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Three essays on investment and information acquisition/disclosure decisions around equity offerings Li, Yinghua 2005

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Three Essays on Investment and Information Acquisition/Disclosure Decisions around Equity Offerings by Y i n g h u a L i B . S . , Northeastern Universi ty , C h i n a , 1997 M . S . , R e n m i n Univers i ty of C h i n a , 2000 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Business Admin i s t r a t i on ) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September, 2005 © Y i n g h u a L i , 2005 A B S T R A C T It is often believed that increased informat ion flow can facil i tate resource allocations and improve market efficiency in the capi ta l market. Equ i ty - i s su ing firms can play significant roles in the capi ta l format ion process, since they are a major provider of informat ion and possess in t imate knowledge about their business. Therefore i t is impor t an t to understand factors that affect their disclosure incentives. In addi t ion , regulators are concerned wi th for-mula t ing appropriate laws and policies to encourage more disclosure of credible information. Previous disclosure models often assume a pure-exchange economy when ana lyz ing equity-issuing firms' disclosure incentives. Such a sett ing might not be descript ive of equity offerings that involve p roduc t ion decisions. It is also commonly assumed that f i rm managers are ex-ogenously endowed w i t h private informat ion. However, i t usual ly takes efforts and resources to produce informat ion. A s stated i n Chris tensen and Fe l tham (2003), "it is a manager's abi l i ty to acquire and process informat ion efficiently that makes h i m an effective manager". T h i s thesis extends the s tandard "new equity" disclosure mode l in- the l i terature by in -t roducing p roduc t ion choices and endogenizing firms' informat ion acquis i t ion decisions. It studies the interact ion between equity-issuing firms' product ive activities- and informat ion acquis i t ion/disclosure decisions. It consists of four parts. Chap t e r 1 provides a general discussion of theoret ical disclosure l i terature, and briefly introduces the m a i n features and results of the subsequent chapters. Chapte r 2 examines how equi ty- issuing firms' disclo-sure incentives affect their investment decisions arid their incentives to acquire pre-decision information. Chapte r 3 examines the impact of different disclosure policies on firms' disclo-sure incentives and investment decisions. Chapte r 4 introduces shareholder l i t iga t ion, and analyzes the resul t ing disclosure equi l ib r ia and efficiencies of p roduc t ion decisions. T h i s research adds to our unders tanding of the subtle interplay of equi ty- issuing firms' disclosure and product ions decisions. It also provides arguments for cau t ion w i t h respect to sett ing disclosure policies. It is shown that i t is difficult to determine the ex ante op t ima l pol icy in a p roduc t ion economy. i i Contents A b s t r a c t i i T a b l e o f C o n t e n t s i i i L i s t o f T a b l e s v L i s t o f F i g u r e s v i A c k n o w l e d g e m e n t s v i i 1 I n t r o d u c t i o n 1 2 A N e w - E q u i t y D i s c l o s u r e M o d e l 15 2.1 In t roduct ion . 15 2.2 M o d e l Se t t ing 17 2.3 Benchmark Case: Se l f -F inanc ing 19 2.3.1 Informat ion A c q u i s i t i o n and Investment Decisions 19 2.3.2 Compara t i ve Stat is t ics 21 2.4 Ana lys i s of E q u i t y - F i n a n c i n g 24 2.4.1 T h e Entrepreneur 's Investment Decis ion when She is Un in fo rmed . . 26 2.4.2 T h e Entrepreneur 's Investment /Disclosure Decisions when She is In-formed 28 2.4.3 T h e Entrepreneur 's Information A c q u i s i t i o n Dec is ion 33 2.5 Efficiency Ana lys i s 35 2.5.1 Af ter the Release of P u b l i c Repor t and Before the Entrepreneur Makes any Decisions (t = 1) . . . 35 2.5.2 Before the Release of P u b l i c Repor t (t = 0) 42 2.6 Conc lus ion 43 i i i 3 C o m p a r i s o n of T h r e e D i sc lo su re Reg imes 45 3.1 In t roduct ion ' 45 3.2 Ins t i tu t ional Backg round 48 3.3 T h e M o d e l Se t t ing 51 3.4 T h e Entrepreneur 's Information Acqu i s i t i on and Investment Decisions . . . . 54 3.4.1 T h e Benchmark Case > 54 3.4.2 Non-Disc losure Regime - 56 3.4.3 V o l u n t a r y Disclosure Regime 61 3.4.4 M a n d a t o r y Disclosure Regime 68 3.5 Compar isons of Disclosure Regimes 69 3.6 Discussion and Conc lus ion 73 4 Impac t of Shareho lder L i t i g a t i o n 76 4.1 In t roduct ion 76 4.2 M o d e l Set t ing and Benchmark Case 82 4.2.1 Set t ing and M a j o r Assumpt ions 82 4.2.2 Se l f -F inanc ing - the Benchmark Case 84 4.3 Ana lys i s of the E q u i t y Offering 85 4.3.1 T h e Lawyer ' s L i t i g a t i o n Decis ion at t=2 85 4.3.2 T h e Entrepreneur 's Disclosure Decis ion at t = 1 if She is Informed . . 87 4.3.3 T h e Entrepreneur 's Investment Decis ion at t — 1 92 4.4 Welfare A n a l y s i s and P o l i c y Implicat ions 95 4.4.1 Soc ia l Welfare 95 4.4.2 Impl ica t ions for S E C ' s Proposed Securities Offering Refo rm 97 4.5 Discuss ion and Conc lus ion 99 B i b l i o g r a p h y 102 A p p e n d i x 110 iv List of Tables 3.1 Efficiencies of Decisions i n Three Disclosure Regimes 75 4.1 Efficiencies of Decisions in Different Disclosure E q u i l i b r i a . 101 v List of Figures 2.1 Sequence of Events when Project is Self-financed 19 2.2 T h e Value of Informat ion as a Func t ion of the Projec t N P V based on the P u b l i c Repor t when Projec t is Self-financed (7 = 0, = 1) 23 2.3 T h e Value of Informat ion as a Func t ion of Informativeness (l=ayi) of the Signal yi when Projec t is self-financed (7 = 0, p = 3) 23 2.4 Sequence of Events when the Entrepreneur Raises E q u i t y C a p i t a l to F inance the Project 25 2.5 Investment /Disclosure Decisions given the P u b l i c Repor t and an Informative Pr iva te Signal 30 2.6 T h e Entrepreneur 's Investment Decisions after She has A c q u i r e d Information and Received an Informative Signal (p > 0, T(p, q, ayi, 7) > 0). . . . . . . . . 39 3.1 Sequence of Events 53 4.1 Sequence of Events 84 4.2 Impact of L i t i g a t i o n R i s k on Disclosure Cutoff (s — 2, q = 10, A — 0.2, 7 = 0.9,(7 = 1 0 , ^ = 1 , 6 ^ = 1): 91 4.3 T h e Entrepreneur 's Investment Decisions i n Different Disclosure E q u i l i b r i a when She is Informed . 93 vi A C K N O W L E D G E M E N T S I am tremendously indebted to Professor Gera ld (Jerry) F e l t h a m (thesis commit tee co-chair) for what I have learned from his two theoretical doctora l seminars! H e has an immea-surable influence on my career by ins t i l l ing in me a love of learning, an apprecia t ion of the beauty of ana ly t ica l models, and a strive for excellence. I want to give m y special thanks to Professor Sandra C h a m b e r l a i n (thesis commit tee co-chair) and Professor Joy. Begley for their valuable support and nur tu r ing throughout m y P h . D . program. I also greatly appre-ciate many insightful discussions and suggestions of m y disser ta t ion commit tee member, Professor R a l p h Win t e r . v i i Chapter 1 Introduction One wel l -known puzzle in the theoret ical disclosure l i terature i n accoun t ing 1 is a counterin-tui t ive but quite robust result on the inefficiencies of account ing disclosures. It is shown that in the pure exchange economy, full and par t ia l disclosure equ i l ib r ia are ex ante less efficient than non-disclosure equ i l ib r ium. Therefore, i f shareholders could commi t f i rm managers to a non-disclosure policy, they would actual ly be better off than grant ing managers discret ion to voluntar i ly disclose. T h e above result follows from the fact that i n a pure exchange set t ing the only role that publ ic informat ion can play is to redistr ibute wealth among market players and i f acquisi t ion and /or disclosure of add i t iona l informat ion is costly, efforts to create a more informative publ ic informat ion system are ex ante inefficient. 2 'In addition to Verrecchia (2001) and Dye (2001)'s review papers, another excellent reference on disclosure literature is Christensen and Feltham (2003). 2 In addition, if the market participants are risk averse, early disclosure can make all the participants collectively worse off if it precludes them from insuring their risks through trading (Hirshleifer 1971). 1 To solve this puzzle, previous l i terature has proposed several approaches (Verrecchia 2001). T h e first approach is to consider the role of pub l ic account ing informat ion in re-ducing costly private informat ion acquisi t ion while ma in ta in ing the assumpt ion of the pure exchange economy. T h e second approach tries to introduce p roduc t ion decisions so that better informat ion can potent ia l ly improve social welfare by fac i l i t a t ing decis ion-making i n product ions. A t h i r d approach is to explore the impact of account ing disclosures on reducing the cost of c a p i t a l . 3 • • T h i s thesis follows the second approach and adopts a product ive set t ing to investigate the disclosure of pre-decision p roduc t iv i ty information. A s Chr is tensen and Fe l tham (2003) point out, as long as the manager chooses p roduc t ion plans to m a x i m i z e the firm's in t r ins ic value, the product markets are compet i t ive , and investors are well-diversified, "achievement of Pareto efficiency does not require that firm-specific productivity information be reported to investors". Therefore, a non-disclosure equ i l ib r ium can continue to dominate a par t ia l or full disclosure equ i l ib r ium even i n a produc t ion economy: . However, firms might prefer to disclose their private informat ion to outside investors under certain circumstances, such as when issuing new equity. T h i s is because disclosure can affect market percept ion of firm value and firms w i t h favorable pr ivate informat ion may want to share the good news w i t h investors to get better prices when sel l ing their stocks. T h e equity offering set t ing is adopted by many disclosure models i n the exis t ing ac-3 See, for example, Ba iman and Verrecchia (1996)>and Verrecchia (1999, 2001). These papers argue that more informative disclosure can lower the cost'of raising equity capital by reducing the premium paid to the l iquidity traders dur ing equity issuances. 2 . count ing l i terature. In these "new equity" disclosure models, i t is usual ly assumed that a r isk-neutral entrepreneur (or a manager who represents the collective interests of risk-neutral shareholders), makes disclosure decisions to max imize the current market value of the firm's equity. One impor tan t result is that when disclosure is. costless and t ruthful , and investors are certain that the manager has private informat ion, a ful l disclosure equ i l ib r ium w i l l prevail (Grossman 1981). O n the other hand, when disclosure is costly, or investors are uncertain about the informat ion endowment.of the f irm manager, there is a pa r t i a l disclosure equi l ib r ium, in wh ich the manager discloses her private s ignal if, and only if, it exceeds a cutoff value. In addi t ion , most of these previous studies assume a pure-exchange sett ing that involves no produc t ion . T h e exis t ing pure-exchange disclosure models have not considered the fol lowing features of the equity offerings in the real economy. F i r s t , one of the most c o m m o n purposes for issuing equity is to raise cap i ta l to finance an investment project such as establishing a new business or expanding an exis t ing business. 4 Therefore, equity offerings often involve product ion decisions. Second, private information held by an issuing firm is l ikely to be related to its future prospects, especially the prof i tabi l i ty of the investment to be financed. T h i s implies that managers can use the information bo th to faci l i tate in ternal p roduct ion decisions, and to influence investors ' perceptions of f i rm value. G i v e n these features, there can be interactions between a f irm's investment and acquisi-t ion/disclosure of informat ion in equity offerings. F i r s t , the pr ivate signal to be disclosed is 4Other reasons for issuing equity include debt repayment and distribution to pre-IPO shareholders, etc. See Leone et al (2003). 3 pre-decision informat ion and knowledge of such informat ion can lead the f irm to change its product ion plan. Second, when a firm raises capi ta l to finance a project, disclosure affects the firm's investment decision through its impact on investors ' va lua t ion and therefore the fraction of equity the firm has to provide in exchange for the capi ta l . W h e t h e r an investment project is implemented depends on whether the firm is able to raise the required capi ta l and the terms of the equity offering (i.e., the fraction of equity exchanged). T h i r d , the firm makes the informat ion acquis i t ion decision i n ant ic ipa t ion of its later investment and disclosure de-cisions. It trades off the acquis i t ion cost against the product ive value of the information and the potent ia l misva lua t ion resul t ing from her inab i l i ty to disclose i f it has not acquired information before issuing equity. T h e misvaluat ion occurs since investors might be unable to dis t inguish whether the non-disclosure occurs because the firm is uninformed or it is wi thhold ing a bad signal . T h e thesis extends pr ior research to analyze the interact ion between firms' product ive activit ies and informat ion acquis i t ion/disclosure decisions. It is organized as follows. C h a p -ter 2 examines this issue by in t roduc ing product ion into a new-equity disclosure model and endogenizing firms' informat ion acquis i t ion decisions. Chap te r 3 analyzes the impact of dif-ferent disclosure policies on firms' disclosure incentives and investment decisions. Chapter 4 introduces shareholder l i t iga t ion , and analyzes the resul t ing disclosure equ i l ib r ia and ef-ficiencies of p roduc t ion decisions. E a c h of these chapters is in t roduced in more detai l as follows. 4 Brief Discussion of Chapter 2 T h e model developed i n Chapte r 2 has the fol lowing fundamental characteristics. There are two players, a r i sk-neutra l entrepreneur (or a firm manager mot iva ted to max imize the current shareholders' interests), and a group of r isk-neural investors. E a c h player makes the following choices sequentially. A t t — 0, the entrepreneur has an investment oppor tun i ty that requires an investment of q. She can.choose to purchase a private signal yi about the prof i tab i l i ty of the new project, at a cost K. A t t = 1, a pub l ic report ya is released. Af ter observing the pub l i c report and the acquisi t ion cost, the entrepreneur decides whether to acquire the s ignal . A t t — 2, based on her informat ion set, the entrepreneur decides whether to invest a n d / o r disclose her private information. If she is uninformed, she has two decision choices: invest or not invest. If she is informed, she s imul taneously decides whether to invest and whether to disclose the private signal. If she decides to undertake the project, she raises capi ta l from the stock market by offering investors a fraction a of the firm's equity in exchange for q. A s s u m e that 6 is the m a x i m u m price the investors are w i l l i n g to pay. T h e investors agree to provide the cap i ta l as long as a > q/5. In a compet i t ive market, the entrepreneur offers a = q/5. T h e investors price the firm based on their informat ion set at t — 2, ty2 = (ya,m,q), where m is the entrepreneur's report (m = yi if the entrepreneur discloses, and m — n if the entrepreneur does not disclose), and q is the entrepreneur's investment decision. A t t = 3, i f the entrepreneur has invested in the project, the payoff is realized and shared between the two players. Otherwise, the 5 te rminal cash flow is zero. . • • Some of the key assumptions are discussed below. 1. Fo l lowing the work of Dye (1985) and Jung and K w o n (1988), the mode l imposes some uncertainty on the entrepreneur's informat ion endowment. Specifically, it is assumed that the informat ion acquis i t ion cost is a r andom variable ex ante and realized before the entrepreneur makes the informat ion purchase decision. W e also assume that w i t h a posit ive p robab i l i ty the entrepreneur w i l l receive a n u l l s ignal after incur r ing the ac-quis i t ion cost. Under these assumptions, in equ i l ib r ium, there is a posi t ive probabi l i ty that the entrepreneur is uninformed. W h e n the investors observe no disclosure from the entrepreneur, they cannot dis t inguish whether it is because the entrepreneur has not acquired informat ion, or she has acquired informat ion but received an uninforma-tive signal, or she has received an informative signal but decides to w i t h h o l d it due to the adverse content. Such uncertainty can prevent unravel l ing from happening, and . result in a pa r t i a l disclosure equi l ib r ium. 2. We assume that the only sources of information for the investors are the pub l ic report, i the entrepreneur's disclosure, and her investment decision. T h a t is, we do not allow for the poss ib i l i ty that the investors could have access to al ternat ive informat ion sources, or the entrepreneur could convey her private informat ion through other mechanisms (such as underwri ter reputa t ion or auditor qual i ty) . W e believe that this assumption is val id as long as the investors could not fully infer or uncover the entrepreneur's private information. Direc t disclosure can be impor tant i f it is incrementa l ly informative be-6 ' . yond al l the other al ternative information. In addi t ion , if other disclosure mechanisms are more costly, direct disclosure can have a posi t ive role in the economy. 3. B o t h players are r isk-neutra l . If, instead, the entrepreneur is risk-averse, we have to consider the s ignal l ing role of the fraction of the equity offered to investors (or the fraction reta ined by the entrepreneur). T h e n in equ i l ib r ium the entrepreneur can use a combina t ion of b o t h equity retention and direct disclosure to convey her private information. B y assuming the entrepreneur is r i sk-neutra l , we s implify the analysis and also focus on the role of direct disclosure. 4. Disclosure is t ru thfu l whenever the 'entrepreneur reports, her pr ivate information to the investors. F i r s t , this assumption is a s tandard assumpt ion in the l i terature and is typ ica l ly just if ied by the anti-fraud legislat ion and reputa t ion concerns. Second, the chapter focuses on disclosure of t ruthful forward- looking informat ion , and how such disclosures affect firms' product ive decisions. T h i r d , ma in t a in ing a balance between encouraging more disclosure and deterring mis leading disclosure has always been one of the biggest challenges i n disclosure regulat ion. T h i s tension becomes even more severe in the case of management forecasts. T h e major reason is that de termining the truthfulness of forward-looking information is difficult, since such informat ion cannot be verified. T h e ac tual result might be used to verify the forecast, bu t a deviat ion between the two can be a t t r ibutable to poor forecast ski l ls , or various r isk factors beyond managers ' control . However, we admit that a l lowing for the poss ibi l i ty of ly ing could potent ia l ly shed more light on firms' incentive to misrepor t i n the real economy. 7 5. There are no agency problems i n the current sett ing. T h e mode l adopts an entrepre-neurial sett ing, and therefore abstracts from many contrac t ing and other agency issues, since the entrepreneur makes decisions to maximize her own interest. In the real wor ld , firms can be managed by a manager hired by in i t i a l owners. There are studies which examine firms' disclosure in an agency setting, such as Gig le r and Hemmer (1998 and 2001). • . • Let us now discuss the m a i n characteristics of the equi l ibr ia . Depend ing on parameter values, there are two potent ia l disclosure equi l ibr ia . One is a pa r t i a l disclosure equ i l ib r ium, in which the entrepreneur discloses if, and only if, the private signal is above a cer tain threshold. ' T h i s result is consistent w i t h that of previous studies that assume investors are uncertain about the manager's informat ion endowment. In the other equ i l i b r ium, the entrepreneur fully discloses whenever she issues equity. T h e latter equ i l ib r ium can. be sustained i f the investors can credibly threaten to offer a very low price i f the entrepreneur issues equity but does not make any disclosure. T h e analysis shows that, firms' ex post disclosure incentives can dis tor t their investment and ex ante informat ion acquis i t ion decisions. F i r s t , overinvestment can be induced when firms' shares are overvalued and the overpr ic ing offsets the loss f rom under t ak ing a negative N P V project. Second, the entrepreneur has incentives to acquire too much private infor-mat ion so that she can strategically use the informat ion to influence the share price of the offering. T h i s result is consistent w i t h that of Shavell (1994) and Pae (2002). B o t h show that voluntary disclosure results i n sellers' social ly excessive incentives to acquire information. 8 Our work contributes to bo th the theoret ical disclosure and the corporate finance l i t -erature. W e extend pr ior research on examining firms' disclosure practices in product ive settings and reconfirm Dye 's caut ion that a product ion economy is not an obvious sett ing for publ ic disclosure to have a posi t ive net social value . 5 O u r analysis also reveals other "side effects" of equity-f inancing. In addi t ion to the possible negative market react ion to the announcement of the equity issuing decision (Myers and Maj lu f , 1984), equity-f inancing can make the current shareholders worse off due to the inefficiencies associated w i t h the issuing firm's subopt imal informat ion acquisi t ion and investment decisions du r ing the offering. A m o n g a smal l number of papers in this area, Pae (2002) is most closely related to our work. Pae (2002) also analyzes the acquisi t ion and disclosure of pre-decision informat ion in a production-based model and shows that the p roduc t ion decisions are dis tor ted by the en-trepreneur's discret ionary disclosure. However, our model differs from Pae 's model in several aspects. F i r s t . Pae (2002) has a dis t inct model setting. In Pae's model , there is a competi-tive market w i t h a large group of entrepreneurs selling their assets. E a c h entrepreneur puts in some effort before the sale of the asset, and after ga in ing the control rights the investors continue to make the capi ta l investment decision. Therefore disclosure not only influences the investors' va lua t ion of the asset, but also effects their post-purchase investment decision. If the private informat ion is not disclosed, the investors w i l l then have to make "uninformed" product ive decisions. In contrast, in our set t ing there is only one entrepreneur who makes al l the information acquis i t ion, investment and disclosure decisions. T h i s implies that the 5See Dye (2001), pages 191-197. 