˆ
? (?) , 1
_
such that
(i) if ? ? [0,
ˆ
? (?)), then
¯
U = q ?c
L
and
¯
V =
¯
U +
B ?e
L
?
;
(ii) if ? =
ˆ
? (?), then
¯
U =
¯
U
0
(?) and
¯
V =
¯
V
0
(?) ;
(iii) if ? ? (
ˆ
? (?) ,
˜
? (?, ?)), then
¯
U ? (
¯
U
0
(?) , p ?c
H
) and
¯
V =
¯
V
0
(?) ;
(iv) if ? ? [
˜
? (?, ?) , 1), then
¯
U = p ?c
H
and
¯
V =
¯
V
0
(?) .
According to Part (i) of Proposition 2, if high-quality production is not sustainable in the
absence of the market for corporate control, then allowing turnover of control block cannot increase
?rm pro?ts. This is because turnover of control block cannot change the fact that the worst possible
punishment payo? to the controlling shareholder is B ?e
L
+?
_
q ?c
L
_
and that such punishment
is not enough to incentivize her. However, Parts (ii)-(iv) of the proposition suggest that as long
as high-quality production is sustainable in the original game without turnover, then turnover can
improve the noncontrolling shareholders’ value and such improvement is increasing in ?. When ?
is su?ciently high, speci?cally when ? ?
˜
? (?, ?), noncontrolling shares attain the maximum value
of p ?c
H
. Figure 3 depicts what the cuto?
˜
? (?, ?) looks like.
15
Several remarks about the proposition and the optimal equilibrium are in order. First, although
the controlling shareholder’s equilibrium payo? remains unchanged, and in both cases she earns less
than B?e
H
+?
_
p ?c
H
_
, there is a notable di?erence in the way she earns that payo?. When the
turnover of control block is not allowed, the controlling shareholder earns the net private bene?t
and her share of the ?rm’s stream of pro?ts, which is less than p ? c
H
per period, because the
?rm has to o?er a price discount to customers in the period following every bad outcome. On
the other hand, with a turnover of control block, the controlling shareholder does not capture the
entire stream of ?rm pro?ts because, once a bad outcome is observed, she is prescribed to sell her
controlling shares at the discounted price. This observation is closely connected to the discussion
on endogenous cost of corporate control discussed in the next section.
Second, in the optimal equilibrium, the incumbent controlling shareholder exits voluntarily.
Were she stays in the ?rm with a damaged reputation, the product market would impose a very
severe punishment on the ?rm, leading to a very low continuation payo? to her. She is thus
willing to sell her control block as long as the transaction price ?T exceeds the continuation payo?
?
ˆ
W. This is possible because the new entrepreneur is not responsible for the bad outcome of the
company, and is not going to be subject to the product market punishment. As a result, her value
for the control block exceeds that of the incumbent. In our terminology, we have ?
ˆ
W > ?W. It
is important to note that the product market’s reaction to the change in controlling shareholder
is NOT exogenously imposed. It is an equilibrium response: customers take optimal action given
their belief, which is consistent with strategy employed by the controlling shareholders.
Third, both the product market and the market for corporate control impose punishment on
a poorly performing controlling shareholder when ? ? (
ˆ
? (?) ,
˜
? (?, ?)).
19
In this case, because the
incumbent enjoys a relatively high bargaining power over the new entrepreneur, she is able to
capture a larger fraction of the gain from trading the block. In order to make the magnitude of
punishment on the incumbent su?ciently large, it is necessary that the new entrepreneur receives
a low enough continuation payo? after taking over the ?rm. Thus, the ?rm will still su?er a phase
of low pro?t under the new leadership. However, the magnitude of this pro?t loss is lower than in
the benchmark case where the market for corporate control is absent.
Last but not least, our theory predicts that turnover of top management is more likely to occur
when the ?rm has performed poorly and the turnover leads to an improvement in ?rm performance.
This prediction is consistent with the empirical ?ndings that CEO/ownership turnover is more
frequently preceded by poor company performance, and that oftentimes the replacement of the
CEO and/or a change in the ownership and the board directors results in successful turnarounds.
20
19
As we will show in Section 6 below, this is sometimes the relevant parameter case when the ownership structure,
i.e., the value ?, is chosen optimally to maximize total shareholder value.
20
See, for example, Barclay and Holderness (1989, 1991), Goodstein and Boeker (1991), Kaplan (1994), Martin
and McConnell (1991), and Volpin (2002).
16
Our model is also able to account for the empirical studies that have found that strategic change is
often not an integral part of turnaround (for example, see Hambrick and Schecter (1983), Robbins
and Pearce II (1992), and Kanter (2003)). Another noteworthy feature of the equilibrium, distinct
from existing management theories, is that even though the new controlling shareholder is no better
at running the company than the incumbent controlling shareholder, we still see an improvement
in the ?rm’s performance following an ownership turnover.
21
The theory proposed here therefore
provides an explanation for change in control even in those cases in which “the potential bene?ts
from changing blockholders are less apparent” (Barclay and Holderness (1991)).
In the remainder of this section, we discuss the model’s implication on the relationship between
the acquisition premium and the post-acquisition performance of the company. Acquisition premi-
ums involved in mergers and acquisitions are often sizeable, so those involved in these activities are
naturally interested to know whether a higher acquisition premium is associated with a better post-
acquisition performance. Traditional management theories suggest a positive relationship between
the acquisition premium and the post-acquisition performance. This is because a manager who is
more capable or has identi?ed a higher value in the target company is willing to pay a higher ac-
quisition premium and the company is also expected to perform better. However, this view cannot
account for the negative relationships between the acquisition premium and the post-acquisition
performance identi?ed in some empirical studies (see for example, Sirower (1994), and Krishnan,
Hitt, and Park (2007)).
Here, we hold ?xed other parameters and study how changes in the bargaining power of the in-
cumbent, ?, a?ects the transfer price and the ?rm’s pro?t margin immediately after the acquisition.
Recall that in the optimal equilibrium constructed above, following a bad outcome of production,
the block of controlling shares is sold to a new entrepreneur at a (per-share) price of T through
Nash bargaining. If ? ? (
ˆ
? (?) ,
˜
? (?, ?)), the ?rm has to o?er a price discount to customers after
the new entrepreneur takes control. Denote the associated discount by D(?, ?).
22
It is immediate
that the value of a noncontrolling share following a bad outcome, denoted by U, is below its value
during the normal phase,
¯
U:
p ?c
H
?(1 ??p) D(?, ?) = U <
¯
U = p ?c
H
?? (1 ?p) D(?, ?) . (7)
De?ne the acquisition premium as the (per-share) transaction price of the block of controlling
shares minus the value of the noncontrolling shares during a downturn, i.e., T ?U. If ? ?
