Financing the Entrepreneurial Venture

Transcription

1 Financing the Entrepreneuria Venture Jean-Etienne de Bettignies y First Draft: September 2, 2002 This Draft: October 7, 2003 Abstract This paper is about nancia contracting choices for the entrepreneur. In an incompete contracts mode, the entrepreneur can design contracts contingent on three possibe contro right aocations: entrepreneur-contro, investor-contro, and joint contro, with each aocation inducing di erent e ort eves by both the entrepreneur and the investor. Four types of contract emerge as potentiay optima: debt with iquidation, debt with reorganization, equity-ike nancing, and preferred-type (convertibe and straight) nancing. The mode: a) highights the importance of ex-ante and expost e ciency in contracting; b) determines optimaity aong two dimensions: the convexity of output as a function of incentives, and the size of the initia capita requirement; c) generates empirica predictions about the e ects of the type of venture, intangibe/tangibe asset ratio, initia capita investment, and investor required rate of return, on optima contracting. Keywords: Entrepreneuria nance, incompete contracts, debt versus equity. JEL Codes: M13, G32. I thank Martin Boyer, Gies Chema, Matt Cements, Doug Cumming, Murray Frank, Keith Head, Bob Hesey, Thomas Hemann, Tom Ross, Raph Winter, and particuary John Ries, for hepfu comments. Abe research assistance was provided by Chris Bidner. A errors are mine. y Sauder Schoo of Business, University of British Coumbia, 2053 Main Ma, Vancouver, BC, V6T 1Z2, Canada. Te: (1-604) Fax: (1-604) Emai: bettignies@sauder.ubc.ca. 1

2 1 Introduction Entrepreneuria ventures pay a crucia roe in the economy: in the U.S. sma rms 1 represent more than 99.7 percent of a empoyers, [...] empoy more than haf of a private sector empoyees, [...and] create more than 50 percent of the nonfarm private gross domestic product (U.S. Sma Business Administration, 2003) 2. The vast majority of the 550,100 new businesses in the U.S. in 2002 required a capita investment to get started. How did the founders nance these initia requirements? The theory of nancia structure of the rm 3 has been one of the centra themes of corporate nance since Modigiani and Mier s (1958) irreevance resut. This paper addresses this theme in the context of sma business: it anayses optima contracting for the entrepreneur. Entrepreneuria ventures have distinctive characteristics reated to project nancing. i) They are subject to far ess restrictive discosure aws reative to arge, pubicy hed corporations, and their income and accounts are not easiy veri abe by a court of aw. ii) Both the entrepreneur and the investor pay an active roe in the management of the venture, but these investments in e ort are di cut to contract upon. The non-veri abiity of pro ts impies non-contractabiity: parties do not want to make contracts contingent on pro ts or cash ows as they woud have no recourse in court in the event of disagreement. Since e ort eves are not contractabe either, the contract signed at the beginning of the game simpy speci es the aocation of property rights and contro rights over the venture. Contro rights, which take the form of board rights, voting rights, veto rights, iquidation rights, etc. pay an important roe because they confer bargaining power in the negotiation over the pro ts generated. This in turn provides anticipating agents with incentives to invest in e ort. Entrepreneur-contro, for exampe, aocates a contro rights and ownership rights to the entrepreneur; in that case the entrepreneur has a bargaining power and can extract 1 The O ce of Advocacy of the SBA de nes a sma business as an independent business having fewer than 500 empoyees. 2 These statistics can be obtained from the frequenty asked questions on how important are sma businesses to the U.S. economy? at 3 See Myers (2002) for an exceent review of this iterature. 2

3 a rent in negotiation. She 4 thus has high incentives to exert e ort. The investor on the other hand anticipates he wi get nothing and does not participate in the management of the venture. Conversey, investor-contro gives a contro to the investor: he exerts high e ort whie the entrepreneur does not participate. Finay, joint-contro aocates enough contro rights to the investor to provide him with some bargaining power, and consequenty with the abiity to extract some rents. The investor may for exampe have enough contro to in uence the entrepreneur s use of rst-cass airine tickets or her access to the company car. As ong as the investor can interfere with the entrepreneur s abiity to enjoy the surpus, he can extract a fraction of that surpus by threatening interference. In that scenario, both the investor and the entrepreneur participate in management, but anticipating they wi have to share the surpus, they have ow incentives and exert ow e orts. This simpe framework generates severa resuts: 1. Ony four types of contract, conditiona on the three contro right aocations described above, are potentiay optima for the entrepreneur to o er to the investor 5. Debt with iquidation assigns contro rights to the entrepreneur (entrepreneur-contro), that revert to the investor (investor-contro) in case of defaut on the debt repayment. Debt with reorganization is simiar to the rst contract except that defaut eads to joint contro. The entrepreneur may aso o er a simpe joint contro contract to the investor. This aternative, despite non-contractibiity of pro ts, yieds an expected cash ow to the investor which ooks much ike that of equity: the investor has enough contro to interfere with the entrepreneur s abiity to enjoy the rents, and can thus extract a fraction of the surpus. Therefore we ca this equity-ike nancing. Finay, the entrepreneur may o er a contract which assigns joint contro conditionay on debt repayment, with defaut resuting in investor-contro. This contract ooks very much ike the preferred equity contracts observed in practice. For this reason we ca it the preferred-type contract. In the paper we distinguish between two sub-categories: straight 4 Throughout the paper we refer to entrepreneurs as femae, and to investors as mae. 5 The entrepreneur initiay has a the bargaining power in negotiation: she makes a take-it-or-eave-it o er to the investor. 3

