The impact of competition from venture capitalists on corporate venturing investment

Bade, Marco Article The impact of competition from venture capitalists on corporate venturing investment The Journal of Entrepreneurial Finance (JEF) Provided in Cooperation with: The Academy of Entrepreneurial Finance (AEF), Los Angeles, CA, USA Suggested Citation: Bade, Marco (2020) : The impact of competition from venture capitalists on corporate venturing investment, The Journal of Entrepreneurial Finance (JEF), ISSN 2373-1761, Pepperdine University, Graziadio School of Business and Management and The Academy of Entrepreneurial Finance (AEF), Malibu, CA and Los Angeles, CA, Vol. 22, Iss. 1, pp. 61-77, https://doi.org/10.57229/2373-1761.1374 , https://digitalcommons.pepperdine.edu/jef/vol22/iss1/3 This Version is available at: https://hdl.handle.net/10419/264413 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ The Journal of Entrepreneurial Finance The Journal of Entrepreneurial Finance Volume 22 Issue 1 Summer 2020 Article 3 July 2020 The Impact of Competition from Venture Capitalists on Corporate The Impact of Competition from Venture Capitalists on Corporate Venturing Investment Venturing Investment Marco Bade Technische Universität Berlin Follow this and additional works at: https://digitalcommons.pepperdine.edu/jef Part of the Business Administration, Management, and Operations Commons, Corporate Finance Commons, Entrepreneurial and Small Business Operations Commons, and the Finance and Financial Management Commons Recommended Citation Recommended Citation Bade, Marco (2020) "The Impact of Competition from Venture Capitalists on Corporate Venturing Investment," The Journal of Entrepreneurial Finance : Vol. 22: Iss. 1, pp. -. Available at: https://digitalcommons.pepperdine.edu/jef/vol22/iss1/3 This Article is brought to you for free and open access by the Graziadio School of Business and Management at Pepperdine Digital Commons. It has been accepted for inclusion in The Journal of Entrepreneurial Finance by an authorized editor of Pepperdine Digital Commons. For more information, please contact bailey[email protected]. The Impact of Competition from Venture Capitalists on Corporate Venturing The Impact of Competition from Venture Capitalists on Corporate Venturing Investment Investment Cover Page Footnote Cover Page Footnote The author would like to thank the editor James C. Brau for handling the paper, and the anonymous referee for his/her helpful feedback. The author also thanks Prof. Dr. Hans Hirth for valuable suggestions. This article is available in The Journal of Entrepreneurial Finance: https://digitalcommons.pepperdine.edu/jef/vol22/ iss1/3 THE JOURNAL OF ENTREPRENEURIAL FINANCE VOLUME 22, NO. 1 (SUMMER 2020) 61-77 Copyright © 2020 Pepperdine Digital Commons and the Academy of Entrepreneurial Finance. All rights reserved. ISSN: 2373-1761. The Impact of Competition from Venture Capitalists on Corporate Venturing Investment Marco Bade Technische Universität Berlin, Germany ABSTRACT This study proposes a model on corporate venturing (CV) investment and examines the impact of venture capital (VC) activity in the economy on CV firms’ investment. The presence of VCs creates competition for entrepreneurs. This reduces CV firms’ expected venturing returns, and thus gives rise to a financial disincentive to CV investment. The empirical prediction of this result is that