Dual Class IPOs,Share Recapitalizations, and Unifications：A

Dual Class IPOs,Share Recapitalizations,and Uni?cations:A

Theoretical Analysis

Thomas J Chemmanur*

and

Yawen Jiao**

First Version:November2004

Current Version:March,2007

*Professor of Finance,Carroll School of Management,Boston College,MA02467.Phone:(617)5523980.Fax: (617)5520431.E-mail:chemmanu@ed7078d3be1e650e53ea9903

**Assistant Professor of Finance,Lally School of Management and Technology,Rensselaer Polytechnic Institute, Troy,NY12180.Phone:(518)2762612.Fax:(518)2768661.E-mail:jiaoy@ed7078d3be1e650e53ea9903

For helpful comments or discussions we thank Anup Agrawal,Sanjay Banerji,Erik Berglof,Sudipto Bhattacharya, Sris Chatterjee,Doug Cook,Amil Dasgupta,Jerome Detemple,Antoine Faure-Grimaud,Laura Field,John Finnerty, Bill Francis,Iftekhar Hasan,Mark Kamstra,Edward Kane,Yrjo Koskinen,Dima Leshchinskii,Paul McNelis,De-barshi Nandy,Jacob Oded,Jun Qian,Phil Strahan,Dimitri Vayanos,David Webb,An Yan,as well as participants at the2005FMA meetings,the2005Asian Corporate Governance Conference,the2005Conference on Paci?c Basin Finance,Economics,and Accounting,and seminar participants at Boston College,Boston University,Durham University,Fordham University,Indiana University at Bloomington,London School of Economics,Rensselaer Poly-technic Institute,University of Alabama,University of Arkansas and York University.We are solely responsible for any remaining errors or omissions.

Electronic copy available at: ed7078d3be1e650e53ea9903/abstract=1108857

Dual Class IPOs, Share Recapitalizations, and Unifications: A

Theoretical Analysis

Abstract

We analyze a firm’s choice between dual class and single class share structures, either at IPO or subsequently, prior to an SEO. We consider an entrepreneur (“incumbent”) who obtains both security benefits and private benefits of control, and who wishes to sell equity to outsiders to raise financing to implement his firm’s project. The incumbent may be either talented (lower cost of effort, comparative advantage in implementing projects) or untalented: the incumbent’s ability is private information, with outsiders observing only a prior probability that he is talented (his “reputation”). The firm’s project may be either long-term (intrinsically more valuable, but showing less signs of success in the short run) or short-term (faster resolution of uncertainty). Thus, under a single class share structure, an incumbent has a greater chance of losing control to potential rivals if he undertakes the long-term project, since outside equity holders may vote for the rival if they believe that the project is not progressing well. A dual class share structure allows the incumbent to have enough votes to prevail against any rival, but may be misused by untalented incumbents to dissipate value by not exerting effort. In equilibrium, the incumbent simultaneously chooses the IPO share structure (dual class or single class), project type (long-term or short-term), and how much effort to exert. Our results help to explain firms’ choices between dual class and single class IPOs and the relative post-IPO operating performance of dual class versus single class IPO firms. We also characterize the situations under which a firm will undergo a share unification or a dual class recapitalization, the announcement effect of these events on the firm’s equity, and their effect on its subsequent operating performance. Finally, our model provides testable predictions for the conditions under which firms will include stronger antitakeover provisions in their corporate charters and the relationship between the prevalence of such provisions in a firm's charter and its post-IPO operating performance.

Key words: Dual Class Shares, Voting Structure, Antitakeover Provisions, Recapitalizations, Unifications JEL Classification: G32, G34

Electronic copy available at: ed7078d3be1e650e53ea9903/abstract=1108857

Dual Class IPOs,Share Recapitalizations,and Uni?cations:A

Theoretical Analysis

1Introduction

When private?rms go public,entrepreneurs and other insiders choose the voting structure of their?rm’s shares and

incorporate these into its corporate charter:while most?rms choose a single class share structure(one share,one vote),a substantial minority(about11%of U.S.IPOs in2001and16.5%in2002)choose a dual class share voting structure,where one class of shares have superior voting rights(we often refer to these as“supervoting”shares from now on)while another class has inferior voting rights(“ordinary”shares).1Typically,the supervoting shares are held by the entrepreneur and other insiders who wish to maintain control of the?rm after the IPO;the ordinary shares are sold to outside investors in the IPO.A prominent recent example of a dual class IPO was that of the internet search?rm Google,which has drawn tremendous media attention.Google’s dual class IPO had class A shares(with one vote per share),which were sold to outsiders in the IPO;it also had class B shares(with ten votes per share), which were retained by the founders,Larry Page and Sergey Brin,as well as other insiders.

Dual class share structures confront?nancial economists with a puzzle.On the one hand,they have been criticized by corporate governance activists and often the media as violating the tenets of shareholder democracy, and for violating the one share-one vote principle(see Grossman and Hart(1988)and Harris and Raviv(1988,1989), and the large academic literature which has followed them,discussed in section2),which states that investors must share a?rm’s cash?ows and voting power in the same proportion.Thus,Google’s dual class IPO share structure came in for considerable criticism from such activists,with the in?uential proxy adviser,Institutional Shareholder Services(ISS)ranking Google near the bottom of its corporate governance rankings,below any company in the S&P500stock index.2On the other hand,the empirical evidence is far from clear that dual class share structures

necessarily destroy shareholder value.The recent empirical evidence,though inconclusive,indicates that the opposite 1Dual class share structures have been growing in popularity in the U.S.About10%or more of all listed companies currently have dual class share structures,almost twice as many as in the1980s.Dual class share structures are even more common abroad:approximately

22%of companies in Canada’s TSX Index have dual class arrangements,and they are at least as common in Western European countries such as Italy,Switzerland,and Sweden(20%of listed companies in the European Union have a dual class share structure),as well as in emerging market countries.

2See,e.g.,the Wall Street Journal,August23,2004,which quotes ISS special counsel Patrick McGurn:“Because Google lacks the usual checks and balances provided at public companies by shareholder votes,holders must closely scrutinize the judgement of the company’s top decision makers.Rank-and-?le shareholders have no meaningful avenue for recourse—other than selling their low-vote shares,of course—if the company loses its way.”