9 information can be used in the p roduc t ion even if it is not pub l i c ly disclosed. Ano the r major difference between ours and Pae's model is that Pae assumes the fract ion of uninformed en-trepreneurs is exogenous and informed entrepreneurs can choose the informativeness of their signals, while we assume that the probabi l i ty the entrepreneur is uninformed is endogenously determined in the equ i l ib r ium and the entrepreneur decides whether to acquire a signal w i t h a given precision. Brief Discussion of Chapter 3 In recognit ion of the impor tance of the legal environment and disclosure regulat ion for equity-issuing firms' disclosure practices, Chapte r 3 investigates the impac t of ex ante disclosure policies on I P O firms' incentives to acquire forward-looking informat ion and their investment decisions. It examines three disclosure policies, Non-Disc losure , V o l u n t a r y Disclosure and M a n d a t o r y Disclosure Regimes. A l l these policies can be found in real countries. T h e model is bu i l t upon the one developed in Chapte r 2, w i t h the fol lowing major differences. F i r s t , the entrepreneur might no longer be able to vo lun ta r i ly choose whether to disclose her private informat ion. Instead she has to comply w i t h a certain disclosure pol icy that cou ld enforce non-disclosure or ful l disclosure. Second, the entrepreneur is now assumed to own bo th an exis t ing asset and a new investment project. In addi t ion to the private forward- looking informat ion about the prof i tabi l i ty of the new project (yi), there is also a signal about the performance of the exis t ing asset (yh)- Such h is tor ica l information is mandated to be disclosed i n the offering. T h e sequence of decisions made by the two 10 players is s imi lar to what is described in Chapte r 2. T h e entrepreneur chooses: (1) whether to acquire informat ion at t = 1; (2) whether to invest and /o r disclose at t = 2. T h e investors choose whether to provide the capi ta l at t = 2. A s to the informat ion sets of the two players, the entrepreneur observes yh, the real izat ion of the r andom informat ion cost K, and yt i f she acquires informat ion; the investors observe yih, q (the entrepreneur's investment decision), and yi if the entrepreneur discloses yi. T h e analysis shows that disclosure regulat ion plays an impor tan t role i n I P O s . It not only affects the to ta l informat ion available to investors, but also has externali t ies on firms' real decisions. In addi t ion , different disclosure policies are associated w i t h different distort ions in firms' informat ion acquis i t ion and investment decisions. Nei ther the M a n d a t o r y or the Volun ta ry Disclosure Reg ime is necessarily more efficient than the Non-Disc losure Regime in equity offerings that involve produc t ion decisions. T h i s chapter extends pr ior studies on how ex post disclosure decisions can distort firms' ex ante incentives to acquire informat ion. Shavell (1994) examines this issue i n a general sales t ransact ion set t ing and one impor tan t insight from his s tudy is tha t vo lunta ry disclosure results in sellers' socia l ly excessive incentives to acquire informat ion . O u r analysis confirms this finding in a financial repor t ing sett ing and generates add i t iona l insights by showing that a Non-Disc losure regime can instead reduce firms' incentives to produce informat ion that has social value. It also contributes to the l i terature on disclosure regulat ion. T h e pr ior studies w i t h which we are familiar focus on the comparison of the voluntary disclosure and the mandatory 11 disclosure policies. T h a t is, the question considered is whether to force firms to disclose or to let them choose whether to disclose. T h i s chapter also analyzes another po l icy choice, a Non-Disclosure Regime that inhibi ts disclosure. Ano the r feature is that the disclosure policies model led in this chapter are not contingent on firms' informat ion endowment. In par t icular , we assume that under the F u l l Disclosure policy, the firm has to satisfy the disclosure requirement even i f i t is uninformed. P r io r studies such as Shavel l (1994) and A d m a t i and Pfleiderer (2000J consider a mandatary pol icy that forces firms to disclose only if they have private informat ion . Such a pol icy wi l l be difficult to enforce, since it requires that any concealment of pr ivate informat ion be detected and punished. However, it is usual ly very difficult to prove i n courts that a firm manager has received cer tain private informat ion and in tent ional ly wi thhe ld i t from investors. O n the other hand, the disclosure regimes model led i n our work are enforceable and axe also consistent w i t h the actual disclosure policies adopted i n various countries. Brief Discussion of Chapter 4 T h e last chapter exp l ic i t ly models shareholder l i t iga t ion as an impor tan t force that affects I P O firms' disclosure incentives. It i s ' m a i n l y mot iva ted by the S E C ' s recent proposal to reform the communica t ion process in securities offerings. T h e analysis is intended to shed light on issues such as whether the regulators should provide a safe harbor for I P O firms' disclosure of forward- looking informat ion and whether I P O firms should be required to file a forecast in their filings. .12 T h e model has three r isk-neutral players, an entrepreneur, a group of investors, and a lawyer. T h e players make the fol lowing choices. A t t = 1, the entrepreneur observes ^ w i t h a posi t ive probabi l i ty . Based on her informat ion set, she decides whether to invest a n d / o r disclose her private s ignal i n the form of a management forecast. If she decides to invest, she offers a fraction of her firm's equity in exchange for q. T h e investors choose whether to accept or reject the offer. A t t — 2, if the project has been implemented , the te rmina l cash flow is realized and observed by a l l players. T h e investors can hire a lawyer to file a lawsuit against the entrepreneur, i f the realized result falls below the forecast disclosed at t —• 1. T h e lawyer decides whether to undertake the legal act ion based on the tradeoff of his l i t iga t ion cost and the fee pa id by the investors. Un l ike the previous chapters, the entrepreneur is assumed to be exogenously endowed wi th a private signal w i t h a posi t ive probabil i ty. In addi t ion , disclosure is no longer costless. In this sense, the mode l is i n line w i t h Verrecchia (1983) wh ich shows that a pa r t i a l disclosure equi l ib r ium can occur i f disclosure incurs a-cost. A major difference between our model and Verrecchia (1983) ;s model is that the disclosure cost in our mode l is endogenously determined by the lawyer's actions, while he assumes that the cost is exogenous. Othe r disclosure models, such as Dar rough (1993), also consider endogenous disclosure costs, but the costs are usually assumed to arise from product market compet i t ion . T h e full and par t ia l disclosure scenarios are endogenously de termined in the equ i l ib r ium depending on the economy parameters. T h e results predict that i f the legal l i ab i l i ty is reduced (for example, if a safe harbor is provided for forward- looking informat ion disclosed 13 by I P O firms), there can be more informat ion flow to the publ ic . However, such a safe harbor could also lead to a higher rate of lawsuits and an increase i n deadweight l i t iga t ion costs. A s for the issue on whether to require issuing firms to file projections, i t is shown that a F u l l Disclosure pol icy is not necessarily op t imal since it is associated w i t h b o t h a social loss due to underinvestment and a higher l i t igat ion-related deadweight cost. 14 Chapter 2 A New-Equity Disclosure M o d e l 2.1 Introduction In this chapter, we develop a s imple one-period model to investigate the interact ion between investment and acquis i t ion/disc losure of pre-decision informat ion. A t the very beginning (date zero), a r i sk-neutra l entrepreneur (or a firm manager mot iva ted to act in the current shareholders' best interests) has an investment oppor tun i ty wh ich requires an investment of q. Assume that she tries to raise capi ta l from the stock market by offering new investors part of the firm's equity in exchange for q. A publ ic report is released before any decisions are made. After observing the pub l ic report, the entrepreneur decides whether to acquire some private informat ion about the project'. We assume that the in format ion acquis i t ion cost is a random variable ex ante and realized before the entrepreneur makes the information purchase decision. We also assume that w i th a posi t ive p robab i l i ty the entrepreneur w i l l 15 receive a nu l l s ignal after incur r ing the acquis i t ion cost. T h e chapter first, examines a benchmark case in which the entrepreneur self-finances the investment project. W e show that the addi t iona l private informat ion is always valuable since it improves economic welfare by helping the entrepreneur make better investment decisions. T h e entrepreneur makes the informat ion acquisi t ion decision according to a cutoff. If the realized value of the acquis i t ion cost- is lower than the cutoff, she acquires the informat ion, and she does not acquire otherwise. We show that in the self-financing case, the acquisi t ion cost cutoff equals the product ive value of the addi t ional private informat ion . We then analyze the case when the entrepreneur issues equity to finance the project. T h e entrepreneur has three possible decisions to make. F i r s t , she chooses whether to acquire addi t ional informat ion. If she acquires the informat ion, then she decides whether to issue equity and undertake the project, and whether to disclose the pr ivate signal to the investors. We have the fol lowing major findings. Ex ante (before observing the pub l i c report, and mak ing a l l t h e decisions), the entrepreneur is worse off i f she has to raise capi ta l to finance the investment project. T h e equity-financing is associated w i t h three potent ia l efficiency losses. F i r s t , the entrepreneur's informat ion acquisi t ion decision can be inefficient. She might overinvest in acqui r ing private p roduc t iv i ty information. Second, when the entrepreneur is uninformed and unable to disclose, she might ha.ve to give up profitable projects due to the severe underpr ic ing by the investors. T h i r d , when the entrepreneur is informed, she might invest in negative N P V projects. Overa l l , such informat ion acquis i t ion and investment decisions make the entrepreneur 16 worse off, because in the ra t iona l expectations equ i l ib r ium the investors on average break even and it is the entrepreneur herself who u l t imate ly bears the efficiency losses incurred by her own decisions. T h i s chapter is organized as follows. T h e next section introduces the basic settings of the model . T h e n , as our benchmark case, we investigate the entrepreneur's information acquisi t ion and investment decisions when she has ample in ternal cap i ta l to finance the project. Section 2.4 examines the informat ion acqusi t ion/disclosure and investment decisions when the entrepreneur employs outside-financing. Section 2.5 compares the entrepreneur's information acquis i t ion and investment decisions w i t h those i n the benchmark case. T h e last section concludes this chapter. 2.2 M o d e l S e t t i n g Consider a set t ing in which a firm is owned by a r isk-neutral entrepreneur. 1 T h e entrepreneur has an investment oppor tun i ty which requires an investment of q and w i l l generate a gross payoff x. x = (1 + 9)q + e, where 9 is the net unit rate of re turn (a constant) , and e is the noise t e rm . 2 Assume that e is normal ly dis t r ibuted, w i t h mean 0 and variance a2. B o t h 9 and q are assumed to be common knowledge. A t the beginning of the per iod , a report ya about e becomes pub l i c l y avai lable . 3 Represent 'Alternatively, we can assume that the firm is owned by well-diversified investors, who hire a manager to operate their'firm. The manager is assumed to be exogenously motivated to act on behalf of current shareholders. 2For a summary of notation used in this paper, please refer to the Appendix. 3Examples of such public reports are Consumer Confidence and Unemployment Report, etc., often issued by government agencies and business research groups. 17 ya as e = ya + ea, where ya ~ N ( 0 , cr^a) and e~a is independent of ya.4 Under such a represen-tat ion, yn is also the entrepreneur's (also the investors') posterior mean w i t h respect to the random component in the gross re turn of the investment project, i.e., ya = E[i\ya = ya\. After observing the pub l ic report , the entrepreneur can choose to acquire informat ion about the remain ing uncertainty, ea, at a cost of K. If she pays K, she w i l l pr ivate ly observe a signal yh which is represented as £a — yi + e~au where & ~ N(0, cr^) and e~ai is independent of 'iji. T h e informat ion acquis i t ion cost, K, is assumed to be a r a n d o m variable ex ante w i t h a cumulat ive d i s t r ibu t ion function of S(K). T h e entrepreneur observes the realized value of K before m a k i n g the informat ion acquis i t ion decision. Assume that after acqui r ing informat ion, there is a p robab i l i ty 7 (7 € [0,1)) that the entrepreneur receives a nu l l s ignal (or uninformative signal) , yf — 0, wh ich does not change the entrepreneur's belief about ea, i.e., E[ea\y^} = E[£a] = 0. Assume that if the entrepreneur decides to invest, she raises cap i ta l from the stock market to finance the investment project. She offers the investors a fract ion of her firm's equity i n exchange for q. ' 'We can also model ya as e plus noise. These two representations are equivalent and one can be easily transformed into the other. However, the form adopted in the paper generally produces neater results. We can.interpret, I = ya + £a as signal ya resolving part of the uncertainty in e. 18 2.3 Benchmark Case: Self-Financing 2.3.1 Information Acquisition and Investment Decisions In this section we briefly examine a benchmark case in which the entrepreneur self-finances the investment project. T h e t ime line of the model is shown i n F igure 2.1. t=0 t=1 t=2 t=3 I , : I l . I Ex ante k is realized; E observes y t or y.° if she payoff ya is available; acquired information; E decides whether E then decides whether to acquire to invest, information. • Figure 2.1: Sequence of Events when Project is Self-financed. T h e entrepreneur's decisions are analyzed using backward induc t ion . A t t = 2, the entrepreneur observes the publ ic report ya and the realized value of the pr ivate information acquisit ion cost. C o n d i t i o n a l on the publ ic report ya, i f the entrepreneur has not acquired information, her expected payoff is U^il/a) = E[x\ya,q = q] — q = 6q + ya if investing (q = q), and zero if she does not invest [q = 0). Therefore, she invests i f 9q + ya > 0 and not invest otherwise. Her expected payoff at t — 1 if not acqu i r ing informat ion then is U[M(yn) = Max{0,6q + ya}. If the entrepreneur has acquired private information and received an informative signal at t = 1, given ya, y^, and her decision to invest, her expected payoff at t = 2 is Ul(ya,yi) — E[x\ya,yi,q = q] — q = 6q + ya + yi- Her expected payoff is zero i f she does not invest. Therefore, she invests i f 6q + ya + > 0 and not invest otherwise. O n the other hand, if she 19 has received an uninformat ive signal, her investment decision is the same as when she has not acquired informat ion and her indirect u t i l i ty at t = 2 is U^iya/yi) = Max{0,9q + ya}. It follows that the entrepreneur's expected payoff at t = 1 f rom acqui r ing informat ion is U?(ya, K) = 7 Max{0, 9q + ya} + (1 - 7) J+£_ya {Oq + ya + Vi) d F(yi) - K , where F(yi) is the cumulat ive d i s t r ibu t ion function of y^. Denote the posterior mean of the project 's N P V (net present value) given ya and invest-ment level q as p(ya), he., p(y„) = E[x\ya, q = q] — q — 6q + ya. T h e value of information, gross of the informat ion acquis i t ion cost, is represented as follows: , ( 1 - 7 ) JZ[-(p + Vi)]dF(Vi) i f p > 0 , V(p) = < ( 1 - 7 ) f^(p + yi)dF(yi) i f p < 0 . It is easy to prove the fol lowing proposi t ion regarding the value of the addi t iona l private in format ion . 5 Proposition 2.1 When investment project is self-financed, additional costless private in-formation is always valuable, i.e., V(p(ya)) > 0 \/ya. In this setting, pr ivate informat ion is valuable because it improves economic welfare through changes in investment decisions. W h e n the project N P V given the pub l ic report is posit ive (p > 0), the entrepreneur, i f uninformed, always invests, whi le i f she is informed, she invests only if E[x\ya, yi} q] — p(ya) + yi > 0. Therefore add i t iona l informat ion yt enables the entrepreneur to avoid invest ing in unprofitable projects. O n the other hand, when 5 T h e proofs for Proposi t ion 2.1 and 2.2 are straightforward, and therefore not provided. 20 p < 0, the uninformed entrepreneur does not invest and therefore receives zero payoff. However, i f she acquires private informat ion ' and the signal is informat ive, she can earn a positive expected profit by invest ing in projects w i t h p + yi > 0. Therefore, as long as the value of the informat ion exceeds its cost, the entrepreneur is better off by acquir ing the private informat ion. T h e fol lowing proposi t ion characterizes the entrepreneur's information acquisi t ion and investment decisions when the project is self-financed. P r o p o s i t i o n 2.2 When the entrepreneur self-finances the investment project, given the pub-lic report, she acquires information according to a cost cutoff K*(p) which equals the value of inforrnaMon V(p) defined above. If K < n*(p); the entrepreneur acquires information, and invests only if p + yi > 0. If n> hz*(p), the entrepreneur does not acquire information, and invests only if p > 0. 2.3.2 Comparative Statistics Now we analyze the impac t of exogenous parameters (p, cr2^ and 7 ) on the entrepreneur's decisions, ho ld ing the variance of ea constant. P r o p o s i t i o n 2.3 (i) The value of information (or information acquisition cost cutoff) in-creases in p when p < 0 and decreases in p when p > 0, where p = 9q + ya. The information is most valuable when p =. 0. (ii) Additional private information is more valuable and the entrepreneur.is more likely to acquire information, if the signal is more informative, i.e., is larger, (iii) Acquiring information is less beneficial, if there is a larger'probability that the entrepreneur will receive a null, signal. 21 T h e in tu i t ion is s traightforward. If the project N P V given the pub l i c report is positive, the value of informat ion arises from the possibil i t ies that it helps the entrepreneur identify posterior unprofitable projects. If the entrepreneur acquires further in format ion and finds out the project is expected to lose money, she does not invest, whi le wi thou t such informat ion, she would have invested i n i t . T h a t is, the investment decision is revoked when £ ( - c o , —p]. T h e larger the project N P V given the publ ic report, the less r o o m for the signal to improve product ion efficiency by avoiding unprofitable projects. O n the other hand, when the project is negative N P V based on the pub l i c report, the entrepreneur, when uninformed, does not invest. B u t she invests and earns posit ive profits i f she is informed and the project is expected to be profitable given bo th publ ic and private signals. T h e no-investment decision is reversed when yt G (— p, +00). T h e larger the project N P V based on the pub l i c report , the more room for the signal to improve p roduc t ion efficiency by recovering posterior profitable projects . 6 Figure 2.2 shows the value of informat ion as a function of the project N P V based on the pub l ic report. To understand the second part of P ropos i t ion 3, recal l that we mode l the signal as £1. = Hi + W h e n the total uncertainty in ia is held constant, the larger the variance of yi, the more uncer ta inty about £ a is resolved by the pr ivate s ignal and the more informative the signal. A n increase in ayi shifts j/j's p robabi l i ty density funct ion towards the tails. Consequently, more unprofitable projects (i.e., projects in the left ta i l ) can be avoided w i t h the pre-decision informat ion when the pr ior project N P V is posi t ive, and more profitable c Remember a larger negative number implies a smaller absolute value. 22 V Figure 2.2: T h e Value of Information as a Func t ion of the Pro jec t N P V based on the P u b l i c Repor t when Projec t is Self-financed (7 = 0, ayi = 1). projects (i.e., projects in the right tai l) can be recovered when the pr ior project N P V is negative, which makes acqui r ing informat ion more at tract ive. F igure 2.3 shows the relat ion between the value of the informat ion and the informativeness (ayi) of the private signal. v F igure 2.3: T h e Value of Informat ion as a Func t ion of Informativeness (l=oyi) of the Signal yi when Project is self-financed (7 = 0, p = 3). T h e t h i rd result of the propos i t ion is quite obvious. T h e higher the p robab i l i ty that the entrepreneur receives a nu l l s ignal when she acquires informat ion, the more l ikely it is that 2 3 ' she ends up m a k i n g the same investment decisions as when she does not acquire information. Therefore, it is less beneficial for her to acquire the informat ion. 2.4 Analysis of Equity-Financing In this section, assume instead that if the entrepreneur decides to invest, she uses the stock market to raise a l l the capi ta l required to finance the investment project . T h e entrepreneur offers a fraction a of the firm's equity to the investors in exchange for q. T h e investors can either accept or reject the offer. Assume that 5 is the m a x i m u m price the investors are wi l l ing to pay. T h e n the m i n i m u m fraction of shares the entrepreneur has to issue is a. = q/5. T h e investors price the firm based on their informat ion set at t — 2, fy2 = [ya, n1, q), where m is the entrepreneur's report (m — yi if the entrepreneur discloses, and m = n if the entrepreneur does not disclose the in format ion) . 7 T h a t is, 5 = E[x\ya,.m,q]. Figure 2.4 shows the sequence of the events and various decisions the entrepreneur makes dur ing the whole per iod . A t t = 1, the entrepreneur and the investors receive a pub l i c report about the noise term of the project 's gross payoff (e). Based on the publ ic report and the real izat ion of the information acquis i t ion cost, the entrepreneur decides whether to spend K to acquire private information about the remain ing uncertainty (ea). A t t = 2, if the entrepreneur has not acquired the informat ion (na) or she has received • 7 I n our model, we assume that the only sources of information for the investors are the publ ic report and the entrepreneur's disclosure/investment decisions. 24 1=0 t=1 t=2 t=3 Ex ante k is realized; y o is available; E decides whether to acquire information. E observes y < or yj° if she acquired information; E then decides whether to invest and/or disclose. payoff Figure.2.4: Sequence of Events when the Entrepreneur Raises E q u i t y C a p i t a l to F inance the Project a nul l signal she chooses between investing (in) and not invest ing (ni). O n the other hand, if she has1 acquired the private informat ion (a) and received an informative signal, she decides whether to invest and whether to disclose her private informat ion . She can choose among three sets of actions: invest ing and disclosing iji (id), invest ing but w i thho ld ing private information (iw), and not invest ing (ni). A t the end of the per iod (t = 3), if the entrepreneur has invested i n the project, the project 's payoff is realized. Otherwise there is zero payoff. In the fol lowing parts, we analyze the sequential game using backward induc t ion . 25 2.4.1 The Entrepreneur's Investment Decision when She is Unin-formed Represent the entrepreneur's informat ion set at t = 2 as *!