competition for talent should decrease CV investment. This prediction contradicts previous statements in the theoretical literature on CV. Keywords: Corporate venturing, Corporate venturing investment, Venture capital JEL Codes: D86, G3, L26, M13 I. Introduction “In the past, corporate interest in creating venture funds tended to wax and wane in sync with the general VC climate” (Lerner 2013, p. 88). Corporate venturing 1 (CV) and venture capital (VC) activity went hand in hand through cyclical boom phases in the late 1960s, mid-1980s, and late 1990s (Bettignies and Chemla 2008, Dushnitsky 2011, Gompers 2002, Gompers and Lerner 1998). In the financial crisis years 2011 and 2012, this longstanding fact has changed (Lerner 2013). In Europe, for instance, the deal value (deal count) of CV activities has risen by 59 percent (15 percent), whereas VC fundraising has fallen by 5 percent (12.5 percent) in those years. In the most recent years, both are rising again in terms of deal volumes. However, growth in the CV sector is stronger (e.g., Pitchbook 2019). The very close link of the past decades appears to be interrupted by new effects. Given the novelty of this development, there is a research 1 This study adopts the Bettignies and Chemla’s (2008, p. 505) definition of CV. They “… define corporate venturing as the financing and development of new business ventures by large established companies, either inside (intrapreneurship) or outside (corporate venture capital) the corporate structure”. Bade The Impact of Competition from VCs on CV Investment 62 62 gap in academic literature on CV. There is no scholarly approach to explain (temporary) opposing trends in CV investment and VC activity. This study presents a model analyzing the investment decision of a CV firm. In order to establish in the market for a new technology, the firm invests and tries to recruit a star entrepreneur with an innovative idea and skill to implement a new venture. In addition, there is a VC in the same market for the new technology who wants to recruit the entrepreneur. The CV investment generates a marginal base return as well as an additional return from the new venture (venturing return) if successful. The venturing return depends on entrepreneurial effort, which the firm may elicit by setting incentives in the contract of the entrepreneur. The model determines the CV firm’s optimal ex-ante investment considering that there is competition for entrepreneurial talent. Only a few papers have addressed CV, particularly CV investment, theoretically. Most closely related, Bettignies and Chemla (2008) present a model on a firm’s choice of organizational form (corporation vs. CV firm). Similar to this model, the authors consider a setting where the firm and a rival investor (e.g., a VC) compete for the recruitment of a star manager with an innovative idea. In the main analysis, they compare the expected payoffs of the firm for the two options and conclude that firms prefer CV to organizing as a corporation in order to benefit from superior managerial incentives in new ventures, and to acquire new knowledge or talent. According to the authors, the model explains why CV is procyclical to entrepreneurial activity. However, the model cannot explain the very recent divergence of trends in CV and VC activity. Moreover, they do not model the investment decision of the firm explicitly but nevertheless predict