1

may,in fact,be true.In a study of dual class IPOs,Bohmer,Sanger,and Varshney(1996)document that?rms

going public with a dual class share structure outperform their matched single class counterparts in terms of stock market returns as well as accounting measures of?rm performance.Similarly,in a study of?rms undergoing dual class share recapitalizations(changing from a single class share structure to a dual class share structure),Dimitrov and Jain(2001)?nd that such?rms exhibit long-term positive abnormal stock returns over the four years after the recapitalization,and also superior operating performance in these years.They conclude that,on average,dual class recapitalizations are shareholder value-enhancing decisions.

There have,of course,been a few notorious recent examples of entrenched managers destroying shareholder value by consuming excessive perquisites(e.g.,Lord Conrad Black,the CEO of Hollinger International,which manages the Chicago Sun-Times and the London Telegraph newspapers).However,some of the best companies,run by highly reputable managers,seem to have adopted a dual class share structure:in addition to Google(which is one of the few companies in the recent past to be pro?table at the time of IPO),examples include Berkshire Hathaway(run by Warren Bu?ett),the New York Times Co.(run by the Sulzberger family),the Washington Post,Inc.,and Dow Jones&Co.(which publishes the Wall Street Journal)and companies like Volkswagan A.G.in Europe.Further,a substantial fraction of“family owned”?rms in the U.S.and abroad have a dual class share structure,which does not seem to have hurt their performance:in a study of the relationship between founding-family ownership and ?rm performance,Anderson and Reeb(2003)document that family owned?rms within the S&P500(about35% of S&P500?rms)exhibit signi?cantly better accounting and stock return performance than those which are not family owned.3In summary,it is by no means clear that,in practice,dual class share structures destroy shareholder value,despite the arguments of corporate governance activists based on existing theoretical analyses implying that one share-one vote is optimal.

Our objective in this paper is to provide a resolution to the above puzzle by developing a fresh theoretical analysis of the equilibrium choice of?rms between dual class and single class share structures.The starting point of our analysis is the rationale that top managers of many?rms give for adopting such a share structure:that it allows

them to focus on long-term value maximization without paying attention to temporary?uctuations in a?rm’s share 3The Ford family controls40%of shareholder voting power with only about4%of the total equity.Supervoting shares in Berkshire Hathaway have two hundred times the voting power of the company’s B shares,with only thirty times the cash?ow rights of the B

shares.

2

value(“the next quarter’s earnings report”).4However,we recognize that,while talented managers may be able

to create considerable shareholder value by focusing on long-run value maximization,the average CEO may not be able to create such long-term value,but will instead use this insulation from the disciplining e?ect of the takeover market to slack o?and enjoy the perquisites of control.Further,the equity market may?nd it di?cult to distinguish perfectly between the two kinds of managers.This is therefore the second ingredient driving our analysis.In such a setting,we characterize incumbent management’s equilibrium choice between dual class and single class IPO share structures.

We distinguish between situations where the incumbent management’s choice of dual class IPO share structure is driven primarily by the incumbent’s desire to maximize his private bene?ts of control,and those in which a dual class IPO share structure is truly value maximizing,so that?rms choosing a dual class IPO can be expected to outperform those choosing a single class IPO share structure(in terms of operating performance).Further,using the dynamic extension of our basic model(section6),we also characterize the equilibrium evolution of?rms’share structures subsequent to the IPO:thus,we study the conditions under which a?rm which undertakes a dual class IPO may choose to have a“share uni?cation”(thus choosing a single class share structure for its seasoned equity o?ering(SEO)),and those under which a?rm will choose to retain its dual class share structure.We also study the conditions under which a?rm that chose a single class IPO share structure will have a dual class recapitalization prior to its SEO(thus choosing a dual class share structure for its SEO)and those under which it will choose to maintain its single class share structure.Finally,we study the announcement e?ects of share uni?cations and dual class recapitalizations on a?rm’s equity,characterizing the conditions under which each of these will have a positive announcement e?ect and those under which each will have a negative announcement e?ect.

We consider an entrepreneur(the incumbent,from now on)who currently owns all the equity in his private?rm, but who wishes to sell equity to outsiders in an IPO to raise external?nancing to implement his?rm’s project.The incumbent obtains both security bene?ts(from the equity he owns in the?rm)and private bene?ts of control.The ?rm can adopt one of two projects(strategies):a long-term project or a short-term project.A long-term project is

intrinsically more valuable than a short-term project,and therefore maximizes long run value.However,adopting 4For example,in their letter to shareholders,Google’s founder managers made clear their desire to continue focusing on long-term value creation even after its IPO.To quote Google’s founders,Larry Page and Sergey Brin:“In our opinion,outside pressures too often

tempt companies to sacri?ce long-term opportunities to meet quarterly market expectations...If opportunities arise that might cause us to sacri?ce short-term results but are in the best long-term interests of our shareholders,we will take these opportunities...”

3

it may cause the?rm’s equity to be undervalued in the short-term,since it may show less signs of success in the short-run compared to a short-term project(in other words,a long-term project takes a longer time to resolve outsiders’uncertainty about project success or failure).Thus,incumbent management has a greater chance of losing control to potential rivals(even those less able than him)if he adopts the long-term project and outside investors believe that the?rm’s project is not progressing well in the short-term,and therefore vote for the rival in a control contest occurring at that time(if the incumbent does not hold enough voting power on his own account to defeat such a rival).The incumbent may be either talented or untalented:talented managers have a lower cost of exerting e?ort,and a comparative advantage in implementing projects relative to the untalented incumbent.In particular, a long-term project yields higher cash?ows than a short-term project only if managed by a talented incumbent. While the incumbent knows his own type,outsiders observe only a prior probability that he is talented(i.e.,his “reputation”).In this situation,the incumbent makes a joint decision regarding the share structure(dual class or single class)for his IPO,the kind of project to adopt(long-term or short-term),and the extent of e?ort to exert in implementing this project.