˜
? (?, ?),
then the new owner does not have to o?er any discount to customers and thus
¯
U = U.
21
In our model, because a turnover of controlling shareholders always occurs after a bad outcome, on the equilibrium
path, the incumbent owner never runs the company after a bad outcome. So this is an improvement over the o?-the-
equilibrium path on which takeover does not occur. If we introduce some friction during takeover so that ownership
does not change hands immediately following a bad outcome, we will see low on-the-equilibrium-path pro?t following
a bad outcome and subsequent improvement following the takeover.
22
The exact formula for the discount can be found in the proof of Proposition 2.
17
Corollary 1 An increase in the bargaining power of the incumbent controlling shareholder ? has
the following e?ect on the ?rm’s optimal equilibrium:
(i) The acquisition premium, T ?U, weakly increases.
(ii) The ?rm’s accounting pro?t in the period after the turnover of the controlling shares, given
by p ?c
H
?D(?, ?), weakly decreases.
Moreover, if ? >
ˆ
? (?), the above relations are strict when ? is su?ciently large.
According to the corollary above, if the source of variation is di?erent allocations of the bar-
gaining power between the incumbent and new controlling shareholders, then our model predicts
a (weakly) negative relationship between the acquisition premium paid by the acquirer and the
?rm’s post-acquisition performance. One descriptive argument used by the authors who empir-
ically identi?ed this negative relationship is that a high acquisition premium is an indication of
bad managerial decision or managerial hubris so the manager also tends to make bad decisions
when running the company (for example, see Hayward and Hambrick (1997)). Our explanation
is di?erent and has more structure; in our model all managers have the same managerial ability.
The negative relationship is a necessary part of the equilibrium to ensure the incumbent controlling
shareholder with a higher bargaining power will not be overpaid so that she has the proper incentive
to maintain the company’s reputation.
5 Endogenous Cost of Corporate Control
In this section, we explore the endogenous cost of corporate control in the model. The classical theory
in asset pricing suggests that share value is determined by the present value of the company’s pro?t
stream. In our model, the role played by the holders of the shares a?ects their value. In particular,
controlling shareholder and noncontrolling shareholders are not entitled to the same pro?t stream.
An endogenous cost of control arises in our model because the controlling shareholder must be
punished following a bad outcome, while the noncontrolling shareholders either do not have to
be punished (if ? ?
˜
? (?, ?)), or they are punished less severely than the controlling shareholder
when they have to be punished (if ? ? (
ˆ
? (?) ,
˜
? (?, ?))). We will show that because of this cost of
control, although the net private bene?t per share, (B ? e
H
)/?, is positive, the control premium,
de?ned as the di?erence between the market value of a controlling share and the market value
of a noncontrolling share, may be negative. Moreover, because the punishment targeted at the
controlling shareholder takes place during di?cult times, the control premium is lower and more
likely to be negative when the ?rm is performing poorly.
For ease of exposition, in the previous section, we focused on equilibria in which controlling
shares are traded only following a bad outcome and noncontrolling shares are never traded. One
can easily construct payo?-equivalent equilibria in which both the controlling and noncontrolling
shares are traded following a good outcome. If controlling shares were traded following a good
18
outcome, the market price would be
¯
V . If noncontrolling shares were traded, the market price
would be
¯
U following a good outcome and U following a bad outcome. Denote the control premium
following a good and bad outcome by ?
H
and ?
L
respectively. Therefore, we have ?
H
?
¯
V ?
¯
U
and ?
L
? T ? U. It is clear that in our simple setting, the measurable control premium de?ned
here and acquisition premium de?ned in the previous section are identical.
Corollary 2 (i) If ? >
ˆ
? (?), then the control premium following bad outcome is lower than that
following a good outcome, i.e., ?
H
> ?
L
.
(ii) If ? >
ˆ
? (?), then there exists a B
?
> e
H
such that the control premium following good
outcome is negative, i.e., ?
H
< 0 if and only if B ? [e
H
, B
?
).
The control premium can be negative if the private bene?t of control is too small relative to the
endogenous cost of corporate control. Negative control premiums have been identi?ed empirically.
Holthausen, Leftwich, and Mayers (1987) found that in large seller-initiated block transactions,
buyers received price concessions. Barclay and Holderness (1989) found that 20% of their sample
block trades were priced at a discount. Relatedly, Lease, McConnell, and Mikkelson (1983), Pinegar
and Ravichandran (2003), Chen (2004), Kruse, Kyono, and Suzuki (2006), and Valero, Gomez, and
Reyes (2008) found that some companies’ shares with superior voting rights were traded at a
discount compared to the shares with inferior voting rights. Some informal arguments for the
observed negative control premiums are that shares with inferior control rights are more liquid
and that the controlling shareholder may have to bear legal liabilities (Dyck and Zingales (2004)).
Nevertheless, the empirical observation of negative control premiums is considered by some to be
puzzling because there is no formal theory that rationalizes it.
23
Furthermore, our theory’s speci?c prediction that the control premium is lower and more likely
to be negative during downturns is also consistent with the empirical ?nding of Barclay and Hold-
erness (1989, 1991) that the average premium is lower following poor performance, and with Kruse,
Kyono, and Suzuki (2006) that the estimated private bene?ts of control in their data are the most
negative when the target ?rm is ?nancially distressed.
6 Optimal Ownership Structure
In this section, we endogenize the ?rm’s ownership structure by ?nding the optimal value of ? from
the company founder’s perspective. The total payo? of the founder consists of two components, the
value of the shares that she retains and the proceeds from the sales of the noncontrolling shares.
We assume there is perfect competition for noncontrolling shares among investors which allows the
company founder to fully capture the value of the noncontrolling shares. Therefore, the total payo?
23
Lease, McConnell, and Mikkelson (1983), Kruse, Kyono, and Suzuki (2006) and Valero, Gomez, and Reyes (2008)
explicitly describe the observation of negative control premiums as a puzzle.
19
of the founder is S = ?V + (1 ??) U. Note that this is the total shareholder value of the company
at the time when the ownership structure is determined. However, it is less than the sum of the
net private bene?t of control and the company’s pro?t. This is because part of the value of the
company is captured through Nash bargaining by future controlling shareholders who take over the
company’s control.