that competition for entrepreneurs encourages CV investment. This prediction is to be taken with care in view of the fact that competition for talent creates pressure on expected payoffs of investors in the market. It seems quite conceivable that less expected payoffs translate to reduced investment volumes. In fact, the model developed in this study will yield an opposite prediction. This study is further related to Amador and Landier (2003), who consider a setting in which a manager chooses between contractual offers of a firm and a VC. The authors argue that the offer of the firm depends on the offer of the VC to the manager. The better the offer of the VC, the more the firm has to pay. Thus, the VC market exerts pressure on the firm, which affects the firm’s innovation effort. Anand et al. (2004) propose a model in which a corporation and a specialist compete for a talented individual, but focus on the different incentives of the two investors to acquire entrepreneurial knowledge. Corporations that incorporate the talent into the main line of business may benefit from the exploitation of synergies, whereas specialists who fund single projects provide stronger incentives and autonomy. Projects in which talent is pivotal might better be financed individually by specialists. The present study contributes to this literature by employing a similar setting, which is extended by an ex-ante investment decision made by a CV firm. The investment The Journal of Entrepreneurial Finance Volume 22, No. 1 Summer 2020 63 provides the firm with an additional tool to elicit the desired effort by the entrepreneur. Remarkably, the results of the model yield an empirical prediction that is in contrast to previous theoretical literature, but is consistent with recent empirical observations. The remainder of the paper is organized as follows. Section 2 presents the model. Sections 3 (Contracting) and 4 (Investment) contain the main analysis of the paper. Section 5 concludes the paper. Note that this paper is intended as a thought-provoking paper in the light of the results of Bettignies and Chemla (2008) and recent empirical observations, and does not claim to be a comprehensive analysis of the topic of CV investment. II. The Model The model is in the spirit of Bettignies and Chemla (2008). In the economy, there are a CV firm 2 investing in a new technology, a rival investor (a female VC) who invests in the same technology 3 , and a star entrepreneur (male) with an innovative idea. Both the CV and the VC aim to recruit the entrepreneur to start a new venture with. The discount rate is normalized to 1. All players are risk-neutral. The timeline of events is illustrated in Table 1. Table 1: Timeline This table provides the timeline of events. Date t=0 t=1 t=2 t=3 Investment in the CV unit Contracting stage Entrepreneur exerts effort Realization of cash flows 2 “CV”, “firm”, and “CV firm” refer to the same player in the model. A neutral gender is assigned to this player. 3 The model does not endogenize the VC’s investment. This could easily be added, but would in no way change or enrich the qualitative results of the model. Bade The Impact of Competition from VCs on CV Investment 64 64 At date t=0, the firm establishes a CV unit and invests. The investment 𝐼𝑐𝑣∈ (0,1) comes at cost 𝐼𝑐𝑣 2 2. This cost can be considered as the cost of raising capital, which is increasing in the amount of capital provided to the CV unit. Alternatively, think of an effort incurred in monitoring the investment that is also increasing in the volume of the investment. 