4 preferred-type contracts and convertibe preferred-type contracts. 2. We show expicity how both ex-ante e ciency and ex-post e ciency contribute to the determination of the optima security. Ex-ante ine ciency arises when fewer projects are nanced reative to the rst-best. Ex-post ine ciency occurs when, conditiona on being nanced, the contract does not yied the highest possibe overa payo. A contract may be ex-ante optima, in that it can be used to nance the argest number of ventures, incuding the ones with the highest initia capita requirements. But at the same time this contract may be ex-post ine cient, in that it returns a ow overa payo. This contract is thus optima for ventures with high capita requirements, but for smaer investments, another, more ex-post e cient contract wi be chosen by the entrepreneur The optima contractua form is mainy determined by two factors: the agents margina e - ciencies at ow incentives reative to their margina e ciencies at high incentives, or convexity of output with respect to incentives 7, and the size of the initia capita requirement. Reative margina e ciency a ects both ex-post and ex-ante reative e ciency of di erent contracts, whie initia capita requirements size a ects the importance of ex-ante reative to ex-post e ciency in the determination of the overa optima structure. We nd that when capita requirements are ow and ex-post e ciency matters most, as the agents ow incentives margina e ciency increases reative to high incentives margina e ciency, the optima contract changes from debt with iquidation to debt with reorganization, to equity-ike nancing. When capita requirements are high and ex-ante e ciency becomes important, a reative increase in ow incentives margina e ciency eads to changes in contractua optimaity, from debt with iquidation to preferred-types contracts (both convertibe and straight). We obtain a convenient two-dimensiona representation where the parameter space can be partitioned into regions in which di erent contracts are optima. 6 Gertner, Scharfstein and Stein (1994) highight both types of (in)e ciency. However they focus on ex-ante e ciency and thus ignore these possibiities. 7 We sometimes (crudey) use convexity to refer to reative margina e ciencies, even though the output function is ony de ned in three points. We coud convexify the function by inking the three points. In that case, moving the midde point up (down) corresponds to making the convexi ed function ess (more) convex. 4

5 4. We provide possibe expanations for the prevaent use of debt contracts to nance ifestye venture, and of equity contracts (common equity, straight and convertibe preferred equity) in cassic startup ventures. We aso conjecture that size of capita requirements as we as investor required rate of return, shoud pay an important roe in optima contracting. Finay, we discuss convertibe preferred contracts in particuar, their current prevaence in the U.S., as we as tempora and geographic di erences. This paper contributes to two areas of the iterature. The theoretica iterature on the nancing of new ventures 8 has focused mainy on venture capita (VC) nancing 9, and has o ered many insights into the use of convertibe preferred equity and its ubiquity in VC deas in the U.S. 10 However venture capitaists nance ony a sma fraction of entrepreneuria ventures: Davis (2003) reports that venture capitaists nance ess than 10 percent of startups in Canada, and that in 2000 Canadian venture capita represented 4 percent of the doar investment in sma rms. Moreover, the prevaence of convertibe preferred equity in VC deas appears to be particuar to the U.S. In other countries such as Canada, Germany, Finand, Taiwan, and Austraia 11, evidence points to the use of a variety of securities. In this paper we deveop a mode where rst, the entrepreneur/investor reationship can be appied to entrepreneuria ventures in genera rather than speci cay to VC nanced ventures, and where second, severa types of contracts commony used in new venture nancing (Cumming, 2002a), such as straight debt, common equity, and preferred equity, emerge as potentiay optima. 8 See, for exampe, Bascha and Waz (2001), Bergöf (1994), Bergmann and Hege (1998), Cornei and Yosha (1997), Gompers (1997), Gompers and Lerner (1999), Hemann (2000), Kapan and Strömberg (2003), Marx (1998), Repuo and Suarez (1998), Schmidt (2002), Trester (1998). 9 Three exceptions come to mind which do not focus on convertibe preferred contracts. Garmaise (2001) show that when investors are better informed than entrepreneurs, the entrepreneur tends to prefer junior equity to debt. Landier (2002) deveops a mode where the choice between bank debt and venture capita nancing depends on the entrepreneur s exit option: a good (bad) exit option tends to favor venture capita nancing (bank debt). Ueda (2002) argues that the tradeo between bank and venture capita nance is that athough banks are better at project evauation, they are more ikey to expropriate the entrepreneur. 10 Evidence of the prevaence of convertibe preferred equity in VC nancing in the U.S. can be found in Bergmann and Hege (1998), Gompers (1995, 1997), Gompers and Lerner (1999), Kapan and Strömberg (2002), Lerner (1994), and Sahman (1990). 11 See Cumming (2002a), Bascha and Waz (2001b), Parhankangas and Smith (2000), Songtao (2000), Austraian Bureau of Statistics (2000). 5

6 Much of the work in the security design 12 iterature anayzes rms which share some of the characteristics described in the second paragraph. As noted in Fuck (1998), this iterature su ers from the drawback that it cannot simutaneousy assume characteristics i) and ii) 13 and incorporate outside equity nancing. Fuck soves this probem by arguing that equity-hoders who have the right to dismiss the manager, and have an unimited time horizon, can discipine the manager into paying out dividends with a credibe threat of dismissa. In contrast, we argue that in entrepreneuria ventures the crucia components of equity contracts are contro rights, such as board rights, voting rights, veto rights, etc. which are typicay associated with it. These contro rights give ex-post bargaining power to the investor, who is thus abe to extract some rents. We incorporate equity not directy through its caim on cash ows 14, but indirecty through the contro rights associated with it, and the bargaining power that they confer in negotiation. Like Fuck (1998), Myers (2000) and Dybvig and Wang (2002) aso use the threat of dismissa to introduce equity in a mode with non-veri abe cash ows. These two papers are somewhat coser to ours, in that they take incentives into account. Dybvig and Wang (2002) in particuar compare debt and equity and argue that whereas debt generates higher (e cient) e ort exertion, it aso give the manager incentives to defaut. Our paper however di ers not ony in context - our focus is on entrepreneuria ventures where the investor as we as the entrepreneur exert e ort - but aso in modeing structure, contracts, and resuts. Dybvig and Wang s tradeo described above, for exampe, does not necessariy hod in our mode, where tota investment in e ort may be higher in with equity than with debt. Our modeing structure is coser to that of Boton and Scharfstein (1990, 1996) and Hart and Moore (1998), but is probaby most cosey reated to Gertner, Scharfstein and Stein 15 (1994) 16. The 12 See for exampe Aghion and Boton (1992), Boton and Scharfstein (1990, 1996), Chang (1992), DeMarzo and Fishman (2000), Dewatripont and Tiroe (1994), Diamond (1984), Gae and Hewig (1985), Hart and Moore (1989), Fuck (1998), Pove and Raith, (2003), Townsend (1979), Wiiams (1989). 13 We refer the reader to the second paragraph. 14 This caim is irreevant when cash ows are not veri abe. 15 Henceforth GSS. 16 We draw our mode of debt from them, and both our modes have agency issues with investors and managers exerting e ort in the second period. 6