/ E , where ^ E = {Vi} if she is informed, $E = {?A°} i f she acquired private informat ion but received a nu l l signal, and \IJE = 0 if she has not acquired private information. A t t = 2, the entrepreneur is uninformed when either she has not acquired informat ion or she has acquired informat ion but received a nul l signal. Assume that the entrepreneur is not able to make any disclosure when she is uninformed. Therefore, when she issues equity, the investors observe no disclosure. Ra t iona l investors know that there are three possibil i t ies when they observe no disclosure and the entrepreneur's decision to invest: (1) the equi ty- issuing entrepreneur is uninformed because she has not acquired private information, (2) she has acquired informat ion but received a nu l l signal, (3) she has received an informative signal from her informat ion acqui-si t ion but is w i thho ld ing the informat ion. T h e investors i m p o u n d a l l these possibil i t ies into their valuat ion of the firm. L e m m a 2 . 1 Assume that the investors believe that with probability A c the entrepreneur has not acquired information. Their ex investment^ valuation of the firm given no disclosure (rn — n) and the entrepreneur's decision to invest (q = q) is then represented as follows: 5n = E[x\p, 777, = ri, q = q, Xc] = p + q + y?(p, Xc) where 26 , c , _ A c - 0 + ( l - A c ) 7 -0 + ( l - A e ) ( I - 7 ) E\e\p,q = q,m = n,VE = {yi}. K ) ~ A c A + (1 - A c ) 7 P2 + (1 - A c ) (1 - 7) -P3 (1 - A c ) (1 - 7) E \i\p,q = q, m = n, VE = M ] " A c + (1 - A c ) 7 P2 + (1 " A c ) (1 - 7) V Px . = Ptob(q = q,rn = n , ^ E = 0) P2 = Prob(q = q,m = n, VE = {y?}) P3 = Prob(q = q, rn = n, i'E = {yi}). To i l lustrate, A c ) is the weighted average of the investors ' posterior beliefs about I in the three possibi l i t ies , and the first equality of its expression follows because the i n -vestors' posterior mean about the noise term given that the entrepreneur is uninformed (either because she has no private informat ion or she has a nu l l signal) is zero. Assume that the entrepreneur conjectures that the investors believe w i t h probabi l i ty A 0 she has not acquired informat ion. W h e n the entrepreneur is uninformed, her expected payoff given the publ ic report and the investment decision then is where p is the project N P V based on the publ ic report (p = 9q+ya, which is ex mite normal ly dis t r ibuted wi th mean 6q and variance <Jya). Therefore, the entrepreneur invests and receives a posi t ive expected payoff i f and only i f p + q > 0 and 5n > q. W h e n , the investors' valuat ion of the firm given the entrepreneur's decision q = q and no disclosure is equal to or less than q (or equivalently, yi(p, A c ) < —p), the entrepreneur does not raise capi ta l if she is uninformed, since she has to give up 100% 27 or more of her firm's equity to obta in q. W i t h o u t capi ta l she cannot invest i n the project even if her project is posi t ive N P V . 2 . 4 . 2 The Entrepreneur's Investment/Disclosure Decisions when She is Informed Suppose that the entrepreneur has acquired informat ion and received an informative signal. A t t = 2, she can choose from the fol lowing three strategies: invest ing and disclosing the information (id), invest ing and wi thho ld ing the informat ion (no) , . and not invest ing (ni). Assume that disclosure is costless and t ru th fu l . 8 C o n d i t i o n a l on A 0 , the pub l ic report and the private signal , the entrepreneur's expected payoff given different investment/disclosure decisions is: Ul2(p,yu\°,q) = { (v + q + Vi) (1 - p + jj+y.) i f Q = q and m = yi: (p + q + V i ) [1 - p + g + y ^ P i X c = x U ) ] if ? = 9 and m = n; 0 if q = 0. Denote A 0 = A 0 + (1 — A 0 ) 7, which is the entrepreneur's conjecture of the investors' belief of the probabi l i ty that she is uninformed. T h e entrepreneur can w i t h h o l d her informat ion in the offering only when 5n(p, \ c = A 0 ) > q, or al ternat ively y"(p , A c = A 0 ) > —p. Otherwise, if she issues equity wi thou t any disclosure, she has to offer investors more than 100% of her 8Following the disclosure literature, we assume that while the entrepreneur can withhold information, she discloses truthfully if she ever reports her private information. 28 firm's shares. 9 Define a function T(p, q, ayi, A 0 ) = pA° + (1 - A 0 ) (p + y-i) d F(yi). It can be proved that T(p,q,ayi, A 0 ) > 0 is a sufficient condi t ion for yf > —p.10 If this condi t ion holds, the entrepreneur believes that ra t ional investors w i l l price the firm at a value higher than q even if she goes out to raise capi ta l wi thout disclosing the pr ivate s i g n a l . 1 1 Therefore, i f the. entrepreneur has received a signal y, > — p — q, she always invests, but 'chooses between disclosing and w i thho ld ing her pr ivate informat ion, whi le i f yt < —p — q she does not invest. W h e n the entrepreneur decides to invest, her disclosure strategies are characterized by a cutoff ( Jung and K w o n 1988) . 1 2 O n the other hand, i f the entrepreneur holds a conjecture such that T(p,q,ayi) A 0 ) < 0, if the entrepreneur ever invests, such a decision signals to the investors that she must be informed. W h e n disclosure is costless and the investors are certain that the entrepreneur is pr ivately informed, the entrepreneur fully discloses her signal as long as she decides to inves t . 1 3 Consequently, the entrepreneur invests and discloses for all signals above- — p and not invest otherwise. T h e fol lowing propos i t ion characterizes the entrepreneur's investment /disclosure deci-sions:-Recall the fraction of shares is a = ^ r . If 611 < q, then a > 1. 1 0Please refer to the Appendix for the proof. .' 1 1 The investors can threaten to believe that the entrepreneur is hiding a very bad signal-when she invests but does not disclose and therefore offer a price lower than q. However, such threat is not credible in this case, since if the investors hold a belief A c such that T(p,q,avi, A 0 ) > 0 and if they are rational, their posterior mean of the firm value given q = q and m — n is higher than q. • 1 2Since the fraction of shares the entrepreneur has to offer in exchange for q is decreasing in yi if she invests and discloses, and the fraction of share offered is independent of yi if she invests but does not disclose, there must exist a lower bound of yi such that she discloses if her signal is above the cutoff and withhold information otherwise. 1 3 This is the standard "unravelling" result when disclosure is truthful and costless and the recipients are certain that the disclosing party is informed (see, e.g., Grossman 1981). 29 Proposition 2.4 Given the public report and the entrepreneur's conjecture X°, ifT(p, q, a y i , A 0 ) > 0, there exists a cutoff yj(p, X°) such that - „t ( 1 - A ° ) / yidFiyi) v; = . ' (2-2) A*° + (l-A°) /--' dFiyi) J-p-q The entrepreneur invests and discloses the private signal if yi G [y\(p, X°),+00), she invests but withholds the information if G (—p — q,yj(p, A 0 ) ) , and she does not invest if she has a signal equal or worse than —p — q. If T(p,q,ayi, X°) < 0, the entrepreneur invests and discloses if her signal is above —p, and does not invest if she has received a worse signal. Partial [ Disclosure . ni -p-q iw y* id Full Disclosure ni -P id ni: not invest; iw: invest and withhold info; id: invest and disclose. Figure .2 .5 : Inves tment /Disc losure Decisions given the P u b l i c Repor t and an Informative Pr iva te Signal In the later analysis, the above two scenarios are referred to as ' P a r t i a l Disclosure" and 30 " F u l l Disclosure" respectively (Figure 2.5). Le t us analyze these two cases separately. In the P a r t i a l Disclosure case, since T ( p , q, ayi, A0) > 0, the entrepreneur believes that ra t ional investors w i l l price the firm at a value higher than q given no disclosure and the investment decision q = q. Therefore, if she wi thholds the informat ion , she is s t i l l able to raise capi ta l to implement the project. W h e n y; e (—p-q, yj(p, A0)), the entrepreneur is better off investing but h id ing the private signal than investing and disclosing. T o see this , when the investors are unsure about whether the entrepreneur is informed, the entrepreneur's expected payoff if invest ing and wi thho ld ing the private information is (p+q+yt) (1 — p + ? + y n ) , which is larger than her expected payoff from investing and disclosing, {p+q+yi) (1 — p + l + y i ) = W h e n she receives a better s ignal than the disclosure cutoff, it is o p t i m a l for the entrepreneur to invest and disclose the informat ion. If the entrepreneur receives a s ignal below — p — q, investing in the project generates a negative expected payoff and therefore she does not invest. T h e disclosure cutoff y\ is a function of p and A0 (or function of ya and A0). T h e following l emma describes its properties. Lemma 2.2 The disclosure cutoff y\(ya, A0) in the Partial Disclosure case has the following• properties: 0) vl < 0; 0; R fe < 0 T h e first two comparat ive statistics are consistent w i t h the results in J u n g and K w o n 31 (1988) (Propos i t ion 1 and 2 ) . 1 4 F i r s t , the disclosure cutoff is no greater than the prior mean (0 m our model) . Second, when the entrepreneur conjectures tha t the investors believe there is a high probabi l i ty that she is uninformed, it is op t ima l for her to hide more i n f o r m a t i o n . 1 5 Let us then expla in why the disclosure cutoff is non-increasing i n the pub l ic report ya. If the entrepreneur conjectures that the investors believe she has not acquired informat ion ( A 0 = 1), it must be true that y"(p, A 0 = 1) = 0. T h e entrepreneur discloses signals above 0 and the disclosure cutoff does not vary w i t h respect to ya. If A 0 ^ 1, first ho ld ing y\ constant, an increase in ya w i l l lead to a higher probabi l i ty of non-disclosure i n the equity offering. T h a t is, the denominator of the expression of y™ increases. A t the same t ime, given m — n and q — q, the investors ' posterior mean of the entrepreneur's pr ivate s ignal wi thhe ld (the numerator) is lower. T h i s is because the non-disclosure region extends downward to include more worse signals. T h e overall effect is an decrease in y " . Since y\ = y™, y\ must also decrease to ma in ta in the equality. In sum, a less opt imis t ic pub l i c report w i l l d r ive .down the investors' posterior belief y- 1 and also y\. Therefore, the entrepreneur is now induced to disclose more unfavorable signals. In the F u l l Disclosure case, the entrepreneur is unable to raise the capi ta l i f she does not disclose her private informat ion. Therefore, as long as the posterior project N P V based on both the pub l ic and pr ivate signals is posi t ive (p + y i > 0), the entrepreneur always invests 1 4 A n important difference between our model and that of Jung and K w o n is that they assume the prob-abil i ty that the entrepreneur is uninformed is exogenous, while in our model A 0 and A c are endogenously determined. . 1 5 W h e n the entrepreneur makes the investment and disclosure decisions, she bases her actions on her conjecture of the investors' beliefs of the probabil i ty that she has not acquired private information. In the rational expectations equi l ibr ia, such conjectures are consistent wi th the investors' actual beliefs, i.e., A 0 = A c . 32 and discloses her private signal and also invest in the project. 2.4.3 The Entrepreneur's Information Acquisition Decision A t t = 1, in an t ic ipa t ion of the subsequent investment and disclosure decisions, the entre-preneur's expected payoff from not acquir ing private informat ion is: (p + q) [1 — ^ —] P a r t i a l Disclosure Ulm(p, \°)= { P + (l + VitP, A°) 0 F u l l Disclosure If the entrepreneur acquires informat ion, her expected payoff is character ized as follows. In the P a r t i a l Disclosure case: a rvHpS0) U?(PI\°,K) = l ( P + q)(l \ n / 0 n J + ( l - 7 ) [ / (p + q + Vi) P + ? + 2/,"(P.A°) J-p-q /•+oo —) d F(yi) + / (1 g . ) {Vi  . (p + Vi) d F(Vi)} - « where y\ and y]L are determined by Equat ions 2.1 and 2.2. In the F u l l Disclosure case: '•+00 E/f(p,A°, «) = (!- 7) / (p + y i ) d F ( y i ) - K Assume that w i th p robab i l i ty A the entrepreneur does not acquire pr ivate information. 33 A ra t ional expectations equ i l ib r ium is characterized by the fol lowing equations: U?(p,\°,K) = C/r°(p,A0) i f« = K (2.3) 1 - A = S(rf) = Prob(K < K]) (2-4) A = A C = A' (2.5) In the equ i l ib r ium, the entrepreneur acquires private in format ion if, and only if, the associated incremental benefit exceeds the acquisi t ion cost. She is indifferent between ac-qui r ing and not acqui r ing the pre-decision signal if the realized value of K equals the cutoff (Equa t ion 2.3), and does not purchase information if K is higher t han the cutoff. There-fore the equ i l ib r ium probab i l i ty that the entrepreneur has acquired informat ion equals S(K^)' (Equat ion 2.4). F ina l l y , in equ i l ib r ium the investors' and the entrepreneur's conjectures are self-fulfilling (Equa t ion 2.5). T h e fol lowing propos i t ion describes the entrepreneur's in format ion acquis i t ion decisions in the ra t ional expectations e q u i l i b r i u m . 1 6 Proposit ion 2.5 The entrepreneur acquires private information if the information acquisi-1 6 E q u a t i n g t/"(p, A 0 , K) and U[la(p, A 0 ) and applying integration by parts yields the expression for « t . 34 tion cost K is below a cutoff rJ^p), which is defined by: «t(p) = ( 1 - 7 ) [f^P (p + q + Vi)(l-$)dF(yt) +GZx°) + y ^ d F ( - y i ) ~ ( p + ^ ( 1 - f ) ] P a r t i a l D i s c l o s u r e (1 - 7) /_ + p°° (P. + d F(yi) F u l l Disclosure -w/iere 5n = p + q + y"(p , A 0 ) , y] and y™ are determined by Equation 2.1 and 2.2, and As satisfy Equations 2.3, 2.4 and 2.5. , She does not acquire information if the cost is equal or above the cutoff. Reca l l that the c r i t i ca l condi t ion which distinguishes the P a r t i a l Disclosure case and the F u l l Disclosure case is whether T(p,q,ayi, A 0 ) > 0 where A 0 = A 0 + (1 - A ° ) 7 . Since the equ i l ib r ium A 0 is determined i n Equat ions 2.3, 2.4 and 2.5, it is a funct ion of exogenous parameters p, q, and 7. In the fol lowing sections we rewrite the cond i t ion T(p, q, cr y i , A 0 ) as T(p,q,<7Vi,'y). 2.5 Efficiency Analysis 2.5.1 After the Release of Public Report and Before the Entre-preneur Makes any Decisions (t = 1) T h e efficiency analysis i n this subsection is for t — 1, i.e., the t ime poin t after the publ ic report is observed and before the entrepreneur makes any decisions. T h e previous sections examine the entrepreneur's informat ion acquis i t ion and subsequent investment and disclosure 35 . decisions. E v e n though we cannot expl ic i t ly solve for the equ i l i b r ium informat ion acquisi t ion cutoff K), we are able to compare it w i t h the first-best cutoff K,*, as shown in the following lemma. L e m m a 2.3 K) > K* if p > 0, and K1 — K* if p < 0. T h e comparisons of bo th the informat ion acquisi t ion and the investment decisions i n the self-financing and the equity-f inancing are summar ized below. P r o p o s i t i o n 2.6 Given a public report ya, there are three possible scenarios: (1) in economies with parameters satisfying p > 0 and T(p, q, ayi, 7) > 0, the entrepreneur overinvests in both information acquisition and investment projects when she issues equity to finance the project; (2) if the economic parameters are such that p > 0 and T(p,q,ayi,^f) < 0, the entrepreneur overinvests in information acquisition but underinvests in projects, and; (3) if p < 0, the entrepreneur's information acquisition and investment decisions are efficient. Let us explore the impl ica t ions of the above proposi t ion i n more details. (1) p > 0 and T{p, q, ayi, 7-) > 0 W h e n the entrepreneur raises equity capi ta l to finance the project, her expected u t i l i ty at t = 1 (after receiving the pub l ic report but before m a k i n g informat ion acquis i t ion and investment decisions) i s : 1 7 17 We use "sF to denote self-financing and "ef" to denote "equity-financing". 36 where U'efl(p,K) and U'^f^p) are defined in Section 2.4.3. If the entrepreneur self-finances the projects, her expected u t i l i t y at t = 1 is UafM = / C / a a / i l ( p , K ) d 5 ( « ) + / ^ ( P ) d S ( « ) JO JK" where U'sj^p.K) and U™}\i(p) are defined in Section 2.3. Before compar ing the two above expressions, we first compare the social welfare in these two contexts. W h e n the entrepreneur self-finances the project, the social welfare at t = 1 equals her own expected payoff: UsfA'P) = USf,i(p) = / [IP + (1 - 7) / (P + Vi) d F(Vl) -K]d S(K) + p [1 - S ( « * ) ] ./0 J -v W h i l e when she has to raise capi ta l to finance the project, the social welfare becomes: U?fA(p) = / [ 7 P + ( l - 7 ) / (p + yi)dF(yi)-K}dS(K)+p{l-S(^)} JO J-p-q It follows t h a t 1 8 = f ( « - « * ) dS(K)- f [ ( l - 7 ) [ P (p + yi)dF(yi)}dS(K) (2.6) A * JO J—p—q 1 8 P r o o f is included in the Appendix . 37 Notice the first t e rm represents the efficiency loss due to the entrepreneur's excessive in -formation acquis i t ion under equity-financing. Such overinvestment occurs when the realized information cost is higher than the efficient information acquis i t ion cutoff K* but lower than K1 . In this case the entrepreneur overinvests in acquir ing the private signal since the cost pa id (« ) exceeds the add i t iona l information 's product ive value (which equals K*). - Here is the in tu i t ion for this overinvestment result. T h e entrepreneur overinvests in information when she has to raise equity capi ta l because her shares w i l l be undervalued if she does not have informat ion to disclose. T o see this, recal l that the investors ' va luat ion of the firm given m = n and q = q is 8n = p + q + yf < p + q.19 T h e second te rm represents another type of inefficiency associated w i t h equity-financing. W h e n the entrepreneur issues equity capi ta l , her investment decisions are also inefficient since she invests in unprofitable projects. T h e fol lowing analysis reveals why the entrepreneur overinvests. i n negative N P V projects. W h e n K < K\ if the entrepreneur employs equity-financing, she invests for signals € (— p — q, —p) since she can take advantage of the investors' overvaluat ion of her firm's shares. To see this, when the investors are unsure about whether the entrepreneur is informed, the entrepreneur's expected payoff if investing and w i t h h o l d i n g the pr ivate information is ip + q + Vi) (1 - p+ g +y») > (P + Q + Vi) (1 - j £ h f e ) = P + Vi > °- Therefore the entrepreneur can earn posit ive profits by w i thho ld ing information and invest ing i n unprofi table projects. a t 1 9 F r o m L e m m a 2, we know i / t n < 0 and ^ > 0. The equi l ibr ium A 0 is less than 1, since A 0 = 1 - S ( « t ) (Equations 2.4 and 2.5) and wt is positive (Proposit ion 5). A lso y™ achieves its max imum when A 0 = 1. Then it must be true that the equi l ibr ium disclosure cutoff y\ is negative. 38 Equity-financing ni iw id 7v V ni Self-financing i: invest; ni: not invest; iw: invest and withhold info; id: invest and disclose. Figure 2.6: T h e Entrepreneur 's Investment Decisions after She has A c q u i r e d Information and Received an Informative Signal (p > 0, T(p,q,ayi,^) > 0). Does the entrepreneur gain from such investment strategy? T h e answer is N o . Remember that in a ra t ional expectat ions equ i l ib r ium, the investors are price-protected and on average break even . 2 0 It is true that the investors overpay for the shares when the entrepreneur issues equity to raise capi ta l whi le w i thho ld ing bad informat ion. O n the other hand, they pay less than the firm's in t r ins ic value when the entrepreneur is uninformed and not able to disclose either because she has not acquired information or she has acquired information but received an uninformat ive signal (5n = p + q + y " < p + q). O n the whole, the investors break even. Since the investors are price-protected, it is the entrepreneur who u l t imate ly bears the losses incurred by her inefficient information acquisi t ion and investment decisions. T h a t is, UefAp) = u?fil(p) < u?fil(p) = uafM For the proof, please refer to the Appendix. 39 In sum, the entrepreneur "shoots herself in the foot" i n her a t tempt t o exploi t the in -vestors and is worse off when she issues equity rather than self-financing the project. Under these condit ions, after the entrepreneur observes the rea l iza t ion of the information acquisi t ion cutoff K, i f K < K*, she. acquires private informat ion under b o t h types of financing. If she has received'an informat ive signal, the entrepreneur's investment strategies is the same irrespective of the financing methods, i.e., investing if the pr ivate s ignal is above — p and not investing otherwise. B u t this is not true if she has received an uninformat ive signal . In the self-financing case, she s t i l l invests i n the project since the posterior N P V remains posit ive. However, if she relies on outside capi ta l , she is unable to raise the cap i t a l required to carry out the project and therefore has to forgo the posit ive N P V project . If K* < K < K\ she acquires private information when us ing equity-f inancing, but does not acquire informat ion if she self-finances the project. If K > K^, the entrepreneur does not acquire informat ion under either f inancing method. A s before, we compare the social welfare at t = 1 instead of d i rec t ly compar ing the entrepreneur's expected payoffs. W h e n the entrepreneur self-finances the project, the social welfare at t — 1 equals her own expected payoff at t = 1: U?JM = U*M= / [7P + ( l - 7 ) / (p + yi)dF(YI)-K}dS(K)+p[l-S(K*)} (2) p > 0 and T{p,q.,ayi,j) < 0 40 W h i l e when she raises capi ta l to finance the project, the social welfare becomes: UseLM = / [ ( 1 - 7 ) / (p + yi)dF(yi)-K]dS(K). JO J-p It follows that L2 = UffiX{p)-U!fil(p) = f ( « - « * ) dS(K)+p{jS(^) + l-S^)) (2.7) J K* A g a i n the first t e rm represents the inefficiency due to overinvestment i n informat ion acquisi-t ion in the equity-financing. T h e second t e rm is the expected loss-from underinvestment due. t o the entrepreneur's inab i l i ty to disclose when she is uninformed, where p is the N P V she has to forgo, and [JS(K^) + 1 — - S ^ ) ] is the equ i l ib r ium probab i l i ty that she is uninformed. W h e n the entrepreneur cannot disclose either because she has not acquired the private signal or she has acquired informat ion but received a nu l l signal, she is not able to invest and her expected payoff is zero. T h i s is because when p > 0 and T(p,q, ayi, 7) < 0, the investors are only wi l l i ng to offer a price less than q, i f the entrepreneur tries to raise capi ta l bu t does not disclose any informat ion. Therefore, the entrepreneur is unable to implement the profitable N P V project . In cases when the loss from giv ing up profitable project is smaller than the acquisi t ion cost of the pr ivate signal, the entrepreneur chooses to not acquire the informa-t ion, and bear the loss from abandoning her project. In other cases when the entrepreneur does acquire private informat ion, i f she unfortunately receives an uninformat ive signal, even though she wants to convince the investors that she has a posi t ive N P V project, she s imply 41 has no means to convey that informat ion. (3) p < 0 In this case, the entrepreneur's informat ion acquis i t ion and investment strategies are the same no matter what k i n d of financing methods she employs. Therefore ex ante, the entrepreneur enjoys the same expected payoffs in bo th contexts. 