The basic tradeo? here is about managing the controlling shareholder’s moral hazard problem
and preserving ?rm pro?t from product market punishment. In the presence of a corporate control
market, a small value of ? helps mitigate the moral hazard problem, as the cost of high-quality
production is lower for the controlling shareholder. This increases the value of the controlling
share block. On the other hand, if ? is small, the turnover mechanism is less e?ective in generating
punishment on the controlling shareholders, resulting in a lower ?rm revenue. To see this, note that
the smaller the value of ?, the more severe the punishment the turnover mechanism must impose
on each unit of controlling share to preserve incentives. However, because of the Nash bargaining
between the incoming and the incumbent controlling shareholders, the e?ectiveness of punishment
is limited, and a product price discount is called for when ? is su?ciently small (recall case (iii) of
Proposition 2). Moreover, this price discount is decreasing in ?.
24
Recall ? (?) is the solution to ? =
ˆ
? (?). De?ne
¯
? (?, ?) as the solution to ? =
˜
? (?, ?).
25
It is
easy to verify that for ? ?
_
ˆ
? (1) , 1
_
, ? < ? (?) <
¯
? (?, ?) (see Figure 4).
Proposition 3 Let ?
?
be the optimal fraction of the controlling shares. If ? ? [
ˆ
? (1) , 1), then
(i) ?
?
is unique and is in the interval (? (?) , min
_
¯
? (?, ?) , 1
_
]. Moreover, ?
?
?? as ? ?1.
(ii) ?
?
is weakly increasing in c
H
? c
L
, e
H
? e
L
, and ?; and it is weakly decreasing in ?.
Furthermore, the above relations are strict if ? ?
_
˜
? (?, 1) , 1
_
.
24
For the explicit formula, see (15) in the proof of Proposition 2.
25
¯
? (?, ?) is well-de?ned because
˜
? (?, ?) is strictly decreasing as a function of ?.
20
The main message of part (i) of Proposition 3 is that the optimal share structure is to convert
some controlling shares, but not as many of them as possible, into noncontrolling shares. The
comparative statics results of part (ii) arise from the tradeo? discussed above. More speci?cally, we
can break down the marginal e?ect of a reduction in ? below
¯
? (?, ?) into (a) the marginal bene?t
that arises from mitigating moral hazard; and (b) the marginal cost that arises from more severe
product market punishment. The marginal bene?t is given by
?
??
_
?
¯
V
0
(?)
_
=
1 ?p
p ?q
_
c
H
?c
L
_
;
whereas the marginal cost is given by
?
??
_
(1 ??)
¯
U
_
=
1 ?p
p ?q
?
1 ??
_
_
?
?1
_
?
?1
?q
_
?(1 ?q)
_
_
e
H
?e
L
?
2
+ c
H
?c
L
_
?(p ?q)
2
_
?
?1
?1
_
_
.
First, it is straightforward to see that an increase in e
H
?e
L
and ? raise the marginal cost without
any e?ect on the marginal bene?t, so ?
?
goes up. Second, if c
H
? c
L
increases, the marginal cost
goes up by more than the marginal bene?t, and ?
?
becomes larger.
26
Finally, if ? increases, the
marginal bene?t is una?ected, whereas the marginal cost goes down, so ?
?
becomes smaller. These
comparative statics results hold strictly whenever ?
?
< 1, or equivalently, ? ?
_
˜
? (?, 1) , 1
_
.
The analysis in this section is related to Zingales (1995), who derives the practice of selling
cash-?ow rights to disperse shareholders and selling control rights through direct bargaining as
the outcome of maximization of total proceeds from the sale of a company. Our model has the
similar feature that disperse shareholders are perfectly competitive and the acquirer of control rights
has substantial bargaining power. Other than that, our analysis is di?erent in several important
ways. In Zingales’s model, the incumbent owner goes public if and only if the incoming controlling
shareholder generates a higher pro?t for the ?rm. Furthermore, the sale of cash-?ow rights is partial
only if the incumbent derives a higher level of private bene?t than the new owner. On the contrary,
in our model, the company founder goes public and chooses selling cash-?ow rights partially even if
every potential controlling shareholder generates the same level of pro?t for the ?rm and derives the
same level of private bene?t. Our results emerge from the consideration of controlling shareholder’s
moral hazard problem and mitigating the impact of product market punishment on ?rm value, while
these factors are absent in Zingales’s analysis.
Finally, we remark that the tradeo? discussed above highlights conditions under which the
optimal ownership structure ?
?
lies strictly below min
_
¯
? (?, ?) , 1
_
, the case in which the turnover
mechanism does not perfectly restore the ?rm’s pro?t. Whether ?
?
< min
_
¯
? (?, ?) , 1
_
holds or not
26
Demsetz and Lehn (1995) and Himmelberg, Hubbard, and Palia (1999) report empirical evidence that managerial
stock ownership is larger in ?rms facing more severe moral hazard problem.
21
is determined by whether the marginal bene?t of cutting ? exceeds the associated marginal cost
evaluated at ? = min
_
¯
? (?, ?) , 1
_
. In particular, observe that if c
H
?c
L
= 0, there is no bene?t in
reducing ? below
¯
? (?, ?), whereas the marginal cost is positive, resulting in ?
?
= min
_
¯
? (?, ?) , 1
_
.
On the other hand, if e
H
? e
L
and/or c
H
? c
L
is too large, the marginal cost of cutting ? always
exceeds that of the marginal bene?t, and ?
?
= min
_
¯
? (?, ?) , 1
_
. Only if the di?erence in monetary
costs c
H
?c
L
is moderate, and the di?erence in e?ort cost e
H
?e
L
is su?ciently small, would ?
?
be strictly interior.
Corollary 3 Suppose e
H
? e
L
<
?(1??)(p?q)
2
1??q???(1?q)
. Then there exists a pair of positive numbers C,
and
¯
C with C <
¯
C such that the optimal structure ?
?
? (? (?) , min
_
¯
? (?, ?) , 1
_
) if and only if
c
H
?c
L
?
_
C,
¯
C
_
. If e
H
?e
L
?
?(1??)(p?q)
2
1??q???(1?q)
, then ?
?
= min
_
¯
? (?, ?) , 1
_
for all c
H
, c
L
.
7 Discussion
For tractability, we have abstracted away from many issues in our analysis. Below, we discuss some
of them.
Competition Among Potential Owners We have ignored the issue of competition among
potential acquirers by assuming that every period only one potential acquirer enters the game.