7 two papers, however, have very di erent focuses: GSS is on the tradeo between interna and externa nancing choices for the rm, whereas ours is on optima security design for the entrepreneur. The paper is structured as foows: section 2 presents the basic mode. Section 3 describes the contractua choices for the investor, and section 4 anayzes optima contracts. Section 5 discusses the main resuts of the paper with exampes, and concudes. 2 The Basic Mode 2.1 Technoogy Consider an entrepreneur who has a two-period, positive NPV project in mind. At the end of the rst period, at date 1, the project produces a payo x with probabiity p, and zero payo with probabiity 1 p. Both x and p are exogenous. At date 2 the project yieds a positive expected payo V 17. The venture requires an outay k at date 0 to purchase some physica assets and the entrepreneur, who is weath-constrained, must turn to an investor to nance the venture. Hence, at date 0, the entrepreneur o ers a nancing contract to the investor. We impicity assume that the entrepreneur has a bargaining power at date 0. There are many more nanciers wishing to invest than there are good entrepreneurs (good projects to be funded). The case where the investor has some initia bargaining power is discussed in section 5. At the beginning of the second period, both the entrepreneur and the investor take two sequentia decisions. First, each agent decides whether to quit or stay invoved with the venture. If one quits, one receives nothing at the end of the second period. If the agent stays invoved, she must take the second decision: both the entrepreneur and the investor make a non-veri abe (and thus non-contractibe) investment, e and f respectivey, to create vaue V (e; f) for the venture. Assumption 1: V (e; f) = e + f. 17 We denote rst period variabes with ower case etters, and second period variabes with capita etters. 7

8 We make this separabiity assumption for simpicity. Simiar resuts hod when technoogy is not additivey separabe. The entrepreneur invests in her area of expertise, e.g. technoogy, and exerts either high e ort e h at cost c e (e h ) = c e h, or ow e ort e at cost c e (e ) = c e. Simiary the investor chooses between high e ort f h at cost c f (f h ) = c f h, and ow e ort f at cost c f (f ) = c f. Investment by the nancier mainy takes the form of manageria hep to the entrepreneur (genera manageria guidance, marketing, access to incubator services, etc.). Assumption 2: c e h = cf h = c h and c e = cf = c ; but e h > f h and e > f. Assumption 2 distinguishes the entrepreneur from the investor. Whie the entrepreneur devotes a his time to the project and has no other activities, the investor typicay is invoved in severa ventures at the same time. Thus he has a higher opportunity cost of investing in one particuar project. Or equivaenty 18, for an equa cost, the investor exerts ess e ort than the entrepreneur. This is the idea captured here. 2.2 Incompete Contracts The payo at the end of the second period, V, represents corporate resources. Athough observabe to entrepreneurs and investors, V is not veri abe by a court, and thus cannot be contracted upon. Boton and Scharfstein (1996, p.5) expain that this assumption is meant to capture the idea that managers have some abiity to divert corporate resources to themseves at the expense of outside investors, and that such perk consumption and investment may be di cut to distinguish from appropriate business decisions and thus impossibe to contro through contracts. Since payo V cannot be contracted upon, the ony contractua too avaiabe in the second period is the aocation of contro rights. There are three possibe aocations of contro rights: joint 18 We coud obtain simiar, though ess convenient resuts by setting the e ort eves equa (e h = f h and e = f ) and by assuming that the investor has higher cost (c f h > ce h and c f > c e ). 8

9 contro, entrepreneur-contro, and investor-contro 19. We describe each one beow. The payo at the end of the rst period, x, is aso observabe but not contractibe. Assumption 3: Entrepreneur-contro 20 is the ony aocation of contro rights avaiabe in the rst period. One justi cation for this assumption woud be to argue that x represents persona ski that accrue to the entrepreneur ony and the vaue of which cannot be interferred with. In that case, the entrepreneur can aways have access to x in the good state of the word, a contro rights aocations yied the same as entrepreneur-contro and can thus be ignored. The purpose of this simpifying assumption is to focus our attention on a imited number of interesting contracts. The resuts of the paper coud be extended to take care of other contro aocations in period 1, abeit without much bene t. 2.3 Joint Contro Joint contro occurs when the investor contros enough board rights, voting rights, inspection/monitoring rights, etc., such that used in combination, these rights provide her with bargaining power. Even though perk consumption by the entrepreneurs is not veri abe in court, the aforementioned contro rights may enabe the investor to interfere with it. Even the abiity to interfere ony sighty with the entrepreneur s perks gives the investor bargaining power, as the two parties must trade over the surpus from no interference. Acting opportunisticay, the investor may be abe to use her contro rights to extract a part of that surpus. In this mode we make the extreme assumption that joint contro gives the investor enough contro rights for maximum interference: the investor can bock competey the entrepreneur s access to perks. If he does that trade breaks down, however, and he can get nothing either. Thus, having an outside payo of zero, both parties bargain over the payo at the end of each period. Assuming Nash bargaining, the two parties spit the surpus from trade and the investor extracts a fraction 21 = We use the same terminoogy as Aghion and Boton (1992). 20 A precise de nition foows beow. 21 The genera resuts of this paper are independent of the vaue of, as ong as 0 < < 1. Throughout the paper we 9

