6 Banks versus Venture Capital
A.4 Proof of Lemma 4
There are three general cases to consider: case A: r? < V C < C, case B: V C < r? < C, case C: V C < C < r?. Due to the continuity of the payo¤ functions in every possible case, it su¢ces to check for strict inequalities.
Case A ( r? < V C < C): The inequality r? C implies r?K C 0.
Case A-1 ( E < r? < V C < C): An entrepreneur’s return by choosing
bank-…nancing is 1 + 2E 2 (1 +r?)K, which is positive because E < r?. On the other hand, his return by choosing VC-…nancing is 1 + 2V C 2 (K + C), which is positive because E < V C < C. Hence, choosing VC-…nancing instead of bank-…nancing delivers the entrepreneur a net payo¤ of ( 2V C 2E) 2 + (r?K C). Because that V C > E and r?K C >0, ( 2V C 2E) 2+ (r?K C)>0. Thus, the entrepreneur’s best response is
BRAE 1 =V C: (A-10)
Case A-2( r? < E < V C < C): An entrepreneur’s return by choosing bank-…nancing
is 2 2E 2, which is positive because E > r?. On the other hand, his return by choosing VC-…nancing is 1+ 2V C 2 (K+C)>0, which is positive because V C > E. Moreover, because that r? < C, we haver?K C > 0. Consequently, 1+ 2V C 2 (K+C)>2 2E 2, because otherwise
0 1+ 2V C 2 (K+C) 2 2E 2
= 1 + 2V C 2 2E 2 (K+C)> 1 2
E 2 (K+C); (A-11) contradicting to E C. Thus, the entrepreneur’s best response is
BRAE 2 =V C: (A-12)
Case A-3( r? < V C < E < C): An entrepreneur’s return by choosing bank-…nancing is 2 2E 2, which is positive because r? < E. On the other hand, his return by choosing VC-…nancing is 1+ 2E 2 (K+C)>0, which is positive because V C < E < C. Thus, bank-…nancing cannot be a best response, because if it were 2 2E 2 1+ 2E 2 (K+C) would result in 1 2
E 2 (K+C) 0, a contradiction to E < C. Thus, the entrepreneur’s best response is
BRAE 3 =V C: (A-13)
Case A-4( r? < V C < C < E): An entrepreneur’s return by choosing bank-…nancing is2 2E 2 >0, which is positive because E > r?. On the other hand, his return by choosing VC-…nancing is 2 ? E( ? E + (1 ?) V C) 2 >0 where ? is the maximal real number in [0;1]that satis…es the equation ((1 ?)2 2V C ?2 2E) 2 =K+C 1. Because that
2 ? E( ? E + (1 ?) V C) 2 <2 ? 2E 2 2 2E 2; (A-14) as a result of E > C > V C and ? 1, the entrepreneur’s best response is
BRAE 4 =B: (A-15)
Case B( V C < r? < C):
Case B-1( E < V C < r? < C): An entrepreneur’s return by choosing bank-…nancing is 1+ 2E 2 (1 +r?)K, which is positive because E < r?. On the other hand, his return by choosing VC-…nancing is 1+ 2V C 2 (K+C), which is positive because E < V C < C. Hence, choosing VC-…nancing instead of bank-…nancing delivers the entrepreneur a net payo¤
of ( 2V C 2E) 2+ (r?K C). Thus, the entrepreneur’s best response is
Case B-2( V C < E < r? < C): An entrepreneurs return by choosing bank-…nancing is 1+ 2E 2 (1 +r?)K > 0, which is positive because E < r?. On the other hand, his
Case B-3( V C < r? < E < C): An entrepreneur’s return by choosing bank-…nancing is 1+ 2E 2 ( 1 2
Case B-4( V C < r? < C < E): An entrepreneur’s return by choosing bank-…nancing is 2 2E 2, which is positive because r? < E. On the other hand, his return by choosing
Case C-1( E < V C < C < r?): An entrepreneur’s return by choosing bank-…nancing is 1+ 2E 2 (1 +r?)K, which is positive because E < r?. On the other hand, his return by choosing VC-…nancing is 1+ 2V C 2 (K+C), which is positive because E < V C < C. Hence, choosing VC-…nancing instead of bank-…nancing delivers the entrepreneur a net payo¤
of ( 2V C 2E) 2+r?K C. Thus, the entrepreneur’s best response is
Case C-2( V C < E < C < r?): An entrepreneurs return by choosing bank-…nancing is 1+ 2E 2 (1 +r?)K > 0, which is positive because E < r?. On the other hand, his
Case C-3( V C < C < E < r?): An entrepreneur’s return by choosing bank-…nancing is 1+ 2E 2 (1 +r?)K > 0, which is positive because E < r?. On the other hand, his implying E > r?, a contradiction. Thus, the entrepreneur’s best response is
BRCE 3 =B: (A-25)
Case C-4( V C < C < r? < E): An entrepreneur’s return by choosing bank-…nancing is 2 2E 2, which is positive because r? < E. On the other hand, his return by choosing
VC-…nancing is 2 ? E( ? E + (1 ?) V C) 2 >0 where ? is the maximal real number in [0;1]that satis…es the equation ((1 ?)2 2V C ?2 2E) 2 =K+C 1. We have that
2 ? E( ? E + (1 ?) V C) 2 <2 ? 2E 2 2 2E 2 (A-26) as a result of V C < E. This also implies ? <1because E > C. Thus, the entrepreneur’s best response is
BRCE 4 =B: (A-27)
References
[1] Admati, A., and P. P‡eiderer, 1994, Robust …nancial contracting and the role of venture capitalists,Journal of Finance 49, 371-402.