The equilibrium in the above situation will be driven by the choices made by a truly talented incumbent(since an untalented incumbent would mimic such choices,in order to not reveal his true type to the equity market).The choice of a talented incumbent between a dual class and a single class share structure depends on three e?ects.First, the insulation from the takeover market provided by a dual class share structure would allow the incumbent to create more value by implementing a long-term rather than a short-term project,without a fear of losing control if a rival for control were to appear before the resolution of uncertainty about such a long-term project.Since project horizon is observable to outsiders,this“long-term value creation”e?ect would be re?ected in the?rm’s IPO share price(and allow him to reduce the dilution in his equity holdings due to the IPO).However,the insulation from the takeover market provided by a dual class share structure also allows untalented incumbents to slack o?by not exerting e?ort, thus dissipating value without any fear of losing control to potential rivals.Since the equity market cannot perfectly distinguish between talented and untalented incumbents,this“loss of discipline”e?ect is also re?ected in the talented incumbent’s?rm’s IPO share price if he adopts a dual class share structure(and favors his adopting a single class share structure instead).Finally,since,regardless of the kind of project adopted,there is a signi?cant chance that the incumbent will lose control to potential rivals under a single class share structure(but only a much lower chance of

4

losing control under a dual class share structure),the expected value of the incumbent’s control bene?ts will always

be greater under a dual class share structure.While this third(“control bene?ts”)e?ect does not directly a?ect share value,it nevertheless enters the incumbent’s objective and favors him choosing a dual class share structure. We show that,when the incumbent’s reputation is high and the di?erence in intrinsic values between the long-term and short-term projects available to a?rm is large,the?rst and third e?ects together dominate the second,so that a dual class IPO share structure is chosen by the incumbent in equilibrium and the?rm implements a long-term project.On the other hand,when the incumbent’s reputation is low,and the di?erence in intrinsic values between long-term and short-term projects is small,the second(loss of discipline)e?ect dominates the?rst and third e?ects, so that the?rm adopts a single class IPO share structure in equilibrium and implements a short-term project.

In our basic model,we assume that the voting ratio(ratio of the voting power of supervoting to ordinary shares) chosen by the incumbent under a dual class share structure is large enough to guarantee the incumbent’s control against all rivals.However,we relax this assumption in an extension to our basic model(section5),where we allow for potential rivals of two di?erent ability levels relative to the incumbent,and also allow incumbents to exert two di?erent e?ort levels(in addition to no e?ort).In this section,the voting ratio(under a dual class share structure) is an endogenous variable,and both the share structure and voting power are chosen simultaneously in equilibrium.5 We show that,when the incumbent’s control bene?ts are large,the talented incumbent chooses a high voting ratio(in a dual class IPO equilibrium),since the incumbent does not wish to lose control of the?rm under any circumstances. On the other hand,when the incumbent’s control bene?ts are small,the incumbent chooses a low voting ratio in equilibrium.In the case of a dual class share structure with a low voting ratio,the risk of losing control to a(high ability)rival exerts a disciplining e?ect on an untalented incumbent(inducing him to exert at least a low level of e?ort),which is re?ected favorably in the share price of even a talented incumbent’s?rm(as discussed earlier).When his control bene?ts are small,the bene?t of a higher share price associated with a low voting ratio dominates the expected value of the control bene?ts lost by the incumbent,so that he chooses a low voting ratio in equilibrium.

While,in our basic model,each?rm has only one project and enters the equity market only once,in a dynamic

(two-period)extension to our basic model we assume that the?rm receives a new project in the second period and 5There is some variation in the voting ratio across?rms adopting dual class share structures in practice.For example,Google has a10to1voting ratio,as have many other?rms.However,the supervoting shares held by Comcast CEO Brian Roberts have85votes

against one vote for each ordinary share;the shares held by Frank Stronach,CEO of Magna International,have a500to1voting ratio; and?nally,the European?rm Erricson’s class B shares have a1000to1voting ratio.

5

therefore re-enters the equity market(by making an SEO)to raise external?nancing to implement it.This allows us

to study the conditions under which share uni?cations and dual class recapitalizations arise in equilibrium.6By the time of the SEO,the cash?ow realization of the?rm’s?rst period project becomes known to outside investors,and they update the incumbent’s reputation upward or downward(according to this realization).We show that,if the projects available to a?rm and the extent of takeover activity in the two periods are similar,then a?rm which had a dual class IPO in the?rst period will have a share uni?cation(and therefore a single class SEO)if its?rst period performance was poor(so that the incumbent’s reputation declines signi?cantly);it will retain its dual class share structure if it performed well in the?rst period(so that the incumbent’s reputation is enhanced).Under similar assumptions,we show that a?rm which had a single class IPO may have a dual class share recapitalization(and a dual class SEO)if its?rst period project was a success,so that the incumbent’s reputation is enhanced considerably; it will retain a single class share structure for its SEO if its?rst period performance was poor.

While we focus only on the e?ects of a?rm’s performance in the?rst period on its subsequent share structure in developing various results in the dynamic extension to our basic model,share uni?cations and dual class recapitaliza-tions may also occur in equilibrium in our setting for reasons unrelated to?rst period performance and managerial reputations.For example,share uni?cations will occur if the?rm matures and the di?erence in the intrinsic values between the long-term and short-term projects available to it is signi?cantly reduced in the second period compared to that in the?rst period.Similarly,dual class recapitalizations may also occur if the extent of takeover activity in the?rm’s industry increases signi?cantly in the second period relative to that in the?rst period(this seems to have been the driving force behind the recapitalizations of the mid-to-late eighties).7

Our analysis generates several testable predictions,which can be summarized as follows.First,our model predicts that dual class IPOs will be more prevalent in three kinds of?rms:First,?rms operating in industries where a considerable amount of value can be created by pursuing long-term goals while ignoring short-term trends(e.g.,the newspaper and media industry,where sacri?cing editorial integrity in pursuit of short-term pro?ts can be disastrous);

second,family owned?rms and?rms run by founder entrepreneurs,who tend to have a high reputation in managing 6Due to space limitations,we will present only an intuitive discussion of our dynamic model in this paper.The formal dynamic model with detailed proofs of various propositions are available in the working paper version of this article.

7While,in our current analysis,we do not allow the extent of takeover activity and the?rm’s investment opportunity set to vary from the?rst to the second period,our analysis can be extended in this direction at the expense of some additional complexity.For example, in a setting where we allow the extent of takeover activity to change from the?rst to the second period,an incumbent who observes an increase in takeover activity in his?rm’s industry after a single class IPO may choose to undertake a dual class recapitalization in the second period even though its?rst period performance was poor(provided that any loss in his security bene?ts due to the recapitalization is dominated by the increase in the expected value of his control bene?ts).

6

the?rm;and third,?rms characterized by large private bene?ts of control.Second,our model makes predictions regarding the relative post-IPO operating performance of dual class versus single class IPO?rms.In particular, it predicts that dual class IPOs will outperform single class IPOs if the reputation of incumbent management is high and the?rm is operating in an industry where the di?erence in intrinsic values between the long-term and short-term projects available to the?rm is large.On the other hand,single class IPOs will outperform dual class IPOs if incumbent reputation is low and the?rm is operating in an industry where the di?erence in intrinsic values between long-term and short-term projects is small.