4 The investment generates a marginal base return Π>0 from the new technology. In addition to the base return, investing in the new technology generates a return from the new venture (venturing return) 𝜋>0 if the entrepreneur exerts effort. In particular, the venturing return is scaled by entrepreneurial effort 𝑒∈[0,1] at date t=2 as well as the ex-ante investment, i.e. √𝐼𝑐𝑣𝑒𝜋. 5 The term √𝐼𝑐𝑣𝑒 represents the probability that the venturing return will be generated. Thus, √𝐼𝑐𝑣𝑒𝜋 is the expected venturing return. The cost of effort is given by 𝑘 2𝑒2. The parameter 𝑘>0 represents the marginal cost of effort. The structure of the expected venturing return captures that both the investment in the technology and the entrepreneur’s effort are crucial for venture success but entrepreneurial effort plays a stronger role. The return structure is the same for the VC (index 𝑣𝑐 instead of 𝑐𝑣). The expected return from the new technology is given by the base return plus the venturing return if the entrepreneur is recruited by investor 𝑖∈ {𝑐𝑣,𝑣𝑐}: 𝐼𝑖Π+√𝐼𝑖𝑒𝑖𝜋. (1) At date t=1, after the investment but before the entrepreneur’s effort, the entrepreneur pitches his idea to the CV and the VC. Both offer a contract to the entrepreneur. The entrepreneur’s compensation 𝑊𝑖, received from either the CV or the VC, comprises two components: a fixed base salary 𝑆𝑖≥0 and a share 𝛽𝑖∈[0,1] of the venturing return √𝐼𝑖𝑒𝑖𝜋. The non-negativity of parameters 𝑆𝑖 and 𝛽𝑖 captures limited liability. Think of a compensation consisting of a fixed and a variable component. The latter can be understood as stock options (calls) issued to the entrepreneur in order to incite his non-contractible effort. In fact, the entrepreneur’s participation 𝛽𝑖∗ in the 4 The convex nature of the cost function ensures that there will be an interior solution when solving the model. 5 The square root √𝐼𝑐𝑣 serves for mathematical simplification. The Journal of Entrepreneurial Finance Volume 22, No. 1 Summer 2020 65 venturing return will determine his effort choice 𝑒𝑖∗. The superscript “∗” denotes variables’ equilibrium values. Moreover, when contracting with the entrepreneur, the firm discloses the capital provided to the CV unit, as this affects the contract and the entrepreneur’s effort. It is difficult to imagine an entrepreneur accepting an offer to implement an innovative idea within a firm without knowing in advance how much capital will be made available for it. In this respect, the timeline (investment before contracting and effort) seems to make sense in the light of reality. 6 The timeline implies that the entrepreneur’s effort choice will not only respond to his participation 𝛽𝑖∗ in the venturing return but also to the size of the investment 𝐼𝑖∗ made by the CV or the VC. Consequently, the CV and the VC have two ex-ante tools to induce non-verifiable entrepreneurial effort 𝑒𝑖∗. Note that the model does not consider the possibility of subsequent adjustments of the investment. The entrepreneur’s utility 𝑈𝑖 if recruited by 𝑖 is given by his compensation minus the cost of effort: 𝑈𝑖=𝑊𝑖−𝑘2𝑒𝑖2=𝑆𝑖+𝛽𝑖√𝐼𝑖𝑒𝑖𝜋−𝑘2𝑒𝑖2. (2) III. Contracting At date t=1, both the CV and the VC offer a contract to the entrepreneur. Payoffs are contractible. The contract signed at date t=1 cannot be