10 of the second period payo V. The second period incentive compatibiity (IC) constraint and the individua rationaity (IR) constraint for the entrepreneur can be described as foows, respectivey: e (U e ) 2 arg max U e (e; f) c e (e) ; (1) U e (e (U e ) ; f) c e (e (U e )) 0; (2) where U e (e; f) is the entrepreneur s expected payo at the end of the second period. With joint contro, U e (e; f) = 1 2V (e; f). Simiary, the second period IC and IR constraints for the investor can be written respectivey in the foowing way: f U f 2 arg max U f (e; f) c f (f) ; (3) U f e; f U f c f f U f 0: (4) where U f (e; f) is the investor s expected payo at the end of the second period. With joint contro, U f (e; f) = 1 2V (e; f). 2.4 Entrepreneur-Contro In this event, the entrepreneur has compete contro over the venture, and a bargaining power in negotiation: she can decide on a actions to be taken regarding the venture. She is thus abe to extract a rents in negotiation; the investor cannot behave opportunisticay and gets nothing. The entrepreneuria equiibrium e ort e (V ) is the e (U e ) that satis es conditions (1) and (2), assume Nash bargaining for simpicity; this yieds =

11 with U e (e; f) = V (e; f). The investor on the other hand expects to get nothing at the end of the second period. Regardess of the eve of e ort f (0) he woud choose, his IR constraint c f (f (0)) 0, which can be obtained simpy by substituting U f (e; f) = 0 into (4), can never hod. Consequenty, with entrepreneur-contro the investor does not participate in the second period. 2.5 Investor-Contro Investor-contro is the ip-side of entrepreneur-contro: the nancier has 100% of the contro rights over the venture and fu bargaining power in negotiation. The investor s equiibrium e ort f (V ) is the f U f that satis es conditions (3) and (4), with U f (e; f) = V (e; f). The entrepreneur s IR constraint c e (e (0)) 0, obtained by substituting U e (e; f) = 0 into (2), can never hod, and hence she does not participate in the second period. 2.6 Stricty Dominating Strategies We focus on vaues of f, f h, e, e h, c f = c e = c, and c f h = ce h = c h, such that there exists a stricty dominating strategy for each payer. These strategies are such that for both the entrepreneur and the investor, the higher the expected fraction of the surpus, the higher the equiibrium eve of e ort. More formay: Assumption 4: 1) 1 2 V (e ; f) c > 1 2 V (e h; f) c h ; 2) 1 2 V (e; f ) c > 1 2 V (e; f h) c h ; 3) 1 2 V (e ; f) c 0; 4) 1 2 V (e; f ) c 0; 5) V (e h ; f) c h > V (e ; f) c ; 11

12 6) V (e; f h ) c h > V (e; f ) c : Conditions 1-4 refer to joint contro. They impy rst that ow investment is the optima choice both agents: e V 2 = e and f V 2 = f (cond. 1,2). And second they impy that both agents choose to participate in the venture (cond. 3,4) in the second period. Conditions 5 and 6 refer to entrepreneur-contro and investor-contro, respectivey. They impy that whenever an agent has fu contro over the venture, he/she has an incentive to make the arge ex-ante investment: e (V ) = e h, and f (V ) = f h. Note that conditions 3 and 4 aso impy that participation of the entrepreneur with entrepreneur-contro, and of the investor with investor-contro, are optima in equiibrium. In sum, from conditions 1)-6) we deduce a stricty dominating strategy for each agent, which we describe in tabe 1: Entrepreneur-contro Joint contro Investor-contro Entrepreneur High e ort Low e ort No participation Investor No participation Low e ort High e ort Tota Output px + V Y c h px + V Q 2c px + V L c h where V Y = V (e (V ) ; 0) = V (e h ; 0), V Q = V e V 2 ; f V 2 = V (e ; f ), and V L = V (0; f (V )) = V (0; f h ). The ast row shows the expected tota net output which resuts from each contro right aocation. Note that by assumptions 1 and 2, we must have V Y c h > V L c h, and thus tota output is aways higher with entrepreneur-contro than with investor-contro. It can easiy be shown that there exists a (arge) set of vaues for parameters f, f h, e, e h, c, and c h, such that conditions 1)-6) in assumption 3 hod. We show in the appendix that for given vaues of f, f h, c, and c h, with f h > 2c h, there exist variabes e min ; e max ; f min ; and f max such that conditions 1)-6) hod for a e 2 e min ; e max and f 2 f min ; f max Thus, with joint-contro the entrepreneur and the investor must share the surpus, and even though they both participate, their individua incentives are ow and they exert ow e ort. With entrepreneur-. 12

13 contro, a ex-post bargaining power is transferred to the entrepreneur, and he has incentives to exert high e ort, whie the investor does not participate. Conversey with investor-contro, the investor has incentives to exert high e ort but the entrepreneur does not participate. First-Best Outcome Let us describe the rst-best (FB) scenario as benchmark. In the FB outcome, which represents the socia optimum, both the entrepreneur and the investor exert e ort to maximize the socia surpus: Max e;f px + V (e; f) c e (e) c f (f) : (5) Conditions 5) and 6) in assumption 3 impy that that the rst-best eves of e ort for the entrepreneur and the investor, respectivey, are e (V ) = e h, and f (V ) = f h. The resuting equiibrium socia surpus can be expressed as: R F B = px + V F B 2c h ; (6) where V F B = V (e (V ) ; f (V )) = V (e h ; f h ). 3 Contractua Choices for the Entrepreneur At date 0, the entrepreneur can combine the possibe aocations of contro rights into a contract to be o ered to the investor. There are two broad categories of contracts avaiabe to the entrepreneur: contingent contracts, and simpe non-contingent contracts. Contingent contracts in our mode are debt-ike contracts in which one aocation of contro rights is contingent on a prespeci ed debt repayment 22 d at date 1, with defaut inducing another, di erent aocation of contro rights. Boton and Scharfstein (1990) have shown that when investor-contro and entrepreneur-contro are the ony two feasibe contro right aocations, the optima contract is one 22 The repayment d is assumed to be veri abe. 13