27
A
simple way to capture the impact of competition is to assume the bargaining power of the incumbent
controlling shareholder increases with the intensity of the competition for the control rights. In
the extreme case where competition is so ?erce that the incumbent has all the bargaining power,
i.e., ? = 1, negotiated block trade fails to act as a disciplinary device. We take the view that it is
unlikely that the incumbent has 100% of the bargaining power. Even when there are simultaneously
multiple buyers seeking control of the ?rm, as long as the incumbent owner cannot commit to a
grand mechanism (say by holding an auction), but instead has to sequentially bargain with one
buyer at a time, there are bargaining protocols with which the seller only receives a fraction of
the total surplus. Moreover, oftentimes the incumbent owner has to face competition from owners
of other companies trying to sell control rights in the market for corporate control, which limits
their bargaining power. We ?nd it comforting that for any interior split of bargaining power, i.e.,
for ? ? (0, 1), allowing turnover of controlling shareholders increases the maximum ?rm pro?t and
total shareholder value for a range of su?ciently high discount factors.
Alternative Turnaround Mechanisms We have focused on the e?ect of negotiated block
trade on turning around a damaged reputation on a ?rm’s pro?t. We have done so not because
27
If the transaction price of controlling shares is publicly observable, then competition among buyers has little
impact on our equilibrium construction. Any equilibrium transaction price of the controlling shares can be supported
by the belief that if any potential owner pays an amount other than the equilibrium price, then the new owner will
receive a continuation payo? equal to the lowest possible equilibrium payo?, supported by the consumers’ self-ful?lling
belief that the ?rm will only engage in low-quality production. This is su?cient to deter any deviation.
22
this is the only possible way to preserve ?rm value from product market punishment. Rather,
our focus is partially motivated by the fact that turnover of ownership and control is common
and empirical ?ndings that ownership and management turnover is an integral part of a successful
turnaround. In fact, if we allow the controlling shareholder to credibly burn money (for example,
by making payments to a third party), then there exist equilibria in which consumers forgive the
?rm’s bad outcome if and only if the controlling shareholder have burnt a large enough amount
of money. Requiring the controlling shareholder to burn money following every bad outcome may
cause her to eventually run into her liquidity constraint because bad outcomes are associated
with low (possibly negative) pro?ts. Even if a few bad outcomes may not cause any trouble, a
su?ciently long streak of bad outcomes, which always happens with a positive probability, will
cause the controlling shareholder’s liquidity constraint to fail and the equilibrium to unravel. By
contrast, under the turnover mechanism proposed here, the controlling shareholder will be receiving
a payment for selling the controlling shares so she will not run into her liquidity constraint.
Probabilistic Availability of New Owners and Costly Turnover In our formal analysis,
the market for corporate control is frictionless in the sense that there is a potential controlling
shareholder available to take over the ?rm’s control every period. In a more realistic setting,
following a bad outcome, there may not be any potential buyers immediately available. In this
case, on-the-equilibrium-path punishment of the ?rm will continue to take place until ownership
changes hands. This will give rise to a more natural empirical implication that when a ?rm’s
reputation is tarnished, the ?rm’s pro?tability will decrease and stay low until a new controlling
shareholder takes over.
8 Conclusion
This paper studies the corporate ?nance of ?rms whose sales and pro?t are sensitive to its repu-
tation in the product market. It analyzes how the product market and the market for corporate
control interact to provide the incentives for the ?rm’s key decision makers to put in e?ort into
maintaining a good ?rm reputation. We ?nd that turnover in the controlling share block can help
a ?rm turnaround its reputation even if all controlling shareholders has the same ability and their
departure from the ?rm is voluntary. The equilibrium property that the controlling shareholder
must be punished for bad outcomes but the noncontrolling shareholders can be spared gives rise to
an endogenous cost of corporate control. The theory’s prediction that the ?rm’s control premium
can be negative, and that it is lower after the company’s reputation is damaged, are consistent with
empirical evidence. Finally, we show that the ?rm’s founder resolves the tradeo? between manag-
ing moral hazard and preserving ?rm value by partially selling cash-?ow rights as noncontrolling
shares.
Appendix
23
Proof of Proposition 1. Plugging P = p into the incentive constraint (2) gives us
W ?
¯
W (?, ?) ?
B ?e
H
?
+
_
p ?c
H
_
?
(1 ??p)
_
e
H
?e
L
?
+ c
H
?c
L
_
? (p ?q)
. (8)
A necessary condition for the sustainability of high e?ort, i.e.,
¯
W (?, ?) ?
_
B ?e
L
_
/?+
_
q ?c
L
_
,
is given by
B ?e
L
?
+
_
q ?c
L
_
?
B ?e
H
?
+
_
p ?c
H
_
?
(1 ??p)
_
e
H
?e
L
?
+ c
H
?c
L
_
? (p ?q)
. (9)
As long as (9) is satis?ed, there exists
W ?
_
_
B ?e
L
?
+
_
q ?c
L
_
,
B ?e
H
?
+
_
p ?c
H
_
?
(1 ??p)
_
e
H
?e
L
?
+ c
H
?c
L
_
? (p ?q)
_
_
such that (8) is satis?ed. One immediate result is that B does not a?ect the sustainability of
high e?ort. This is because the controlling shareholder receives B regardless. This inequality can
be rewritten as
? ?
ˆ
? (?) =
e
H
?e
L
+ ?
_
c
H
?c
L
_
q (e
H
?e
L
+ ? (c
H
?c
L
)) + ? (p ?q)
2
.
Note that
ˆ
? (?) is decreasing in ?,
ˆ
? (0) = 1/q > 1 and
ˆ
? (1) =
e
H
?e
L
+ c
H
?c
L
q (e
H
?e
L
+ c
H
?c
L
) + (p ?q)
2
.
If
ˆ
? (1) > 1, then
ˆ
? (?) > 1 for all ? and high e?ort is unsustainable for discount factors.
Therefore, for the analysis to be nontrivial, it is necessary that
ˆ
? (1) ? 1, which is equivalent to
(3). When (3) holds, there exists ? such that
ˆ
? (?) ? 1 if and only if
? ? ? ?
(1 ?q)
_
e
H
?e
L
_
(p ?q)
2
?(1 ?q) (c
H
?c
L
)
.
For ? ?
ˆ
? (?), the maximum value of the controlling share can be obtained by plugging W =
¯
W(?, ?) from (8) into (1). Since W is enforced by a discounted price, setting W =
¯
W (?, ?) means
the ?rm gives a discount just large enough to support the incentive to engage in high-quality
production. In other words, setting W =
¯
W (?, ?) maximizes U and V , which in turn maximizes
S.
Proof of Proposition 2. (i) If ? <
ˆ
? (?), then
¯
W (?, ?) <
_
B ?e
L
_
/? +
_
q ?c
H
_
. Therefore,
there does not exists T ? [
_
B ?e
L
_
/? +
_
q ?c
H
_
,
¯
W (?, ?)]. In other words, when high-quality
24
production is not sustainable in the absence of transfer of controlling shares, allowing transfer of
these shares will not improve the performance of the ?rm because the possibility of ownership
turnover cannot lower the controlling shareholder’s continuation payo? below B ?e
L
+?