The dynamic extension to our basic model also has predictions for the prevalence of dual class recapitalizations and share uni?cations,for the abnormal returns in the equity market to the announcement of these events,and for the operating performance of?rms subsequent to these events.Regarding the prevalence of uni?cation,our prediction is that,after a dual class IPO,?rms will undergo share uni?cations under three di?erent situations:First, if the performance subsequent to the IPO has been poor(or if?rm management’s reputation has declined for any other reason);second,following a change in incumbent management(e.g.,retirement of the founding entrepreneur and transfer of control to professional management);third,due to maturing of the?rm’s industry(e.g.,from an industry characterized by innovative products requiring risky long-term investments to one characterized by less risky investments with smaller changes across product cycles).Regarding the prevalence of dual class recapitalizations, our prediction is that?rms undergoing dual class share recapitalizations will be those in three di?erent situations: First,?rms whose management reputation has increased,either due to good performance in the past,or due to reputable new management;second,?rms in industries with a signi?cant increase in takeover activity;third,?rms undergoing drastic changes in the product market(e.g.,signi?cant technological change,entry into a new market) requiring them to start making risky long-term investments with no guarantees of success in the short-run.Our model predicts that the announcement e?ect of a share uni?cation will be positive if the current reputation of incumbent management is low enough;it will be negative if this reputation is high enough.Further,it predicts that operating performance will improve following share uni?cations.In contrast,it predicts that the announcement e?ect of a dual class recapitalization will be positive(and the?rm’s operating performance will improve subsequently)if incumbent management’s reputation is high;the announcement e?ect will be negative(and the?rm’s operating performance will deteriorate subsequently)if incumbent management’s reputation is low.Finally,our analysis has testable predictions

7

for the voting ratio between supervoting and ordinary shares in?rms adopting dual class share structures.It also

has policy implications for regulators for controlling management abuses under a dual class share structure.

While,for concreteness,we model dual class share structures,our paper can also be thought of as providing a theory of anti-takeover provisions in general,since the focus of our paper is on the relationship between the quality and reputation of a?rm’s management and the costs and bene?ts of entrenching that management in control:clearly, such management entrenchment can also be accomplished through antitakeover provisions other than dual class share structures.8Our model answers the following questions related to antitakeover provisions:What are the costs and bene?ts of incorporating various antitakeover provisions in a?rm’s charter?Under what conditions are antitakeover provisions value-destroying and under what conditions do they enhance shareholder value?What is the relationship between the quality and reputation of a?rm’s management and their propensity to incorporate antitakeover provisions in their charter at the time of IPO?What is the relationship between the strength(or intensity)of the antitakeover provisions in a?rm’s charter and its subsequent operating performance?Our model generates testable predictions related to many of the above questions(see implication7in section7).

The rest of the paper is organized as follows.Section2describes how our paper is related to the existing theoretical and empirical literature.Section3describes the essential features of our basic model.Section4characterizes the various equilibria of our basic model and develops results.Section5develops an extension of the basic model to allow for rivals of two di?erent ability relative to the incumbent,and characterizes the equilibrium voting ratio under a dual class share structure.Section6discusses a two-period(dynamic)extension to our basic model where each?rm obtains a second project at the end of the?rst period and raises additional?nancing to implement this project by making a seasoned equity o?ering.Section7describes the testable and policy implications of our analysis.Section 8concludes.The proofs of all propositions in our basic model(proposition1,2,3,and4),as well as those in section 5,are in the appendix.The proofs of the propositions in our dynamic model are omitted due to space considerations and are placed in appendix B,available to interested readers upon request.We also con?ne the speci?c parametric

restrictions and threshold values for various propositions to hold to the appendix.

8In addition to dual class share structures,other commonly observed antitakeover provisions are:anti-greenmail provision,blank check preferred stock,staggered boards,fair price provision,poison pills,stakeholder clause,various shareholder meeting restrictions (e.g.,meetings can be called only by directors or executives),various supermajority vote requirements(e.g.,supermajority required to approve mergers),miscellaneous antitakeover provisions(e.g.,directors can be removed only for cause).See Field and Karpo?(2002)or Chemmanur,Paeglis,and Simonyan(2005)for a detailed listing.

8

2Relationship to the Existing Literature

Our paper is related to several strands in the theoretical and empirical literature.As discussed before,the seminal

theoretical analyses of the optimal design of?rms’share structures is by Grossman and Hart(1988)and Harris and Raviv(1988,1989),whose analyses come to the conclusion that the optimal share structure in terms of shareholder wealth maximization involves allocating a?rm’s cash?ow and voting power in the same proportion(one share, one vote)since it minimizes the chance that a value increasing takeover by a rival would not be consummated (in a setting where incumbent management obtains private bene?ts from control).9However,in the symmetric information analysis of Grossman and Hart(1988)and Harris and Raviv(1989),all agents:incumbent,rival,and outside investors,share the same information about the actions to be taken to maximize?rm value,and the focus is only on the incentive problem between incumbent management and outsiders.In contrast,in our setting,there is asymmetric information between the incumbent and outside shareholders about the incumbent’s ability(talent), and later,regarding how e?ective the incumbent has been in implementing the?rm’s project.This asymmetric information interacts with the incentive problem faced by the incumbent in our setting,so that in some situations, it is a dual class share structure which maximizes shareholder wealth while in others,a single class share structure maximizes shareholder wealth.

Subsequent to the seminal analyses of Grossman and Hart(1988)and Harris and Raviv(1988,1989),there have been relatively few theoretical analyses directly dealing with the design of share structure by?rms.10However,to the extent that a dual class share structure can be thought of as one among many di?erent antitakeover provisions in corporate charters,our paper is also related to the law and economics literature explaining why companies may go public with corporate governance arrangements that are known to be ine?cient by both investors and by those taking ?rms public.There is also a large literature that has studied the costs and bene?ts of a complete ownership(CO)

structure(where the company remains private and the initial owner retains complete ownership)to a controlling 9Grossman and Hart(1988)also suggest,however,that,in the case of competition,departing from one share-one vote can result in higher bid prices for the?rm,though in their setting one share-one vote is always socially optimal(unlike in our paper).See also Burkart, Gromb,and Panunzi(1998),who study a setting with post-takeover moral hazard by the acquirer and free-riding by target shareholders,

and demonstrate that deviating from the one share-one vote rule can help current majority shareholders achieve higher bid prices for the ?rm.