renegotiated. However, as is typical in the literature on contracting models in entrepreneurial finance research, the entrepreneur’s effort is non-verifiable in court and thus non-contractible (see, e.g., Anand et al. 2004, Bettignies 2008, Bettignies and Chemla 2008, Bettignies and Duchêne 2015, Casamatta 2003). The expected aggregate return from investment and recruitment of the entrepreneur depends on the entrepreneur’s best response in terms of effort at date t=2. Thus, the contracts offered by the CV and the VC at date t=1 also depend on the entrepreneur’s best response 𝑒𝑖(𝐼𝑖,𝛽𝑖). Consequently, as the CV and the VC can only provide imperfect incentives to entrepreneurial effort, the first-best level of effort will not be achieved, but the second-best level of effort. 6 In addition, this timeline facilitates the comparability of this model with the most closely related literature, which makes statements about CV investment before recruiting entrepreneurs. Bade The Impact of Competition from VCs on CV Investment 66 66 Given that the CV and the VC compete for the entrepreneur’s talent, the CV’s (VC’s) offer additionally depends on the VC’s (CV’s) offer, which is expressed in the entrepreneur’s reservation payoff. As a result, the offers by the CV and the VC are sets of contracts {𝑆𝑖∗,𝛽𝑖∗,𝑒𝑖∗} depending on the entrepreneur’s reservation payoffs 𝑈𝑣𝑐 and 𝑈𝑐𝑣, respectively. Lemma 1 illustrates the set of contracts offered by the CV to the entrepreneur. The formal proof of Lemma 1 can be found in the Appendix. Lemma 1: The CV firm offers the following set of contracts to the entrepreneur: {𝑆𝑐𝑣 ∗,𝛽𝑐𝑣 ∗,𝑒𝑐𝑣 ∗}= { {0,12,√𝐼𝑐𝑣𝜋 2𝑘 } ∀ 𝑈𝑣𝑐∈[0,𝐼𝑐𝑣𝜋2 8𝑘 ) {0,√2𝑈𝑣𝑐𝑘 √𝐼𝑐𝑣𝜋,√2𝑈𝑣𝑐 𝑘} ∀ 𝑈𝑣𝑐∈[𝐼𝑐𝑣𝜋2 8𝑘 ,𝐼𝑐𝑣𝜋2 2𝑘 ) {𝑈𝑣𝑐−𝐼𝑐𝑣𝜋2 2𝑘 ,1,√𝐼𝑐𝑣𝜋 𝑘} ∀ 𝑈𝑣𝑐∈[𝐼𝑐𝑣𝜋2 2𝑘 ,∞). (3) 𝑈𝑣𝑐 represents the reservation payoff of the entrepreneur, which he receives if recruited by the VC. As explained above, the entrepreneur’s compensation in the CV firm depends on the VC’s offer, expressed by 𝑈𝑣𝑐. As formally shown in the Appendix, there are three relevant areas. If the reservation payoff is relatively small (first area, first part of expression 3), the entrepreneur is able to extract rents from the venture. The CV, however, can elicit the desired effort by setting 𝛽𝑐𝑣 ∗=1 2 and paying no fixed salary. As the VC’s offer and thus the reservation payoff of the entrepreneur increases, the CV’s offer remains the same but the entrepreneur’s rent vanishes. If the reservation payoff is in the second area (second part of expression 3), the CV must increase the entrepreneur’s share of the venture returns to outbid the VC, which induces higher effort in favor of the CV firm. If the reservation payoff reaches the third area (third part of expression 3), the CV must pay a fixed salary in addition to the variable compensation that reaches 100 percent to ensure that the entrepreneur participates. Note that, due to the symmetric payoff structure from the technology, the VC offers a similar set of contracts (only with swapped indices 𝑐𝑣 and 𝑣𝑐 in expression 3). The compensation structure illustrated above is in line with prior research (e.g., Amador and Landier 2003, Bettignies and Chemla 2008). The novel feature in this model is the explicit inclusion of the ex-ante investment. As mentioned above, the investment is made before contracting, as the entrepreneur’s decision with respect to the selection The Journal of Entrepreneurial Finance Volume 22, No. 1 Summer 2020 73 REFERENCES Amador, M., & A. Landier. (2003). Entrepreneurial pressure and innovation. Working paper, Stanford Graduate School of Business, Stanford University, Stanford. Anand, B., A. Galetovic, & A. Stein. (2004). Incentives versus synergies in markets for talent. Working paper, Harvard Business School, Boston. Bettignies, J.