Active hot hands investors vs. the crowd: trading-o investment horizon, support quality and the allocation of control rights in entrepreneurial nance

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1 Active hot hands investors vs. the crowd: trading-o investment horizon, support quality and the allocation of control rights in entrepreneurial nance Guillaume Andrieu and Alexander Peter Groh January 8, 014 Abstract We focus on the choice of the entrepreneur between active hot hands and rather passive long term investors - such as the crowd - with a two-staged model in which an innovative venture requires external equity for start-up and expansion nancing. We assume that active investors provide better support but have a shorter investment horizon than the crowd. We search the NPV-maximizing contract for the entrepreneur, taking into account the active investors' potential moral hazard. They might try selling their claim in an unsuccessful venture to an uninformed outside investor at interim stage even if the project should be abandoned. The likelihood of success depends on the entrepreneurial eort which is boosted by the investor's support. Hence, success chances are eventually higher with the active investor than with the crowd. The abandonment decision can be taken by the party which controls the venture, i.e. either the nancier or the entrepreneur. There exist several equilibria in this game and we show that entrepreneurs can trade-o important contract parameters when seeking external nancing. Contingent on the allocation of the control rights, on the investor's support quality and investment horizon, on the success by chance, and on the venture's expected liquidation value either type of investor is preferable. We particularly thank Catherine Casamatta for her recommendations and support. We are also grateful for important comments by Philippe Desbrières, Pascal François, Ulrich Hege, Antoine Renucci and by our discussant at the 01 FMA European Conference in Istanbul and the 013 AFFI Conference in Lyon. Group Sup de Co Montpellier Business School, 300 avenue des Moulins, Montpellier Cedex 4, France; Tel: +33 (0) ; g.andrieu@supco-montpellier.fr. Corresponding author, EMLYON Business School, 3 Avenue Guy de Collongue, Ecully, France, groh@em-lyon.com. 1

2 JEL classication: D81; G1; G4; G3 Keywords: Allocation of Control Rights, Investment Horizon, Entrepreneurial Finance, Venture Capital, Business Angels, Crowd Funding

3 1 Introduction If an entrepreneur requires outside nancing for an innovative start-up project she has the choice among several sources of capital. The alternatives vary between friends and family, crowd funding, banks, public subsidies, business angels, and professional venture capital rms. All alternatives have dierent characteristics with respect to typically available nancing volumes, terms, duration, cost for the entrepreneur, and support provided by the nancier during the relationship. Distinguishing the sources of equity capital, we can assume that friends and family or the crowd do not take any active role in supporting or controlling the venture, unlike venture capitalists or business angels. These are active investors and highly involved in managing and supporting their investees. Their support can encourage entrepreneurs and help them to achieve important milestones. On the other side, active investors, but especially venture capitalists, have rather hot hands: They have an incentive to divest early to present a successful track record to their investors. This characteristic results from their funds' limited lifetime which requires new fund raising. The shorter investment horizon is a disadvantage because it might create hazards when the venture is not yet mature for an exit but needs expansion nancing beyond the venture capitalist's fund life-cycle. In this paper, we focus on trading-o the benets and disadvantages of active hot hands and passive investors. We set up a two staged model where an innovative entrepreneurial venture requires external equity for start-up and expansion nancing. The entrepreneur can select among two types of nancial ressources: rather passive long term investors such as the crowd or active hot hands investors such as professional venture capital rms. The active hot hands investor monitors tightly and provides a higher support quality but has a shorter investment horizon than the long term investor. He does not want to or cannot provide the expansion capital and rather exits when arriving at the venture's expansion stage. We search the NPV maximizing contract for the entrepreneur taking into account that the active hot hands investor might have a moral hazard. He would try selling his claim after the seed phase to an uninformed outside investor as a claim in a successful venture even if it is a failure and should be abandoned. The likelihood for being successful depends on the entrepreneur's eort which is boosted by the support quality of the investor while the decision to abandon can be taken either by the nancier or the entrepreneur, contingent on who holds the controlling majority. There exist several equilibria in this game and we show that entrepreneurs can trade- 3