_
q ?c
L
_
.
Therefore, if ? <
ˆ
? (?), only low e?ort can be supported in equilibrium even when turnover is
allowed. Consequently,
¯
V =
B?e
L
?
+
¯
U and
¯
U = q ?c
L
.
(ii) When ? =
ˆ
?(?), in order to support high e?ort, the continuation payo? to the controlling
shareholder must be set at ?
_
q ?c
L
_
+ B ? e
L
following a bad outcome, for incentive provision.
When controlling shares turnover is allowed, it requires a transaction price of ?
_
q ?c
L
_
+ B ?e
L
to sustain e?ort. When the incumbent has positive bargaining power, this is possible only if the
surplus from the trade of controlling shares is zero, i.e. the newly arrived entrepreneur has to be
punished as severely as the incumbent after he takeovers the ?rm. Thus, the ?rm’s pro?t cannot
be increased by turnover. Consequently,
¯
U and
¯
V stay at
¯
U
0
(?) and
¯
V
0
(?) respectively.
(iii) ?(iv) In order to construct the optimal equilibrium, we look for PPE that maximizes the
total shareholder value S = ?V + (1 ??) U.
An upper bound on the equilibrium value of U in any PPE is p ?c
H
.
Equation (5), which determines the value of controlling share, V , in those equilibria with own-
ership turnover and high-quality production, can be rewritten as
V =
1 ??
1 ??p
_
B ?e
H
?
+
_
p ?c
H
_
_
+
? (1 ?p)
1 ??p
T (10)
Thus, the equilibrium value of V is increasing in the transaction price of controlling shares T,
as long as T is small enough to sustain incentive for high-quality production. More precisely, the
following incentive constraint must be satis?ed to motivate high-quality production
T ?
¯
W (?, ?) ?
B ?e
H
?
+
_
p ?c
H
_
?
(1 ??p)
_
e
H
?e
L
?
+ c
H
?c
L
_
? (p ?q)
(11)
Therefore, the maximum possible value of V in any PPE with turnover of control block and
high-quality production is given by equation (10) with T =
¯
W (?, ?). Consequently, an upper bound
on the equilibrium value of V in any PPE is
¯
V
0
(?).
Now, we show the upper bounds on U and V can be achieved if the discount factor is large
enough. This then implies that when the discount factor is large enough, the optimal equilibrium
yields
¯
U = p ?c
H
and
¯
V =
¯
V
0
(?).
First, in order for the controlling share to achieve the value
¯
V
0
(?), we have to set T =
¯
W (?, ?).
Next, recall
ˆ
W is the value of controlling shares to the new controlling shareholder following an
ownership turnover. Suppose high-quality production can be supported with
ˆ
W =
¯
V
0
(?). Then no
price cut is needed in the equilibrium punishment phase and from equation (6), the noncontrolling
shares achieve the value
¯
U = p ? c
H
. Substituting
ˆ
W =
¯
V
0
(?) and T =
¯
W (?, ?) into equation
(4) and rearrange, we can express the value of controlling shares to the incumbent following an
25
o?-equilibrium negotiation breakdown, W, as
W =
¯
W (?, ?) ??
¯
V
0
(?)
1 ??
This o?-equilibrium value of controlling share can be supported by requiring the incumbent to
o?er a price discount to customers for one period. The discount is given by
¯
V
0
(?) ?W
1 ??
=
¯
V
0
(?) ?
¯
W (?, ?)
(1 ??) (1 ??)
The equilibrium described above is feasible if and only if
W ?
B ?e
L
?
+
_
q ?c
L
_
(12)
This translates into the following condition:
? ?
˜
? (?, ?) ?
e
H
?e
L
+ ?
_
c
H
?c
L
_
((1 ?q) ? + q) (e
H
?e
L
+? (c
H
?c
L
)) + (1 ??) ? (p ?q)
2
. (13)
In sum, if ? ? [
˜
? (?, ?) , 1),
¯
U = p ?c
H
and
¯
V =
¯
V
0
(?) in the optimal equilibrium. The equilib-
rium takes the form described in the text, with T =
¯
W (?, ?). On the o?-equilibrium path punish-
ment phase in which the controlling shares are retained by the incumbent, a price cut
¯
V
0
(?)?
¯
W(?,?)
(1??)(1??)
is o?ered to customers for one period. This concludes the proof for part (iv) of the proposition.
Next, suppose ? ? [
ˆ
? (?) , ? (?, ?)). In the optimal equilibrium,
¯
V >
ˆ
W, and a price discount is
o?ered in the on-the-equilibrium punishment phase. It is therefore immediate that
¯
U < p ? c
H
.
We now proceed to construct the optimal equilibrium.
Equation (4) can be written as
ˆ
W =
T ?(1 ??) W
?
(14)
Using (14) and (10), the price cut, denoted by D(?, ?), can be written as
D(?, ?) ?
V ?
ˆ
W
1 ??
=
1
1 ??p
_
B ?e
H
?
+
_
p ?c
H
_
_
?
1
1 ??
_
1
?
?
? (1 ?p)
1 ??p
_
T +
1 ??
? (1 ??)
W (15)
Note that because ? ? [
ˆ
? (?) , ? (?, ?)), the price cut D(?, ?) is positive for all T and W such
that T ?
_
0,
¯
W (?, ?)
¸
(by (11)) and W ?
_
B ?e
L
_
/? +
_
q ?c
L
_
(by (12)). The price cut is
therefore increasing in W and decreasing in T (since 1/? > 1 > ? (1 ?p) /1??p). Therefore, to get
the minimum equilibrium price cut, we should set W =
_
B ?e
L
_
/? +
_
q ?c
L
_
and T =
¯
W (?, ?).
Note that by setting T =
¯
W (?, ?), we also achieve the upper bound on the equilibrium value of
controlling shares V =
¯
V
0
(?). Thus,
¯
V =
¯
V
0
(?).
26
By setting W =
_
B ?e
L
_
/? +
_
q ?c
L
_
and T =
¯
W (?, ?), the value of noncontrolling shares in
the optimal equilibrium is
¯
U =
_
p ?c
H
_
??
1 ?p
1 ??
_
e
H
?e
L
?
+ c
H
?c
L
p ?q
_
?
?1
_
?
?1
?q
_
?(1 ?q)
¸
?(p ?q)
_
?