10A prominent recent example of this literature is Bebchuk(2002).He shows that,in a setting where?rm insiders have private infor-mation about the true value of the?rm’s projects and the cash?ows of the?rm are positively correlated with incumbent managements’s control bene?ts,?rms may adopt ine?cient corporate governance arrangements to signal their true value to outsiders.Unlike the analysis of Bebchuk(2002)where such antitakeover provisions are ine?cient,and are adopted only to“burn money”and thus signal credibly to outsiders,in our setting,dual class share structures are often e?cient(shareholder value maximizing).Thus,the motivation for adopting dual class share structures is quite di?erent in our setting from that in the above literature.

9

shareholder(CS)structure(where the initial owner retains control of the?rm but sells some of the cash?ow rights to

public investors:see,e.g.,Bolton and von Thadden(1998),Holmstrom and Tirole(1993),Pagano and Roell(1998), and Zingales(1995).In particular,Bebchuk and Zingales(2000)argue that dual class share structures exacerbate the distortions associated with the socially excessive use of controlling shareholder structure,since they enable the initial owner to retain a majority of the voting rights in the?rm while selling a majority of the cash?ow rights to public investors.Further,our paper is also indirectly related to the broader literature on a?rm’s going public decision:see,e.g.,Chemmanur and Fulghieri(1999)or Boot,Gopalan,and Thakor(2006).11 In contrast to the relative paucity of theoretical analyses,there is a substantial empirical literature dealing with?rms’adoption of a dual class share structure,either at IPO or subsequently.Field and Karpo?(2002)and Daines and Klausner(2001)study the characteristics of IPO?rms adopting dual class share structures and other antitakeover provisions,and compare them with those adopting single class share structures:they arrive at the conclusion that such?rms are not necessarily of lower quality.Bohmer,Sanger,and Varshney(1996)compare the performance of dual class IPO?rms and an industry and size-matched sample of single class IPO?rms.12There is also a large literature studying long-term stock return and operating performance of?rms following dual class recapitalizations(e.g.,Dimitrov and Jain(2001),Mikkelson and Partch(1994),and Lehn et al(1990)),and the short term abnormal stock returns to the announcements of these events:see,e.g.,Partch(1987),who found a signi?cantly positive announcement e?ect,and Jarrell and Poulsen(1988),who found a signi?cantly negative announcement e?ect. Finally,a small literature has studied the announcement e?ect of the abolition of dual class share structures(share uni?cation):these include Dittman and Ulbricht(2004),who?nd a signi?cantly positive announcement e?ect for German?rms.In summary,the existing empirical literature seems to be undecided so far as to whether dual class share structures create or destroy shareholder value:our theoretical analysis can help to resolve these inconsistencies in the empirical literature by suggesting sharper empirical tests and by generating new hypotheses for empirical

research.

11A number of important papers have also made informal arguments regarding the bene?ts and costs of dual class share structures and other corporate governance arrangements that entrench top management to some degree.These include Alchian and Demsetz(1972), who argue that dual class share structure may deter outside shareholders from incorrectly replacing competent incumbent management, and DeAngelo and DeAngelo(1985),Fischel(1987),and Denis and Denis(1994)who conjecture that e?ective defenses against change in control can enhance managers’incentive to make?rm-speci?c investments,thus adding to?rm value.See also Partch(1987)and Jarrell and Poulsen(1988)for summaries of alternative arguments.

12In this context,our paper is also related to the broader theoretical literature on IPOs(see,e.g.,Alan and Faulhaber(1989), Chemmanur(1993),or Welch(1989))as well as the large empirical literature on the post-IPO operating and stock return performance of?rms(see Ritter and Welch(2002)for a review).

10

3The Basic Model

The basic(single-period)model has two dates:time0and time1.There are three types of agents in this model:the incumbent,passive(outside)investors,and the rival.Consider a?rm initially set up by a risk-neutral entrepreneur (the incumbent hereafter)as an all-equity?rm.The incumbent holds all of the?rm’s equity at the beginning of the game,and obtains not only the cash?ows accruing to this equity(“security bene?ts”)but also private bene?ts of control(“control bene?ts”)from managing the?rm which are not obtainable by any other equity holder.

At time0,the incumbent undertakes one of two possible projects available to his?rm:a long-term project(l)or a short-term project(s).The terminology“long-term”and“short-term”project do not necessarily refer to the length of the project itself;instead,they refer to the horizon over which they maximize stock value.Thus,a long-term project is one which maximizes stock value in the long-run,but in the short-run may not show any signs of project success,potentially leading to the?rm’s equity being undervalued in the short-run.A short-term project has a lower NPV than a long-term project,but has a faster resolution of uncertainty(and information asymmetry)than a long-term project,thus potentially leading to a higher stock price for the?rm in the short-run(we discuss the resolution of information asymmetry in the two kinds of projects in detail later).The incumbent can implement only one of the two projects.Both of these two projects require an investment amount I to implement at time0,which the incumbent wishes to raise from outside investors through an initial public o?ering(IPO)of equity(at time0), since the?rm has no internal capital available.When taking his?rm to the IPO market,the incumbent can either have a dual-class(D)or a single-class(S)share structure.

If he chooses to have a dual-class IPO,the incumbent will hold all the supervoting shares(with t votes per share), and sell all the ordinary shares(with one vote per share)to outside investors.13If he chooses to have a single-class IPO,both he and outside investors will hold shares with equal voting rights(one vote per share)and cash?ow rights.To begin with,the equity in the?rm is assumed to be pided into a large number of shares,all owned by the incumbent.After choosing the IPO share structure for his?rm,the incumbent sells a certain number of additional shares to outside investors.Both the investment horizon(long-term project or short-term project)and the IPO share structure are publicly observable.

Shortly after its IPO at time0,outside investors receive a noisy intermediate signal about the potential success or 13Note that the supervoting shares and ordinary shares have the same cash?ow rights.

11

Figure1:Sequence of events in the single-period model

failure of the?rm’s project chosen at time0.After outside investors observe the realization of this signal,a rival will arrive with probabilityφand try to take over the?rm currently run by the incumbent by buying outside investors’shares using her own wealth(φcan be thought of as the probability capturing the extent of takeover activity in the industry the?rm is operating in).The outcome of the control contest at this time will a?ect the time1cash?ow to the?rm,since it determines the identity of the management team(incumbent or rival),that will be in charge of the ?rm.