4 o important contract parameters when seeking external nancing. Depending on the allocation of the control rights, on the investor's support quality and investment horizon, on the required expansion capital, on the success by chance, and on the venture's expected liquidation value either investor is more appropriate. Our results allow another interpretation: There is no cannibalization among crowd and venture capital nancing. The two sources of capital are rather complementary in the set of available nancing opportunities for young ventures. The mechanisms we discuss are not only relevant for the theory of entrepreneurial nance. They also should be carefully considered by entrepreneurs who raise start-up capital because they directly impact their wealth from the intended venture. Our model is based on two important aspects in early stage nancing relationships. The rst one is the observation that there are dierences with respect to monitoring and controling activities of the investors in start-ups. Some of them are rather passive but some are highly involved in supporting and controlling their investees. Gorman and Sahlman (1989), Sahlman (1990), Hellmann and Puri (00), argue that investors often hold control rights in order to prevent hold-ups by entrepreneurs who may seek private benets from running the venture and being the CEO. This control is usually gained if the board majority is allocated to the investors. Kaplan and Strömberg (004) document that investors hold control rights to mitigate their investment risks. However, Kaplan and Strömberg (003) note that sophisticated investors transfer control rights from/to entrepreneurs contingent on the venture's performance. The better the performance, the more the entrepreneurs gain control via vesting schedules. Hellmann (1998) highlights that entrepreneurs can also select investors with less expertise who may be willing to leave them more control. He develops a model in which an entrepreneur relinquishes control to an investor with strong expertise. His model reveals that wealth-constrained entrepreneurs may give up control even if this imposes a greater loss of private benet than a monetary gain to the company. The model also explains why entrepreneurs accept vesting of their shares. Aghion and Bolton (199) show that, in particular situations, entrepreneurs have no choice but to accept relinquishing their control if they want to obtain nancing. Other papers relate control and exit channels. For example, Bacha and Walz (001), Bayar and Chemmanur (011), and Cumming (008) show that entrepreneurs prefer an IPO to a trade sale in order to keep a controlling position in the venture. Similar to the interest of keeping a powerful position after an investor's exit, Marx (1998) develops a model in which entrepreneurs benet from non-liquidation decisions. Her model explains why entrepreneurs refrain 4

5 from liquidating or delay liquidation even if it would be appropriate to pursue. The second important aspect of our model is the principle of staged investments. Future nancing rounds are usually contingent on the achievement of specic objectives in order to mitigate moral hazards. 1 The drawback of investment staging is that investors may focus on short-term returns that can damage long-term protable projects. Cornelli and Yosha (003) focus on this window-dressing problem. Their model shows that the entrepreneur may prefer to meet short-term expectations to the detriment of long-run success; for instance, by developing a prototype without considering the business aspects. Furthermore, an investor already present in a venture may extract rents based on the private information he receives. In the model of Admati and Peiderer (1994), the informed investor may use his bargaining power to require too much income at the expense of the entrepreneur. Even further, Dessi (005) shows that under certain conditions, the seed investor and the entrepreneur may collude at the expense of new outside expansion investors. These ndings put the importance of the role of actively monitoring investors in a dierent perspective. They show that these investors might also use their privileged information to extract rents at the expense of other outside investors or entrepreneurs. Our model builds on Rajan (199) and Aghion and Bolton (199). In Rajan's (199) model, an entrepreneur can choose nancing from a bank or from an arm's length investor. The bank obtains private information and may liquidate the project subsequently. Unfortunately, this also alters the allocation of the surplus between the bank and the entrepreneur in case the project is successful. The arm's length investor does not ask for control rights and is less costly. Rajan (199) nds that there is ambiguity about the benets of both investors and entrepreneurs can trade-o the ecient continuation decisions of banks, against the less costly alternative. However, Rajan (199) does not consider investor's support and its eect on the project's NPV and hence, does not capture an important aspect in entrepreneurial nancing relationships. Similarly, Aghion and Bolton (199) study the optimal allocation of control rights to entrepreneurs and investors. Their two-staged model is based on the idea that some future decisions about a project can not be determined in the initial contract and that entrepreneurs and investors might have conicting interests with respect to the future of the venture. Therefore, a trade-o in the allocation of control rights arises: If voting equity is issued, then the entrepreneur gives up the integrity, which she actually attaches 1 See empirical papers such as those from Sahlman (1990) and Kaplan and Strömberg (004), as well as theoretical papers from Gompers (1995), Cornelli and Yosha (003) and Wang and Zhou (004). 5

6 a high value to being preserved. If the entrepreneur raises debt, then the full ownerhsip is preserved in principle, but bankruptcy might yield the exact inverse scenario: the complete loss of control. However, the model also ignores the potential support of investors which increases the venture's NPV. Our paper shows that the models presented in Rajan (199) and Aghion and Bolton (199) can be extended in this respect. Hellmann (00), presents a theory which addresses investors' support but also the conicts of interest with an entrepreneur. He focuses on two dierent types of investors, independent and corporate venture capital rms. The corporate venture capital fund has strong experience related to the product and market of the investee and hence, can provide higher support quality than the independent fund. Nevertheless, Hellmann (00) does not discuss the allocation of control rights nor does he consider the impact of abandonment of unsuccessful projects. Other related models are discussed by Ueda (004) and Winton and Yerramilli (008). They compare ordinary bank debt with venture capital nancing. Ueda (004) assumes that a venture capitalist has better skills than a bank manager to evaluate projects but can expropriate the entrepreneur after learning details about her idea. However, Ueda (004) also does not acknowledge the abandonment option nor does she elaborate on control rights or the dierences among the investors with respect to the investment horizon, support quality or risk and reward expectations. To our knowledge, the only study which incorporates investment horizon and the option to abandon is by Winton and Yerramilli (008). However, their paper does not consider that early stage sponsors may actively support their investees and thus increase success chances nor do the authors discuss the impact of control allocation. The paper is organized as follows: in the following section we introduce the model. In section three, we derive the optimal contracts if investors with a long-term or with a short-term horizon hold the controlling stake in the venture. Section four repeats the analysis for the case where the entrepreneur has the control rights. In the fth section, we compare the contract parameters and provide a discussion. The sixth section concludes. All proofs are provided in appendix. Hsu (004) shows that entrepreneurs even accept discounts on new equity issues and trade-o support quality against valuations. 6