14 which assigns entrepreneur-contro if a debt repayment d is paid out to the investor at date 1; and assigns investor-contro in the event of defaut. Here however, another possibe contro aocation exists, joint contro; and thus two other feasibe contingent contracts arise. One is debt with entrepreneur-contro if d is paid out, joint contro otherwise. The other is joint contro if d is paid out, investor-contro otherwise. In addition, three di erent contingent contracts are theoreticay possibe 23, but we show in the appendix that these are never optima. There are aso three types of non-contingent contracts, which simpy correspond to the three avaiabe aocations of contro rights: entrepreneur-contro, investor-contro, and joint contro. We show in the appendix that unconditionay assigning entrepreneur-contro or investor-contro is never optima 24. Thus the ony non-contingent contract eft is joint contro, which we ca equity-ike nancing. We ook at joint contro before discussing contingent contracts in greater detai. 3.1 Equity-Like Financing Probaby the simpest contractua form is the one in which the entrepreneur chooses joint contro unconditionay for the second period. In that case both the investor and the entrepreneur have some bargaining power in negotiation and spit the supus equay at the end of period 2. Even though in our mode an equity contract per se woud not yied any payo to the investor (since by assumption cash ows are not veri abe, the entrepreneur woud stea them), joint contro (with or without equity) generates a stream of payo s to the investor which is simiar to the one typicay obtained in a standard equity contract. For that reason we ca this equity-ike nancing. Focusing on the contro rights associated with equity (joint contro) rather than the cash ow rights, 23 These contracts are: 1) joint contro conditionay on debt payment d, entrepreneur-contro otherwise; 2) investorcontro conditionay on debt payment d, entrepreneur-contro otherwise; 3) investor-contro conditionay on debt payment d, joint contro otherwise. 24 Giving contro right to the entrepreneur in the second period unconditionay is not an option because the investor woud anticipate he wi nothing from the venture, and thus woud be unwiing to invest anything upfront. Moreover, as in Boton and Scharfstein, (1990), unconditiona investor-contro in the second period is aways dominated by one of the debt contracts. 14

15 we are abe to introduce an equity-ike contract in the mode and to compare with other contracts, a the whie keeping our assumptions of non-veri abiity of cash ows and performance necessary for debt to be interesting. In an interesting study of venture capitaists however, Kapan and Strömberg (2003) found evidence that the contro rights aocated to venture capitaists through covenants are independent of the nancia contracts o ered. One may thus argue that this impies that contro rights cannot be used as a good instrument for equity since the two are assigned independenty. We argue that even if contro rights are separatey aocated within the cass of VC equity nancings observed by Kapan and Strömberg, 25 on average the VC has much ess contro than woud a creditor in a debt contract foowing defaut, and much more contro than the creditor in a debt contract where the contracted debt repayment has been made. These are the important di erences in our mode. The date 0 return on investment for the nancier is: R f E = 1 2 V Q c k t 0; (7) where t 0 is a date 0 transfer from the investor to the entrepreneur. The optima equity-ike contract has the foowing characteristics: 1) If k is too arge for (7) to hod, even with t = 0, the contract is not feasibe and the venture is not undertaken. 2) If k is sma enough for (7) to hod, the entrepreneur, who has a bargaining power ex-ante, chooses a vaue of t such that R f E = 0, and extracts a ex-ante surpus. Her return from a date 0 perspective is : R e E = px + V Q 2c k: (8) 25 Kapan and Strömberg ony ook at entrepreneuria ventures nance with venture capita, and thus where private equity is used. They do not ook at entrepreneuria ventures in genera, incuding the ones nanced with debt by commercia banks. 15

16 3.2 Debt with Liquidation As shown in Hart and Moore (1998), and Boton and Scharfstein (1990, 1996), when ony investorcontro and entrepreneur-contro are feasibe aocations of contro rights, the optima contract is a debt contract with the foowing features: 1) At date 0, the investor invests k into the new venture. 2) At date 1, the entrepreneur makes a debt repayment d to the investor, and keeps compete contro over the project in period 2. As discussed above, the investor then eaves the venture, the entrepreneur exerts e ort e (V ) = e h, and he receives an expected second period payo of V Y. We ca this the continuation scenario. 3) In the iquidation scenario, which occurs if the entrepreneur fais to make the repayment d at date 1, tota contro of the project is transferred to the investor, who then proceeds to either manage the venture himsef in period 2, or to se (iquidate) it to another identica investor/entrepreneur. Both aternatives then yied an expected payo V L. We ca this debt with iquidation nancing (DL). There are two possibiities at date 1. If the project does not generate any cash, the entrepreneur must defaut on payment d, the investor iquidates the assets and gets V L. If at date 1 the project generates payo x (which occurs with probabiity p), the entrepreneur pays d to the investor, keeps x d for himsef, and gets an expected payo of V Y at the end of period 2. For a given vaue of d, the return on investment R D for the nancier is: R f DL = pd + (1 p) (V L c h ) k: (9) If possibe, at date 0 the entrepreneur set d such that R f D = 0. However she is constrained: d must be ow enough to be renegotiation-proof. In the good state of the word for exampe, when the rst period payo is x, the entrepreneur may be tempted to defaut on the debt repayment. In that event, iquidation is ine cient since V Y c h > V L c h. Thus, renegotiation between investor and entrepreneur occurs. In the event of renegotiation, the payment s DL from the entrepreneur to the 16