-E. de. (2008). Financing the Entrepreneurial Venture. Management Science 54, 151–166. Bettignies, J.-E. de, & G. Chemla. (2008). Product Market Competition and the Financing of New Ventures. Management Science 54, 505–521. Bettignies, J.-E. de, & A. Duchêne. (2015). Corporate Venturing, Allocation of Talent, and Competition for Star Managers. Management Science 61, 1741–2011. Casamatta, C. (2003). Financing and Advising: Optimal Financial Contracts with Venture Capitalists. The Journal of Finance 58, 2059–2085. Chesbrough, H. (2002). Making sense of corporate venture capital. Harvard Business Review 80, 90–99. Covin, J.G., & M.P. Miles. (2007). Strategic use of corporate venturing. Entrepreneurship Theory and Practice 31, 183–207. Dushnitsky, G. (2011). Riding to the Next Wave of Corporate Venture Capital. Business Strategy Review 22, 44–49. Gompers, P.A. (2002). Corporations and the financing of innovation: The corporate venturing experience. Federal Reserve Bank of Atlanta Economic Review 87, 1–17. Gompers, P.A., & J. Lerner. (1998). The determinants of corporate venture capital successes: Organizational structure, incentives, and complementarities. Working Paper 6725, National Bureau of Economic Research, Cambridge. Hellmann, T. (2002). A theory of strategic venture investing. The Journal of Financial Economics 64, 285–314. Lerner, J. (2013). Corporate Venturing. Harvard Business Review 91, 85–94. Bade The Impact of Competition from VCs on CV Investment 74 74 Ma, S. (2020). The Life Cycle of Corporate Venture Capital. The Review of Financial Studies 33, 358–394. Mathews, R.D. (2006). Strategic alliances, equity stakes, and entry deterrence. The Journal of Financial Economics 80, 35–79. Pitchbook (2019). European VC trends in 9 charts. Available at: https://pitchbook.com/news/articles/european-vc-trends-in-9-charts. Last access: February 14, 2020. Siegel, R., E. Siegel, & I. MacMillan. (1988). Corporate venture capitalists: Autonomy, obstacles, and performance. Journal of Business Venturing 3, 233–247. APPENDIX Proof of Lemma 1: The CV aims to maximize its net expected payoff from recruiting the entrepreneur: max 𝑒𝑐𝑣 𝐼𝑐𝑣Π+√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−(𝑆𝑐𝑣+𝛽𝑐𝑣√𝐼𝑐𝑣𝑒𝑐𝑣𝜋)−𝐼𝑐𝑣 2 2. (12) The entrepreneur chooses effort level to maximize his expected utility: 𝑒𝑐𝑣∈argmax𝑆𝑐𝑣+𝛽𝑐𝑣√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−𝑘2𝑒𝑐𝑣 2, (13) subject to: 𝑆𝑐𝑣+𝛽𝑐𝑣√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−𝑘2𝑒𝑐𝑣 2≥𝑈𝑣𝑐. (14) The entrepreneur’s optimal effort level is given by: 𝑒𝑐𝑣=𝛽𝑐𝑣√𝐼𝑐𝑣𝜋 𝑘 ⟺𝛽𝑐𝑣=𝑘𝑒𝑐𝑣 √𝐼𝑐𝑣𝜋. (15) Substituting this into the CV’s objective function yields: The Journal of Entrepreneurial Finance Volume 22, No. 1 Summer 2020 75 max 𝑒𝐼𝑐𝑣Π+√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−(𝑆𝑐𝑣+𝑘𝑒𝑐𝑣 2) 𝑒𝑐𝑣 ∗=√𝐼𝑐𝑣𝜋 2𝑘 . (16) Hence, 𝛽𝑐𝑣 ∗=1 2 and 𝑆𝑐𝑣 ∗=0 if 𝑈𝑣𝑐<𝐼𝑐𝑣𝜋2 8𝑘 . If, however, 𝑈𝑣𝑐≥𝐼𝑐𝑣𝜋2 8𝑘 , condition 14 is violated. The CV increases 𝛽𝑐𝑣 ∗, thus 𝑒𝑐𝑣 ∗, such that the condition is satisfied again: 𝑆𝑐𝑣+𝛽𝑐𝑣√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−𝑘2𝑒𝑐𝑣 