7 The model.1 The investment environment We consider a risk-neutral world with no discounting. A penniless entrepreneur has an innovative venture which attracts many potential outside investors. She has unique technological knowledge and is irreplaceable. The project lasts two periods and its innovative nature does not qualify for traditional debt nancing. It requires seed capital I 0 at t = 0 and expansion money I 1 at t = 1 in exchange for a cash ow right δ in the company. Instead of continuing the project at the interim state (t = 1) and providing expansion nancing, it may be abandoned, which yields liquidation proceeds L. If continued it either qualies for selling at R after the expansion period, i.e. t =, or needs to be written o. The probability for a successful trade sale or IPO depends on the state of nature determined at the interim stage. We distinguish two states of nature: If the state of nature is favorable, then the divestment generates cash-ow R with probability 1. If the state of nature is unfavorable, then there is still a chance to receive payo R at probability q, or otherwise 0 with probability (1 q). We require that it is optimal to abandon the project when the state is unfavorable and to continue when the state is favorable: R I 1 > L qr I 1 < L In case of liquidation, the investor cannot recover his investment cost, i.e. I 0 + L < 0. However, the investor insists on a liquidation preference to minimize his loss. The incentive for the investor is R > I 0 + I 1. If the favorable state is reached or not at interim stage depends on the eort e provided by the entrepreneur. She can exert between zero and full eort and decides about her eort during the seed period. For simplicity, we dene the probability of reaching a good state to be equal to the eort, i.e. e [0; 1]. Eort is costly and we denote the cost in the following way: cost(e) = c e In this setting, the entrepreneur has full bargaining power due to her unique project and makes a take-it-or-leave-it oer to an investor. We dierentiate two types of in- 7

8 vestors. First, there is a rather passive investor who provides long term capital, e.g. the crowd, denoted by the subscript L. Second, there is an active hot hands investor who ips his exposure on a shorter horizon (e.g., business angels or professional venture capitalists) - denoted with subscript S. The short term investor aims to leave at t = 1 while the long term investor can back the venture through the seed and expansion stages. Both investors also provide support to the investee. However, the level of support quality may dier. The investor's support aects the entrepreneur's unit cost of eort which we denote c L, and respectively. We assume that the active short term investor takes better care about his investments than the crowd and he has more experience in building and developing start-up ventures. Hence, his contribution results in lower unit cost of eort for the entrepreneur, i.e., < c L. At the end of the seed stage, the entrepreneur and the investor are privately informed about the state of the project and the party which holds the majority of the board seats rights decides if the project is continued or abandoned. Continuation requires expansion capital I 1 which is not supplied by the active hot hands investor. Hence, if the active investor backs the venture and if the project continues, then he must be bought out at t = 1. Since the short term investor knows ex ante that he would leave the project prior to its maturity he requires ex ante a price P S to be bought ought of the venture. 3 expansion investor needs to take over the shares of the seed venture capital rm and also needs to inject I 1 at the same time. 4 The The long term investor does not incur such a limitation. He can stay with the venture throughout the seed and expansion stages and can contribute I 0 and I 1. He expects to be rewarded at the project's maturity. Figure 1 represents the game: ===================== Insert Figure 1 here ===================== 3 Such a claim is typically structured as preferred equity. It provides a liquidation preference and a certain return to the investor. Preferred equity is most commonly used in venture capital nancing. The assumption that the entrepreneur and the active hot hands investor sign a complete contract at t = 0 determining the future price P S for the investor's claim may seem unrealistic. However, the assumption is purely formal and only necessary to derive the result. We assert that all agents are rational and use their information for decision making. At t = 0, the entrepreneur perfectly estimates the price the expansion investor will pay according to the set of information the new agent will get. This is strictly equivalent to negotiating this price at t = 1. Therefore, renegotiation at t = 1 would not change the initial contract parameters. 4 This assumption rules out that the outside investor could buy out the rst one and then wind-up the company prior to injecting I 1. 8

9 . First-best solution The net present value of the project in the rst-best equilibrium is: I 0 + e(r I 1 ) + (1 e)l e. The social optimum is attained if the surplus is maximized. The optimal level of eort is such that: e max I 0 + e(r I 1 ) + (1 e)l e We denote e FB the rst-best solution to this equation. To maximize the surplus, it needs to be e F B = R I 1 L 5. For consistency, we also assume that e FB < 1: Assumption 1. R I 1 L <. Subsequently, we analyze the optimal contracts in this game. Therefore, we distinguish two principle ownership structures of the venture: Either the entrepreneur or the investor holds the majority of the board seats and controls the company. We dene the allocation of the control rights independently of the nancial structure. The separation of control from the nancial structure is important: For any given sharing arrangement about the cash ows of a venture it is possible to allocate the control rights independently. This is a common characteristic in entrepreneurial nancing relationships and comprehensively discussed in Kaplan and Strömberg (003). 3 Optimal contracts if the investor controls We initially assume that the investor has the controlling power over the venture which also entitles him to liquidate it. The entrepreneur selects between the passive long term and the active hot hands investor and trades-o the contract parameters that provide her the highest benet. We derive and analyze the optimal contracts with the long and short term investor. 3.1 Backing by a passive long term investor An investor with a long term investment horizon is able to accompany the venture through the seed and expansion phase and stages the investments I 0 and I 1 according to the project requirements. Therefore, he receives a cash ow right δ in the venture 5 We assumed that R I 1 L > 0 and thus, e FB > 0. 9