17 investor, using the Nash bargaining soution, is: s DL = arg max ((V Y c h ) z) (z (V L c h )) (10) which yieds s DL = 1 2 (V L c h ) (V Y c h ). The debt repayment d must be ower than s DL, otherwise it is in the interest of the entrepreneur to defaut, renegotiate, and pay out s DL : the contract woud not be renegotiation-proof. Hence, for the debt payment to be incentive compatibe, we must have: d 1 2 (V L c h ) (V Y c h ) : (11) The maximum return the investor can receive is: R f 1 DL = p 2 (V L c h ) (V Y c h ) + (1 p) (V L c h ) k 0: (12) The optima debt with iquidation contract can be described as foows: 1) If k is too high for (12) to hod, this contract is not feasibe and the venture is not undertaken. 2a) If k is ow enough for (12) to hod, d > 0 is chosen such that R f DL = 0, and the entrepreneur extracts a rents from a date 0 perspective: R e DL = p [x + V Y c h ] + (1 p) (V L c h ) k: (13) 2b) In the specia case when k is so ow that (1 p) (V L c h ) k, the entrepreneur set d = ", with "! 0, and requests a transfer t from the investor at date 0 such that (1 p) (V L c h ) k t = 0. 17

18 3.3 Debt with Reorganization Another possibe debt contract is to have entrepreneur-contro if the entrepreneur makes the debt repayment d at date 1, and joint contro if she defauts. In that case the debt contract is in some sense converted into equity in bankruptcy, and reorganization occurs, with both agent sharing contro. We ca this debt with reorganization (DR). This contract is very simiar to the debt with iquidation contract, the main di erence being the aocation of contro rights in bankruptcy. This di erence in contro rights a ects the entrepreneur s bargaining power in renegotiation, and hence the maximum payment she can commit to repay at date 1. Here the entrepreneur can commit to pay at most 26 s DR = 1 2 (V Y c h ), and the maximum return the investor can receive is: R f 1 1 DR = p 2 (V Y c h ) + (1 p) 2 V Q c k 0: (14) Simiar to debt with iquidation, the optima debt with reorganization contract is as foows: 1) If k is too high for (14) to hod, this contract is not feasibe and the venture is not undertaken. 2a) If k is ow enough for (14) to hod, d > 0 is chosen such that R f DR = 0, and the entrepreneur extracts a rents from a date 0 perspective: R e DR = p [x + V Y c h ] + (1 p) (V Q 2c ) k: (15) 2b) In the specia case when k is so ow that (1 p) 1 2 V Q c k, the entrepreneur set d = ", with "! 0, and requests a transfer t from the investor at date 0 such that (1 p) 1 2 V Q c k t = 0. The distinction we make between debt with iquidation and debt with reorganization is not as cear in the rea word. Indeed most contracts tend to ook ike the DL contract in that in the event 26 Using the Nash bargaining soution, we have: s DR = arg max (V Y c h ) z yieds s DR = 1 2 (VY c h). 1 2 VQ c z 1 2 VQ c, which 18

19 of defaut the investor takes contro over the assets. Ony after taking contro the investor decides whether to a) manage the venture himsef or iquidate it, or b) reorganize, keep the entrepreneur on board, and manage the venture jointy. We coud thus have set up the probem with one type of debt contract, which in the bad state sometimes eads to iquidation, other times to reorganization. From a date 0 perspective, the two ways to present are identica: the date 1 payment d aways re ects the agents expectation about whether iquidation or reorganization wi occur. We choose to present the two contracts separatey for carity purposes. 3.4 Preferred-Type Contracts: Redeemabes and Convertibes A third category of debt contracts assigns joint contro conditionay on a prespeci ed debt payment d at date 1; and investor-contro in the event of defaut. These are preferred-type contracts (P). By now it shoud be cear how to determine the optima contract within that category. First, we must determine the incentive compatibe debt repayment d. If the entrepreneur vountariy defauts in the good state of the word, renegotiation occurs, and in equiibrium she transfers an amount 27 s P = 1 2 (V L c h ) to the investor. This is thus the maximum she is wiing to forfeit at date 1, consequenty the most the investor can receive: R f 1 P = p 2 V Q c (V L c h ) + (1 p) (V L c h ) k 0: (16) The optima preferred-type contract can be described as foows: 1) If k is too high for (16) to hod, this contract is not feasibe and the venture is not undertaken. 2a) If k is ow enough for (16) to hod, d > 0 is chosen such that R f DP = 0. The entrepreneur extracts a future rents at date 0: R e P = p [x + V Q 2c ] + (1 p) (V L c h ) k: (17) 27 With Nash bargaining, we have: s P = arg max 1 2 VQ c 1 2 (VL c h). z 1 2 VQ c + z (VL c h ), which yieds s P = 19

20 2b) In the specia case when k is smaer than p 1 2 V Q c + (1 p) (VL c h ), the entrepreneur set d = ", with "! 0, and requests a transfer t from the investor at date 0 such that p 1 2 V Q c + (1 p) (V L c h ) k t = 0. Note the resembance between this contract and the preferred equity nancings observed in practice. There are two main categories of preferred stock: redeemabe (or straight ) preferred, and convertibe preferred. Redeemabe ( straight ) preferred contracts (SP) typicay specify the redemption vaue of the investment (say d), the redemption date (say date 1), and the amount of common stock to be issued in combination with the preferred stock. This common stock gives the investor some rights over the future cash ows, in addition to the pre-speci ed redemption vaue; this is the so-caed doubedipping. If the company cannot make the redemption payment, the assets are iquidated, with the proceeds accruing to the investor rst ( iquidation preference ). Convertibe preferred contracts (CP) give the investor the choice between redeeming his stock at the pre-speci ed redemption vaue d, and converting it into common stock. Obviousy, in the bad state of the word the investor woud not convert, thus forcing iquidation and making use of the iquidation preference attached to his security to extract as much out of the iquidation vaue as possibe. In contrast in the good state of the word it makes sense for him to convert, as ong as the caim on a fraction (say 1 2 ) of the proceeds he can get with the common stock after conversion is higher than the redemption vaue. The reason why we ca this contract the preferred-type contract shoud now be cearer: for sma investments, when k is so ow that in equiibrium d tends to zero, our contract mimicks the payo of convertibe preferred stock. In contrast, when k is arger and the equiibrium date 1 payment d is stricty positive, our contract mimicks the payo of redeemabe preferred stock: doube-dipping occurs as the payment d is foowed by joint-contro and a sharing of the surpus. Thus we ca this preferred-type contract convertibe preferred when equiibrium d tends to zero, and redeemabe (or 20