?1
?1
_
_
(16)
In sum, if ? ? [
ˆ
? (?) , ? (?, ?)),
¯
U is given by (16) and
¯
V =
¯
V
0
(?) in the optimal equilibrium. The
equilibrium takes the form described in the text, with T =
¯
W (?, ?). On the o?-equilibrium path in
which the controlling shares are retained by the incumbent, a price cut of
¯
V
0
(?)?[(B?e
L
)/?+(q?c
L
)]
(1??)(1??)
is o?ered to customers for one period.
Finally, because ? ? (
ˆ
? (?) ,
˜
? (?, ?)), it can readily veri?ed that
¯
U ?
_
_
_
p ?c
H
_
?(1 ?p)
_
_
_
_
e
H
?e
L
?
+ c
H
?c
L
_
(p ?q)
_
_
_
, p ?c
H
_
_
=
_
¯
U
0
(?), p ?c
H
_
.

Proof of Corollary 1. Fix a ? ? ?. If ? ?
ˆ
? (?), then ? has no e?ect on
ˆ
W and hence no
e?ect on the acquisition premium and the post-acquisition accounting pro?t. For the rest of the
proof, we consider the case ? >
ˆ
? (?).
Recall that
˜
? (0, ?) =
ˆ
? (?) and that
˜
? (?, ?) is strictly increasing in ?, we can thus de?ne its
inverse: let
¯
? (?, ?) be the solution to ? =
˜
? (?, ?). When ? ?
¯
? (?, ?), we have ? ?
˜
? (?, ?).
Therefore, according to the proof of Proposition 2,
ˆ
W =
¯
V
0
(?) and T =
¯
W (?, ?). Both the
acquisition premium, T ?U, and post-acquisition pro?t, p ?c
H
, are locally invariant to ?.
When ? >
¯
? (?, ?), we have ? <
˜
? (?, ?). According to the proof of Proposition 2, T remains at
¯
W (?, ?) and
ˆ
W =
¯
W (?, ?) ?(1 ??)
_
B?e
L
?
+
_
q ?c
L
_
_
?
Therefore,
ˆ
W is equal to
¯
V
0
(?) when ? ?
¯
? (?, ?) and is strictly decreasing in ? for ? ?
_
¯
? (?, ?) , 1
_
. The result then follows because the acquisition premium varies inversely with
ˆ
W
while the post-acquisition accounting pro?t varies positively with
ˆ
W.
Proof of Corollary 2. Based on Proposition 2, if ? ?
˜
? (?, ?), then
¯
V =
¯
V
0
(?),
¯
U = U =
p ? c
H
, and T =
¯
W (?, ?). The expressions for ?
H
and ?
L
then follow by direct substitution. It
follows immediately that ?
H
> ?
L
. Also, ?
H
< 0 if
B ?e
H
?
is su?ciently small.
Next, if ? ? (
ˆ
? (?) ,
˜
? (?, ?)), then
¯
V and T remain at
¯
V
0
(?) and
¯
W (?, ?), respectively. The
expressions for
¯
U and U are given by (7). According to the proof of Proposition 1,
ˆ
W =
¯
W (?, ?) ?(1 ??)
_
B?e
L
?
+
_
q ?c
L
_
_
?
.
27
Direct substitution gives the expressions for ?
H
and ?
L
. Note that the term in the brackets is
negative if and only if
? > ?
1
(?) =
c
H
?c
L
+
e
H
?e
L
?
(p ?q)
2
+ q
_
c
H
?c
L
+
e
H
?e
L
?
_.
It can be readily veri?ed that ?
1
(?) <
˜
? (?, ?) under (3). Thus, if ? ?
_
?
1
(?) ,
˜
? (?, ?)
_
and
B?e
H
?
is su?ciently small, then ?
H
can be negative. Finally, note that
?
H
??
L
=
_
¯
V
0
(?) ?
¯
U
_
?
_
¯
W (?, ?) ?U
_
=
ˆ
W ?
¯
W (?, ?) .
Because
ˆ
W ?
¯
W (?, ?) > 0, we obtain that ?
H
> ?
L
as in the former case.
Straightforward calculation yields the following expressions for ?
H
:
?
H
=
_
¸
_
¸
_
B ?e
H
?
?
1?p
p?q
_
e
H
?e
L
?
+ c
H
?c
L
_
if ? ?
˜
? (?, ?)
B?e
H
?
?
(1?p)(?
?1
?1)
1??
_
? (p ?q) ?
1??q
p?q
_
e
H
?e
L
?
+ c
H
?c
L
__
if ? ? (
ˆ
? (?) ,
˜
? (?, ?))
It is immediate to see that in both cases, ?
H
< 0 if B is su?ciently small.
Proof of Proposition 3. (i) First, it is immediately apparent that when ? =
ˆ
? (1), ?
?
is
unique and equal to one as any lower ? cannot support high-quality production. Similarly, for any
? ?
_
ˆ
? (1) , 1
_
, it is suboptimal to set ? below ? (?).
Next, when ? = ? (?) or equivalently, ? =
ˆ
? (?), we have that
¯
U =
¯
U
0
(? (?)) and
¯
V =
¯
V
0
(? (?)),
according to Proposition 1. Therefore,
¯
U ?
¯
V = ?
B?e
H
?(?)
< 0 and non-controlling shares is less
valuable than controlling shares. Since the value of each kind of shares is strictly increasing in ?
when ? ?
_
? (?) , min
_
¯
? (?, ?) , 1
_¸
and ? ?
_
ˆ
? (1) , 1
_
, the optimal ownership structure ?
?
strictly
exceeds ? (?).
Moreover, if
¯
? (?, ?) < 1 and ? ?
¯
? (?, ?), then according to Proposition 1,
¯
U (?) = p ?c
H
and
¯
V (?) =
¯
V
0
(?). This gives
S (?) = B ?e
H
+
_
p ?c
H
_
?
1 ?p
p ?q
_
e
H
?e
L
+?
_
c
H
?c
L
_¸
.
Therefore, S is strictly decreasing in ? for ? ?
¯
? (?, ?) and it is suboptimal to set ? above
¯
? (?, ?).
We have thus established that ?
?
(?) ? (? (?) , min
_
¯
? (?, ?) , 1
_
].
To see why ?
?
(?) is unique when when ? ?
_
ˆ
? (1) , 1
_
, recall by de?nitions, ? ? (? (?) , min
_
¯
? (?, ?) , 1
_
]
if and only if ? ? (
ˆ
? (?) ,
˜
? (?, ?)]. Using part (iii) of Proposition 1, the total shareholder value
28
S (?) = ?
¯
V (?) + (1 ??)
¯
U (?) for this range of ? is given by
S (?) = ?
_
B ?e
H
?
+
_
p ?c
H
_
?
1 ?p
p ?q
_
e
H
?e
L
?