2.5.2 Before the Release of Public Report (t = 0) Let us move further backward to t = 0. T h e ex ante expected payoffs of the entrepreneur under the self-financing and the equity-financing are /•+oo Uaf,i(p(ya)) d F(ya), -oo and /• + C O Uef,i(p(ya)) d F(ya), -co respectively. U s i n g the previous results, we can compute the difference as, Us/,0 - Ueffi = / Lx dF{ya) + I L2 dF{ya) < 0 where Y] = {ya : 0q+ya > 0, T(ya, 6, q, ayi, 7) > 0}, F a 2 = {ya : 6q+ya > 0, T(ya, 6, q, ayi, 7) < 42 0}, and L i and L 2 are defined in Equat ions 2.6 and 2.7, respectively. T h e ex ante (t = 0) welfare analysis is summarized in the fol lowing proposi t ion . P r o p o s i t i o n 2.7 E x ante (before observing ya, making information acquisition and invest-ment decisions), the entrepreneur is. worse off if she issues equity to finance the investment project rather than using self-owned capital. The equity-financing is associated with three potential efficiency losses. First, her information acquisition decision can be inefficient. She might overinvest in searching for private productivity information. Secondly, when the entre-preneur is uninformed and unable to disclose, sometimes she has to forgo profitable projects due to the severe underpricmg by th.e investors. Thirdly, when the entrepreneur is informed, she might invest in negative NPV projects. 2.6 Conclusion In this chapter we develop a new-equity disclosure mode l to investigate the interact ion be-tween equity-issuing firms' informat ion acquis i t ion/disclosure decisions and their investment activit ies. B y in t roduc ing the poss ibi l i ty that, the investors are unsure whether the entre-preneur is informed, we obta in interesting results regarding several inefficiencies that could arise when the firm raises equity capi ta l to finance the projects. A s a benchmark case, when the entrepreneur self-finances the project, she is better off by acquir ing add i t iona l private informat ion as long as the value of pre-decision information exceeds the informat ion acquis i t ion cost. In addi t ion, the entrepreneur invests only if the project has a posterior posi t ive N P V based on her informat ion set. 43 W h e n the entrepreneur issues equity in the stock market , she po ten t ia l ly incurs three efficiency losses. She could excessively invest in informat ion when the project N P V based on the publ ic report is posi t ive. E v e n though she is ex ante better off by p recommi t t i ng to not acquir ing private informat ion when the acquisi t ion cost is equal or above the efficient cutoff, ex post the entrepreneur has unavoidable incentives to acquire pr ivate informat ion. T h i s is because if she does not acquire informat ion, she is unable to make disclosures at the t ime of equity issuance and her firm's shares are undervalued. If the informat ion acquis i t ion cost is smaller than the sum of product ive value of the informat ion and the expected mispr ic ing result ing from the inab i l i ty to disclose, ex post she purchases the pr ivate informat ion. Moreover, the entrepreneur's investment decisions can be inefficient. W h e n the entrepre-neur receives an informative private signal, under certain circumstances she overinvests in unprofitable projects i n her a t tempt to take advantage of the investors ' overvaluation. O n the other hand, when she is uninformed, she might have to give up profitable projects due to her inabi l i ty to correct the investors' underpricing. These inefficient investment /disclosure decisions eventually make the entrepreneur worse off, because in the ra t ional expectations equi l ib r ium the investors on average break even and it is the entrepreneur herself who bears a l l the efficiency losses. 44 Chapter 3 Compar ison of Three Disclosure Regimes 3.1 Introduction Chapter 2 develops a new equity model to .examine the in terac t ion between firms' infor-mat ion acquis i t ion/disc losure choices and their investment decisions. In that model , the equity-issuing entrepreneur/manager is assumed to voluntarily choose whether to disclose a forward-looking signal that she pr ivately observes. In pract ice, however, equity-issuing firms and their underwri ters ' disclosure practices are often subject to securities laws and regulation. For example, countries such as Singapore, M a l a y s i a , and Greece require their firms to disclose an earnings forecast when they go publ ic . O n the other hand, i n the U n i t e d States, equity-issuing firms are extremely cautious w i t h their disclosures of prospective in -45 formation, since a misstep could violate the so-called "Quiet P e r i o d " regulat ion and lead regulators to impose a delay on their offerings. 1 T h i s chapter extends the new equity disclosure model developed i n the previous chapter to analyze the impac t of different disclosure regimes on corporate dec is ion-making du r ing in i t ia l publ ic offerings ( I P O s ) . 2 Specifically, it investigates how disclosure rules affect firms' incentives to acquire forward-looking information, their disclosure practices and investment strategies. T h e disclosure regimes examined are Non-Disc losure , Volun ta ry , and M a n d a t o r y Disclosure. T h e analysis yields a number of insights. It shows that a Non-Disc losure Regime for management forecasts, as is found in the U S , can impa i r firms' ab i l i t y to reduce information asymmetry through disclosure. B y depr iv ing firms of the oppor tun i ty to convey private infor-mat ion to investors, such a po l icy results i n undervaluat ion of firms w i t h profitable projects and overvaluat ion of firms wi thou t such projects. Mi sva lua t i on also alters the condit ions un-der which firms make their investment decisions. In par t icular , investors ' overvaluat ion can give firms incentives to invest in negative N P V projects. Fur thermore , a non-disclosure rule 'Lang and Lundholm (2002) analyze several types of costs associated with a forced delay in the offering. First, the issuing firms have to postpone the investment plan. Second, the issuers have to incur additional costs to revise and refile the prospectus. Third, a delay might be interpreted negatively and reduce the proceeds from the offering. 2 The insights generated by our model should also apply to seasoned equity offerings, and any other asset sales setting that involves productive decisions. We focus on IPOs mainly because the legal environment for SEOs is more complicated. For example, in the US, on one hand, SEO firms must not breach the gun jumping prohibition. On the other hand, they must also maintain their normal disclosures mandated by the 1934 Securities Exchange Act. That is, they should continue to send out periodic financial reports and make press releases with respect to firms' business and financial development etc. (Lang and Lundholm 2000). In addition, there is usually a much larger total mix of information around SEOs, such as previous press releases especially previous management forecasts, analysts' reports, etc. The incremental information content of management forecasts is likely to be smaller. 46 reduces equity-issuing firms' incentives to acquire valuable p roduc t ive informat ion . However, the other two disclosure regimes also ' induce distortions. B o t h overinvestment and underin-vestment can occur under the Vo lun ta ry Disclosure Regime. In add i t ion , w i t h the discret ion to disclose, firms tend to acquire too much information so tha t they can strategical ly use it in the later offerings. T h e M a n d a t o r y Disclosure Regime has the highest price efficiency, but it also imposes burden on firms to produce informat ion to meet the disclosure requirement. F ina l ly , a welfare analysis shows that each of the three disclosure regimes can emerge'as. the socially op t ima l regime under some condit ions. T h e chapter is organized as follows. Section 3.2 discusses the regulatory requirements and disclosure practices of forward- looking information around equi ty offerings i n the U n i t e d States, and also defines the three disclosure regimes. T h e basic settings of the model and the major assumptions are in t roduced in Section 3.3. Sect ion 3.4 first briefly analyzes the entrepreneur's information acquisi t ion and investment decisions when she has ample internal capi ta l to finance the project as a benchmark case,, and then examines the entrepreneur's decisions under each of the three regimes. Section 3.5 compares the ex ante efficiencies of different disclosure regimes and explains the pol icy impl ica t ions of the results. T h e last section concludes the paper w i t h a discussion of several key assumptions and l imi ta t ions of the model , and provides suggestions for future research. 47 3.2 Institutional Background In the U n i t e d States, an equi ty- issuing firm and its underwriters are p roh ib i t ed from mak ing certain types of marke t ing efforts dur ing a "quiet per iod" that roughly starts from the issuing firm's first meeting w i t h the underwriters un t i l 40 calendar days after the I P O . 3 Specifically, Section 5(c) of the 1933 Securities A c t , enti t led "Necessity of filing regis trat ion statement", prohibi ts any "offer to sell" a new security prior to filing a regis t ra t ion statement w i t h the S E C . V i o l a t i o n of 5(c) is usual ly cal led "gun j u m p i n g " . 4 T h e major basis of this regulat ion is to preclude issuers and their underwriters from hyping the stock and to encourage investors to consider the full disclosures contained w i t h i n the prospectus and regis trat ion statement (Coffin 2002). In addi t ion to Sect ion 5(c), the S E C also provides some guidelines on informa-t ion releases dur ing the equity offerings. In par t icular , Release N o . 5180 advises that issuers should main ta in their normal and routine communicat ions such as adver t is ing products and services. However, they should avoid " 1 . Issuance of forecasts, projections, or pre-dictions relating but not l imited to revenues, income, or earnings per share. 2. Publishing opinions concerning values" by means other than a s ta tuary prospectus. . Even though no forecasts are allowed outside the prospectus, firms can s t i l l legi t imately 3 In July 2002, the quiet period was extended from 25 to 40 calendar days after the IPO. 4 The following incident highlights the SEC's strict enforcement on inappropriate or suspicious disclosure practices in the "quiet period". Salesforce.com, a customer relationship management software vendor, delayed its IPO due to an interview of its C E O with the New York Times just prior to its planned IPO. The interview was published on May 9, 2004. Eleven clays later, a Wall Street Journal article reported that Salesforce would delay its IPO due to its potential violation of the "quiet period" regulation (Bank 2004). As a matter of fact, in the New York Times interview, the Salesforce CEO sidestepped questions relating to the pending IPO, citing the restrictions from the SEC (Rivlin 2004). However, because the article was high-profile and published within two weeks of the company's IPO date, the SEC and Salesforce "reached a mutual agreement" to delay the offering. 48 disclose such informat ion i n their S E C filings. However, a s ty l ized fact about U S I P O s is that forecasts are v i r tua l ly non-existent in the prospectuses. 5 One frequently c i ted reason for this phenomenon is U S ' s h ighly l i t igious environment. T h a t is, if a firm inc luded a forecast in its prospectus and u l t imate ly failed to meet the target after the I P O , there wou ld be a high risk of l i t i ga t i on . 0 In add i t ion , disclosure of forward- looking informat ion from I P O firms is excluded from the "Safe Harbor" protect ion in t roduced by the 1995 Pr iva te Securities L i t iga t ion Reform A c t ( P S L R A ) . 7 F ina l ly , even though firms must provide sufficient and meaningful disclosure of their risk factors, they have no obl iga t ion to make forecasts or projections on future events, inc lud ing their l ikely performance. 8 T h i s shields firms that wi thho ld private forward- looking informat ion against po tent ia l charges of misrepresentat ion. 9 A most recent move by the S E C revealed the pol icymakers ' concern w i t h the insuffi-cient communica t ion in the equity offerings caused by the "quiet pe r iod" regulat ion. In its November 3, 2004's Release 33-8501 on Securities Offering Reform, the S E C proposed to 5 The IPO prospectus often contains some forward-looking information, mainly in the discussion of risk factors and/or the Management's Discussion and Analysis (MD&A) section. However, almost all of them are qualitative "soft information" or vague statements, such as "We anticipate sales and marketing expenses will increase in dollar amount and may increase as a percentage of net revenues in 2004 and future periods". See, for example, Google Inc.'s 2004 IPO Prospectus. 6Another possible reason is that, given the scarcity of forecasts or projections in the IPO prospectus in the US, it can be imprudent for an IPO firm to include a forecast to expose itself to the potential risk of becoming a conspicuous target in the securities litigations. 7 The 1995 Act created a statutory safe harbor that applies to both written and oral forward-looking statements. Under this provision, a defendant is not liable with respect to any forward-looking statement if it is identified as forward-looking and is accompanied by "meaningful" cautionary language identifying the factors that could cause actual results to differ. However, this safe harbor does not apply to certain forward-looking statements such as those "made in connection with an initial public offering" (Section 27A of the 1993 Securities Act). 8See the September 1996's Corporate and Securities Litigation Bulletin of Hale and Dorr L L P , http://www. lntledorr.com/publications/pub_detail.aspx?ID=251&type=5545. 9Misrepresentation in the equity offering settings is defined as the registration statement containing an untrue statement of a material fact or omitting to state a material fact required to be stated or necessary to make the statement not misleading. See Section 11(a) of the 1933 Securities Act. 49 eliminate "unnecessary and ou tmoded restrictions on offerings" and "provide more t imely investment informat ion to inves tors" . 1 0 T h e S E C proposed to provide a safe harbor from the gun- jumping provisions for the release of forward-looking statements from repor t ing issuers (i.e., firms that file reports pursuant to the 1934 Securities Exchange A c t ) , as long as they regularly disseminate such informat ion prior to the offerings. However, the S E C is not p lan-n ing to extend this safe harbor to non-report ing issuers (usually I P O firms) "because of the lack of such informat ion or his tory for these issuers in the marketplace" , and the potent ia l abuse of the safe harbor to inflate the market prices. . To summarize, in the U n i t e d States, I P O firms' disclosure of forward- looking informat ion is constrained by the quiet per iod regulat ion, and is vulnerable to shareholder l i t iga t ion due to the lack of safe harbor protect ion for I P O forecasts. T h e overal l t ime between the beginning of an issuing firm's preparat ion of the registrat ion statement and the closing of its I P O could easily exceed six months, and is rarely less than three m o n t h s . 1 1 G i v e n the usually l imi ted al ternative pub l ic informat ion around an I P O and the considerable length of the quiet per iod, the disclosure regulat ion and the legal environment cou ld significantly affect the informat ion m i x available to investors. A s a mat ter of fact, i n the U n i t e d States, investors (especially smal l investors) have very l imi ted access to numer ica l forward-looking information from I P O firms and their affiliated ana lys t s . 1 2 W e characterize such a legal environment that inhib i t s I P O forecasts as a "Non-Disc losure Reg ime" . 1 0 The full text of this release is available on the SEC's official web site: http://www.sec.gov/rules/proposecl/33-8501 .htm. u See, for example, http://www.boselaw.com/bizJaq.shtml. 1 2 I t is alleged that the issuing firms could privately disclose information such as management forecasts, to selected institutional investors during closed-door meetings (see, e.g., Hennessey and Plitch 2004). 50 O n the other hand, I P O firms in the U K , Canada , A u s t r a l i a , and other B r i t i s h C o m m o n -wealth countries in the As ia -Pac i f i c region, can voluntar i ly choose whether to issue forecasts in the prospectus, whi le the inclusion of forecasts in the I P O prospectus is mandatory in countries such as Greece, Singapore and M a l a y s i a (How and Yeo 2000; B i l s o n et al 2003; Gounopoulos 2002). We refer to these two types of disclosure environments as "Voluntary Disclosure Regime" and " M a n d a t o r y Disclosure Regime" respectively. 3.3 The Model Setting To explore the impact of different disclosure regimes on firms' real decisions, we use a mod-ified version of the s imple one-period N e w E q u i t y disclosure mode l developed. in Chapter 2. Assume that there is a r i sk-neutra l entrepreneur who considers issuing equity to finance a new project. T h e entrepreneur has one exis t ing asset, wh ich generates a t e rmina l cash flow u, which is normal ly d i s t r ibu ted w i t h mean u and variance c r 2 . 1 3 T h e new project requires an investment of q and generates a gross payoff x = (1 + 0)q + e, where 8 is the net uni t rate of expected re turn (a constant) , and e is the noise term. Assume that e is no rmal ly dis t r ibuted, wi th mean 0 and variance cr2.. B o t h 6 and q are assumed to be c o m m o n knowledge. P r io r to the investment decision, the entrepreneur has an oppor tun i ty to acquire a signal about the new project at a cost of K. If she pays K, she w i l l receive a signal y;, which , is represented as e = y~i + z/j, where y~j ~ N(0 , of) and Vi is independent of y^. We can interpret this as the signal y.; resolving part of the uncertainty i n e. In addi t ion , under such 1 3 For a summary of the notation used in this chapter, please refer to Appendix A. 51 a representation, the realized value of & is also the entrepreneur's posterior mean about the noise in the project 's re turn, i.e., E[e\y~i — yi] = T h e informat ion acquis i t ion cost, K, is assumed to be a r a n d o m variable ex ante and has a cumulat ive d i s t r ibu t ion function of S(K). T h e entrepreneur observes the realized value of K before m a k i n g the informat ion acquisi t ion decision. If the-entrepreneur decides to invest in the project, she issues equity and offer the in -vestors a fraction of her firm's shares in exchange for q. D u r i n g the equity offering, the entrepreneur is required to disclose her firm's previous years' opera t ing results. Assume that the entrepreneur observes these his tor ical financial results from the firm's accounting sys t em. 1 4 T h e his tor ica l informat ion is represented as a signal yh wh i ch is informative about u. Specifically, u = yh + uh, where yh ~ N ( u , al) and vh is independent of yh. It follows that yh is the entrepreneur's posterior mean w i t h respect to the re turn of the asset-in-place, i.e., E[u\y~h = yh] = Vh- T o simplify, assume that cov(yh,y~i) = 0, cov(u,y~i) = 0, and cov(x, yh) = 0. T h a t is, the two signals are uncorrelated; i n addi t ion , the his tor ica l account-ing information is informative only about the return of the o ld asset, whi le the private signal to be acquired is informative only about the future cash flows of the new investment p ro jec t . 1 5 Under these assumptions, we have .Efely/i] = 0 and E[u + x\yh, yi] = + £ [ a % i ] . Fur-ther, to focus on the acquis i t ion of the product ive informat ion about the new project, we assume that the entrepreneur does not acquire or have any private informat ion about the u T h e setup cost of the accounting system is sunk and therefore yh can be regarded as a signal with which the entrepreneur is exogenously endowed. 1 5 T h e s e three assumptions do not imply that the returns of the asset-in-place and the new project are uncorrelated. T o see this, cov(u, x) — cov(y~h + Vh^Vi + ^i), which can be nonzero even if cov(y~h,y~i) = 0. 52 future re turn of the asset-in-place other than y^. t=0 t=l t=2 t=3 Ex ante b y E ; • E decides whether to • E receives y h; • k is realized and observed acquire yt. E observes y ( if she acquired information; E decides whether to invest in the project; If E decides to invest, she will issue equity; In the offering, E must disclose yh, but she may or may not disclose y ; Payoffs are realized Information Sets: E observes: • k and y, prior to the information acquisition at t=l; " following a decision to acquire information -- the value of the signal y ; prior to the investment decision at t=2. Investors observe: * E's investment decision (q), a signal about the existing asset (yh), and a signal about the new project (y ;) if E discloses y r T h e sequence of the events and various decisions the entrepreneur makes du r ing the whole per iod are summar ized in F igure 3.1. Specifically, at t = 1, the entrepreneur observes the historical informat ion about the o ld asset, y\x. She also observes the real ized value of the information cost, K. Based on K, she then decides whether to acquire private information about the new project. A t . i = 2, if the entrepreneur has acquired informat ion , she observes F igure 3.1: Sequence of Events . 53 a private signal y.; about the project. Based on her informat ion set, she decides whether to invest. If she decides to invest, she issues equity to the pub l ic w i t h a prospectus which con-tains previous years' financial results and possibly her private signal about the new project. A t t = 3, the payoffs are realized. 3.4 The Entrepreneur's Information Acquisition and Investment Decisions 3.4.1 The Benchmark Case We first briefly examine the case in which the entrepreneur self-finances the project. T h e entrepreneur's decisions are analyzed using backward induc t ion . In this benchmark case, the only decision that the entrepreneur makes at t = 2 is whether to invest in the project. Le t q 6 {0, q} represent her investment decision. A t t = 2, if the entrepreneur has not acquired informat ion about the project, she is informed w i t h only one signal, y/ t . Her expected payoff is c7 2(y/i) = E[u + x\yh, 1 = q] — Q — Uh + dq if she invests (q = q), and U2(yh) = Vh i f she does not invest (q — 0 ) . 1 6 Therefore, she invests i f 9 > 0 and does not invest otherwise. If the entrepreneur acquired private informat ion. about the new project at t = 1, she is informed wi th bo th and y% at t = 2. G i v e n these two signals, her expected payoff is 1 G F o r exposit ional ease, throughout the paper, mathematical expressions are represented only as a function of a few key parameters. For example, in addit ion to yu, Ui{-) is also a function of two other parameters q and 6. However, only y^ is made explicit in the expression since it is a key parameter on which we want to focus. 54 U2{'!Jh, Vi) = E[u + x\ijh,yi,q = q] - q = yh + 6q + yi i f she invests, and yh if she does not invest. Therefore, she invests if dq + yi > 0 and does not invest otherwise. A t t = 1 the entrepreneur decides whether to acquire yi i n an t i c ipa t ion of the subsequent investment decisions. Represent the entrepreneur's informat ion acquis i t ion decision at t = 1 as a function of the real ized acquis i t ion cost, a : K —> {0 ,1} . T h a t is, the informat ion acquisit ion strategy maps from the acquisi t ion cost into a choice of either acqui r ing private information (a = 1) or not acquir ing (a = 0). T h e entrepreneur expects that acquir ing information generates an expected payoff of Ui(yh, a = 1, /_) = yh + {Oq + yi) d F(yi) — K, where F{yi) is the cumula t ive d i s t r ibu t ion function of j / j . Her expected payoffs from not acquir ing informat ion is Ui(yh,a = 0) = yh + Max{0,dq}. Denote the p r io r mean of the N P V of the new project as s, i.e., s = E[x\q = q] — q — dq. T h e entrepreneur's information acquisi t ion and investment decisions are characterized in the fol lowing p r o p o s i t i o n . 