21 straight) preferred when d > 0. We show in the appendix that these 4 types of contract, namey equity-ike, debt with iquidation, debt with reorganization, and preferred-type contracts, are the ony ones which can potentiay be optima. In this section we have determined the optima contract within each type. We now determine which type is optima. 4 Optima Contracting Ex-Ante and Ex-Post E ciency 28 In this paper we distinguish between ex-ante and ex-post (in)e ciency 29. We de ne ex-post ine - ciency as the di erence between the rst-best return and the entrepreneur s return, XP = R F B R e. The entrepreneur s return R e measures the tota expected surpus from project, and reative ex-post e ciency, conditionay on the investor agreeing to nance the project (i.e. ignoring the investor s return). Even conditionay on the project being nanced, ine ciency arises ex-post due to agency costs. To understand, reca that with any contract, the entrepreneur can extract a future rents from a date 0 point of view, with a date 0 transfer payment t and/or date 1 repayment d. Thus the revenue to the entrepreneur at the end of the game is one of the three outputs described in the ast row of tabe 1, depending on the contro aocation and the state of the word. Note that these outputs are a ower than the FB revenue. This is Grossman and Hart s (1986) we known resut: with incompete contracting, bargaining at the end of period 2 and the sharing of the surpus eads to ine cient eves of investments at the beginning of that period. For a given eve of e ort, the margina return to the agent (entrepreneur or investor) is now weaky ower than the margina product of e ort in the FB. In other words, because the entrepreneur and the investor can never reap 100% of the surpus at the same 28 I greaty bene tted from a discussion with Raph Winter on this subject. 29 The same distinction was made in Gertner, Scharfstein and Stein (1994). 21

22 time, they never both exert the rst-best eve of e ort in period 2, and vaue created is suboptima. In order to be nanced, a project must generate a non-negative return R f to the investor. Some projects require such a ow initia capita outay k that a contracts yied a non-negative return to the investor. With these projects the entrepreneur o ers the contract that gives her the highest return: the ex-post optima contract. In contrast, other projects require much arger initia investments, so arge in fact that not a contracts aocate su cient rents for the investor to make a non-negative return. In these cases the entrepreneur o ers the contract which maximizes her expected payo, among the contracts she knows the investor wi accept. She may not be abe to o er the ex-post optima contract, uness it yieds R f 0. She must take ex-ante e ciency into account. We de ne ex-ante ine ciency as the di erence between the rst-best return and the investor s return, XA = R F B R f. Ex-ante ine ciency measures the fact that not as many projects are to be nanced, reative to rst-best. In the rst-best, a project is undertaken as ong as the initia outay k is ow enough for R F B to be positive. In contrast, in the second best k must be ow enough for the investor s return to be positive. Since the investor s return is ower than the FB return, the threshod eve of k above which a project cannot be nanced is ower, and in equiibrium fewer projects are undertaken. Thus, the higher R f for a given outay k, the more ex-ante e cient the associated contract: the higher the number of projects that coud potentiay be nanced by such a contract. A usefu way to think this is as foows: whereas ex-post e ciency measures the size of the pie to be created, ex-ante e ciency measures the size of the sice of that pie that the entrepreneur can commit to give to the investor. When that sice is higher than the initia outay k, the project is nanced. Of course, the two measures are not independent: a bigger pie makes bigger sices in absoute terms, even keeping the reative sice size constant. The distinction between ex-ante and ex-post ine ciency is crucia: a contract may be ex-post e cient because it gives a high return to the entrepreneur, but at the same time ex-ante ine cient: unikey to be nanced because it attributes so itte to the investor. We anayze ex-post and ex-ante 22

23 e ciency in turn. 4.1 Ex-Post E ciency Let us assume for now that the initia investment required k is so sma that a of the contracts described above are feasibe: each contract Z, Z = E, DL, DR, P, yieds a positive return R f Z for the investor. Since in that case the entrepreneur knows that the investor wi participate, she simpy chooses the contract which maximizes her return R e : the ex-post optima contract. Which contracts yieds the highest return for the entrepreneur evidenty depends on the reative vaues of V Y, V Q, and V L. For simpicity we treat V Y and V L as xed, and we anayze optima contracting for varying eves of V Q. We divide the set of vaues for V Q (V Q 2 e min into three regions, and anayze optima contracting in each one in turn. Region 1: V Q 2 e min + f min ; V L c h + 2c. + f min ; e max + f max ) It shoud be immediatey cear - upon comparing the return to the entrepreneur associated with the di erent contracts, (8), (13), (15), and (17) - that the ex-post optima contract in this region is debt with iquidation: RDL e > Re Z, with Z = E, DR, P. The intuition is simpe: when the payo associated with joint contro, V Q is ow, contracts which incude joint contro in some (or a) contingencies, tend to perform poory. DL yieds the highest return to the entrepreneur because it never assigns the poory performing joint contro. In contrast, it gives fu contro to the entrepreneur in the good state, and fu contro to the investor in the bad state, both of which yied a higher payo than V Q. h Region 2: V Q 2 V L c f h + 2c ; V Y c e h + 2c. In region 2, the net expected payo with joint contro is higher than with investor-contro, but ower than with entrepreneur-contro. Again we compare the returns to the entrepreneur for the di erent contracts, and nd that RDR e > Re Z, with Z = E, DL, P : debt with reorganization is ex-post optima. Debt with reorganization dominates debt with iquidation. Both assign entrepreneur contro in 23