[2] Aghion, P., and P. Bolton, 1992, An incomplete contracts approach to …nancial contracting, Review of Economic Studies 59, 473-494.
[3] Akerlof, G., 1970, The market for “lemons”: quality uncertainty and the market mechanism, Quarterly Journal of Economics 84, 488-500.
[4] Becker, R., and T. Hellmann, 2005, The genesis of venture capital: lessons from the German experience, in C. Keuschnigg and V. Kanniainen, ed.: Venture Capital, Entrepreneurship, and Public Policy, Chapter 2 (MIT Press), 33-67.
[5] Bergemann, D., and U. Hege, 1998, Venture capital …nancing, moral hazard, and learning, Journal of Banking and Finance 22, 703-735.
[6] Berger, A, and G. Udell, 1998, The economics of small business …nance: the roles of private equity and debt markets in the …nancial growth cycle, Journal of Banking and Finance 22, 613-673.
[7] Berglof, E., 1994, A control theory of venture capital …nance,Journal of Law, Economics and Organization 10, 247-267.
[8] Black, B., and R. Gilson, 1998, Venture capital and the structure of capital markets: banks versus stock markets, Journal of Financial Economics 47, 243-277.
[9] Bottazzi, L., M. Da Rin, and T. Hellmann, 2008, Who are the active investors?: evidence from venture capital, Journal of Financial Economics 89, 488-512.
[10] Brander, J., E. Egan, and T. Hellmann, 2008, Government sponsored versus private venture capital: Canadian evidence. in J. Lerner and A. Schoar, ed.: NBER Conference Volume on
“International Di¤erences in Entrepreneurship”.
[11] Brander, J., R. Amit, and W. Antweiler, 2002, Venture capital syndication: improved venture selection versus value-added hypothesis, Journal of Economics and Management Strategy 11, 423-452.
[12] Casamatta, C, 2003, Financing and advising: optimal …nancial contracts with venture capi-talists, Journal of Finance 58, 2059-2086.
[13] Chan, Y., D. Siegel, and A. Thakor, 1990, Learning, corporate control and performance re-quirements in venture capital contracts,International Economic Review 34, 365-381.
[14] Cornelli, F., and O. Yosha, 2003, Staged …nancing and the role of convertible securities,Review of Economic Studies 70, 1-32.
[15] Cumming, D., 2008, Contracts and exits in venture capital …nance,Review of Financial Studies 21, 1947-1982.
[16] Cumming, D., and S. Johan, 2008, Preplanned exit strategies in venture capital, European Economic Review 52, 1209-1241.
[17] Cumming, D., G. Fleming, and A. Schwienbacher, 2006, Legality and venture capital exits, Journal of Corporate Finance 12, 214-245.
[18] de Bettignies, J., and J. Brander, 2007, Financing entrepreneurship: bank …nance versus venture capital, Journal of Business Venturing 22, 808-832.
[19] Dyck, A. and L. Zingales, 2004, Private bene…ts of control: an international comparison, Journal of Finance 59, 537-600.
[20] Gompers, P., 1996, Grandstanding in the venture capital industry, Journal of Financial Eco-nomics 42, 133-156.