1 7 Proposition 3.1 When the entrepreneur can self-finance the investment project, she decides whether to acquire information about the new investment project by comparing the realized value of k with a cutoff n*{s). The cutoff is represented by A t t = \ , the entrepreneur acquires yi if K < K*(S), and does not acquire otherwise. At t = 2, if the entrepreneur is informed with yiy she invests if, and only if, s + yi > 0. 1 7 For a. more detailed analysis, please refer to Chapter 2. 55 // the entrepreneur is uninformed about the project, she invests if, and only if, s > 0. In the fol lowing analysis, we analyze the entrepreneur's decisions i f she raises cap i ta l from the equity market to finance the new project: 3.4.2 Non-Disclosure Regime In this section, assume that the entrepreneur never discloses her private signal to the in -vestors. Represent the entrepreneur's information set as ^E, where — {yinVi} i f s h e has acquired private informat ion and ^E — {'Uk} otherwise. T h e investors ' informat ion set is {L>i = (v//i,r/), i.e., the h is tor ica l results disclosed i n the prospectus and the entrepreneur's investment dec i s ion . 1 8 If the entrepreneur decides to invest and goes publ ic , the investors price the firm as Vn = E[u + x\yiu q = q] = y^ + s + q + E[e|<j = q].19 Assume that the investors believe that w i t h probabi l i ty A c the entrepreneur has not acquired private informat ion. Based on the entrepreneur's decision to issue the stock, the investors cannot te l l whether she is uninformed or w i thho ld ing her private s i g n a l . 2 0 Under the assumption that the investors are ra t ional and update their beliefs according to the Bayes Rule , their posterior belief about e given q = q is the weighted average of their posteriors in these two possible si tuat ions. Denote the investors' posterior mean about the noise term in 1 8If the entrepreneur is risk-averse, it is 'possible that she could communicate her private information through costly signals, such as equity retention. However, we assume away this possibi l i ty to focus on the impact of direct disclosure. We believe that the results on the Non-Disclosure Regime are valid as long as the signall ing device does not perfectly reveal the entrepreneur's private information. L 9 T o be complete, V' is a function of y^, s, q, A c , a\. In part icular, it depends on not only what the investors observe (i.e., yh) but also what they believe (i.e., A c as defined later). However, for expositional ease, Vn is referred to as V n ( j / / t , A c ) , or sometimes simply as Vn. 2 0 A s s u m e that the entrepreneur only issues stock if she decides to invest in the project. 56 the new project 's re turn given q — q as y" , which can be represented as: <y7(Ac) = E [ e | g = 9 ,A c ] (1 - A c ) E [% = <?, a = 1 ] A c Prob(q = q\a = 0) + (1 - A c ) Prob(q = q\a = 1) where a-G {0,1} represents the entrepreneur's informat ion acquis i t ion decision. T h e E n t r e p r e n e u r ' s Investment Dec is ions at t = 2 Assume that the entrepreneur's conjecture of A c is A. G i v e n A, the entrepreneur believes that the investors' va lua t ion of the firm is Vn(y/L, A) = yh + s + q + J/"(A), if she decides to invest and issues the stock. If the entrepreneur is uninformed, given A, her expected payoff at t = 2 is If the entrepreneur is informed w i t h a signal yit given A, her expected payoff then is Denote the investment cutoff as tN, which is the worst s ignal w i t h wh ich the entrepreneur Therefore, if she is informed, she invests if, and only if, (y^ + s + q + yi)(l — Sn) > Vh-57 invests. It is easy to show tN = -s - y,fl_ -{s + y?): T h e posterior mean of the private signal y\l, given the entrepreneur's decision to invest, should then equal /• + CO yidF(yi) y i [ A } = -JL (3:1) A Prob(q = q\a = 0) + (1 — A) / d F(yi) JtN T h e fol lowing l e m m a characterizes the investment cutoff tN .21 Lemma 3.1 Under the Non-Disclosure Regime, when the entrepreneur is informed, she invests in negative NPV projects, i.e., tN < —s. T h e in tu i t ion is as follows. Under the Non-Disc losure Regime, the entrepreneur's i n -vestment choice q is the only mechanism for her to convey the pr ivate informat ion to the investors. Since higher investments lead to inferences of higher profi tabi l i ty , the lower-type entrepreneur has incentives to m i m i c the higher-type by overinvesting, as long as the gain from the investors' overpr ic ing exceeds the loss from under tak ing the unprofi table project. Further , because the investment level is dichotomous while the pr ivate informat ion is a con-t inuum, there does not exist a separating s ignal l ing equ i l ib r ium. T h e investment decision only serves as a very coarse signal for the entrepreneur's pr ivate informat ion . The Entrepreneur's Information Acquisi t ion Decision at t = 1 In ant ic ipat ion of her investment decisions, the entrepreneur makes the informat ion acquisi-t ion decision by compar ing the fol lowing expected payoffs. 2 1 T h e proof is provided in the Appendix . 58 If she does not acquire private information yit her expected payoff at t = 1 is Ui(yh,X,a = 0) = Max{{yh + s + q) (1 - ^),yh}. O n the other hand, if the entrepreneur acquires yi, her expected payoff at t — 1 is Ux{yh, A, a = 1, K) = y, t + / + s + q + Vi) (1 - ^ ) d Ffo) - «: Assume that w i t h p robab i l i ty A w the entrepreneur does not acquire private information. A ra t ional expectat ions equ i l ib r ium is characterized as follows: U1(yli,X,a = l,K) = Ul(yh,X,a = 0) i f « = K n (3.2) • 1 - A N = = P r o 6 ( « < « N ) (3.3) A == A^ = A N (3.4) In the ra t ional expectations equi l ib r ium, the entrepreneur acquires private information if, and only if, the incremental benefit from acquir ing informat ion exceeds the information cost. She is indifferent between acqui r ing and not acquir ing i f the real ized value of K equals the cutoff (Equa t ion 3.2), and does not acquire if K is higher than the cutoff. Therefore the equ i l ib r ium probab i l i ty that the entrepreneur has acquired informat ion equals S{KN) (Equa t ion 3.3). A l s o , in equ i l ib r ium, the investors' and the entrepreneur's conjectures are self-fulfilling (Equa t ion 3.4). 59 T h e fol lowing propos i t ion describes the entrepreneur's in format ion acquis i t ion decision in the ra t ional expectations equ i l ib r ium. Proposition 3.2 Under the Non-Disclosure Regime, the entrepreneur acquires private in-formation yi if the information acquisition cost K is below a cutoff Kn, which is defined by: Kn =-yh F(tN) + j {yh + s + q + y i ) ( l - ± l ) d F(yi) - Max{(yh + s + q) (1 - ^),yh}, where y!tl is determined by Equation 3.1, and As satisfy Equations 3.2, 3.3 and 3-4-And she does not acquire information if the cost is equal to or above the cutoff. C o m p a r i n g the informat ion acquisi t ion cost cutoff w i t h tha t of the first-best case, we have the fol lowing proposi t ion: Proposition 3.3 KN < K*, i.e., the entrepreneur underinvests in the acquisition of the productive information under the Non-Disclosure Regime. To understand this result, recal l that under the Non-Disc losure Regime, the entrepreneur is not able to disclose her private information about the new project to the investors. There-fore, informat ion has only one type of value: faci l i ta t ing p roduc t ion decisions. However, as shown previously, even though her private signal indicates the project is negative N P V , the entrepreneur invests as long as the investors' overvaluation exceeds the loss from the project. Therefore, the acquired informat ion has not been efficiently incorpora ted into investment de-cisions. A s a result, these ex post inefficient investment decisions make the information less 60 valuable ex ante, which reduces the entrepreneur's incentives to acquire informat ion. 3.4.3 V o l u n t a r y D isc losu re R e g i m e In this sect ion, ' assume that the entrepreneur can choose whether to. disclose her private signal about the new project in the prospectus. Chapter 2 has analyzed a s imi lar model and the results can be easily adapted to the current setting. T h e investors' informat ion set i n the equ i l ib r ium is = ( ? / / i , m , q ) , i.e., the his torical results disclosed in the prospectus, the entrepreneur's disclosure of the pr ivate signal (m = y i if the entrepreneur discloses and m = n i f the entrepreneur does not disclose), and the entrepreneur's investment decision. If the entrepreneur decides to invest and issues equity but does not disclose any forward- looking information, the investors price the firm as Vn(yh, X°) ! + x\yh, rn = n, q = q, Xc] = yh + s + q + E[e\rn — n,q = q, Xc]. If the entrepreneur issues equity w i th a disclosure of bo th his tor ical results and a forward- looking signal about the new project, her firm's shares are valued as Vd{yh, yi) = E[u + x\yh) m — yt, q = q] — yn + s + q+yi-Assume that the investors believe that w i t h probabi l i ty A c the entrepreneur has not acquired information. G i v e n the entrepreneur's decision to issue the stock but not disclose, the investors update their beliefs on e according, to the Bayes Ru le . T h a t is, y ,r (A<) = E[e\m = n,q = q,Xc] (1 - A c ) E [e\m = n , q = q, a = 1] A c Prob{rn = n,q — q\a = 0) + (1 — A c ) Prob(m = n,q = q\a = 1 ) ' 61 w here a : K —> {0 ,1} represents the entrepreneur's informat ion acquis i t ion decision. The Entrepreneur's Investment Decisions at t = 2 Assume that the entrepreneur's conjecture of A c is A. G i v e n A, the entrepreneur believes that the investors' va lua t ion of the firm is Vn(yh, A) = yh + s + q + _/ t"(A), if she decides to invest and issues the stock. If the entrepreneur is uninformed, given A, her expected payoff is U2(yh,'\,q) = (vh + s + q)(i-Tr%) i f q = q Vh i f q = 0. If the entrepreneur has acquired informat ion and received a s ignal yi, she can make three possible decisions: invest and disclose yi (id), invest and w i t h h o l d the informat ion (iw), and not invest (ni). Assume that disclosure is costless and t r u t h f u l . 2 2 G i v e n A, yil} and the private signal, the entrepreneur's expected payoff is U2(yii,yi,'ni,\,q) = (yh + s + q + yi)(l - -^) = yh + s + iji i f m = yi and q = q, ('<Jh + s + q + yt)(l - ^n) if m = n and q = q, if q = 0. Depending on different parameter values, there are two possible equi l ibr ia . 2 2 Fo l low ing the disclosure l i terature, we assume that while the entrepreneur can wi thhold information, she discloses truthful ly if she ever reports her private information. 62 Part ia l Disclosure Equi l ib r ium If V" > q and (yh + s + q)(l - ^n) > yh, the entrepreneur invests i f she is uninformed, and if she is informed, she invests and discloses her private s ignal i f yi > y j , invests and withholds private informat ion i f y* 6 (tv ,y\), where tv = -s - yrfl_ -(s + y " ) , and does not invest otherwise. T h e following l emma characterizes the necessary condi t ion for a P a r t i a l Disclosure E q u i -l i b r i u m . 2 3 Lemma 3.2 Under the Voluntary Disclosure Regime, the Partial Disclosure Equilibrium only exists for s > 0. In this equ i l ib r ium, when the investors observe the entrepreneur issuing equity but only disclosing his tor ical results, they infer that the entrepreneur is either uninformed or informed wi th a signal above the investment cutoff but below the disclosure cutoff. T h e disclosure cutoff y\, and the investors ' posterior mean of e given q = q and no disclosure about the project in the offering, y " , are determined by T h e fol lowing l e m m a characterizes the disclosure and investment cutoffs. Lemma 3.3 In the Partial Disclosure Equilibrium under the Voluntary Disclosure Regime, 2 3 A s proved later, yj > — s. Also from Lemma 3.3, y\ < 0. It follows that s > 0. That is, the Partial Disclosure Equilibrium only exists for s > 0. ( 1 - A ) (3.5) 63 when the entrepreneur is privately informed, both her investment and disclosure decisions a/re characterized by cutoffs, which have the following properties: (i) The' disclosure cutoff is below the prior mean of the private signal, i.e., y\ < 0; (vi)The investment cutoff is lower than the efficient cutoff, i.e., tv < —s. That is, the entrepreneur invests in negative NPV projects when she is informed. These results are s imi lar to those, in Chapter 2.. T h e first result i n L e m m a 3.2 is a s tandard result for the disclosure cutoff when disclosure is costless and there is uncertainty about the entrepreneur's informat ion endowment ( Jung and K w o n 1988) . 2 4 T h e second part of L e m m a 3.2 is the "overinvestment" result, which is induced by the investors ' overpricing of the firm's equity. A g a i n , overvaluat ion occurs due to the investors ' i nab i l i ty to dis t inguish whether the non-disclosure is because the entrepreneur has no pr ivate informat ion about the new project, or because she is w i thho ld ing bad information. Full Disclosure Equilibrium If Vn > q and (yh + s + q)(l — -r%) < yh, the entrepreneur does not invest i f she is uninformed. Therefore, i f the entrepreneur issues stock but does not disclose forward-looking informat ion, the investors infer that the entrepreneur must be w i thho ld ing private information. In other words, issuing stock signals to the market that the entrepreneur, is informed w i t h a private s ignal . In equ i l ib r ium, when the entrepreneur is informed, she always discloses her private signal if she issues equity and invests . 2 5 In add i t ion , the investment 2 4 T h e proof for y\ < 0 is provided in the appendix for Chapter 2, wi th only minor changes in the notation. 2 a T h i s is the standard "'unravelling"' result when disclosure is costless and the investors are certain that 64 cutoff is tv = — s, (i.e., her investment decisions are efficient). If V"' < q, it is not op t ima l for the entrepreneur to raise the capi ta l to undertake the project since she has to offer the investors more than 100% of her f i rm's shares, i f she invests but does not disclose any forward-looking information. Therefore, the entrepreneur issues equity and invests in the project if, and only if, she is pr iva te ly informed w i t h a signal yx > —s. In addi t ion , when she issues equity, she always reports her pr ivate signal . Under each of these two scenarios, the entrepreneur fully discloses her private information when she issues equ i ty . 2 6 However, when the entrepreneur is uninformed, she is unable to invest even though her project can be posit ive N P V . T h e E n t r e p r e n e u r ' s I n f o r m a t i o n A c q u i s i t i o n D e c i s i o n a t t = 1 In ant ic ipat ion of her investment decisions, the entrepreneur makes the informat ion acquisi-t ion decision by compar ing the fol lowing expected payoffs. If the entrepreneur does not acquire private informat ion, her expected payoff at t — 1 is { ('[Ik + s + q) (1 - - S n ) P a r t i a l Disclosure V yii F u l l Disclosure the entrepreneur is informed. 2 6 B o t h cases can be sustained by a threat from the investors that they wi l l believe the entrepreneur is hiding a very bad signal and offer a price V " < q if the entrepreneur issues stocks but does not disclose forward-looking information about the new project. 65 A n d if the entrepreneur acquires the private signal, her expected payoff is Ui(yh,X,a = 1,K,) = < Vh d F(yi) + $ {yh + s + q + Vi) (1 - ^n) d F(Vi + Ij°°(yii + s + yi) d F(yt) - K I Z Vh d F(Vi) + f+~(yh + s + yi)d F(yi) - « P a r t i a l Disclosure F u l l Disclosure Assume that w i th p robab i l i ty Xv the entrepreneur does not acquire p r iva t ion information. T h e following condit ions characterize a ra t ional expectations equ i l ib r ium: Ui(yk, A, a = 1,K,) = Ui{yh, A, a = 0) i f K = KX \ - \ V = S(KV) = Prob(K < KV) Xc = A 1 (3.6) (3.7) (3.8) T h e following propos i t ion describes the entrepreneur's in format ion acquis i t ion decisions in the ra t ional expectat ions equ i l ib r ium. Proposition 3.4 Under- the Voluntary Disclosure Regime, the entrepreneur acquires private information if the information acquisition cost K is below a cutoff n v , which is represented by: Vh d F(Vi) + f$ (yh -rs + q + yt) ( l - f i ) d F(Vi) + I^iVh + s + Vi) d F{yf) - (yh + s + q ) ( l - jfa) . I T 0s + Vi) d F(Vl) P a r t i a l Disclosure F u l l Disclosure 66 where y\ and y™ are determined by Equation 6, and As satisfy Equations 3.6, 3.7, and 3.8. She does not acquire information if the cost is equal or above the cutoff. C o m p a r i n g the informat ion acquis i t ion cost cutoff w i t h tha t of the first-best case, we have the following proposi t ion: Proposition 3.5 Under the Voluntary Disclosure Regime, if s > 0, then KV > K*; and if s < 0, then KV = K* . T h a t is, under the Vo lun t a ry Disclosure Regime, the entrepreneur has incentives to ex-cessively acquire private informat ion prior to the offering. Intui t ively, informat ion has two types of values in this case. F i r s t , it can s t i l l facili tate p roduc t ion decisions, bu t is less valu-able. T h e lower product ive value results from the entrepreneur's ex post inefficient decisions. However, informat ion also has a second role. T h e entrepreneur can use it to influence the investors' valuat ion. A s shown previously, in the P a r t i a l Disclosure E q u i l i b r i u m , shares are overpriced when the entrepreneur wi thholds her pr ivate informat ion , and underpriced when she is uninformed. Therefore, w i t h the information, the entrepreneur can avoid underpric-ing and can even take advantage of overvaluation. • In the F u l l Disclosure E q u i l i b r i u m , the entrepreneur has to forgo posit ive N P V projects when she is uninformed. Therefore, by ac-qui r ing informat ion, she can avoid losing profitable investment oppor tuni t ies . Overa l l , under the Volun ta ry Disclosure Regime, the private value of informat ion exceeds its social value (i.e., its product ive v a l u e ) , 2 7 which induces the entrepreneur to overinvest in her information acquisi t ion. 2 7 I n the benchmark case, the private value of information equals its social value. 67 3.4.4 Mandatory Disclosure Regime In this section, assume that the entrepreneur is required to include an informative forward-looking signal in the prospectus (either in the form of a forecast about the cash flows gen-erated by the new project, or in the form of a forecast about the firm's to ta l future cash f lows) . 2 8 Therefore i f the entrepreneur has not acquired the pr ivate s ignal , she is not able to issue equity at t — 2 since she fails to satisfy the disclosure requ i rement . 2 9 Her expected payoff at t = 1 then is U\(yh, a = 0) = y^. If the entrepreneur has acquired private informat ion, given y^\ yi} and her decision to invest, her expected payoff at t = 2 from invest ing is [^ (zz/t, Vi, ? = <?) = E[u + x\yh, yi, q = q]—q = yil + s + yi, and her expected payoff is yh if she does not invest. Therefore, she invests if s+'iji > 0 and does not invest otherwise. Her expected payoff from acqui r ing information at t: = 1 then is Uy(yil, a = 1. K) — yu + J^™ (s + yi) d F(yl) — K. T h e entrepreneur's information acquisi t ion and investment decisions are characterized in the fol lowing proposi t ion. Proposition 3.6 Under the Mandatory Disclosure Regime, when the entrepreneur issues equity to finance the investment project, she acquires information according to a cost cutoff 2 S A n "informative" signal refers to a signal that leads the investors to revise their beliefs about the firm value. On the other hand, an "uninformative" or a null signal results in no revisions of beliefs. 29VV'hen analyzing the Voluntary Disclosure Regime, we implicitly assume that the entrepreneur who does not acquire information cannot convince the investors the fact she is uninformed. To be consistent, we assume that the entrepreneur cannot credibly disclose a null forecast in the prospectus. Otherwise, the entrepreneur, when uninformed, could simply issue a null signal to convince the investors that- she indeed has no private information. We will discuss later how things change if this assumption is relaxed. 68 Km , which is represented by /+oo (s + yi) dF(Vi). •s If K < Km , the entrepreneur acquires information, and invests if, and only if, s + yi> 0. If K > Km , the entrepreneur does not acquire information, and not invest. 3.5 Comparisons of Disclosure Regimes Table 3.1 and P ropos i t i on 3.7 summarize the comparisons of the ex ante efficiencies of the investment and informat ion acquis i t ion decisions in the three disclosure regimes. P r o p o s i t i o n 3.7 If s > 0, then KN < K* < nv < Km, and if s < 0, then Kn < n* = KV = A s can be seen in Pane l A of Table 3.1, the investment decisions are inefficient relative to the first-best case in a l l disclosure regimes, except in the Vo lun t a ry and M a n d a t o r y Disclosure Regimes w i t h 5 < 0. Furthermore, Pane l B of Table 3.1 and Propos i t ion 3.7 compare the entrepreneur's i n -formation acquis i t ion decisions in different equi l ibr ia . W h e n 5 > 0, the entrepreneur un-derinvests in her acquis i t ion of product ive information in the Non-Disc losure regime, and overinvests in informat ion in bo th the Volun ta ry and M a n d a t o r y Disclosure Regimes. T h e excessive informat ion acquis i t ion in the M a n d a t o r y Disclosure Reg ime tends to be more 69 severe than that in the V o l u n t a r y Disclosure Regime (nv < KM)-. W h e n s < 0, the V o l u n -tary and M a n d a t o r y Disclosure Regimes induce the social ly o p t i m a l incentives to acquire information, while the Non-Disc losure Regime motivates the entrepreneur to produce less information. T h e in tu i t ion is as follows. If firms are mandated to include numer ica l forward-looking information in the offering prospectus, they tend to overinvest i n the informat ion acquisi t ion to comply wi th the disclosure regulat ion. However, if the informat ion is too costly (possibly due to the high uncertainties around their future cash flows), firms w i l l choose not to acquire information. These uninformed firms w i l l have to give up positive- N P V projects since they are unable to make a forecast that is required by the Regulators . O n the other hand, under the Non-Disc losure Regime, firms are not al lowed to share their private forward- looking informat ion w i t h investors. Therefore, when their shares are misvalued, they are deprived of the oppor tuni ty to achieve a fair va lua t ion th rough disclosure. T h e mispr ic ing can dis tor t firms' investment decisions, which u l t ima te ly results i n a decrease in the value of the informat ion to firms' internal p roduc t ion decisions and makes firms less incl ined to acquire addi t iona l informat ion. T h e Volun ta ry Disclosure Regime induces excessive incentives to acquire information. T h i s is because informat ion has a second role in addi t ion to its value of i m p r o v i n g product ion decisions. F i r m s could also strategically use the information to influence investors ' valuat ion. W h e n their shares are undervalued relative to their private knowledge, firms disclose the information to achieve a higher price; however, they w i t h h o l d their private . information 70 when their shares' are overvalued. T h e following propos i t ion summarizes the welfare comparisons of the ex ante efficiencies of three disclosure regimes. P r o p o s i t i o n 3.8 When s > 0, each of the three regimes can emerge as the efficient regime under some condition's.