24 the good state, but in the event of defaut DR assigns joint contro, which yieds a higher payo than investor contro assigned with the DL contract. Simiary, the equity-ike contract yieds the same as DR in the bad state, but not as much in the good state, since joint contro (with E) generates ess than entrepreneur-contro (with DR). Finay, the DR contract aso dominates the preferred-type contract: in the good state entrepreneur-contro dominates joint-contro, and in the bad state joint contro dominates investor-contro. Region 3: V Q 2 [V Y c e h + 2c ; e max + f max ). In this region, joint contro generates the highest possibe output, even more than entrepreneurcontro. Obviousy the highest tota surpus, and hence the highest return to the entrepreneur, is obtained by the contract which assigns joint contro in as many contingencies as possibe. The equityike contract, which assigns joint contro in a contingencies, does just that We summarize these resuts in the foowing tabe: Region Name Region Description Optima Contract Region 1 V Q 2 (V Q min ; f 1 (V L )) Debt with Liquidation Region 2 V Q 2 [f 1 (V L ) ; f 2 (V Y )) Debt with Reorganization Region 3 V Q 2 [f 2 (V Y ) ; V Q max ) Equity-ike Financing We de ne V Q min = e min + f min, f 1 (V L ) = V L c h + 2c, f 2 (V Y ) = V Y c h + 2c, and V Q max = e max +f max. We make these abreviations, as we as f 3 (2V L ) = 2V L 2c h +2c, to simpify the reader s anaysis of gures 1-5 beow. Interpretation: In this mode we treat V Y, V L, c, and c h as xed, and we anayze optima contracting for varying eves of V Q. More speci cay we take the high e ort eves as given and study optima contracts for vaues of e 2 e min ; e max, and f 2 f min ; f max. Here is why. A change in e can be interpreted as a change in high-incentive margina e ciency reative to ow-incentive margina e ciency. Margina e ciency refers to the increase in e ort/output which 24

25 resuts from an increase in incentives. There are two margina e ciencies for an agent, say the entrepreneur, in this mode. i) When contro rights switch from investor-contro to joint contro, date 2 bargaining power is transferred from the investor to entrepreneur, from no bargaining power at a (with investor-contro) to some bargaining power (joint contro). Consequenty the entrepreneur s incentives increase and his e ort/output, net of e ort cost, rises from 0 (no participation) to e c ; margina e ciency in that case is (e c ) 0 = e c. ii) When the aocation of rights switches from joint-contro to entrepreneur-contro, more bargaining power is transferred from the investor to the entrepreneur. The entrepreneur s incentives increase even more and her margina e ciency is (e h c h ) (e c ). Thus, for a given e h, c h, and c, a ow e impies a ow ow-incentive margina e ciency and a high high-incentive margina e ciency. Conversey, a high e impies a high ow-incentive margina e ciency reative to a ow high-incentive margina e ciency. Simiary for the investor, the ow incentive eve of margina e ciency, which resuts from a switch from entrepreneur-contro to joint contro, is (f c ) 0 = f c, whie the high incentive eve of margina e ciency, which occurs with a switch from joint-contro to investor-contro, is (f h c h ) (f c ). For both the entrepreneur and the investor, the tradeo between the two margina e ciencies measures the importance of high e ort reative to mere participation in the venture. A high (ow) high incentive margina e ciency reative to ow incentive margina e ciency, means that the agent s high e ort has a arge (ow) impact on performance reative to mere participation. We measure this reative margina e ciency for each agent with the vaues of e and f, and consequenty with V Q = e + f. The ower V Q, the more important the entrepreneur s and the investor s skis and e orts, reative to mere participation in the venture 30. In other words, the ower V Q the more convex the output as a function of incentives. 30 Keeping V Y = e h and V L = f h as we as c h, c h, and c, xed, the ower V Q = e + f, the higher (e h c h ) (e c ) reative to (e c ), and the higher (f h c h ) (f c ) reative to (f c ). 25

26 In ight of this, the resuts of tabe 1 can be interpreted as foows: In region 1, high incentive margina e ciency is arge reative to ow incentive margina e ciency, i.e. high e ort matters much more than mere participation. Consequenty the ex-post optima contract, debt with iquidation, is one which gives high incentives to the entrepreneur (in the good state) as we as to the investor (in the bad state). In region 2, participation by both agents matters more than inducing high e ort by the investor, but ess than the entrepreneur s high e ort and ski. Unsurprisingy, the optima contract, debt with reorganization, gives fu incentives to the entrepreneur in the good state, but induces participation by both agents in the bad state. Finay, when participation by both agents matters a ot reative to expertise and high e ort, as in region 3, the optima contract (equity-ike nancing) generates this coaboration in both states of the word. Comparing with Grossman-Hart-Moore 31 : In order to nd the optima ex-post contract, we impicity compare the margina e ciency of the entrepreneur with that of the investor in each contingency. In region 1 for exampe, the optima contract assigns investor-contro in the bad state of the word, because the (high incentive) margina e ciency of the investor, (f h c h ) (f c ), is higher than the (ow incentive) margina e ciency of the entrepreneur 32 (e c ). This is a we known resut from Grossman-Hart-Moore: more contro shoud be given to the agent with higher margina e ciency. When comparing ownership structures, in the context of the theory of the rm, the Grossman- Hart-Moore resut is simpe and intuitive: aocate property rights over the asset to the most e cient agent 33. It is more di cut, however, to compare nancia contracts on the basis of reative margina e ciency, because as in our mode, nancia contracts can be state contingent in equiibrium, and 31 Grossman and Hart (1986) and Hart and Moore (1990). 32 Very simpy, V L c h > V Q 2c if and ony if (f h c h ) (f c ) > (e c ). 33 See aso Aghion and Tiroe (1994), and de Bettignies (2002) for exampes in the context of vertica integration. 26