[21] Gompers, P., and J. Lerner, 1998, Venture capital distributions: short-run and long-run reac-tions, Journal of Finance 53, 2161-2183.
[22] Gompers, P., and J. Lerner, 1999.The Venture Capital Cycle (MIT Press, Cambridge, MA).
[23] Gompers, P., and J. Lerner, 2000, Money chasing deals?: the impact of fund in‡ows on the valuation of private equity investments, Journal of Financial Economics 55, 281-325.
[24] Gorman, M., and W. Sahlman, 1989, What do venture capitalists do?, Journal of Business Venturing 4, 231-248.
[25] Grossman, S., and O. Hart, 1988, One share-one vote and the market for corporate control, Journal of Financial Economics 20, 175-202.
[26] Harris, M., and A. Raviv, 1988, Corporate governance: voting rights and majority rules, Journal of Financial Economics 20, 203-235.
[27] Hart, O., 1995.Firms, Contracts, and Financial Structure (Oxford University Press, Oxford).
[28] Hellmann, T. 1998, The allocation of control rights in venture capital contracts,RAND Journal of Economics 29, 57-76.
[29] Hellmann, T., and M. Puri, 2000, The interaction between product market and …nancing strategy: the role of venture capital,Review of Financial Studies 13, 959-984.
[30] Hellmann, T., and M. Puri, 2002, Venture capital and the professionalization of start-up …rms:
empirical evidence, Journal of Finance 57, 169-197.
[31] Hellmann, T., L. Lindsey, and M. Puri, 2008, Building relationships early: banks in venture capital,Review of Financial Studies 21, 513-541.
[32] Holmstrom, B., and J. Tirole, 1989, The theory of the …rm. in R. Schmalensee and R. Willig, ed.: Handbook of Industrial Economics, Chapter 2 in Part 1 (Elsevier Publishing B.V, Ams-terdam).
[33] Holmstrom, B., and P. Milgrom, 1991, Multitask principal-manager analyses: incentive con-tracts, asset ownership and job design,Journal of Law, Economics, and Organization 7, 24-52.
[34] Inderst, R., and H. Muller, 2003, The e¤ect of capital market characteristics on the value of start-up …rms, Journal of Financial Economics 72, 319-356.
[35] Kaplan, S., and P. Stromberg, 2001, Financial contracting theory meets the real world: an empirical analysis of venture capital contracts, Review of Economic Studies 70, 281-315.
[36] Landier, A., 2003, Start-up …nancing: from banks to venture capital. Unpublished working paper, University of Chicago, Chicago, IL.
[37] Lerner, J., 1994, The syndication of venture capital investments, Financial Management 23, 16-27.
[38] Lerner, J., 1995, Venture capitalists and the oversight of private …rms,Journal of Finance 50, 301-18.
[39] Lindsey, L., 2008, Blurring …rm boundaries: the role of venture capital in strategic alliances, Journal of Finance 63, 1137-1168.
[40] Marx, L., 1998, E¢cient venture capital …nancing combining debt and equity, Review of Eco-nomic Design 3, 371-387.
[41] Repullo, R., and J. Suarez, 2004, Venture capital …nance: a security design approach,Review of Finance 8, 75-108.
[42] Rothschild, M., and J. Stiglitz, 1976, Equilibrium in competitive insurance markets: an essay on the economics of imperfect information, Quarterly Journal of Economics 90, 629-649.
[43] Sahlman, W., 1990, The structure and governance of venture-capital organizations,Journal of Financial Economics 27, 473-521.
[44] Schmidt, K., 2003, Convertible securities and venture capital …nance, Journal of Finance 58, 1139-1165.
[45] Schwienbacher, A., 2008, Innovation and venture capital exits, Economic Journal 118, 1888-1916.
[46] Schwienbacher, A., 2009, Venture capital exits. in D. Cumming, ed.: Companion to Venture Capital, Robert W. Kolb Companion to Finance Series (Wiley/Blackwell).
[47] Thomson, W., 1981, Nash bargaining solution and utilitarian choice rules, Econometrica 49, 535-538.
[48] Ueda, M., 2004, Banks versus venture capital: project evaluation, screening, and expropriation, Journal of Finance 59, 601-621.
[49] Winton, A. and V. Yerramilli, 2008. Entrepreneurial …nance: banks versus venture capital, Journal of Financial Economics 88, 51-79.