At time1,all cash?ows from the?rm’s?rst period project are realized.We assume that all agents are risk-neutral and normalize the risk free rate of return to zero.The sequence of events in the basic(single-period)model is depicted in Figure1.

3.1Project Technology and Information Structure

Incumbents are of two types:type T(“talented”)or type U(“untalented”).The talented incumbent has two advantages over the untalented incumbent.The?rst advantage is that the talented incumbent has a lower personal cost of exerting e?ort compared to the untalented incumbent.For simplicity,we assume that the cost of exerting e?ort for the talented incumbent is0,while that of the untalented incumbent is e>0.We assume that incumbents may choose to exert one of two possible e?ort levels:a high(positive)level of e?ort or a low level of e?ort(which we normalize to be zero).The incumbent can improve the expected cash?ow from a project by exerting e?ort. Given that the talented incumbent has an e?ort cost of0,he will always exert e?ort in implementing a project. Whether an untalented incumbent exerts e?ort or not depends on his trade-o?between his monetary and control

12

bene?ts from the project and his e?ort cost.The incumbent’s e?ort level is not publicly observable.The second advantage of the talented incumbent over the untalented one is his superior ability in implementing projects:this comparative advantage is especially pronounced when implementing long-term projects,as we discuss in detail below. In other words,for a given level of e?ort,the talented incumbent can generate a higher cash?ow on average than an untalented incumbent,regardless of the type of project chosen.

We model the cash?ow generated by a?rm’s projects as follows.Each project implemented by a?rm generates a high cash?ow C H with a certain probability and a low cash?ow C L with the complementary probability.Given our earlier assumptions,the probability of a high cash?ow from the?rm’s projects depends on three variables:(i) whether incumbent management is talented or not;(ii)whether the incumbent exerts e?ort or not;(iii)whether the project is long-term or short-term.We denote the probability of a high cash?ow from a long-term project under a talented incumbent exerting e?ort byηl;βl<ηl denotes the corresponding probability under an untalented incumbent(i.e.,an untalented incumbent managing a long-term project,also exerting e?ort).Similarly,η0l and β0l respectively denote the high cash?ow probabilities when the talented and untalented incumbents manage the long-term project without exerting e?ort,η0l>β0l.The corresponding high cash?ow probabilities for a short-term project are:ηs andβs depending on whether this project is managed by a talented incumbent(exerting e?ort) or an untalented incumbent(exerting e?ort),respectively;andη0s andβ0s give the same probability depending on whether this project is managed by the talented or untalented incumbent without exerting e?ort.As in the case of the long-term project,the talented incumbent’s advantage in managing a short-term project is captured by assuming thatηs>βs andη0s>β0s.

It now only remains to specify how the expected cash?ows from the long-term and short-term projects relate to each other.We assume that while the talented incumbent can manage a long-term project to generate higher cash ?ows than a short-term project(ηl>ηs andη0l>η0s),long-term projects o?er no such advantage over short-term projects if managed by an untalented incumbent(βl=βs andβ0l=β0s).In summary,our parametric assumptions are as follows:ηl>ηs>βl=βs>β0l=β0s(note that we do not include the high cash?ow probabilities when the talented incumbent does not exert e?ort,η0l andη0s,in the above summary,since given that his e?ort cost is zero and that exerting e?ort creates value,the talented incumbent always exerts e?ort,so thatη0l andη0s are unimportant for our analysis from now on).

13

The equity market is characterized by asymmetric information.While incumbents know their own true types at time0,outside investors only have a prior probability distribution on the incumbents’types:they believe that with a probabilityθthe incumbent is of type T,and is of type U with the complementary probability.We will refer toθas the incumbent’s reputation at time0.

3.2Intermediate Signal About the Incumbent’s Progress in Project Implementation Between time0and time1,outside investors receive an intermediate signal about how successful the incumbent has been so far in implementing the?rm’s project.This intermediate signal has two possible realizations:it can be either “good”(G)or“bad”(B).14We assume that,while this intermediate signal is informative about the success of project implementation,the signal is less informative about the long-term project than about the short-term project.Thus, consistent with the assumptions we made in section2.1about the probability of a project yielding a high cash?ow,we assume that the probability of a project receiving a good intermediate signal if implemented by a talented incumbent (denoted byδwith subscripts indicating project horizon,and primes indicating the case where the incumbent does not exert e?ort)is higher than the corresponding probability if implemented by an untalented incumbent(denoted byψ,with subscripts indicating project horizon,and primes indicating the case where the incumbent does not exert e?ort).Thus,we assume,for the long-term project:δl>ψl,andδ0l>ψ0l;and for the short-term project:δs>ψs, andδ0s>ψ0s.Similarly,we assume that the probability of getting a good signal is greater when the incumbent exerts e?ort compared to the case where he does not:thus,we assume thatδl>δ0l andδs>δ0s(for the talented incumbent); similarly,ψs>ψ0s andψl>ψ0l(for the untalented incumbent).However,we assume that this intermediate signal is less informative(i.e.,has a greater chance of being erroneous)about the long-term project than about the short-term project.Thus,we assume:δs>δl andδ0s>δ0l(for the talented incumbent with or without e?ort,respectively). Similarly,we assume thatψs>ψl andψ0s>ψ0l(for the untalented incumbent,with or without e?ort,respectively). In summary,we assume:δs>ψs>δl>ψl>ψ0s>ψ0l(we do not mentionδ0l andδ0s in the above summary since

the talented incumbent always exerts e?ort,so that these are unimportant for our further analysis).

14An equivalent speci?cation is to assume that a good signal is received with a certain probability and no signal is received with the complementary probability.