+ c
H
?c
L
__
+ (1 ??)
_
_
p ?c
H
_
??
1 ?p
1 ??
_
e
H
?e
L
?
+ c
H
?c
L
p ?q
_
?
?1
_
?
?1
?q
_
?(1 ?q)
¸
?(p ?q)
_
?
?1
?1
_
__
.
Direct computation gives the second derivative:
S
??
(?) = ?2?
?3
_
?
1 ?p
1 ??
e
H
?e
L
p ?q
_
_
?
?1
_
?
?1
?q
_
?(1 ?q)
_
< 0.
Since S is strictly concave in ? in the interval (? (?) , min
_
¯
? (?, ?) , 1
_
], ?
?
is unique when ? ?
_
ˆ
? (1) , 1
_
.
Finally, it is easy to verify that both ? (?) ? ? and
¯
? (?, ?) ? ? as ? ? 1. Therefore, ?
?
converges to ?.
(ii) By the strict concavity of S (?) in the interval (?, min
_
¯
?, 1
_
], ?
?
is characterized by the ?rst
order condition S
?
(?
?
) = 0, which can be simpli?ed into
˜
? =
¸
¸
¸
_
(e
H
?e
L
) (1 ??q ??? (1 ?q))
(1 ??)
_
? (p ?q)
2
?(c
H
?c
L
) (1 ??q)
_.
From the proof of part (i), we know that the optimal ownership structure ?
?
is given by
?
?
= min
_
1,
¯
?,
˜
?
_
,
where
¯
? ?
_
e
H
?e
L
_
((1 ?q?) ??? (1 ?q))
? (1 ??) (p ?q)
2
?(1 ?? (q + ? (1 ?q))) (c
H
?c
L
)
.
Note here,
¯
? is the inverse of
˜
?. Furthermore, if ? ?
_
˜
? (?, 1) , 1
_
, then ?
?
< 1.
It is obvious that both
¯
? and
˜
? are strictly increasing in e
H
?e
L
and c
H
?c
L
. Thus, ?
?
is weakly
increasing in e
H
?e
L
and c
H
?c
L
if ? ? (0, 1). It is strictly decreasing in e
H
?e
L
and c
H
?c
L
if
? ?
_
˜
? (?, 1) , 1
_
.
Direct computation shows that
?
¯
?
??
,
?
˜
?
??
< 0. Thus, ?
?
is weakly decreasing in ? for ? ? (0, 1),
29
and strictly decreasing in ? if ? ?
_
˜
? (?, 1) , 1
_
.
?
¯
?
??
=
?
_
e
H
?e
L
_
(1 ??) (p ?q)
2
_
? (1 ??) (p ?q)
2
?(1 ?? (q + ? (1 ?q))) (c
H
?c
L
)
_
2
< 0,
?
˜
?
??
=
1
2?
?
e
H
?e
L
1 ??
?(p ?q)
2
+
_
c
H
?c
L
_
? (1 ?q)
_
? (p ?q)
2
?(c
H
?c
L
) (1 ?q?)
_
2
< 0.
Direct computation shows that
?
¯
?
??
,
?
˜
?
??
> 0. Thus, ?
?
is weakly increasing in ? for ? ? (0, 1),
and strictly increasing in ? if ? ?
_
˜
? (?, 1) , 1
_
.
?
¯
?
??
=
? (1 ??)
_
e
H
?e
L
_
(p ?q)
2
_
? (1 ??) (p ?q)
2
?(1 ?? (q + ? (1 ?q))) (c
H
?c
L
)
_
2
> 0,
?
˜
?
??
=
1
2?
?
_
e
H
?e
L
_
? (p ?q)
2
?(c
H
?c
L
) (1 ??q)
1 ??
(1 ??)
2
> 0.

Proof of Corollary 3: Using the de?nitions in the proof of Proposition 3, the optimal own-
ership structure is strictly interior if and only if
˜
? < 1 and
˜
? <
¯
?. Upon straightforward algebra
manipulation, the inequalities can be written as
c
H
?c
L
<
1
(1 ??q)
_
? (p ?q)
2
?
_
e
H
?e
L
_
_
1 ??q ??? (1 ?q)
1 ??
__
?
¯
C, and
0 > ? (1 ??) (p ?q)
2
_
? (1 ??) (p ?q)
2
?
_
e
H
?e
L
_
((1 ?q?) ??? (1 ?q))
_
+(1 ??) (1 ?q? ??? (1 ?q))
_
(1 ??q)
_
e
H
?e
L
_
?2? (p ?q)
2
_
_
c
H
?c
L
_
+(1 ??q ??? (1 ?q))
2
_
c
H
?c
L
_
2
. (17)
The condition e
H
? e
L
<
?(1??)(p?q)
2
1??q???(1?q)
ensures that
¯
C is positive. It also ensures that inequality
(17) holds at c
H
? c
L
=
¯
C. Combined with the observation that inequality (17) does not hold at
c
H
?c
L
= 0, the system of inequalities above hold for some c
H
?c
L
?
_
C,
¯
C
_
, where C > 0. Finally,
direct computation shows that the e?ciency requirement (3) holds for all c
H
?c
L
<
¯
C.
References
[1] Anderson, Ronald C. and Reeb, David M. (2003), “Founding-Family Ownership and Firm
Performance: Evidence from the S&P 500,” The Journal of Finance, 58, pp. 1301—1327.
30
[2] Bar-Isaac, Heski and Steven Tadelis (2008), “Seller Reputation,” Foundations and Trends in
Microeconomics, 4(4); pp. 273-351.
[3] Barclay, Michael J., and Cli?ford G. Holderness (1989), “Private Bene?ts from Control of
Public Corporations,” Journal of Financial Economics, 25, 371-395.
[4] Barclay, Michael J., and Cli?ford G. Holderness (1991), “Negotiated Block Trades and Cor-
porate Control,” Journal of Finance, 46, Issue 3, pp. 861—878
[5] Chen, Yinghong (2004), “Valuation of Voting Scheme Changes: The cases of Electrolux AB
and SKF AB,” working paper.
[6] Demsetz Harold and Kenneth Lehn (1985), “The Structure of Corporate Ownership: Causes
and Consequences,” Journal of Political Economy, 93, No. 6, pp. 1155-1177.
[7] Dyck, Alexander and Luigi Zingales (2004), “Private Bene?ts of Control: An International
Comparison,” The Journal of Finance, 59(2), pp. 537-600.
[8] Fama, Eugene F. and Michael C. Jensen (1983), “Separation of Ownership and Control,”
Journal of Law and Economics, 26(2), pp. 301-325.