2≥𝐼𝑐𝑣𝜋2 8𝑘 , (17) if 𝑒𝑐𝑣 ∗=√2𝑈𝑣𝑐 𝑘, 𝛽𝑐𝑣 ∗=√2𝑈𝑣𝑐𝑘 √𝐼𝑐𝑣𝜋, and 𝑆𝑐𝑣 ∗=0. If 𝑈𝑣𝑐≥𝐼𝑐𝑣𝜋2 2𝑘 , the firm can no longer ensure that condition 14 is satisfied through the incentive parameter, because increasing 𝛽𝑐𝑣 ∗ along with 𝑈𝑣𝑐≥𝐼𝑐𝑣𝜋2 2𝑘 would induce an inefficiently high effort by the entrepreneur. Instead, the firm pays a fixed salary 𝑆𝑐𝑣 ∗=𝑈𝑣𝑐−𝐼𝑐𝑣𝜋2 2𝑘 , which ensures that the condition is satisfied again. The variable compensation reaches its maximum possible value 𝛽𝑐𝑣 ∗= 1. This elicits the first-best effort 𝑒𝑐𝑣 ∗=√𝐼𝑐𝑣𝜋 𝑘. The contract offered by the VC is similar (only with swapped indices 𝑣𝑐 and 𝑐𝑣) due to the symmetric return structure. QED Proof of Lemma 2: The expected recruitment payoff of the CV is given by: 𝐸(𝑃𝑐𝑣)=𝐼𝑐𝑣Π+√𝐼𝑐𝑣𝑒𝑐𝑣𝜋−𝑊𝑐𝑣−𝐼𝑐𝑣 2 2. (18) If the CV does not recruit the entrepreneur, its expected payoff is 𝐼𝑐𝑣Π−𝐼𝑐𝑣 2 2. Similarly, for the VC, we have the following recruitment payoff: 𝐸(𝑃𝑣𝑐)=𝐼𝑣𝑐Π𝑣𝑐+√𝐼𝑣𝑐𝑒𝑣𝑐𝜋−𝑊𝑣𝑐−𝐼𝑣𝑐 2 2. (19) Bade The Impact of Competition from VCs on CV Investment 76 76 If she does not recruit the entrepreneur, her expected payoff is 𝐼𝑣𝑐Π𝑣𝑐−𝐼𝑣𝑐 2 2. Note that the entrepreneur’s effort 𝑒𝑖 and the compensation 𝑊𝑖 depend on his reservation payoff. From the firm’s perspective, the expected recruitment payoff is greater than the norecruitment payoff if the reservation payoff 𝑈𝑣𝑐 is sufficiently small, i.e. 𝑈𝑣𝑐≤𝑈𝑣𝑐. The weak inequality captures that the entrepreneur would choose the firm if indifferent. If, however, 𝑈𝑣𝑐>𝑈𝑣𝑐, the firm’s expected payoff is negative and the firm does not recruit the entrepreneur. Therefore, there is a reservation payoff to the entrepreneur 𝑈𝑣𝑐, such that the recruitment payoff equals the no-recruitment payoff. Replacing 𝑊𝑖 yields the following equation, which implicitly determines 𝑈𝑣𝑐: 𝐼𝑐𝑣Π +√𝐼𝑐𝑣𝑒𝑐𝑣(𝑈𝑣𝑐)𝜋−𝑈𝑣𝑐−𝑘2𝑒𝑐𝑣 2(𝑈𝑣𝑐)−𝐼𝑐𝑣 2 2=𝐼𝑐𝑣Π 𝑐𝑣−𝐼𝑐𝑣 2 2. (20) For the VC, the recruitment payoff equals the no-recruitment payoff if 𝑈𝑐𝑣=𝑈𝑐𝑣. If 𝑈𝑐𝑣<𝑈𝑐𝑣, the VC recruits the entrepreneur. Otherwise, the VC does not recruit the entrepreneur. If both the CV firm and the VC bid for the entrepreneur, the CV firm can offer a more attractive contract if 𝑈𝑐𝑣≤𝑈𝑣𝑐. In this case, the CV firm offers contract 𝑊𝑐𝑣=𝑈𝑐𝑣 and recruits the entrepreneur, as the VC cannot outbid the CV. Then, the firm’s expected payoff is given by: 𝐸(𝑃𝑐𝑣(𝑈𝑐𝑣))=𝐼𝑐𝑣Π𝑐𝑣+√𝐼𝑐𝑣𝑒𝑐𝑣(𝑈𝑐𝑣)𝜋−𝑈𝑐𝑣−𝑘2𝑒𝑐𝑣 2(𝑈𝑐𝑣)−𝐼𝑐𝑣 2 2. (21) The payoff of the entrepreneur is 𝑊𝑐𝑣=𝑈𝑐𝑣, and the VC expects to receive the norecruitment payoff. If, however, 𝑈𝑐𝑣>𝑈𝑣𝑐, the VC offers 𝑊𝑣𝑐=𝑈𝑣𝑐 and recruits the entrepreneur. The VC’s payoff is: 𝐸(𝑃𝑣𝑐(𝑈𝑣𝑐))=𝐼𝑣𝑐Π𝑣𝑐+√𝐼𝑣𝑐𝑒𝑣𝑐(𝑈𝑣𝑐)𝜋−𝑈𝑣𝑐−𝑘2𝑒𝑣𝑐 2(𝑈𝑣𝑐)−𝐼𝑣𝑐 2 2. (22) The entrepreneur gets 𝑊𝑣𝑐=𝑈𝑣𝑐, and the firm expects to receive the no-recruitment payoff. Note that, by definition of 𝑈𝑐𝑣: 𝐸(𝑃𝑣𝑐(𝑈𝑐𝑣))=𝐼𝑣𝑐Π𝑣𝑐+√𝐼𝑣𝑐𝑒𝑣𝑐(𝑈𝑐𝑣)𝜋−𝑈𝑐𝑣−𝑘2𝑒𝑣𝑐 2(𝑈𝑐𝑣)−𝐼𝑣𝑐 2 2 =𝐼𝑣𝑐Π 𝑣𝑐−𝐼𝑣𝑐 2 2. (23) The Journal of Entrepreneurial Finance Volume 22, No. 1 Summer 2020 77 Hence, 𝑈𝑐𝑣=√𝐼𝑣𝑐𝑒𝑣𝑐(𝑈𝑐𝑣)𝜋−𝑘2𝑒𝑣𝑐 2(𝑈𝑐𝑣). (24) We can substitute this into the CV’s expected payoff and obtain: 𝐸(𝑃𝑐𝑣 ∗(𝑈𝑐𝑣))=𝐼𝑐𝑣Π𝑐𝑣+𝜋(√𝐼𝑐𝑣𝑒𝑐𝑣 ∗(𝑈𝑐𝑣)−√𝐼𝑣𝑐𝑒𝑣𝑐 ∗(𝑈𝑐𝑣)) −𝑘2(𝑒∗𝑐𝑣 2(𝑈𝑐𝑣)−𝑒∗𝑣𝑐 2(𝑈𝑐𝑣))−𝐼𝑐𝑣 2 2. (25) Given the symmetric payoff structure, the CV and the VC elicit the same effort by the entrepreneur. Thus, 𝑈𝑐𝑣=√𝐼𝑣𝑐𝑒𝑣𝑐(𝑈𝑐𝑣)𝜋−𝑘2𝑒𝑣𝑐 2(𝑈𝑐𝑣)=√𝐼𝑣𝑐𝑒𝑣𝑐(𝑈𝑐𝑣)𝜋−𝑘2𝑒𝑣𝑐 2(𝑈𝑐𝑣). (26) Given the assumptions in the text, the CV recruits the entrepreneur in equilibrium. This yields the expected payoffs given in Lemma 2 in the text. QED