14

3.3The Rival

After outside investors receive the intermediate signal about the incumbent’s progress in project implementation, a rival may arrive and try to take over control of the?rm.At time0,the incumbent and outside investors are uncertain about whether any rival will arrive or not:they only observe the probabilityφthat a rival will arrive;no rival will arrive with the complementary probability.We denote the rival’s wealth by W R.There is no uncertainty about the ability of the potential rival in the basic model(we will relax this assumption by introducing multiple rival ability levels in section5).If the rival succeeds in taking over the?rm,she will generate a time1cash?ow of C R with probability1(regardless of project horizon).We assume that the rival,if she arrives,has a higher ability than an untalented incumbent in implementing a short-term project,and a lower ability than a talented incumbent in implementing the same project:i.e.,ηs C H+(1?ηs)C L>C R>ψs C H+(1?ψs)C L.Further,we assume that the intermediate signal received by outsiders is precise enough that the expected cash?ow from the?rm’s project under the incumbent conditional on a good intermediate signal is higher than the expected cash?ow under rival management;on the other hand,the expected cash?ow under the incumbent conditional on a bad intermediate signal is worse than that under rival management:

Pr ob(T|G)[ηs C H+(1?ηs)C L]+Pr ob(U|G)[βs C H+(1?βs)C L]>C R,(1) and

Pr ob(T|B)[ηs C H+(1?ηs)C L]+Pr ob(U|B)[βs C H+(1?βs)C L]

The rival’s objective in investing her wealth W R in the?rm’s equity is to maximize the sum of her security and control bene?ts(assumed to be positive).We assume that the rival can only buy equity from passive investors. Outside investors(and the incumbent)observe all the features of the rival immediately after she arrives.Thus the rival has to pay a“fair price”for the equity she buys from passive investors,who price the?rm’s equity competitively based on their equilibrium beliefs.In other words,the price paid by the rival for the?rm’s equity depends on her own ability and the expected outcome of the control contest.

15

3.4Passive Investors and the Control Contest

We now specify the voting behavior of passive investors.Whether or not the?rm chooses a single class or dual

class share structure,passive investors’shares have only one vote per share(i.e.,in a dual class share structure,the incumbent holds all supervoting shares).We assume that outside investors vote for the party which maximizes their long-term share value.Given our earlier assumptions,this means that all passive investors vote for the incumbent if they receive a good intermediate signal,and for the rival if they receive a bad intermediate signal about the incumbent’s progress in implementing the?rm’s project.We assume that the incumbent’s wealth(subsequent to the dilution of his equity holding due to the?rm’s IPO)is small enough that,under a single class share structure he needs passive investors’votes to maintain control:i.e.,he cannot maintain control solely by relying on voting for himself in the control contest against any rival.At the same time,the rival’s wealth W R is also not large enough to buy up enough equity to ensure success in the control contest by relying only on voting her own shares:in other words,the rival also needs passive investors’votes to prevail in the control contest.Thus,passive investors’votes are pivotal in determining whether it is the incumbent or rival who controls the?rm subsequent to the control contest.

Passive investors’votes,however,are not important to the incumbent under a dual class share structure.This is because,under a dual class share structure,the incumbent can always structure the voting ratio between supervoting and ordinary shares(denoted by t)such that he will never lose to a rival in a control contest.Regardless of how small his share holding in the?rm,the incumbent can always choose t such that he retains at least50%control of the?rm.15In summary,if a dual class IPO is chosen at time0,the incumbent is always able to maintain control regardless of the realization of the intermediate signal,even if a rival arrives and attempts to take over control.In contrast,if a single class IPO is chosen at time0,the incumbent loses control if a rival arrives and outsiders receive a bad intermediate signal(since all outsiders will vote against him in this case);he maintains control if either no rival arrives,or a rival arrives but outsiders receive a good intermediate signal(since all outsiders vote for the incumbent

in this case).16

15Note that in the basic model,we assume that the incumbent always chooses t to ensure control against any rival,so that t is not a choice variable.In section5,where we solve for the optimal voting ratio in dual class IPOs,we will relax this assumption,and allow the incumbent to choose the optimal level of t.

16The underlying assumption here is that all outsiders vote for the management(incumbent or rival)which will maximize the expected value of their equity in the?rm(conditional on the information set of outsiders).Our results go through qualitatively even if we assume instead that a majority of outsiders(rather than all outsiders)vote for the management team that outsiders perceive as value-maximizing.

16

3.5The Incumbent’s Objective

The incumbent obtains both security(cash?ow)bene?ts and control bene?ts from managing the?rm under his

control.17The incumbent’s security bene?ts arise from the cash?ows of the projects accruing to the share of the ?rm’s equity held by him(such cash?ows accrue to all equity holders in proportion to their equity holdings in the ?rm).In contrast,control bene?ts(which are non-contractible)accrue only to the management team in control.

We useαi,i∈{D,S},to denote the fraction of equity retained by the incumbent in his?rm’s IPO(a dual-class or a single-class IPO),and F mi,m∈{T,U},i∈{D,S},to denote incumbent’s expectation(conditional on his private information about his own talent)of the future cash?ows from the?rm.Therefore,the security bene?ts the

incumbent gets isαi F mi,i∈{D,S},m∈{T,U}.Further,we use o i∈{0,1},i∈{D,S},to denote the outcome of the control contest(o i=0if the incumbent loses control to a rival,and o i=1if the incumbent maintains control).

Thus the expected value of the incumbent’s control bene?ts is o i B.We use e m,m∈{T,U}to denote the cost of e?ort for the two types of the incumbents.As discussed before,we assume that the talented incumbent has an e?ort cost of zero,and the untalented incumbent has a positive cost of e?ort(i.e.,e T=0,and e U=e>0).Whether the incumbent exerts e?ort or not is unobservable to outsiders and is thus non-contractible.Whether the incumbent exerts e?ort or not is captured by w∈{0,1}:w=1if he exerts e?ort and0otherwise.

In summary,the objective of each type of incumbent is to make a choice of IPO share structure(i∈{D,S}), project horizon(p∈{l,s}),and whether to exert e?ort or not(w∈{0,1}),in order to maximize the expected value of the sum of his time1security and control bene?ts,net of any personal e?ort costs incurred by him.This is given by:

Max

(αi F mi+o i B?w mi e m).(3)

i,p i,w mi

Note that,in the incumbent’s objective(3)above,αi is an endogenous variable which depends upon the share structure chosen by the?rm(and thus the market value of its equity)and the amount of external?nancing I that the?rm wishes to raise in the equity market;similarly,o i and w mi are also endogenous variables.We discuss the incumbent’s problem in detail in the next section.

17This assumption is standard in the corporate control literature.See,for example,Grossman and Hart(1988)or Harris and Raviv (1988).