10 which determines a fraction of the trade sale or IPO proceeds δr. Since we assume that the investor controls the company he may decide about its continuation at the interim stage. He learns about the venture's state during the seed phase and this information determines the continuation decision. Let us rst assume that the state of the project is unfavorable in t = 1. If the project is continued the investor can expect δqr I 1. If liquidated he receives the liquidation preference L L. We assume L L = L and verify this later. Since qr I 1 < L, the investor winds-up the business. We now analyze the state if the project is favorable in t = 1. In this case, liquidation is not appropriate because it is loss creating L L I 0 L I 0 0, while continuation oers δr I 1. Nevertheless, to motivate an investment in the venture at t = 0 the investor requires to at least break even on average, i.e.: 6 e(δr I 1 ) + (1 e)l L I 0 0 (P C) The entrepreneur anticipates this behavior and calculates her prot by solving: e maxe(1 δ)r + (1 e)(l L L ) c L δ,e,l L The maximization program is thus, the following: e maxe(1 δ)r + (1 e)(l L L ) c L δ,e,l L s.t.e argmax e(1 δ)r + (1 e)(l L L ) c L e s.t.e(δr I 1 ) + (1 e)l L c L e This contract is possible if the expected payo is large compared to the costs. The following assumption describes this: Assumption 3. R I 1 L c L (I 0 L) Proposition 1 If the entrepreneur selects the passive long term investor she will sign a contract such that: δ = R + L + I 1 (R I 1 L) + 4c L (L I 0 ) R 6 If this condition is true, then δr I 1 > 0 as L L < I 0. 10

11 L L = L Corollary 1 Then the entrepreneur provides an eort e = R I 1 L+ which is lower than rst-best. (R I 1 L) +4c L (L I 0 ) c L, 3. Backing by an active hot hands investor An active hot hands investor does not want to or cannot nance the venture through the expansion phase and aims selling his stake at the interim stage. The contract signed at t = 0 needs to set the values of the investor's liquidation preference L S, of his claim P S and of the fraction of his cash ow right δ. 7 At interim stage, the hot hands investor is privately informed about the state of the project (i.e. good or bad). Since we assumed that he holds the majority of the control rights, he decides wether to liquidate the venture or to sell at P S to the expansion investor. If it was P S < L S, this would imply that the investor always liquidates the venture independent of a good or bad state. He would receive his liquidation preference L S in return for the initial investment I 0. However, we required that L I 0 < 0. Hence, this would be loss making and the investor would never invest ex ante. Consequently, this assumption is false and it needs to be P S > L S. Accordingly, the investor contributes I 0 and prefers selling his shares in a secondary transaction at t = 1 for price P S. However, he only accepts ex ante to invest if this condition is true: P S I 0 0 (P C) Since the hot hands investor never liquidates the venture but systematically sells his stake, the expansion nancier cannot infer the venture's success due to the pooling equilibrium which is reached. He computes his expected payo by assessing the probability of a good or a bad state. We dened that the probability that the venture is not a lemon is equal to the entrepreneur's eort e. Therefore, the secondary transaction can only happen if: eδr + (1 e)δqr I 1 P S 0 (P C) 7 We assume that δ is initially negotiated between the hot hands investor and the entrepreneur, and proposed to the second investor at the interim stage against paying P S. The cash ow stake is determined according to the information set that the second investor will have. The second investor may only accept or reject the proposed transaction. This approach is stricly equivalent to negotiate the price with the second investor at the interim period. 11

12 The entrepreneur maximizes her prot by solving: Then, the maximization program is: e max e(1 δ)r + (1 e)(1 δ)qr δ,e,p S e max e(1 δ)r + (1 e)(1 δ)qr δ,e,p S,L S, s.t.e argmax e(1 δ)r + (1 e)(1 δ)qr e, s.t.eδr + (1 e)δqr I 1 P S 0, s.t. I 0 + P S 0. The following assumption derives [ the parameters ] of the optimal contract: R Assumption. i = (1 q) + qr 4 R (1 q) (I 0 + I 1 ) 0 and i [ ] R R(1 q) q. Hence, the trade sale or IPO proceeds R must be suciently high to compensate for the costs while the unit cost of eort should not be too large. Proposition If the entrepreneur selects an active short-term investor she signs a contract such that P S = I 0 and δ = 1 + (qr i ) R (1 q), [ ] R with i = (1 q) + qr 4 R (1 q) (I 0 + I 1 ). This contract yields inecient continuations of the project in its unfavorable state because the investor has no incentive to wind it up. The total output qr I 1 at project maturity is smaller than what would be obtained if the investor had decided to liquidate (i.e. L). However, the active investor needn't consider this because the uninformed outsider buys him out at P S. Therefore, he always prefers to sell his stake and not to disclose his private information. In the optimum, he receives a payo equal to his initial investment and independent of the state of nature. 8 8 In the optimum, parameter P S veries our initial assumption P S I