[9] Gadhoum, Yoser, Larry H. P. Lang, and Leslie Young (2005), “Who Controls U.S.?,” European
Financial Management, 11, no. 3, pp. 339-363.
[10] Goodstein, Jerry and Warren Boeker. 1991. “Turbulence at the Top: A New Perspective on
Governance Structure Changes and Strategic Change.” Academy of Management Journal, 34
(2), pp. 306-330.
[11] Green, Edward J. and Robert H. Porter (1984), “Noncooperative Collusion under Imperfect
Price Information,” Econometrica, 52(1), pp. 87-100.
[12] Hambrick, Donald C. and Steven M. Schecter (1983), “Turnaround Strategies in Mature
Industrial-product Business Units,” Academy of Management Journal, 26, pp. 231—248.
[13] Hayward, Mathew L. A. and Hambrick, Donald C. (1997), “Explaining the premiums paid for
large acquisitions: evidence of CEO hubris,” Administrative Science Quarterly, 42, 103 - 27.
[14] Himmelberg, Charles P., R. Glenn Hubbard, and Darius Palia (1999), “Understanding the
Determinants of Managerial Ownership and the Link between Ownership and Performance,”
Journal of Financial Economics, 53, pp. 353-84.
[15] Holderness, Cli?ord G. (2003), “A Survey of Blockholders and Corporate Control,” Economic
Policy Review, 9, no. 1, pp. 51-64.
31
[16] Holderness, Cli?ord G., Randall S. Kroszner, and Dennis P. Sheehan (1999), “Were the Good
Old Days That Good? Changes in Managerial Stock Ownership since the Great Depression.”
Journal of Finance, 54, pp. 435-69.
[17] Holthausen, Robert W., Richard W. Leftwich, and David Mayers (1987), “The E?ect of Large
Block Transactions on Security Prices: A Cross-sectional Analysis,” Journal of Financial Eco-
nomics, 19.2, pp. 237-267.
[18] Jensen, Michael C., and Richard S. Ruback, (1983), “The Market for Corporate Control: The
Scienti?c Evidence,” Journal of Financial Economics, 11.1, pp. 5-50.
[19] Kanter, Rosabeth M. (2003), “Leadership and the Psychology of Turnarounds,” Harvard Busi-
ness Review, 81(6): 57—66.
[20] Kaplan, Steven N. (1994), “Top Executives, Turnover, and Firm Performance in Germany,”
Journal of Law, Economics, and Organization, 10, pp. 142-159.
[21] Klein, Benjamin, and Keith B. Le?er (1981), “The Role of Market Forces in Assuring Con-
tractual Performance,” The Journal of Political Economy, pp. 615-641.
[22] Kreps, David M. (1990), “Corporate Culture and Economic Theory,” in J. E. Alt and K. A.
Shepsle, eds., Perspectives on Positive Political Economy, Cambridge, England: Cambridge
University Press.
[23] Krishnan, Hema A., Michael A. Hitt and Daewoo Park (2007), “Acquisitions Premiums, Sub-
sequent Workforce Reductions and Post-acquisition Performance,” Journal of Management
Studies 44 (5), 709-732.
[24] Kruse, Timothy A., Takuya Kyono, and Kazunori Suzuki (2006), “Discounted Tender O?er
Bids and the Value of Target Shareholders: the Source of Negative Control Premium,” working
paper.
[25] La Porta, Rafael, Florencio Lopez-de-Silanes, and Andrei Shleifer (1999), “Corporate Owner-
ship around the World,” Jounral of Finance, Vol 54, No. 2, pp. 471-517
[26] Lease, Ronald C., John J. McConnell, and Wayne H. Mikkelson (1983), “The Market Value of
Control in Publicly-traded Corporations,” Journal of Financial Economics, 11, pp. 439-471.
[27] Mailath, George J. and Larry Samuelson (2001), “Who Wants a Good Reputation?,” Review
of Economic Studies, 68, 415—441.
[28] Manne, Henry G. (1965), “Mergers and the Market for Corporate Control,” Journal of Political
Economy, 73, No. 2, pp. 110-120.
32
[29] Martin, Kenneth J. and John J. McConnell (1991), “Corporate Performance, Corporate
Takeovers, and Management Turnover,” The Journal of Finance, 46, pp. 671—687.
[30] Mikkelson, Wayne and Megan Partch (1989), “Managers’ Voting Rights and Corporate Con-
trol,” Journal of Financial Economics, 25, pp. 263-90.
[31] Pinegar, J. Michael and Ravichandran R. (2003), “US Investors’ Perceptions of Corporate
Control in Mexico: Evidence from Sibling ADRs,” Journal of Financial and Quantitative
Analysis, 38(1), pp. 213-230.
[32] Robbins, D. Keith and John A. Pearce II (1992), “Turnaround: Retrenchment and Recovery,”
Strategic Management Journal, 13(4), pp. 287—309.
[33] Shleifer, Andrei and Robert W. Vishny (1986), “Large Shareholders and Corporate Control,”
Journal of Political Economy, 94, No. 3, Part 1, pp. 461-488.
[34] Shleifer, Andrei and Robert W. Vishny (1997), “A Survey of Corporate Governance,” The
Journal of Finance, 52(2), pp. 737-783.
[35] Sirower, Mark L. (1994), “Acquisition Behavior, Strategic Resource Commitments and the
Acquisition Game: a New Perspective on Performance and Risk in Acquiring Firms,” Ph.D.
dissertation, Columbia University, New York
[36] Tadelis, Steven (1999), “What’s in a Name? Reputation as a Tradeable Asset,” American
Economic Review, 89, pp. 548—63.
[37] ––– (2002), “The Market for Reputations as an Incentive Mechanism,” Journal of Political
Economy, 110(4), pp. 854-882.
[38] ––– (2003), “Firm Reputation with Hidden Information,” Economic Theory, 21, 2-3, pp.
635-651.
[39] Valero, Magali, Manuel Gomez, and Edmundo Reyes (2008), “Price Di?erences between Dual-
class Stocks: Evidence from Mexico,” Journal of International Finance and Economics, 8(4),
pp. 120-130.
[40] Volpin, Paolo F. (2002), “Governance with Poor Investor Protection: Evidence from Top
Executive Turnover in Italy,” Journal of Financial Economics, 64(1), pp. 61—90.
[41] Zingales, Luigi (1994), “The value of the voting right: A study of the Milan stock exchange
experience,” Review of Financial Studies, 7(1), pp. 125-148.
[42] ––– (1995), “Insider Ownership and the Decision to Go Public,” Review of Economic Stud-
ies, 62, pp. 425-448.
33

doc_980289897.pdf