- However, when s < 0, the Mandatory and Voluntary Disclosure. Regimes dominate the Non-Disclosure Regime. T h e welfare analysis of the regimes involves complex tradeoffs of product ive value of information, informat ion acquis i t ion costs and efficiency losses from investment and infor-mat ion acquisi t ion decisions associated w i t h equity f inancing. P r opos i t i on 3.8 shows that neither M a n d a t o r y nor Vo lun t a ry Disclosure Regime is necessarily more efficient than the Non-Disc losure Regime. T h i s finding supports Dye 's (2001) argument that a product ion economy is not an obvious sett ing for publ ic disclosure to have a net posi t ive social value and the interplay between disclosure and product ion is subtle. Our results also have po l icy impl icat ions on the disclosure regula t ion of i n i t i a l publ ic offerings. In addi t ion to concerns for market efficiency and investor protect ion, regulators should also take into account the impact of disclosure policies on firms' real decisions. These policies not only affect the to ta l information available to the general pub l ic , but also have other externalities. O u r analysis shows that firms' p roduc t ion plans and informat ion acqui-si t ion decisions can be dis tor ted under different disclosure rules, and the d i rec t ion of the dis tor t ion varies. 71 Second, i t is difficult to determine which disclosure regime should be preferred from an ex ante point of view. T h e M a n d a t o r y and Volun ta ry Disclosure Regimes are associated w i t h efficiency losses resul t ing from excessive information acquisit ions and inefficient investment decisions, while the Non-Disc losure Regime suffers from the efficiency losses from under-product ion of informat ion and overinvestment in unprofitable projects. T h e tradeoffs of excessive and inadequate information product ion , and various forms of investment inefficien-cies depend on different parameter values, and none of the disclosure regimes dominates the other two in a l l s i tuations. However, our results also show that a Non-Disc losure Regime can compromise firms' abi l i ty to reduce informat ion asymmetry and correct potent ia l misva lua t ion through disclo-s u r e 3 0 and such restr ict ions can be detr imental . P ropos i t ion 3.8 shows that when s < 0, the M a n d a t o r y a n d Vo lun t a ry Disclosure Regimes are ex ante more efficient t han Non-Disc losure Regime. Reca l l that s is the pr ior mean of the project N P V , i.e., the market 's prior belief about the prof i tabi l i ty of the new investment project. Therefore this propos i t ion implies that l i n n s facing unfavorable pr ior pub l ic op in ion should be al lowed to t ru th fu l ly disclose their private forward-looking informat ion. Otherwise, issuing firms not only have less incentives to"acquire valuable product ive informat ion, but also invest inefficiently. 3 0 A n example in the appendix of L a n g and Lundholm (2000) illustrates how firms generally feel about the strict "quiet period" regulation. When facing negative news reports about his firm's proposed I P O , the C E O of Wired Ventures emailed his employees complaining how he felts hampered in his ability to defend their firm by the S E C regulation. Similar remarks have also been made by Salesforce's C E O in his M a y 2004 interview with the New York Times. 72 3.6 Discussion and Conclusion In this chapter, i t is assumed that the uninformed entrepreneur cannot credibly disclose that she has no private informat ion about the p ro jec t . 3 1 If this assumpt ion were relaxed, the results of bo th the Vo lun t a ry Disclosure and the M a n d a t o r y Disclosure regimes would change. It is s t raightforward to show that the M a n d a t o r y Disclosure Regime would be the same as the first-best case. Further , it is not difficult to show that when disclosure of forward-looking signal is voluntary, the entrepreneur fully discloses her pr ivate s ignal whenever she issues equi ty . 3 2 Therefore, bo th the M a n d a t o r y and Vo lun t a ry Disclosure Regimes would dominate the Non-Disc losure Regime. Another key assumption is that disclosure is t ruthful if the entrepreneur ever reports to the investors. T h i s assumpt ion is usually warranted by the threat of l i t iga t ion imposed on the misleading or unt ruthful I P O prospectus. T h i s assumpt ion is imposed to focus on the impact of disclosure policies on the avai labi l i ty of t ruthful forward- looking informat ion to the investors and how too much or too l i t t le informat ion affects the p roduc t ion efficiency of the economy. Our analysis is a pa r t i a l equ i l ib r ium analysis since we take al l the other factors which might affect firms' decisions as exogenous. In par t icular , we have not exp l ic i t ly model led the 1 1 The same assumption is made by previous studies such as Dye (1985), Jung and Kwon (1988), and Pae (1999, 2002). 3 2 I f the entrepreneur is uninformed, her firm's shares are correctly priced and her ex ante expected payoff is the same as in the first-best case. And if she is informed but issues equity without disclosing, the investors know that she is withholding information. A credible threat of offering a very low price will force the entrepreneur to fully disclose if she ever wants to issue equity. Therefore a Full Disclosure Equilibrium will prevail under the Voluntary Disclosure Regime. 73 threat of securities l i t iga t ion . Moreover , we have not considered the s ignal l ing effect of own-ers' decisions (such as the equity retention and the amount of cap i ta l investment) , and other i information accessible to the pub l ic around in i t i a l pub l ic offerings (such as economic-wide and industry-specific informat ion, and unaffiliated analysts ' reports and forecasts, etc.). For example, one relevant quest ion is to what extent management forecasts add to investors' knowledge given these al ternative information sources . 3 3 A n o t h e r quest ion is if the firm managers can convey their private information through al ternat ive mechanisms, how impor-tant disclosure policies are in the capi ta l market. Richer insights may be obta ined if future research extends, this line of research by incorpora t ing these elements. That is, there can be a subst i tut ion effect between these other mechanisms and direct disclosure. 74 Table 3.1: Efficiencies of Decisions in Three Disclosure Regimes P a n e l A : I n v e s t m e n t D e c i s i o n s Non-Disc losure Regime Voluntary Disclosure Regime M a n d a t o r y Disclosure Regime s > 0 overinvest i n negative N P V projects. Par t i a l Disclosure E q u i l i b r i u m : overinvest in negative N P V projects. Underinvest in posi t ive N P V projects. Fu l l Disclosure E q u i l i b r i u m : underinvest in positive N P V projects. s < 0 overinvest i n negative N P V projects. F u l l Disclosure E q u i l i b r i u m : no efficiency loss. N o efficiency loss. P a n e l B : I n f o r m a t i o n A c q u i s i t i o n D e c i s i o n s Non-Disc losure Regime Volun ta ry Disclosure Regime M a n d a t o r y Disclosure Regime s > 0 Underp roduc t ion of informat ion. Excessive informat ion acquisi-t ion. Excessive information acquisi-t ion. 5 < 0 Underp roduc t ion of informat ion. N o efficiency loss. N o efficiency loss. Chapter 4 Impact of Shareholder L i t iga t ion 4.1 Introduction A s mentioned previously, the threat of shareholder l i t iga t ion is a major force that affects an equity-issuing firm's disclosure incentives. It is often alleged that firm managers are reluctant to issue forecasts since they might be sued by shareholders i f the ac tual results fall short. Li t iga t ions can be very costly to firms. T h e costs of defending against lawsuits, even those without merits, could be substant ial . There can also be damage to corporate and personal reputations and d is t rac t ion of management from product ive act ivi t ies (Revsine et al . 2001). Pol icymakers have long been aware of the negative impact of the l i t iga t ion risk on firm managers' incentives to provide voluntary disclosure of forward- looking informat ion. One of the most impor tant legal reforms to address this issue is the 1995 P r iva te Securities L i t i ga t i on Reform A c t ( P S L R A ) . T h i s act created a s tatutory safe harbor that applies to bo th wr i t t en 76 and oral forward- looking statements. Under such a safe harbor, a defendant is not l iable w i th respect to any forward- looking statement if it is identified as forward- looking and is accompanied by "meaningful" caut ionary language ident ifying the factors that could cause actual results to differ. 1 However, this safe harbor does not app ly to i n i t i a l pub l ic offerings ( I P O s ) . 2 O n November 3, 2004, the S E C proposed a new rule to reform, the registrat ion, com-municat ions, and offering processes of the securities offerings ( S E C Release N o . 33-8501). 3 T h e major intent of this proposal is to promote more t imely investment informat ion to the investors, and to continue the efforts to integrate disclosure requirements on equity-issuing firms and publ ic firms. One of the S E C ' s proposals is to grant safe harbor protect ion from the gun- jumping provisions for forward- looking informat ion disclosed by repor t ing issuers (i.e., exist ing pub l ic firms) if they regularly release such informat ion before the offering. 4 However, the S E C d id not propose a same safe harbor for non-repor t ing issuers (mainly I P O firms). B u t i t remains an open question whether the S E C should provide a safe harbor for forward-looking informat ion released by I P O firms. In the release, the S E C specifically requested comments on the fol lowing issues: 5 o "In in i t i a l pub l ic offerings by non-report ing issuers, should we consider using our au-L Foi ' a detailed review of the 1995 Private Securities Litigation Reform Act, please refer to Johnson, Kasznik, and Nelson (2001). 2Other forward-looking statements excluded from the safe harbor provision include those statements in connection with tender offers, or made by firms issuing penny stock. 3 The full text of this release is available on the SEC's official web site: http://www.sec.gov/rules/proposed/33-8501.htm. 4Please refer to Section 3.2 in Chapter 3 for a discussion of the "gun-jumping" provisions. 5See Section III of SEC Release No. 33-8501. 77 thority,. . . to propose a projections and forward-looking informat ion safe harbor from l iabi l i ty for the forward- looking statements that wou ld be s imi la r to the l i ab i l i ty safe harbor ... in Securities A c t Sect ion 2 7 A ? " « "If we (the S E C ) determine to propose a safe harbor of this type for i n i t i a l publ ic offerings, what k inds of condit ions should we consider for its use?" • " A s a condi t ion for this safe harbor or one for i n i t i a l pub l i c offerings, should we require the issuer to file projections or other forward-looking informat ion as part of the regis-t ra t ion statement? Shou ld the projections be required to follow I tem 10 of Regula t ion S - K or S-B as applicable? Should projections be required to be accompanied by an accountant 's report on the projections or forecasts?" • " W o u l d a l i ab i l i ty safe harbor for i n i t i a l publ ic offerings cause issuers to provide more projections pub l i c ly? W o u l d there be concerns about the qua l i ty of these projections in light of the safe harbor?" Mot iva t ed by these questions, this chapter investigates the potent ia l impact of share-holder l i t iga t ion on the vo lunta ry disclosure of forward-looking informat ion i n in i t i a l publ ic offerings. It also analyzes the impl ica t ions of legal l iabi l i t ies on firms' p roduc t ion decisions. Specifically, we introduce a potent ia l cost of a law suit for "failure to meet the forecast". We assume that shareholders could hire a lawyer to file lawsuits against the equity-issuing firm if the subsequent actual performance falls below the management forecast disclosed dur ing the offering. W i t h an exogenous posit ive probabi l i ty , the court w i l l rule in favor of 78 the shareholders and award damages to them. T h i s posi t ive p robab i l i ty is used to capture the litigiousness of the legal environment, or the legal l i ab i l i t y associated w i t h the issuance of a forecast. 6 T h e paper has the fol lowing major findings. F i r s t , under different sets of economic para-meters, the entrepreneur has two possible equ i l ib r ium disclosure strategies: F u l l Disclosure and P a r t i a l Disclosure. Specifically, i n a F u l l (Par t ia l ) Disclosure E q u i l i b r i u m , a l l (part) of the signals w i l l be disclosed when the informed entrepreneur issues equity. O f par t icular interest is the latter equ i l ib r ium, in which shareholder l i t iga t ion plays a significant role. T h e l i t igat ion threat can give the entrepreneur incentives to only pa r t i a l ly disclose her private prospective in fo rma t ion . 7 W h e n the legal environment is sufficiently l i t igious, the entrepre-neur rarely discloses a forecast in the offering, which is descript ive of the s i tua t ion in the Un i t ed States. Second, the entrepreneur's p roduct ion decisions might be d is tor ted by her disclosure in -centives. In the F u l l Disclosure E q u i l i b r i u m , the entrepreneur, if informed, could give up some posit ive N P V projects i f the expected l i t iga t ion cost outweighs the expected invest-ment profit. O n the other hand, if she is uninformed and unable to issue a forecast, she has to forgo the investment oppor tun i ty even though the project is posi t ive N P V , since the in -vestors severely underprice the firm's stock when they observe no disc losure . 8 In contrast, in 6 These two are not mutually exclusive, since a higher legal liability on firms could induce investors to file lawsuits more often, which in turn makes the legal environment more litigious. 7 B y "partially", we mean that the entrepreneur discloses only if her signal is above a certain threshold. 8 I t is assumed that if the entrepreneur is uninformed, she cannot issue a "null" forecast which does not change investors' prior-beliefs about the firm value. Alternatively, we can assume a "null" forecast and a "no disclosure" are treated as equivalent by the investors. 79 the Paxt ia l Disclosure. E q u i l i b r i u m , the entrepreneur could invest i n negative N P V projects. T h i s is because when the investors have uncertainty about the entrepreneur's informat ion endowment, in equ i l i b r ium they overpay for the firm's shares when the pr ivately- informed entrepreneur issues equi ty . 9 Such overvaluation induces the entrepreneur to take on unprof-itable projects and incur an efficiency loss. T h e model is then used to examine the effect of regulatory polices on firms' disclosure incentives. T h e analysis shows that re laxing the legal l i ab i l i ty (for example, by prov id ing a safe harbor for forward- looking informat ion disseminated by I P O firms) can result in more information flow to the pub l ic and facilitate the capi ta l format ion process. O n the cost side, however, such a safe harbor could lead to a higher rate of lawsuits and an increase in deadweight l i t iga t ion costs. A s to the issue on whether to require issuing firms to file projections, the s tudy suggests that the F u l l Disclosure po l icy is not necessarily op t imal since it is associated w i t h bo th a social loss due to underinvestment and a higher l i t iga t ion-related deadweight cost. We extend previous ana ly t ica l research on the l ink between shareholder lawsuits and man-agerial disclosure of prospective information. T h e s tudy is most closely related to Trueman (1997), but our model differs from his in the fol lowing impor tan t ways. T rueman examines a sett ing in which the manager has an affirmative duty to disclose forward- looking infor-mat ion, and f a i l u r e t o d i s c l o s u r e w i l l potent ia l ly trigger lawsuits when there is a stock price decline after the actual result reveals the informat ion that was wi thhe ld . B u t in our 9 T h e investors on average breaks even, since they also underpay for the firm's shares when the entrepreneur is uninformed and issues the equity. 80 setting, the firm manager has no legal obl igat ion to make a forecast and it is the disclosure o f the prospective information that can lead to future lawsuits i f the actual result falls below the forecast. O u r results also differ significantly. T r u e m a n demonstrates shareholder l i t igat ion can motivate managers to disclose bad news. In contrast, we show that l i t iga t ion risk can suppress manageria l disclosure of forward-looking informat ion . Our w o r k complements the empir ica l l i terature on the re la t ion between shareholder l i t i -gation and voluntary disclosure. Ear l ie r studies (Skinner 1994, 1997) have investigated the impact of shareholder l i t iga t ion on firm management 's vo lunta ry disclosures of forecasts, and produce two general findings (as summarized i n Bag insk i , Hassel l , and K i m b r o u g h 2002). F i rs t , the threat of l i t iga t ion reduces the manager's incentives to vo lun ta r i ly disclose man-agement forecasts. Second, fear of legal l i ab i l i ty motivates managers to hasten disclosure of bad news to "preempt" potent ia l l awsu i t s . 1 0 Later , Johnson, K a s z n i k , and Nelson (2001) examine how the safe harbor provis ion int roduced by the 1995 Pr iva te Securities L i t i ga t i on Reform A c t changes the managers ' disclosure practices of prospective informat ion. Bag insk i et al . (2002) compare the characteristics of management forecasts i n two different legal en-vironments, U . S . and Canada . A l m o s t a l l these studies examine management forecasts'from exist ing publ ic companies, and how l i t iga t ion affects I P O firms' disclosure incentives are largely unexplored. T h i s cou ld be a t t r ibutable to the fact that I P O forecasts are v i r tua l ly non-existent in the U n i t e d States. T h i s chapter employs a theoret ical approach and thereby circumvents the da ta problem. W e argue that in the I P O settings shareholder l i t iga t ion l 0 F o r example, Skinner (1994) provides evidence that managers voluntar i ly disclose bad news to preempt bad quarterly earnings news. 81 deters disclosure of prospective informat ion, rather than induces more disclosure. Further-more, this approach also allows us to provide predictions for the potential consequences of a l leviat ing the legal l i ab i l i ty for forecasts associated w i t h i n i t i a l pub l i c offerings. T h i s chapter is organized as follows. Section 4.2 introduces the basic settings of the model and the major assumptions, and briefly analyzes a benchmark case. Section 4.3 investigates the entrepreneur's possible disclosure strategies i f she-is informed. T h e n the entrepreneur's investment decisions in different disclosure equ i l ib r i a (Fu l l and Vo lun ta ry Disclosure Equ i l i b r i a ) are examined. Section 4.4 compares the ex ante efficiencies of different disclosure equi l ibr ia and discusses the pol icy impl ica t ions of the results. T h e last section concludes. 4.2 Model Setting and Benchmark Case 4 . 2 . 1 Setting and Major Assumptions We incorporate the features of the U.S . ' s legal environment into the new equity disclosure model developed i n previous chapters to analyze the impact of shareholder l i t iga t ion on firm managers' disclosure strategies. Specifically, we consider a set t ing w i t h a r isk-neutral entrepreneur who owns a private firm, and a group of well-diversified investors. T h e firm has an investment oppor tuni ty , which requires an in i t i a l investment of q and generates a gross payoff x = (1 + 6)q + e, where 9 is the net uni t rate of re turn (a constant) , and e is the noise 82 . t e r m . 1 1 Assume that e is normal ly dis t r ibuted, w i t h mean 0, variance o2 and a cumulat ive d is t r ibut ion function of G(e). Assume that the entrepreneur decides to issue equity to finance her project. She w i l l offer investors a fraction of her firm's shares in exchange for q. Before she makes the investment decision, however, w i t h a p robabi l i ty 1 — A, the entrepreneur receives a signal about the project 's future return. T h e signal , denoted as yiy is represented as e = y~i.+ u, where yt ~ N(0 , of) and v is independent of y~i. T h e residual uncer ta inty is captured by v, which follows a normal d i s t r ibu t ion N ( 0 , o f ) w i t h o2v = o2 - of . T h e cumula t ive d i s t r ibu t ion functions of yt and v are denoted as F(yi) and H{v) respectively. A t t = 1, based on her informat ion set, the entrepreneur decides whether to invest. If she decides to invest, she w i l l issue equity to the publ ic w i th a prospectus that includes general information about her firm's business and possibly a forecast of her firm's t e rmina l cash flow. Denote the forecast as F. Under the t ruthful disclosure assumpt ion, i t must be true that F = - E ^ l i / i ] = (1 + 9)qJryi. Since F is informational ly-equivalent to yx, in the later analysis, we w i l l sometimes refer to the inclus ion of a forecast as disclosing yx. A t the end of the per iod , if the entrepreneur d id not invest i n the project at the previous date (t = 1), the cash flow'is zero; otherwise the firm's cash flow is real ized as x = (\ + 9)q + e. If the realized cash flow falls short of the pr ior forecast F, the shareholders who purchased the shares at t = 1 might successfully sue the entrepreneur for the "inflated forecast". Fol lowing Trueman [1997], we assume that the shareholders who want to take legal ac t ion against the " F o r a summary of the notation used in this paper, please refer to the Append ix . 83 entrepreneur w i l l approach a r isk-neutral lawyer who decides whether to take on the suit. Assume that 9, q, and the structure of the game are common knowledge. T h e t ime line of the model is shown in F igure 4.1. t=0 t=l t=2 E x ante W i t h an exogenous probability, E observes y ( ; E decides whether to invest and/or disclose y {. x is realized i f E has invested; a lawyer decides whether to sue E . F igure 4.1: Sequence of Events . 4.2.2 Self-Financing - the Benchmark Case We first briefly examine the case i n which the entrepreneur self-finances the project. Let q G {0,q} represent the entrepreneur's investment decision. A t t = l s i f the entrepreneur has no private informat ion about the investment 's profi tabil i ty, her expected payoff is U\ = E[x\q = q] — q = 9q if she invests, and U\ = 0 i f she does not invest. Therefore, she invests if 9 > 0 and does not invest otherwise. If the entrepreneur is pr ivate ly informed, her expected payoff at t = 1 is U\(yi) = E{x\'tji,q = q] — q = 9q + yi if she invests, and 0 if she does not invest. Therefore, she invests if 8q + yi > 0 and does not invest otherwise. Denote the pr ior mean of the N P V of the investment project as s, i.e., s = E[x\q = q] — q = dq. T h e n when the entrepreneur is informed, her investment decisions are characterized by an investment cutoff — s. T h a t is, 84 investment is undertaken if, and only if, -y^ € (—s,+oo). 4.3 Analysis of the Equity Offering From now on, assume that the entrepreneur decides to raise cap i ta l from the equity market to finance the project. 