13 Corollary The entrepreneur provides the following level of eort: e = This eort is lower than rst-best. (1 q)r ( 1 (qr ) i ) R (1 q) The corollary expresses the eort provided by the entrepreneur. eort than rst-best. She exerts less 3.3 Comparison of the two nancing alternatives We realize that nancing by an active short term investor incurs a disadvantage if he has the controlling majority. Unsuccessful projects might not be abandoned but receive additional ressources because the investor has an incentive to sell a lemon instead of liquidating the venture. However, we also argued that support quality is important and this sponsor might take better care of his investments. This encourages the entrepreneur to exert higher eort and increases the success chances. Therefore, we rst compare the investors' impact on the project NPV. Given that all participation constraints are binding in the optimum, the entrepreneur receives the full NPV. The following proposition describes the condition that makes the long-term investor the better choice: Proposition 3 The NPV created with a long-term investor is higher than with a short term investor if I. R L I 1 > c L γ(e S ) and e L R I 1 L (R I 1 L) c L γ(e S ) c L, with γ(e S ) = e S R + (1 e S )qr I 1 L e S. Hence, there is a trade-o for the entrepreneur between support quality and possible inecient continuations. The proposition highlights that either of both nanciers is preferable under certain conditions. Most importantly, inecient continuation decisions can be compensated by higher support quality while the benets of appropriate liquidation diminish with lower support quality. 13

14 4 Optimal contracts if the entrepreneur controls Now we require that the entrepreneur has controlling power over the venture and the discretion whether to continue or liquidate the project at t = 1. We derive the optimal contracts with both investors and discuss incentives to liquidate if it is appropriate. 4.1 Backing by the long-term passive investor If the entrepreneur chooses the long-term passive investor there is no impact on the above discussed equilibrium, independent of her controlling stake. If the project's state is good at t = 1, then both parties will agree to continue developing the venture to maturity. If the state is bad, then she is obliged to liquidate the venture for two reasons. First, the investor will refuse to invest I 1 since he knows the bad state of the project. Second, any new outside investor would refuse to buy out the long-term investor because he infers that the rst investor only sells in a bad state. Since the liquidation is forced by the impossibility to raise expansion money I 1, the situation does also not change if the entrepreneur has any potential private benet from continuing the venture. Therefore, the entrepreneur decides optimally and continues the project in good and liquidates in bad states. 4. Backing by an active hot hands investor We assumed that the active hot hands investor is either obliged or wants to exit the venture at the interim stage, when both, the entrepreneur and the investor know about the project's state of nature. If it is continued, then the hot hands investor needs to be bought out by a new outside investor according to the conditions established in the initial contract. The second investor can only take or leave this oer. If the entrepreneur decides to liquidate, then the proceeds L are shared between both parties, also according to the initial contract conditions. We show that there exist two equilibria that characterize the entrepreneur's actions. In the rst one, she replicates the pooling equilibrium obtained when the investor holds the controlling majority. In the second one, she takes optimal continuation decisions, i.e., she liquidates in bad states of nature. 14

15 4..1 Contract preventing liquidation Not to liquidate would be a reasonable strategy for the entrepreneur if it is always more attractive for her to continue the venture. In this case, her incentive constraint must be: (1 δ)qr L E (IC), with L E denoting the liquidation proceeds for the entrepreneur and L = L S + L E. We presume that this condition be true. 9 by solving: The entrepreneur will then maximize her prot e max e(1 δ)r + (1 e)(1 δ)qr δ,e,p S The outside investor does not know about the state of nature at t = 1 before entering into the transaction. Hence, he calculates his expected prot and invests if and only if: eδr + (1 e)δqr I 1 P S 0 (P C) Since the hot hands investor always sells at t = 1, he intially required: P S I 0 0 (P C) We note that these constraints yield the same maximization program as if the investor holds the majority of the board seats. Consequently, the parameters of this contract are the same. The following proposition summarizes this nding: Proposition 4 When the entrepreneur holds the controlling majority, she may sign a contract with a hot hands investor that incentivizes her to never liquidate the venture. The contract parameters are equal to those if the investor holds the majority. 4.. Contract allowing liquidation More important than the contract that prevents liquidation is that one which allows optimal continuation decisions and eliminiates the ineciency of the previous one. We assume that it is preferable for the entrepreneur to liquidate the project if its state is unfavorable: L E (1 δ)qr (IC) 9 This incentive constraint is easily fullled by setting L E = 0. 15