17

4Equilibrium in the Basic Model

In this section,we characterize the equilibria of our basic model.The equilibrium concept we use is that of Perfect

Bayesian Equilibrium.18An equilibrium consists of(i)a choice of IPO share structure by the incumbent,along with his choices of IPO share price,the number of shares to be o?ered to outside investors,project horizon,and the level of e?ort to exert in implementing the?rm’s project;(ii)a decision by each outside investor about whether or not to participate in the IPO and a choice of management team to vote for in the event of a control contest;and(iii)a decision by the rival(if she arrives)about whether or not to purchase the?rm’s shares from outside investors in an attempt to take over the?rm.Each of the above choices must be such that:(a)The choices of each party maximize their objectives,given the equilibrium beliefs and choices of others;(b)The beliefs of all parties are consistent with the equilibrium choices of others;further,along the equilibrium path,these beliefs are formed using Bayes’rule;(c) Any deviation from his equilibrium strategy by any party is met by beliefs by other parties which yield the deviating party a lower expected payo?compared to that obtained in equilibrium.

In propositions1and2,we characterize the equilibria in our basic model for di?erent model parameters.We discuss the nature of these equilibria at some length,since we build on these basic equilibria in subsequent sections of the paper.19

Proposition1(Dual Class IPO Equilibrium).For a given level of takeover activityφ,and control bene?ts B,there exists an equilibrium where the incumbent chooses a dual class IPO if his reputation is high enough and

the di?erence in the intrinsic value between the long-term and the short-term projects is large enough(the speci?c 18See Fudenberg and Tirole(1991)for a detailed description of this equilibrium concept.In section4we will make use of a dynamic model where there is a second round of equity?nancing,possibly a second control contest,and an adjustment of share structure after the

cash?ows of the?rst period project are realized.In section6we will also characterize the equilibrium while allowing the incumbent to choose the optimal voting ratio in addition to the share structure.However,the general de?nition of equilibrium used in these sections will be same as the one described here.

19Throughout this paper,our focus will be on pooling equilibria,where the two types of incumbents pool by making similar decisions on IPO share structure,equity pricing,number of shares to o?er to outside investors,and project horizon.We will not focus on equilibria where the actions taken by the two types of incumbents are di?erent in equilibrium,so that the equilibrium is fully separating,and the choice of IPO share structure is a signal of the incumbent’s true type.Two potential separating equilibria are as follows.The?rst separating equilibrium is the case where the talented incumbent chooses a single class share structure for his IPO while the untalented incumbent chooses a dual class share structure.This equilibrium is not very plausible,since it occurs only when the bene?ts to the talented incumbent of undertaking a long-term versus a short-term project is small enough(relative to the value bene?t of separating from the untalented incumbent),and the incumbent’s control bene?ts are large enough that the untalented incumbent does not wish to mimic the talented one(while at the same time,not so large that the talented incumbent is better o?choosing a dual class share structure due to the reduction in his control bene?ts under a single class share structure).The second separating equilibrium involves the talented incumbent choosing a dual class share structure while the untalented incumbent separates by choosing a single class share structure.This equilibrium is equally implausible,since it arises only when the increased security bene?ts to the untalented incumbent of committing to exert e?ort through his choice of single class share structure is greater than the sum of the bene?ts of mimicking the talented incumbent and the greater expected value of control bene?ts under a dual class share structure relative to a single class share structure.Thus,the pooling equilibria studied here are the“natural”equilibria that arise in our setting.Further,separating equilibria are not interesting in our setting,since the most important issues that we analyze here do not arise in these equilibria.Never the less, details of the above separating equilibria are available to interested readers upon request.

18

parametric conditions are speci?ed in the appendix).Such an equilibrium involves the following:

The talented(T)incumbent:He sells a fraction(1?αD)of the?rm’s equity(in the form of ordinary voting shares carrying one vote per share)to outsiders at a price P D(P D is given by(4)andαD by(5)).He retains the remaining fractionαD of equity in the form of supervoting shares carrying a fractionαD

of the total voting

αD t+(1?αD)

power of the?rm’s equity.20He implements the long-term project and exerts e?ort.

The untalented(U)incumbent:He mimics the talented incumbent by selling a fraction(1?αD)of equity at a price P D,retaining a fraction ofαD of equity as supervoting shares.He also implements the long-term project,but exerts no e?ort.

Outside investors:They participate in the?rm’s IPO,paying(1?αD)P D for a fraction(1?αD)of the?rm’s shares.If there is a control contest at time1,they vote for the incumbent if they get a good realization of the intermediate signal,and for the rival if they get a bad realization.

The rival:If she arrives,she invests all of his wealth,W R,in buying shares from outside investors,but will not be able to take over the?rm.21

The incumbent chooses between a dual class and a single class IPO share structure based on the costs and bene?ts of each over the other.The equilibrium in this case is driven by the choices made by the talented incumbent,since the untalented incumbent?nds it optimal to mimic the talented incumbent.The choice of a talented incumbent between a dual class and a single class share structure depends on three e?ects.First,the insulation from the takeover market provided by a dual class share structure would allow him to create more value by implementing a long-term rather than a short-term project,without a fear of losing control if a rival for control arrives before the resolution of uncertainty about such a long-term project.Since project horizon is observable to outsiders,this “long-term value creation”e?ect would be re?ected in the?rm’s IPO share price(and allow him to reduce the dilution in his equity holdings due to the IPO).However,the insulation from the takeover market provided by a dual class share structure also allows untalented incumbents to slack o?by not exerting e?ort in implementing the

20Throughout this paper,whenever we refer to a fraction of a?rm’s“equity,”we refer to the cash?ow rights associated with this equity;on the other hand,we will speci?cally refer to the“voting power”of equity when this is the subject of discussion.

21There are two dimensions in which an incumbent can make an out-of-equilibrium move observable to outsiders in our setting.The?rst dimension is the incumbent’s choice of share structure:i.e.,an incumbent may choose a single class IPO in a dual class IPO equilibrium, or a dual class IPO in a single-class IPO equilibrium.The second dimension is the incumbent’s choice of project horizon:the incumbent may choose a short-term project when the equilibrium behavior calls for his choosing a long-term project(as in proposition1)or he may choose a long-term project when the equilibrium behavior calls for his choosing a short-term project.Throughout this paper,the out-of-equilibrium beliefs we specify are such that if outsiders observe a?rm taking an out-of-equilibrium action,they believe with probability1that the incumbent of that?rm is untalented,and will not exert any e?ort in implementing that?rm’s project.

19

本文来源：https://www.bwwdw.com/article/0j4q.html