4.3.1 T h e L a w y e r ' s L i t i g a t i o n Dec i s i on at t = 2 U s i n g backward induc t ion , we first analyze the lawyer's suing decision at date 2. Assume that the necessary condit ions for a lawsuit are that (1) the entrepreneur issued a forecast at t = 1, and (2) at the end of the per iod the realized cash flow x falls below the forecast. Such an assumption is based on the following two observations. F i r s t , many disclosure-related lawsuits are filed fol lowing a sharp decline in the stock price and firms are rarely sued after large stock price increases (Trueman 1997; B r o w n et a l . 2004). Secondly, in the Un i t ed States, I P O firms have no affirmative duty to disclose numer ica l forward-looking information in the prospec tus . 1 2 T h e above assumpt ion implies that the entrepreneur w i l l not be sued i f she d i d not include a forecast in the prospectus when she issued equity at date 1. O n the other hand, i f a forecast was inc luded i n the prospectus (i.e., y,; was disclosed) and the realized cash flow is x, the lawyer agrees to take on the lawsuit i f the fee he receives from the shareholders l 2 A n affirmative duty to disclose exists either because the manager's information pertains to M D & A . statement or would serve to update or correct a previous disclosure (Trueman 1997). 85 exceeds his l i t iga t ion cost (denoted as C/j). Assume that the shareholders pay the lawyer a fraction 7 of the damage a w a r d . 1 3 7 is assumed to be an exogenous constant, wh ich implies that the market for legal services is not compet i t ive and in equ i l ib r ium the lawyer could earn a positive profit. It is also assumed that when a lawsuit is filed, the court holds the entrepreneur l iable wi th a posit ive p robab i l i ty /3.14 We can interpret (3 as a measure of the lit igiousness of the legal environment, or the legal l i ab i l i ty for disclosure of a forecast. T h e damage award to the shareholders is assumed to be set to equal to max{0, E[x\yi] — x}, i.e., the alleged "price i n f l a t i o n " . 1 5 If the lawsuit is unsuccessful, the shareholders receive noth ing . T h e lawyer's expected payoff from pursuing a lawsuit is TTL = 7 j3 max{0, E[x\yi] - x} - CL. It is easy to show that he w i l l agree to sue the entrepreneur if, and only if, e < y^ — L, where C e is the realized noise term in x and L =-—Jj. - 7/3 1 3 H o w the damage award is determined wil l be discussed later. 1 4 F i r m managers could be held liable for forecasts that are truthful but in hindsight are too optimistic. Th is is because firm managers have the legal responsibil i ty to make the forecasts wi th best judgement and reasonable care and ski l l . However, what constitutes "due care" is not specifically stated in the current law. Therefore, a manager can be held liable for failure to forewarn the investors about the future poor performance, even though the forecast was consistent with the manager's private information set at the time of making the projection. The legal rules on auditor l iabil it ies are also ambiguous in defining "due care". 1 , r jDamages in securities l i t igation cases are most commonly based on the difference between the security's alleged inflated purchase price and a subsequent price that reflects the correct information (Schwartz 1997). 86 4.3.2 The Entrepreneur's Disclosure Decision at t = 1 if She is Informed Reca l l that we assume that the entrepreneur can choose whether to disclose her private signal in the prospectus. We can follow the same procedure used i n Chap te r 2 to analyze the entrepreneur's decisions. Represent the entrepreneur's informat ion set as tyE, where tyE — {Vi} i f s n e is informed and tyE = 0 otherwise. T h e investors' information set is ty/ = {m, q], i.e., the entrepreneur's disclosure of the private signal (m = y i if the entrepreneur discloses and m = n i f the entre-preneur does not disclose), and the entrepreneur's investment decision. If the entrepreneur decides to invest and issues stocks but does not disclose any forward- looking information, the investors price the f irm as 5n = E[x\m = n , q = q] = s + q + E[i\m = n , q — q}. If the entrepreneur issues equity and also discloses a forward-looking signal about the project, her firm's share is valued as 5d = E[.x |m = yi: q = q] = s + q + y^. G i v e n the entrepreneur's decision to issue the stock but not disclose, the investors update their beliefs on e according to the Bayes Ru le as follows, Vi = E [ e | ™ = n, q = q] (1 - A) E [e|m = n, q = q, tyE = {yi}] A Prob(m = n,q = q, tyE = 0) + ( 1 - A) Prob(m = n,q = q,tyE = {yi})' In ant ic ipat ion of the investors' responses, the entrepreneur believes that the investors' valuat ion of the firm is Sn = s + q + y " , if she decides to invest and issues equity but makes 87 no forecast. • If the entrepreneur is uninformed, her expected payoff is Ur(X,q) = (s + q)(l - $1) i f Q = 9, 0 if q = 0. If the entrepreneur is informed with a signal yit she can make three possible decisions: invest and disclose y i (id), invest and withhold the information (iw), and not invest (ni). As-sume that disclosure is truthful. The entrepreneur's expected payoffs from these alternative actions can be characterized as follows. Given yi, and in anticipation of the potential future litigation, the entrepreneur's expected payoff at t = 1 is s + yi - 7 D(yt, (5) if m = y{ and q = q, U{(yi,m,\,P,q) = \ (g + g + ^)(1 - ? ,) if m = n and q = q, i> -r q -r (/j 0 if g = 0, where D(yi,(3) = (3 (yi — e) d G(e\yi), i.e., the expected damage award.16 There are two points worth noting. First, let us try to understand the expected payoff when the entrepreneur issues equity and discloses her signal in the form of a forecast. The term 7 D(v/7;, (3) represents the portion of expected damage award that the investors use to pay the lawyer. In a rational expectations equilibrium, the investors endogenize their expected 3 T h e proof for this expected payoff functions is provided in the Append ix . legal fees into their p r i c ing function, and get fully reimbursed from the entrepreneur for this legal expenditure. Second, it can be shown that the expected damage award D(yi,B) is independent of the forecast disclosed, as summar ized in the fol lowing l e m m a . 1 7 Lemma 4.1 The expected damage award D(yi,B) is independent ofyi. T h i s might sound counter intui t ive. In tu i t ion suggests tha t the more op t imis t i c the fore-cast is, it is more difficult for the entrepreneur to meet or beat the target. T h e expected damage award should also be larger, since it is. more l ikely tha t the ac tua l result falls widely below the forecast. However, recall that yt is informative about the noise te rm e. W h e n the entrepreneur issues a favorable forecast and the forecast is t ru thfu l , it implies that the terminal cash flow is expected to be higher. A s a mat ter of fact, t h e signal shifts the mean of e from zero to j / j . 1 8 Therefore, the condi t ional p robabi l i ty tha t the t e rmina l cash flow falls below the forecast is independent of the forecast. So is the expected damage award. In the subsequent analysis, we refer to the expected damage award as D(B). If s + q + y-i < 0, the entrepreneur does not invest. N o r does she need to access the capi ta l market or make any disclosure. If s + q + y i > 0 and 5n < q, the entrepreneur fully discloses her signal whenever she issues equity, since the fraction of shares she has to sell is equal to or larger than 100% if she makes no disclosure. 1 7 T h e proof is as follows. Recal l that e = yt + D. Therefore, D(yi,P) = (3 (yi - e) d G(e\yi) = P (—u) d H{v) = P av where </>(•) is the P .D .F . of a standard normal distr ibut ion. It follows that D(yi,p) is independent of j/j. We are thankful to Prof. Jerry Fel tham for raising this point: 1 8 G i v e n e = y-i + v, it must be true that .E[e|i/;] = y;. ' 8 9 If s + q + yt > 0 and 5n > q, she invests in the project and also chooses whether to issue a forecast to the investors. Her disclosure strategy is characterized by the fol lowing lemma. Lemma 4.2 If s + q + yi > 0 and 5n > q, the entrepreneur's disclosure strategy is charac-terized, by a lower bound. T o understand this l emma, note that the entrepreneur makes the disclosure decision by compar ing Ui(yi,rn, — yu\,B,q = q) w i t h Ui(yi,m — n, X,j3,q = q). It is easy to see that both expected ut i l i t ies are a linear increasing function of yi for a l l yi > —s — q.19 T h e two straight lines intersect once and the disclosure region must be character ized by a single lower cutoff. Lemma 4.3 // the parameters are such that 5n > q, the disclosure cutoff increases in the Oy^ litigation risk, i.e., > 0. To explain , in our sett ing, disclosure of the private s ignal involves a cost. T h a t is, it can result in shareholder lawsuits at the end of the per iod . Several previous studies (such as Verrecchia 1983) show that a par t ia l disclosure equ i l i b r ium exists when there is a disclosure cost. A major difference between our model and Verrecchia (1983)'s model is that the disclosure cost in our model is endogenously determined by the lawyer 's actions, while lie assumes that the cost is exogenous. 2 0 In addi t ion , the disclosure cost is increasing in the l i t iga t ion risk. Therefore, when the l i t iga t ion risk is higher, the entrepreneur has less incentive to disclose her private signal. 1 9 Note that s + q + j / " is a constant. 2 0Some disclosure models have considered endogenous disclosure costs arising from product market com-petition. See, for example, Darrough (1993). 90 Figure 4.2 shows a, numerica l example on the impact of the l i t iga t ion r isk on the disclosure cutoff. T h e vert ical axis represents the value of the function T(yi) = (p+q + Vi) _ ^pj^ ~ (p + q + Viiyi)), and the intercepts are disclosure cutoffs under different values of B. It can be shown that B = 0.45 results in a disclosure cutoff y\ = 1.65. T h e equ i l ib r ium probabi l i ty that the entrepreneur issues' a forecast when issuing equity is about 5 % . 2 1 T h a t is, when the threat of l i t iga t ion is sufficiently high, it can result in l i t t le disclosure of forward-looking information, which is consistent what we now observe in in i t i a l pub l i c offerings in the U n i t e d States. Figure 4.2: Impact of L i t i g a t i o n R i s k on Disclosure Cutoff (s = 2, q = 10, A = 0.2, 7 = 0.9, a = 10, ^ = 1,CL = 1). T h e following propos i t ion fully characterizes the entrepreneur's disclosure decisions: 2 1 In the numerical example, the signal yi follows a standard normal distr ibut ion. W h e n (3 = 0.45, the probabil i ty that the entrepreneur issues equity is Prob(yi > — s — q) = Prob(yi > —12) = 1, and the probabil i ty that she discloses a forecast is Prob(yi > y\) = Prob(yi > 1.65) = 0.05. Therefore, the condit ional probabil i ty of observing a forecast in the offering is about 5%. P P P P 0.1 0.3 0.5 0.7 0.9 91 P r o p o s i t i o n 4.1 If the entrepreneur is informed and decides to raise capital to invest in the project, she coidd possibly make the following disclosure decisions: (1) Full Disclosure: If the parameters are such that 5n < q, the entrepreneur always discloses her private signal if she is informed.2'1 (2) Partial Disclosure: If the parameters are such that 5n > q, the entrepreneur makes disclosure decisions according to a cutoff. Specifically, the entrepreneur's disclosure strategy rn is as follows, m(yi) = | y% ifyi e [yh+oo), n ifyi€(s-q,y}), v where y\ is determined by the following two equations: s + y \ - l D { B ) = (5 + g + y ? ) ( l - g ) (4.1) fVi y? = ^ (4.2) A Prob(m = n, q = q, tyE = 0) + (1 - A) / ' d F{Vi) J—s — q 4.3.3 The Entrepreneur's Investment Decision at t = 1 F u l l D i sc losu re If 5n < q, the entrepreneur is not able to raise the capi ta l needed, i f she invests but does not disclose any forward- looking informat ion. Therefore, i f the entrepreneur is not informed, she does not invest. W h e n the entrepreneur is informed, she invests and discloses her private 2 2 T h e complete list of parameters includes s, q, a2, a2, 7 , A, CL, and (3. 92 signal if s + yl — 'yD(p) > 0 and does not invest otherwise. Denote the solut ion to s + yt = jD((3) as y_i, which is bo th the investment cutoff and the disclosure cutoff. Lemma 4.4 In the Full Disclosure Equilibrium, yi > —s. That is, the entrepreneur under-invests in positive NPV projects. Equity-Financing: Full Disclosure Equilibrium Self-Financing Equity-Financing: Partial Disclosure Equilibrium iw , id Vi Self-Financing i: invest; ni: not invest; iw: invest and withhold into; id: invest and disclose. Figure 4.3: T h e Entrepreneur 's Investment Decisions in Different Disclosure E q u i l i b r i a when She is Informed. Intuit ively, since the entrepreneur can only invest if she discloses her private signal, she has to weigh the expected investment payoff against the potent ia l future loss caused by 93 shareholder l i t iga t ion . If the project 's expected re turn is not large enough tb compensate for the expected l i t iga t ion cost, the entrepreneur does not invest. Part ial Disclosure If 5n > q, the investment cutoff for the informed entrepreneur is — s - q. T o expla in , when 5n > q, if the entrepreneur is informed w i t h a signal better t han y\, she receives a posit ive expected payoff from investing. T h e proof is as follows. Ui(yi, m = yi} \,q = q) > U\{yi,m = n,X,q = q)-= (s + q + yi)(l - J j ) > 0 = U[(yi,m = yi,\,q = 0). Similar ly , when the private signal is between — s — q and y\, the entrepreneur is better off by investing than not investing, since U\(yi,m =.yi, \,q = q) > 0. O n the other hand, i f the entrepreneur is uninformed, she chooses to invest i n the project if s + q > 0 and does not invest o therwise . 2 3 To 'summarize, if the entrepreneur is uninformed, she invests i n project if, and only if, s + q > 0. If she is informed, she invests and discloses her pr ivate signal i f y i > y\, invests and withholds private informat ion if yi G ( —s — q,yj), and does not invest otherwise. 2 3 R e c a l l that C/J"(A, q = q) = (s + q)(l - ^ r ) . If s + q < 0, the investors infer that the entrepreneur must be informed and withholding the private signal if she invests but does not make any forecast. In this case, even though the investors are certain that the entrepreneur is informed if they observe m = n and q = q, partial disclosure continues to be an equilibrium since there exists an endogenous disclosure cost. • 94 4.4 Welfare Analysis and Policy Implications 4.4.1 Social Welfare We can compare the ex ante efficiencies of investment decisions i n the two disclosure equi-l ibr ia . . T h e ex ante efficiency, or equivalently, ex ante social welfare, is defined as the sum of expected uti l i t ies at t = 0 of the three players: the entrepreneur, the investors and the lawyer. For each disclosure equ i l ib r ium, its social welfare is compared to the social welfare in the first-best (i.e., self-financing) case. T h e decrease in social welfare is ca l led a social loss or inefficiency. P ropos i t i on 4.2 summarizes our findings from the previous section. Proposit ion 4.2 In the Partial Disclosure Equilibrium, the entrepreneur overinvests in neg-ative NPV projects relative to the first-best case; she underinvests in positive NPV projects in the Full Disclosure Equilibrium. We can further calculate the ex ante inefficiency of the investment decisions as below: A max{s, 0} + (1 - A ) [ J ^ (5 + Vi) d F(yi)] F u l l Disclosure , —A s I — (1 — A)[/Jss__ (s + yi) d F(yi)] P a r t i a l Disclosure, where I = 1 if s G (—q, 0] and 1 = 0 otherwise. To explain , in the F u l l Disclosure E q u i l i b r i u m , there are two scenarios i n which the entrepreneur underinvests: (1) when the project N P V is posi t ive (s > 0), but she has no private informat ion and cannot issue equity; (2) when she is p r iva te ly informed, but the expected investment payoff cannot offset the expected l i t iga t ion cost (—s <yx < y{). In the • 95 Par t i a l Disclosure E q u i l i b r i u m , recal l that the entrepreneur's expected payoff from investing when she is uninformed is (s + cy)(l — J^). Since 5n > q, the entrepreneur invests i n the project as long as s + q > 0 when she uses equity-financing, whi le she invests only when s > 0 in the first-best case. Therefore overinvestment occurs when s € (—q, 0] and the result ing efficiency loss is the project 's net loss — s. O n the other hand, when the entrepreneur is informed, she invests in a negative N P V project when her private signal falls between —s — q and -s.2A T h e other inefficiency is related to the deadweight loss incurred in shareholder lawsuits, which is represented by ( 1 - A ) H(-L) CL [1 - F(yi)] F u l l Disclosure , L2 = { (1 - A) H(-L) CL [1 - F(yj)} P a r t i a l Disclosure. where y i is the solut ion to s + yi = 7-D(/3), and y\ is the disclosure cutoff established in Equat ions 4.1 and 4.2. To understand, recal l that a lawsuit w i l l be filed whenever the entrepreneur is informed and issues a forecast in the equity offering (?/, > in the F u l l Disc losure E q u i l i b r i u m , and •iji > y\ in the P a r t i a l Disclosure E q u i l i b r i u m ) , and the por t ion of the damage award pa id to the lawyer exceeds her l i t iga t ion cost {iyB{yi — e) > CL or equivalently, v < —L ). Reca l l that the C . D . F . of v is H{v). T h e n , H(—L) is the equ i l ib r ium probab i l i ty that a lawsuit occurs condi t ional on disclosure of a forecast and CL is the deadweight loss caused by the 2 4 Cond i t i ona l on the private signal j / ; , the intrinsic project NPV equals yi + s. Thus a private signal yi £ (—s — q, — s) implies that the project is negative NPV. 96 l i t iga t ion. It is easy to compare the expected l i t igat ion-related efficiency loss i n the two equi l ibr ia . P r o p o s i t i o n 4 .3 The Full Disclosure Equilibrium is associated with a higher expected dead-weight litigation cost than the Partial Disclosure Equilibrium.25 T h e above propos i t ion follows from the fact that y\ > yi2& T h e to ta l inefficiency associ-ated w i t h the equi ty-f inancing set t ing relative to the self-financing set t ing is L = USfto — Uef]0 = L\ + Li-4 . 4 . 2 Implications for SEC's Proposed Securities Offering Reform Safe H a b o r for P r o s p e c t i v e In fo rma t ion Disc losu re f rom I P O F i r m s Given the scarcity of management forecasts in the in i t i a l pub l ic offerings, the S E C is consid-ering whether to relax the current legal l i ab i l i ty and provide a safe harbor for the disclosure of forward-looking informat ion by I P O firms. Such a po l icy corresponds to reducing the parameter (3 in the context of our model . A s shown in bo th L e m m a 4.3 and Figure 4.2, a decrease in (3 could induce the issuing firms to pub l i c ly issue more forecasts and the investors would have more access to prospective informat ion to facili tate their investment decisions. 2 r jEndogenizing the entrepreneur's information acquisition could make it difficult to compare the expected litigation welfare loss in the Full and Partial Disclosure Equilibria. This is because relative to the Partial Disclosure Equilibrium, in the Full Disclosure Equilibrium, the entrepreneur could be less inclined to acquire information (the equilibrium A is higher), even though she discloses more often (j/.; < y\). 2 6 The proof is provided in the Appendix. 97 However, the overall effect of a safe harbor pol icy on the social welfare is ambiguous. T h e reasons are as follows. F i r s t , when the market is efficient and investors are ra t ional , they on average break even. M o r e information available to investors has no impact on their collect ive welfare. Second, the product ion efficiency remains the same as well , as can be seen from our previous analysis. Las t but most impor tant ly , under certain circumstances the impos i t i on of a safe harbor could induce an increase i n shareholder lawsuits, and more social resources expended i n the l i t igat ion process. R e c a l l that the equ i l ib r ium probabi l i ty of lawsuits equal H( — L) [1 — F(yj)] where L = It is easy to see that a lower l i t iga t ion risk w i l l decrease the probabi l i ty that the lawyer files a lawsuit against the forecast, but also increase the p robab i l i ty that the entrepreneur discloses a forecast. W h e n the second effect dominates the first effect, re laxing the legal l iab i l i ty on voluntary disclosure of prospective informat ion could actual ly decrease the social welfare. Optimal E x Ante Disclosure Policy One of the issues for wh ich the S E C is seeking comments is whether i t should require the issuer to file projections or other forward-looking informat ion as par t of the registration statement. To answer this question, we have to determine whether a F u l l Disclosure is the op t imal ex ante disclosure pol icy in the I P O setting. Under such a policy, full disclosure of forward-looking informat ion is enforced if a firm ever wants to raise equity. It can be easily seen that the social welfare under this ex ante 98 disclosure pol icy is the same as that under the F u l l Disclosure E q u i l i b r i u m analyzed previ-ously. However, compared to the welfare under the P a r t i a l Disclosure E q u i l i b r i u m , the F u l l Disclosure pol icy might not be op t ima l ex ante. Fi r s t of a l l , even though the P a r t i a l Disclosure E q u i l i b r i u m is associated w i t h an efficiency loss in p roduc t ion due to overinvestments, a F u l l Disclosure po l icy induces underinvestments. Second, the F u l l Disclosure is also associated w i t h a larger l i t igat ion-re la ted social loss than the Pa r t i a l Disclosure E q u i l i b r i u m . Therefore, there exists condi t ions i n which each equil ib-r i um could be o p t i m a l ex ante. To sum up, it might not be o p t i m a l for the regulators to mandate al l issuing firms to include projections of their future performances. 4.5 Discussion and Conclusion We conclude our paper w i t h the fol lowing remarks. F i r s t , one major l i m i t a t i o n of this paper is that we assume disclosure is t ruthful if the entrepreneur ever discloses. E v e n though this assumption is warranted by the integri ty requirements on the I P O prospectus, the possibi l i ty of l y ing can s t i l l arise if the legal l i ab i l i ty for forward-looking informat ion is relaxed and firms start to issue projections. Therefore, an interesting extension of the analysis is to draw on cheap-talk or persuasion game models to introduce untruthful repor t ing , and reinvestigate the effect of shareholder l i t iga t ion on I P O firms' disclosure incentives of prospective infor-mat ion and the potent ia l consequences of p rov id ing a safe harbor for forecasts i n connection w i t h in i t i a l pub l ic offerings. Secondly, we have assumed that capi ta l markets are compet i t ive and investors are ratio-99 rial. A s a consequence, the investors are indifferent to different l i ab i l i t y rules on disclosure since they are assumed to always break even in the equ i l ib r ium and it is the entrepreneur who u l t imate ly bears a l l the consequences of the change in the legal system. T o the extent that this assumption is not descriptive of the real wor ld , we might underest imate the potent ial benefits of p rov id ing a safe harbor to induce more manageria l disclosure of forward-looking information. F ina l ly , one salient feature of this paper is that we have exp l i c i t ly model led shareholder l i t iga t ion and its role in affecting issuing firms' incentive to disclose prospect ive information. However, the p robab i l i ty that the firm is held l iable by the court (the measure of the l i t iga t ion risk) is assumed to be an exogenous constant, which could ac tua l ly be a funct ion of the magnitude of the forecast error. 