16 This rules out inecient continuation and the expansion investor can rely on the good state of the venture. For his investment, he needs: δr I 1 P S 0 (P C) The hot hands seed investor knows that the project will be abandoned if the state of nature will be bad and requires his expected prot to be: ep S + (1 e)l S I 0 0 (P C) The resulting maximization program is thus, the following: max δ,e,l e,p S e(1 δ)r + (1 e)l E (e /), s.t.e argmax e(1 δ)r + (1 e)l E (e /), s.t.l E (1 δ)qr, s.t.δr I 1 P S 0, s.t.ep S + (1 e)l S I 0 0. Here, the entrepreneur's stategy is equivalent as with the long term investor, regardless of the uninformed outside expansion investor who steps into the transaction. However there is a notable dierence between the two contracts: In the venture's bad state, the entrepreneur receives L E = 0 liquidation proceeds with a long term investor. This is ruled out with the hot hands investor given that one necessary condition is L E (1 δ)qr. It also implies that the liquidation proceeds L (which are exogenous) need to be suciently large to meet the incentive constraint L (1 δ)qr. If not the contract is impossible. The contract parameters must be as follows: Proposition 5 If the entrepreneur holds the controlling majority of the venture, she may sign a contract that incentivizes her to continue the project in good states and to liquidate in bad states. The parameters of this contract are: δ = R + L + I 1 L E (R I 1 L) + 4 (L S I 0 ), R P S = R I 1 + L L E (R I 1 L) + 4 (L S I 0 ), 16

17 and L E = (R I 1 P S )q and L S = L L E. Corollary 3 With this contract, the eort provided by the entrepreneur is e = R I 1 L+ which is below the rst-best eort. This contract allows the entrepreneur to optimally decide about the venture's continuation. However, it does not replicate the rst-best equilibrium since she will receive some of the liquidation proceeds. Sharing the abandonment value is necessary to incentivize her to liquidate in bad states of the venture but reduces her willingness to exert eort. (R I 1 L) +4 (L S 4.3 Comparison of the two nancing alternatives We show that the contract with the long-term investor yields the same parameters and the same decision behavior regardless of a shift of decision power. Equivalent to the investor, the entrepreneur also decides optimally about the project's continuation and liquidates in bad states. Together with the hot hands investor, there are two possible contracts. The rst one is characterized by the incentive to never liquidate the project. Hence, the entrepreneur replicates the decision of the hot hands investor (if he held the majority of the voting rights), leading to the same ineciency: bad projects are continued instead of being liquidated. However, it is possible to design a second contract that eliminates this ineciency. In this situation, the entrepreneur needs to be set better-o from liquidation compared to continuation. She must receive a payo equivalent to the opportunity cost of liquidating: L E = (1 δ)qr, where (1 δ)qr is her share of the exit procceds that she can still receive by chance, even if the venture's state is bad. Nevertheless, we realize that the less the entrepreneur receives in an unfavourable state, the more she is encouraged to exert eort to turn the venture into a success. Therefore, she provides less than rst-best eort with this contract. We recall that in the rst-best case, the entrepreneur has no claim on the abandonment value L. 5 Comparative statics and discussion We have derived four equilibria with optimal contracts for the entrepreneur, contingent on the allocation of the control rights in the game and on the choice of investor. All 17

18 equilibria are below the rst-best level because either the contract incites inecient continuation or lower support quality decreases the likelihood for success and hence, the project's NPV. Independent of the allocation of the decision power over the venture, the project will always be eciently liquidated in its bad state if it is backed by the long term investor. This is due to the principle that the long term investor would refrain from providing expansion capital in the project's bad state and likewise could not sell his claim to an outsider. Any potential new investor would infer the venture to be a lemon. However, we assumed that the level of support provided by the long term nancier is lower than that of the hot hands investor and therefore, the rst-best NPV is not reached. If the entrepreneur selects the hot hands investor, then the allocation of control rights makes a dierence. In case the investor has descretion, he would ineciently continue the project in its unfavorable state because he has no incentive to wind it up. We reach a pooling equilibrium where the investor always sells at P S to an uninformed outsider and does not disclose his private information. In the optimum, he receives a payo equal to his initial investment and independent of the project's state of nature. If the control rights are allocated to the entrepreneur the equilibrium becomes more complex. Two situations are possible: In the rst one, the entrepreneur replicates the above pooling equilibrium yielding inecient continuation of bad projects. In the second situation she makes optimal continuation decisions. Therefore, the entrepreneur needs an incentive, i.e. receiving a payo in unfavorable states equal to her reserve utility (i.e. the expected value of continuing a bad project). However, this requires certain parameter values. The liquidation proceeds need to be above a threshold L (1 δ)qr. This favors, in principle, the alternative to allocate the control rights to the entrepreneur as she would make ecient liquidation decisions. However, providing her with a fraction of the liquidation proceeds likewise encourages shirking. Therefore, the project NPV decreases and we conclude that none of the alternatives dominates. The trade-o depends on the model primitives and we discuss it subsequently in more detail. We rst derive propositions for the most important model implications. Next, several gures present additional mechanics. For these comparisons, we dene the following notation: The superscripts E and I denote the allocation of the decision power to the entrepreneur or the investor, respectively. The subscripts L and S denote the short and long term investor, as previously dened. 18

19 5.1 Level of eort The level of entrepreneurial eort is a central implication of our model. The more the entrepreneur is incentivized the higher the eort she will spend. Her eort increases the chances for success and the project's NPV. Nevertheless, in any of the possible contracts, her eort is always below rst-best as we showed before. We assumed that the support quality of the passive long term investor is lower than that of the active short term sponsor and this reduces her incentive to work. If she selects a hot hands investor and relinquishes control, then the support quality is elevated, but inecient continuation decisions destroy value and make shirking more attractive. Even if the entrepreneur selects the same investor but keeps control her eort will remain below the rst-best. Unsuccessful projects are liquidated then, but this requires an incentive for the entrepreneur equal to her reserve utility, while she would receive nothing in the rst-best situation. The following proposition compares the level of eort for both possible allocations of decision power and with respect to the parties' cash ow rights: Proposition 6 The level of eort provided by the entrepreneur is higher in case she has the controlling power if and only if: δ I S > δ E S Hence, the level of entrepreneurial eort will be higher if she has control compared to not having it only if she has higher cash ow rights. We subsenquently illustrate the levels of eort induced by the possible contracts and the the main variables of the model (i.e., L, the quality of support, and I 1 ). ================= Insert Figure ================= Figure presents the rst-best eort and the levels of eort according to the dierent contracts and contingent on the liquidation proceeds. The rst-best eort decreases with higher liquidation proceeds as we have already shown by e F B = R I 1 L. If the venture is backed by the hot hands investor and if liquidation is ruled out, then the level of eort is independent of the potential liquidation proceeds. Continuing with what we discussed above, the contract with the hot hands investor which allows liquidation is only possible if she controls the venture and if the liquidation proceeds are above a threshold L t. In this case, she can exert higher eort relative to a contract with the 19

20 long term investor. In general, entrepreneurial eort increases with L if the entrepreneur chooses the long term investor or if she controls the venture. In both scenarios, the increase of the liquidation proceeds does not make shirking more attractive to her. The higher the liquidation proceeds the smaller the potential loss for the investor in a bad state of nature. This lowers his required cash ow rights leaving a larger stake for the entrepreneur, thus encouraging her to exert eort. Figure 3 relates the entrepreneurial eort to the dierence of the support quality cl of the two investors. ================= Insert Figure 3 ================= The gure illustrates the eect on the entrepreneurial eort if the long term investor increases his support quality up to the level of the active hot hands investor. The rstbest eort and both contracts with a hot hands investor are not aected because they do not depend on c L. However, the entrepreneurial eort backed by the long-term investor increases with his support quality. If his level of support quality reaches that of the hot hands investor, then the entrepreneurial eort becomes even rst-best. Finally, we analyze entrepreneurial eort with respect to the required expansion capital I 1. ================= Insert Figure 4 ================= Figure 4 emphasizes that the entrepreneurial eort decreases with the required capital for all contracts because the more nancial resources are necessary the more cash ow rights the investors demand. This lowers the NPV for the entrepreneur and she will be less prepared to exert eort. The contract with the hot hands investor allowing liquidation always encourages higher eort than the contract with the long term investor. 10 If liquidation is prevented, then entrepreneurial eort can be higher or lower compared with the long term investor. 5. Cash ow rights for the entrepreneur A second central model implication is the allocation of the cash ow rights between entrepreneur and investor. A fair allocation secures that the entrepreneur is rewarded 10 Remark: at reasonable levels of and c L. 0

21 for her eort and the investor for putting capital at risk. Both parties can benet from the support provided by the investor which enhances the entrepreneurial eort and the project's NPV. Proposition 7 The entrepreneur's cash ow rights are higher in case she has the descretion about the project continuation if and only if: [ ] e I S < (1 q) e E S + LE S The proposition shows that for reasonable values of q, and if the level of eort when the entrepreneur decides is suciently high, 11 then the entrepreneur receives more cash ow rights if she controls. Figure 5 presents the entrepreneur's cash ow rights over the liquidation proceeds according to the possible contracts. ================= Insert Figure 5 ================= The gure reveals that liquidation proceeds do not impact the contract with a hot hand investor who controls simply because the venture never gets liquidated. If liquidation is possible and the higher the proceeds the lower the investor's required cash ow rights. The rationale is as follows: Liquidation proceeds lower investor's losses in bad states of nature. Hence, the investor demands less compensation in the favorable state, leaving higher cash ow rights to the entrepreneur. There is an additional eect with the long term investor: Since all of the liquidation proceeds ow to the investor, the entrepreneur is highly incentivized to avoid liquidation by spending much eort. Figure 6 presents the relation between the entrepreneur's cash ow rights and the dierence of support quality of the two investors according to the possible contracts. ================= Insert Figure 6 ================= The gure depicts that if the entrepreneur receives nancing from a hot hands investor, then her fraction of the cash ow rights is higher with a contract allowing liquidation compared to a contract preventing it. If she is backed by a long term investor her stake in the venture can be smaller or larger than with a hot hands investor 11 Remark: This is likely to be the case due to the absence of inecient continuation decisions. 1