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"Essays on Disclosure," Journal of Accounting and Economics 32, 97-180. 109 APPENDIX Appendix 1 Notation and Proofs for Chapter 2 Appendix 1.1 Summary of Notation q = the required investment capi ta l of the project. q • = the entrepreneur's investment decision. x = the gross t e rmina l payoff of the investment project, x = (1 + 6)q + e. 6 = the net unite rate of return of the investment project . e = the noise te rm in the gross payoff of the project, e ~ N(0, a2). ya = the pub l ic report about the noise term in the gross payoff of the project, e = ya + £„., where ya ~ N(0, a2ja). y~i = the private signal acquired by the entrepreneur about the remain ing uncer ta inty i n the noise term. ea. T h a t is, £a = y~i + e~ai, where y i ~ AT(0, cr^). T h e cumulat ive d i s t r ibu t ion funct ion of & is F(yi). p = the posterior mean of the project 's net payoff given the pub l i c report and an investment level of q, i.e., p(ya) = E[x\ya, q — q] — q = 6q + ya-' Ex ante p is normal ly d is t r ibuted wi th mean 6q and variance a2a. K — the informat ion acquisi t ion cost, which is assumed to be a random variable ex ante w i t h a cumulat ive d i s t r ibu t ion funct ion of S(K). y° = the nu l l s ignal (or uninformative signal), wh ich does not change the entrepreneur's belief about £ a . 7 = the p robab i l i ty that after acquir ing the private informat ion , the entre-preneur w i l l receive a nul l signal. A c = the investors' conjectured probabi l i ty that the entrepreneur has not acquired pr ivate information. 8n = the investor 's ex investment valuat ion of the f i rm given no disclosure and the entrepreneur's decision to invest. 110 Appendix 1.2 Proofs P r o o f for P r o p o s i t i o n 2.4 T h e investors' posterior belief about the entrepreneur's pr ivate s ignal given the invest-ment decision and no disclosure is ( L e m m a 1): % „ / , C N C1 - A C ) (1 ~ 7) E [yi\p, q = q,rn = n] Vi (P, A ) = A c A + (1 - A c ) 7 P 2 + (1 - A c ) (1 - 7 ) P 3 If y"(p, A c ) > —p and + q > 0, the entrepreneur w i l l always invest i f she is uninformed and both Pi and P2 equal 1. A l s o , if she is informed, the entrepreneur w i l l invest for a l l signals above —p — q. Assume the entrepreneur conjectures that the investors believe w i t h probabi l i ty A 0 that she has not acquired private informat ion. G i v e n the publ ic report and her conjecture A 0 , if the entrepreneur believes investors w i l l price the firm at a value higher than q (or al ternat ively y"(p , A c — A 0 ) > — p), she w i l l make disclosure decisions according to a cutoff yl(p, A 0 ) , which is determined by the following equations: yi ( 1 - A ° ) / 1 mdF(yi) A° + ( l - A ° ) r dF(Vi) J-p-q where A 0 = A 0 + (1 - A°)7. To be consistent w i t h the entrepreneur's belief, the solut ion to the above equations must satisfy y?(p, A 0) > -p. I l l Define the fol lowing function: ( 1 - A ° ) f yidFiyi) H(x) = x. J - ^ f x A° + ( l - A ° ) / dF(Vi) . J-p-q A ° s + ( 1 - A ° ) f • ( x - y i ) d F ( y i ) _ J-p-q A° + ( l - A ° ) f dF(Vi) J-p-q Denote its numerator as G(x). It can be shown that G(x) is increasing i n x, since G'(x) = x \ ° + (1 - A 0 ) jZv_C!dF{yi) > 0. G i v e n y? = y\, G'(x)> 0 and G{y\) = 0, the necessary and sufficient condi t ion for T / J 1 > -p is G{-p) < 0. T h a t is, p A° + ( l - A ° ) / J p p _ _ {p+m) d F(yi) > 0 (oi-T(p,q,ayuX0) > 0 ) . If the above condi t ion does not hold and if the entrepreneur believes that the investors' posterior belief of her private signal given no disclosure and the investment decision q = q is no greater than — p, she cannot invest if she is uninformed or w i t h h o l d i n g private information and she w i l l invest and disclose for a l l signals above —p. In equ i l ib r ium, the investors w i l l always see disclosure i f the entrepreneur ever invests. Therefore invest ing but not disclosing is an off-equil ibrium act ion. If the investors can threaten to believe that the entrepreneur is h id ing a very bad signal and therefore offer a price less than .q i f the entrepreneur invests but does not disclose, a F u l l Disclosure equ i l ib r ium can be sustained. Q . E . D . P r o o f for Lemma 2.2 0 implies that y\ < 0 (G(x) is defined as i n the (i) G'(x) > 0, G(0 ) > 0 and G(yj) = above proof). (ii) P roo f for M > 0. 112 ( 1 - A ° ) / VidFfa) ,„t _ J-p-q y. _ . A° + (l-A°) dF{Vi) J —p-q t AO y t _ ( 1 _ A"o) F ( _ p _ g -) ( p + g + y t } + ( 1 _ A o } j i/i__ F ( y . ) d y . = o ( Differentiate the above equation w i t h respect to A 0 and solve for n t -vt + / [F(yt) - F(~P - ?)] d V l OVi J-p-q d\° . A° + (1 - AO) [F(y}) - F(-p - q)\ . ' . It is easy to see that bo th the denominator and the numerator are posi t ive. Therefore, > 0. A n d since A° = A 0 + (1 - A 0 ) 7, it must be true that | f [ > 0. (iii) P r o o f f o r ' < 0. Differentiate equat ion (**) w i t h respect to ya and solve for dy\ _ (1 - A°) / ( - p - q) (y\ + p + q) 8ya • AO + (1 - A°) [F(yj) - F(-p - q)} Q . E . D . Proof for Lemma 2.3 • < 0 If p < 0, it must be-true that T ( p , q, ayi, A 0 ) < 0 VA°. Therefore, « t = (1 - 7) (p + yi) d F(yi) = K * , according to P ropos i t ion 2 and 5. If p > 0 and T(p, q,o~yi, A 0 ) < 0, « t = (1 _ 7 ) ( p + <,.) d F ( y i ) , whi le K * -113 - ( 1 - 7 ) / _ £ (P + J/t) d F(iji). U s i n g integration by parts, «t = ( 1 - 7 ) [P+ / " ^(z/i) d J - c o «* - ( 1 - 7 ) / ? n</0 </ —co It is easy to see that > K*. If v > 0 and T ( p , c], cr y i , A 0 ) > 0, the two cutoffs are, Q « f = ( 1 - 7 ) [/ (p + cj + y i ) ( l - ^ ) d F ( y i ) -P-Q " + C O + jT°° (P + "</>) - (P + 9) (1 - J r ) ) . «* = - ( 1 - 7 ) / ' (p + yOdFd/i) . J — C O Using integrat ion by parts, they can be rewri t ten as ^ = (1 - 7) [/ " " F(Vi) d V i + q n ( / ' F(Vi) d V l - y?)] J —oo P ~> Q ' Hi J—p—q «* = ( 1 - 7 ) / ' ^ ( y . ) rfyi.' Thus , « f - «* = ( 1 - 7 ) [ _5 » ( F(y,) d y< - y?) - / " F(Vi) d V i P + Q + Vi J-p-q J-p-q ^ ' [ - f t m / _ \ .1 . _.T\ i r- , _.t\ / F{yi)dyi-y\)-{p + q + y\) f F{Vi) d V l Ik J-v-d J-p-q P + Q + Vi -J-P-Q J P Q Denote the numerator of the above expression as (1 — 7 ) J ( y | ) . It can be shown that J'{y\) = q [F(yl) - i] - / " F(Vi) dVi<o J-p-q 114 Since y\ < 0 ( L e m m a 2), it must be true that J{y\) > J (0 ) = q J°_p_q F{Vi) d Vi — (p + q) F(yt) d V i . Let us then examine the sign of J (0 ) . Define the fol lowing funct ion: B(x) = q J^x_^ F{yi)dyi (x + q) J_^_(1 F(yi) d yi. B(x) is increasing in x , since B'{x) = q F(-x -q)- j * F(yi) d y i + (x + q) [ F ( - x ) - F(-x - q)) J — x—q > (x + q) F(-x) - x F(-x -q)-q F'(-x) = x[F(-x)-F(-x-q)] > 0 Since B(0) = 0, B'(x) > 0, it must be true that B(p) > 0 i f p > 0. It follows that J(yj) > J(0) = B(p) > 0. Therefore, K\P) > «*(p) . Q . E . D . Proof for Equation 2.6 Rewri te U^j t (p) as /•«t r + co U?JM = / [7P + ( l - 7 ) / (p + J / i j ^ ^ - z c j ^ W Jo J-p + f [ (1-7) l V (P + yl)dF(yl))dS(K)+p{l-S(^)] Jo J-p-q 115 T h e n , +00 [TP + (1 - 7). 7 {P + Vi) d F(yt) - K] d S(K) J-P [(1-7) / (p + yi)dF{yi)]dS{K)+p[S{^)-.S(K*)} 0 J-p-q /'«t r + 00 = . / { K - [ 7 P + ( 1 - 7 ) / [p + Vi) d F{yi) - p]} d S{K) J K." J—p -V [ ( l - 7 ) / (p + yi)dF(yt)}dS(K) 0 J-p-q (K-K*)dS(K)^ [ ( 1 - 7 ) . / + . K * J O J-p-q where the last equal i ty follows from n* = jp + (1 - 7) J^00 (p + y%) d F{y{) - p when p > 0. Q . E . D . Proof for Footnote 19 G i v e n the publ ic report ' ya, the investors' ex ante expected payoff is Uifil(p) = £ M(p + q)£-q\ + (l-'V) £ _[(p + q + yi)^-q]dF(yi)}dS(K) + l+0°[(p + q)^-q}dS(K) Rearranging terms we have UljM = -hS(^) + 1 - q Vf + (1 - 7) J * (Vi - Vi)-$s d F(y%) 116 Using the results in Equa t ions 2.4 and 2.5, = r 3 / i d F ( y i ) - y r ( A ° + ( i - A ° ) r d r y ] 0 7—n-17 J-p-q • (1 - AO) y _ s f c d . F f o ) It must be true that Ulf^(p) = 0, since y " = y] = t (Equat ions A ° + ( I - A ° ) r d % ) J-p-q 2.1 and 2.2). Therefore, even though investors overpay when the entrepreneur invests and withholds private informat ion and underpay when the entrepreneur is uninformed, in the ra-t ional expectations equ i l ib r ium they on average break even because they are price-protected. Q . E . D . 117 Appendix 2 Notation and Proofs for Chapter 3 Appendix 2.1 Summary of Notation q = the required investment capi ta l of the investment project . q = the entrepreneur's investment decision. u = the t e rmina l cash flow generated by the asset-in-place. x . = the gross payoff of the investment project, x = (1 + 6)q + e.. 6 = the net unite rate of re turn of the investment project . e = the noise te rm in the gross payoff of the project, e ~ N(0, a2). y~ii = the pub l i c report about the noise term in the payoff of the asset-in-place, u = y~h + eh, where yh ~ (0, al). yi = the private signal acquired by the entrepreneur about the noise term in the gross payoff of the project, e. T h a t is, e = y~i + i>i, where ~ 7Y(0,a, 2 ) . T h e cumula t ive d i s t r ibu t ion function of 7/,-is F(yi). s = the pr ior mean of the net payoff (or N P V ) of the project given an investment level of q. s = E[e\q = q] — q = 6q. K — the informat ion acquisi t ion cost, which is assumed to be a random variable ex ante and its cumulat ive d i s t r ibu t ion funct ion is S(K). Xc = the investors ' conjectured probabi l i ty that the entrepreneur has not acquired private informat ion. 118 Appendix 2.2 Proofs Proof for Lemma 3.1 Depending on different parameter values, there are two possible equi l ibr ia , in bo th of which the investors' va luat ion of the firm is greater than q. It can be shown that Vn < q w i l l not exist in the equ i l ib r ium. If Vn < q, the entrepreneur w i l l never issue equity, since she lias to y ie ld 100% or more of her firm's equity in exchange for the cap i ta l needed, no matter whether she is informed or not. G i v e n this investment strategy, the market price Vn is not ra t ional . T h i s is because i f the entrepreneur never issues equity, the investors w i l l not make, any conjectures on the firm's value. Therefore there is no basis for a va lua t ion as Vn < q. T h e two equi l ib r ia differ in that i n Case N l the entrepreneur invests when she is un in-formed, while in Case N 2 she does not invest if she has no private informat ion . (i) C a s e N l : T h e necessary and sufficient condit ions for Case N l are Vn > q and U2(yh, X,q = q)> U2(yh, X,q = 0), or equivalently, Vn > q and (yk + s + q)(l - —r) > yh, where Vn = y^ + s + q + y™ and yf is represented in E q u a t i o n 3.1. Rearranging the terms yields, y't > max[-yh - s, - j ^ y h - s] i f s > -q ( Vi > ~Vh - s a n d yh < 0 if s = -q y\'€ (-yh- s,-j^yh-s) and yh < 0 i f s < -q 119 In this case, the entrepreneur invests if she is uninformed. If she is informed, she invests only if (jjh + s + q + — yn) > yih. Hence, when investors observe the entrepreneur issuing equity, they infer that the entrepreneur is either uninformed or informed wi th a signal above the investment cutoff tN. T h e posterior mean of the pr ivate s ignal y f , given the entrepreneur's decision to invest, equals (A2.1) It is easy to show that y " > 0, since If s > 0, then y'f > 0 > -s. If s e (-<?, 0) and yh > 0, then y f > max.[-yh - s, — yh - s] => y " > — yh s + q s + q — s => y? > s If s < 0 and y/ t < 0, then Vn > q y\l > -yh - s Since tN = —s — v i f l _ -{s + y , n ) , it must be true that tN < —s. (ii) Case N2 : 120 T h e necessary and sufficient condit ions for Case N2 are Vn>q and (yh + s + q)(l - ^) < yh, where yf is represented in E q u a t i o n 3.1. Rearranging the terms y ie ld , Vi e (-yh ~ s, - sTgyh ~ s^ a n d i f s > _l? Vi > -Vh - s and yh > 0 i f s = - g ( > - 5 and y™ > - j ^ y h -s if s < -q In this case, the entrepreneur does not invest if she is uninformed, and i f she is informed, she invests only if (yh + s + q+yi)(l - p^r) > yh- Therefore, issuing stock signals to the market that the entrepreneur is informed w i t h a signal above the investment cutoff tN. Therefore the posterior mean of the private signal y " based on the stock issuance decision is /•+oo / Vi d F('iji) V? = ^ • (A2.2) / dF(Vi) JtN To prove tN < —s, let us assume instead tN > -s. Since tN = — s — yn^_ -(s + y" ) , i t follows that y " < — 5. F r o m the above expression of y- 1 , we have p+oo r+oo / y?dF(Vi) = / y i d F ( y i ) . JtN JtN However, r+°° y» d F(Vl) < Jt+N°°(s) d F(Vl) < ft+N°° tN d F(yt), whi le ^ d F(Vl) > J^°°tN d F(iji). Con t rad ic t ion ! Therefore it must be true that tN < -s. Q . E . D Proof for Proposi t ion 3.3 121 (i) Case N I . T h e information acquis i t ion cost cutoff is determined by Ui(yh, X,a = I, K) = U\(yh, X, a = 0). Therefore, f + OO J yhdF{yi) + j (yh + s + q + Vi) (1 - ^)dF(Vi) - (yh + s + q) (1 -—) I [yh - (yh + s + q + yl)(l-^i)}dF(yl) J-oo If s > 0, the first-best informat ion acquisi t ion cost cutoff is K* = JTJIJ—(s + Vi)] d F(yi). It can be proved that the shares of the firm are overvalued i f the entrepreneur issues equity when uninformed. T o see this, U2(Vh, A, q = q) = (yh + s + q) (1 - ^ ) = (yh + s + q) ( i q > (yh + s + q) (1 -y / t + s + <? + ^ 9 ^ y ; i + 5 + g . since y " > 0. O n the other hand, when the entrepreneur is informed, ex ante her shares are underval-122 ued. To see this, from E q u a t i o n A 2 . 1 , r+oo (1-A C) / yidF(yi) v? = ^ i l l r+oo A c + ( 1-A c) / dF(Vl) JtN / + C O VidF{yi) ^ Ut ^ / - + C O +co r+oo r + OO i yyF(Vl) < / VidF(yi) tN JtN It follows that r + oo -J (Vu + s + q + yi) (1- ^ ) d F ( y f ) /+ C O (yh + s + q + yi)dF(yi) I VUh -ts-rq^m) a r { V i ) - q— V / (yh+* + q + y?)dF(yi) JtN r + oo < / (Vh + s + q + Vi) d F(Vl) — q (1 — F(tN)) JtN f + OO {yil + s + Vi) d F{yi) (A2.3) 123 T h e information acquis i t ion cost cutoff KN must satisfy j VhdFivi) + J (yh + s + q + yi)(l- fodHVi) ~ (Vh + s + (1 - ^ r ) rt N r + OO < / yhdF{yi) + / {yh + s + yi)dF(yi) - (yh + s) J-oo • JtN I-+00 = / (s + yi)dF(yi) - s /• + OO < / (s + yi)dF(yt) - s •1 -s S{-(s + yi))d,F(yl) -co * since £ w < — s. If 5 < 0, the first-best informat ion acquisi t ion cost cutoff is K* — f T ( s + 2/*) ^ F(yi). In Case N l , when the entrepreneur-is uninformed, her expected payoff from investing is larger than the expected payoff from not investing, i.e., U2(Vk, \q = q) = (yh + s + q ) ( l - f y > U2(yh, \,q = 0)=yh (A2.4) . T h e informat ion acquis i t ion cost cutoff KN must satisfy KN = I yhd F(yL) + / (yh + s + q + Vi) (1 - ^ ) d F{yi) - (yh + 5 + q) (1 - ^ I-LN y + co < < = K r+00 1 yh d F(Vi) + / — C O Jl N ftN r+00 1 'Uh d F(yi) + / - c o JtN r+oo / (s + Vi) d nvi) t N r+00 1 (s + yt) d F(Vi) —s since t < —s (where the first inequal i ty follows from inequali t ies A 2 . 3 and A2 .4 . ) . 124 (ii) Case N 2 . Fi r s t we can prove that Case N 2 only exists for s < 0. Recal l that when the entrepreneur is uninformed, her expected payoff from investing is U2(yh, A, q = q) = (yh + s + q)(l - p^rr). It is easy to shown that U2(yh, X,q = q) > yh + s, because Vn = y\x + s + q + y'l > yh + s + q (since y " > 0). Therefore, i f the pr ior mean of the N P V of the new project is zero or posi t ive (s > 0), it must be true that t / 2 ( y / i , A , g = q) > yh. T h a t is, it is always o p t i m a l for the uninformed entrepreneur to invest because the firm's shares are overvalued and invest ing generates a higher expected payoff than not investing. However, this contradicts the second condi t ion that sustains Case N 2 . To be consistent, we must have s < 0. Since Case N 2 only exists for s < 0, the first-best informat ion acquis i t ion cost cutoff is In this case, in the ra t iona l expectations equ i l ib r ium, the entrepreneur's shares w i l l be on average correctly pr iced. T o see this, from E q u a t i o n (**), 125 It follows that r + oo (-' (yh + s + q + yi) (1 - 7 ^ ) d ,N V r+oo , + o o ( 1 - ^ ) ) I {yh + s + q + yi)dF{y%) I (yh + S + q + yi)d F{Vi) - q J+oo : +oo ('Uh + s + q + Vi) d F(yi) - 9(1 - F(tN)) tN +oo (yii + s + yi) d F(yi) T h e informat ion acquis i t ion cost cutoff KN is determined by U\(yh, A, a = 1, « ) = U\(yh, A, a Therefore, / • / , A ' /-(-oo / 'Uh d F{Vi) + (yh + s + q + Vi) ( l - - ^ ) d F(yi) - yh . 7 - c o JtN V r+oo r+oo / (yh + s + y^ d F(yi) - / yh d F(yi) JtN JtN + o o (s + y^ d F(yi) tN +oo (s + y'l) d F(yi) tN N A s proved i n the m a i n text , t A < — 5 < y'"', it follows that K + C O tN + o o (s + iji) d F{yi) /O0 (s + Vi) d F(yi) •s Q . E . D . Proof for Proposit ion 3.5 126 (i) Par t ia l Disclosure Equi l ibr ium If s > 0, the first-best informat ion acquisi t ion cost cutoff is K* = / J ^ f — ( s + Vi)] d F{Vi)-T h e informat ion acquis i t ion cost cutoff KV is determined by Ux(yh, A, a = 1, K) = Ui(yk,\, a 0). Therefore, ,v „.„t / y h d F(Vl) + [ ' (yh + s + q + yi) d F{Vi) J-oo Jtv V + / + 5 + Vi) d F(Vl) - (yh + s + q){l-^) A p p l y i n g integrat ion by parts yields Kv = yhF{tv) + (yh + s + y\)F{y\) - yhF(tv) - jT (1 - X ) F ( y i ) d y . + + s) - / (y / t + 5 + yi)dF(yi) - (yh + s + ( l - J L ) • / — C O . ^ = / F ( y i )<* y < + i - • n (/ ^(y,) d N - y?) Thus , * K - «* = ^ n ( / * F ( y , ) d V l - y?) - / ^ y< y / t + s + <? + y ; y t v Jtv I 1 / ' ? ; , t f~s = 77^ [9 ( / F(Vi) rf 2/i - 2/1) -(Vh + s + q + y\) / . F(y0 d Vi) v Jtv Jtv Denote the numerator of the above expression as J(y\). U s i n g tv = — s — yifl_ ^{s,+ y™ 127 and y\ = y" , we can show that r)tv l'~s J\y\) = Q [ F ( y l ) - 1] + (yh + a + yl)F(tv)^ - / F(Vl) d V l dy] Jtv = g [Hvl) - i] + F(tv) ~~qVh - r F(Vi) d V l yh + s + y\ Jtv < q [F(y] ) - 1] + F{tv) - (tv + s)F(tv) Vh + s + y\ = q[F(yl)-l}-qF(tv) < 0 Since y\ < 0 ( L e m m a 3.3), it must be true that J(y\) > J (0 ) = q as F(yi) d yi — Vh+S (yh + s + q) /r,"__iH_ F(yL)dyi. Vh +s Let u s then examine the sign of J (0 ) . Define a function B(x) = q J qX F(yi) d yi — Vh+X (yh + x + q) ( * ifx F(yi) d y i . B(x) is increasing in x, since Vh+'J: B'(x) = q F(-x - - ^ - ) ( 1 + . q V h . 2 ) - lX F(yi) d V l + (yh + x + q) [F(-x). y/i + x (yh + x) J-x-^r-j? I qx \ / T I qVh \ i -F(-x )(1 + -?)\ yh + x'K (yh + x)2!l = -(yh + x)F(-x - + qV" 2 ] + ( y , + x + g)F(-x) - / * F(Vl) d V i > ~(y h + - + T - ^ r d + (ifo + x + q)F(-x) + - ^ - F ( - x - -^-] yu + x (yh + xy yh + x yh + x = (yh + x + q)[F(-x)-F(-x--^-)} yh + x > 0 V.x > max[0, - y / J Since 73(0) = 0, B'(x) > 0, it must be true that 73(5) > 0 if 5 > 0. It follows that J(vt) > J(0) = 73( 5) > 0. Therefore, KV > K*. (ii) F u l l D i sc lo su re E q u i l i b r i u m 1 128 T h e information acquis i t ion cost cutoff KV is determined by £/" = C / 1 i a . Therefore, / • + 0 O ^ - / (s + Vl) d F(yt) JtN If s > 0, the first-best informat ion acquisi t ion cost cutoff is = f T ( s + ^ F(Vi) ~~ s--s r + OO , Thus KV > K*. If s < 0, the first-best information acquis i t ion cost cutoff is K* — J_ s °° ( s + yi) d F(v/i) . It follows that KV = K*. Q . E . D . Proof for Proposi t ion 3.7 Since comparisons of other cost cutoffs are provided i n proofs i n P ropos i t i on 3.3 and 3.5, and it is obvious that KV = K,M for the F u l l Disclosure E q u i l i b r i u m , we only need to show KV < KM for the P a r t i a l Disclosure E q u i l i b r i u m . Us ing the expression KV — K* and the result KM = K* + S (if s > 0) i n the proof for Propos i t ion 3.5, r<V - KM = ~ [ q ( lV' F(Vi) d V l - y\) - (yh + s + q + y\) [ * F(Vl) d Vi) - s v Jtv Jtv Denote the numerator of the above expression as W{y\). W e can show that W'(yl) = q[F(yl)-l}-qF(tv)-s < 0 the Pa r t i a l Disclosure E q u i l i b r i u m only exists for s > 0. Since y\ > —s (see proof for L e m m a 4), it must be true that W(yj) < W(—s) = qs - sVn < 0. It follows that W{y\) < W(-s) < 0. Therefore, KV < KM. Q . E . D . 129 Appendix 3 Notation and Proofs for Chapter 4 Appendix 3.1 Summary of Notation q = the required investment capi ta l of the investment project . q = the entrepreneur's investment decision. x = the gross payoff of the investment project, x = (1 + 0)q + e. 0 — the net unite rate of re turn of the investment project. e = the noise te rm in the gross payoff of the project, e ~ N(0,a2). T h e cumula t ive d i s t r ibu t ion function of e is G(e) . y~i = the private signal acquired by. the entrepreneur about the uncertainty in the noise te rm. e. T h a t is, e = yi + v, where y i ~ A^(0, o f ) , v ~ iV(0 , o2) and a2 = al + a2. T h e cumulat ive d i s t r ibu t ion functions of yi and u are denoted as F(yi) and H{v) respectively. F = the informed entrepreneur's forecast of the firm's t e rmina l flow based on her private signal F = E[x\yi\ = (1 + 6)q + y% s = the pr ior mean of the net payoff (or N P V ) of the project, i.e., s = Qq^-ya-X — the exogenous probabi l i ty that the entrepreneur is uninformed. 7 = the lawyer 's share of the damage award pa id by the investors. (j = the p robab i l i ty that the court w i l l ho ld the entrepreneur l iable when a lawsuit is filed due to a fall in the stock price. 130 Appendix 3.2 Proofs P r o o f for Foo tno te 16 We only provide the proof for the case when the entrepreneur invests and discloses her private signal, since the proof of the other two cases are s t raightforward. Since the investors are ra t ional , they w i l l endogenize their damage awards from the future . lawsuits into their p r i c ing of the firm's shares at t = 2. Denote the fract ion of the shares the entrepreneur w i l l offer the investors in exchange for q as a. Under the compet i t ive market assumption, it must be true that g = a[s + g + yi-D(yi,fi)] + (l-y) D{yi7/3), (43.1) where s + q + yi — D(yi,8) is the firm's expected residual cash flow after deduct ing the l i t igat ion damages. T h e entrepreneur's expected payoff at t = 2 if she invests and discloses yi w i l l be (1 — a) of the firm's expected residual cash flow: UKyum = yu A, q = q) =' [s + q + iji - D(yi} (3)] (1 - a). Subs t i tu t ing a from the E q u a t i o n A 3 . 1 into the above u t i l i t y funct ion yields, U{(yu m =.Vi> A, q = q) = s + Vi- lD(yu(3). Q . E . D . P r o o f for L e m m a 4.3 In the P a r t i a l Disclosure E q u i l i b r i u m , the disclosure cutoff y\ is determined by the fol-131 lowing equations: s + yl- 7 D(f3) = ' s + q + y})'i-—-!—) (A3.2) „t ( 1 - A ) I'1 yidYiyi) J — s—a Vi- = =^ (A3.S) A Prob(m = n , g = 9, = 0) + (1 - A) / d F(y*) J—s-Q Rewri te E q u a t i o n A 3 . 2 as [5 + y\ - 7 D({3)} (s + q. + y?) = (s + q + y\) (s + y?). Differentiate it w i t h respect to (3, keeping in m i n d that bo th y\ and y™ are functions of (3. We have [ ^ - l ^ ] ( s + q + y-) + [s + yl-jD(P)}^ = d-^(s + y7) + (s + q + ylJ g p or alternatively, It is easy to show that ^ " ^ ^ > 0 and D((3) > 0. It must be true that dy[>dyl d(3 d(3 T h e n differentiate E q u a t i o n A 3 . 3 w i t h respect to (3. W e have r)'iin l'Vi Bv^ [X Prob(m = 77, q = q, * B = 0) + (1 - A) J _d F(Vl)] = (1 - A) (y l - y?) f(y\) From E q u a t i o n A 3 . 2 , i t is easy to see that y i > yf. T h e n it must be true that sign(-^) = sign(^). It follows that either 2^ > ^ > 0 or ^ < ^ | < 0. 132 Define a funct ion M(t) = t{XProb{m = n,q = q,tyE = ®) + (l-X) f d Ffa)} - (1 - A) / yidF{Vi). J—s—q J—s—q It can be proved that M(t) is an increasing function. Define y\ = y\(B = 0). It is easy to see that M(y\) > 0 when B > 0, and M(y\) = 0 when Q = 0. Since M ' ( - ) > 0, i t must be true that y\(B) > y\ when B > 0. We must have > > 0. T h a t is, the disclosure cutoff is increasing in the l i t iga t ion risk. Q . E . D . Proof for Proposi t ion 4.3 Reca l l that one necessary condi t ion for the existence of the P a r t i a l Disclosure E q u i l i b r i u m is 5n > q, which also impl ies that s + y\ > jD(B) (from E q u a t i o n 4.1). Since J(iji) = s + yt — 'yD(B) is increasing in y i and J(yi) = 0, i t must be true that 'III > Vi- Therefore L2 is higher in the F u l l Disclosure E q u i l i b r i u m than in the P a r t i a l D i s -closure E q u i l i b r i u m . Q . E . D . 133 

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