22 depending on the dierence of the support quality. If the long term investor can provide as good support as the hot hands investor he would be the better choice. Figure 7 shows the entrepreneur's cash ow rights over the required expansion capital I 1. ================= Insert Figure 7 ================= In general, the higher the required expansion capital the more cash ow rights the entrepreneur needs to relinquish. If the investor's exposure increases he demands a higher compensation. We note that especially with a contract preventing liquidation and high expansion nancing requirements, the entrepreneur needs to give up a large stake of her venture. 5.3 Comparison of NPVs A third pivotal model implication is the NPV of the project because it is particularly important for the entrepreneur to assess the impact of her choice of investor and control right allocation on her personal wealth. Therefore, we compare the NPVs generated with the two investors and according to the two possible allocations of control rights. We required that the investors compete in a competitive market. Consequently, the entrepreneur recovers the full NPV. We assume rst that the entrepreneur contracts with a hot hands investor. If the investor controls, then the project gets never liquidated. This corresponds to a pooling equilibirum where bad projects are ineciencily continued. If the entrepreneur controls two situations are possible. In the rst one, she perfectly replicates the former equilibrium. In the second one, she makes optimal continuation decisions. However, this situation requires the existence of high enough liquidation proceeds to give her an incentive to liquidate.the following proposition summarizes this result: Proposition 8 With a hot hands investor, the allocation of control to the entrepreneur creates the same or more NPV compared to allocating control to the investor. If the entrepreneur selects a long-term investor the allocation of control rights has no impact. Whatever happens, the investor forces her to liquidate by refusing to inject additional capital in bad states of nature. This signals the quality of the venture to any potential outside investor and prohibits a new nancing round. The long term investor

23 has in fact the abandonment option for the project and descretion about its future, independent of the formal allocation of the decision power. Proposition 9 If an investor with a long-term horizon backs the venture, the investor controls directly or indirectly and optimal continuation decisions are made. Since the entrepreneur has full bargaining power according to one of our initial model assumptions, she receives the project's NPV and weighs the comparative benets of the hot hands and the long term investor. The following proposition sets up the determinants of her choice: Proposition 10 A contract with a long term investor generates a higher NPV than a contract with a hot hands investor in which i) the entrepreneur has control rights and ii) the entrepreneur liquidates if and only if the following two conditions are true: [ ] I. (R I 1 L) c L e E S (R I (e 1 L) c E S ) S e I L R I1 L (R I 1 L) c L c L e E S (R I 1 L) ( ee S ) In both cases, optimal continuation decisions are made. With a hot hands investor, and if the entrepreneur controls the venture, then she has an incentive to liquidate bad projects because she obtains an equal payo as if she decided to continue. With a long term investor, it would be the investor who triggers liquidation of bad projects. The main determinants are the level of support eciency c L and, the value of liquidation proceeds L, and the value of the required expansion capital I 1. Figure 8 presents the entrepreneur's NPV over the liquidation proceeds of the venture. ================= Insert Figure 8 ================= Below the threshold L t, liquidation is ruled out and either the long term or the active hot hands investor may be preferable according to Figure 8. However, above the threshold, the contract allowing liquidation with the hot hands investor maximizes the project NPV. In Figure 9, we present the project's NPV contingent on the dierence of the support quality of the two investors according to the possible equilibria at a given level of. 3

24 ================= Insert Figure 9 ================= We realize that with large dierences of the support quality among both investors the long term investor is less benecial. However, if the dierence diminishes the NPV with the long term investor reaches the rst-best level. The gure also reveals that the NPV of the contract with the hot hands investor that allows liquidation is above that one which prevents it. Nevertheless, the NPVs of the possible contracts with the hot hands investor are independent of the support quality dierence. Finally, we focus in Figure 10 on the link between the NPV of the project and the required expansion money. ================= Insert Figure 10 ================= In principle, the larger the expansion capital requirement the lower is the venture's NPV. We also recognize that the contract with the hot hands investor, which prevents liquidation, is inferior to all other possibilities if the venture's nancing needs are large. Contrarily, if the expansion investment is low, then the project's NPV can approach the rst-best level if the hot hands investor is chosen. 5.4 Empirical predictions and discussion Our model reveals that if liquidation proceeds are not too low and if the investor has a short-term horizon preference, then it is optimal to allocate control rights to the entrepreneur because she will make optimal continuation decision, unlike the investor. If the entrepreneur selects an investor with a long-term horizon preference, she can relinquish control rights and the investor makes optimal decisions. This nding adds to the existing literature. First of all, literature on venture capital emphazises that investors should have control rights to prevent entrepreneurs from obtaining private benets that may damage value. Aghion and Bolton (199) is one of the founding models that elaborates on the allocation of control rights to investors. They show that entrepreneurs have to relinquish control in certain cases. Otherwise they will not obtain nancing. However, unlike our model, their study does not deal with the support of investors that aects entrepreneurial performance. Hellmann (1998) completes Aghion and Bolton (199), by suggesting that entrepreneurs may voluntary accept to relinquish their con- 4