Venture Capital Contracting: Staged Financing and Syndication of Later-stage Investments

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Venture Capital Contracting: Staged Financing and

Syndication of Later-stage Investments

Zsuzsanna Fluck

Eli Broad School of Business

Michigan State University

and

The William Davidson Institute

Kedran Garrison

Department of Economics

Massachussetts Institute of Technology

Stewart C. Myers

Sloan School of Management

Massachussetts Institute of Technology

and

The National Bureau of Economics Research

November 26, 2006

We are grateful for helpful comments from Ulf Axelson, Amar Bhide, Francesca Cornelli, Paul Gompers, Steve Kaplan, Josh Lerner, Tom Noe, David Scharfstein, Per Str¨omberg, Michael Weisbach and participants at presentations at LSE, MIT, University of Michigan, Michigan State University, the University of Min-nesota, University of Western Ontario, and the RICAFE II Conference on Entrepreneurship and Venture Capital, the Conference on Venture Capital and Private Equity (Stockholm), the Financial Intermediation Research Society Conference (Capri).

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Abstract

This paper develops a model to study the design of financial contracts between entrepreneurs and venture capitalists. We argue that contractual provisions that alle-viate one market imperfection often exacerbate another. We demonstrate this tradeoff in the context of stagedfinancing. We show that staged financing alleviates the effort provision problem by trading it off for the hold-up problem. The hold up problem arises because staged financing gives disproportionate bargaining power to the initial venture capitalist. In venture capital practice a new contract is issued at each stage of investment and the presence of a series of previously issued contracts creates a hold-up problem between participants. The hold-hold-up costs we document are not negligible. For a wide range of parameter values the hold up costs of staged financing are so high that they actually overwhelm the benefits of staged financing relative to full up-front financing. We then show that an ex ante commitment to syndication of later stages of investment alleviates the hold-up problem of staged financing by reducing the incumbent venture capitalist’s incentive to dilute the entrepreneur’s stake ex post and improves efficiency. Since in practice staged financing is a provision of venture capital term sheets and syndication of later-stage investment is induced by covenants in partnership agreements, our theory suggests that venture capital term sheets and partnership agreements complement each other.

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1

Introduction

This paper develops a model to study the design offinancial contracts between entrepreneurs and venture capitalists. While many individual provisions of venture capital contracts have been previously studied in thefinance literature, the interactionbetween different provisions is not yet well understood. For example, we know from previous research that stagedfi nanc-ing can induce optimal effort provision, and so can equity and option-based compensation and convertible preferred equity financing. One cannot help but wonder that if each clause induces optimal effort provision on its own, then why do venture capitalists put them all in one contract? Aren’t these clauses substitutes? Wouldn’t any one of these provisions be sufficient and the others redundant? If each of these provisions is so effective on its own, then what is the rationale for the practice of writing extensively long venture capital contracts?

We argue that the reason these provisions coexist in venture capital contracts is because entrepreneurs and venture capitalists face multiple market imperfections in their relation-ships. These include moral hazard, effort provision, agency, asymmetric information and holdup problems. While each provision alleviates some of these problems, it also exacer-bates others. Focusing on individual contractual provisions, the venture capital contracting literature was able to obtain key insights into the benefits of these provisions by identifying the particular market imperfection that they were designed to alleviate. However, we argue that the benefits of individual provisions may have been overstated by not explicitly taking into account the costs, i.e. the extent to which particular contractual provisions trade offone market imperfection for another. By combining specific provisions in very particular ways, venture capital contracts effectively span the space of market imperfections that the parties face and thereby add value.

In this paper we show that venture capital contract provisions do not necessarily solve or eliminate particular market imperfections but instead they trade off one problem for another. Demonstrating and quantifying this tradeoffin the context of stagedfinancing and the hold up problem is the novel contribution of our paper. In venture capital practice a new contract is issued at each stage of investment (Series A, Series B, Series C, etc.) and the presence of a series of previously issued contracts creates a hold-up problem between participants. Theoretical models in the venture capital literature have not studied this hold-up problem, they typically focused on the impact of a single early-stage financial contract on the later-stage incentives and efforts of the entrepreneur and the venture capitalist. One of the novelties of our paper is modeling the interaction of subsequently issued financial contracts and studying the differential impact of these contracts on the parties’ efforts and incentives ex ante and ex post.

We show that stagedfinancing alleviates the effort provision problem by trading it offfor the hold up problem. The hold up problem arises because stagedfinancing gives dispropor-tionate bargaining power to the incumbent venture capitalist in later stages of investment since an incumbent venture capitalist is potentially better informed about the project than outsiders. Anticipation of a potential hold up ex-post reduces the entrepreneur’s willingness to exert optimal effort ex ante. Once the cost of the potential hold-up is taken into account, the effort incentives provided by stagedfinancing are no longer optimal. The loss is not even negligible: for a wide range of parameter values we find that the cost of staged financing (the value loss due to the hold-up problem) is so high that it actually exceeds the benefits

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(improved effort incentives from efficient continuation).

There are contractual provisions that can alleviate the hold up problem of stagedfi nanc-ing and improve efficiency. We argue that syndication of later stages of financing reduces value loss by improving effort incentives. We find that when later stages of investment are syndicated, then the benefits of staged financing (improved effort incentives) outweigh the hold-up costs for all parameter specifications. We demonstrate that syndication of later stage investment adds value because it shifts the terms offinancing in the entrepreneur’s fa-vor. A commitment to syndication of later-stage investment reduces the incumbent venture capitalist’s incentive to dilute the entrepreneurs’ stake ex post and aligns his interest with the entrepreneur’s. In our model commitment to syndication of later rounds offinancing can protect the entrepreneur from ex post hold up by incumbent investors and thereby encourage ex ante and ex post effort provision. In other words, syndication of later stage investment creates value ex ante by tying the hands of the incumbent venture capitalist ex post. Con-sistent with thefinding of Kaplan and Str¨omberg (2003) the entrepreneur’s ownership share increases with the value of the project when later stages of investments are syndicated. This is not the case, however, when staged financing is provided by the incumbent venture cap-italist alone. In the latter case the entrepreneurs’ share would decrease as project value increases.

In the United States staged financing is a common feature of venture capital “term sheets”, the contracts between entrepreneurs and venture capitalists (Gompers (1995)). With a few exceptions all later-stage venture capital investments are syndicated (Lerner(1994)). Partnership agreements between venture capital firms and their limited partners commit funds to syndicate later stages of their investments by requiring the venture capital fund not to invest more than a small percentage of the fund (typically 5 percent) in any portfolio com-pany or by specifying the maximum dollar value of an investment round (Sahlman (1990)). We argue that by rationing the amount funds can invest in any portfolio company in any given round, partnership agreements precommit venture capitalists to syndicate later-stages of investments. These covenants are binding since fund size is chosen to be proportional to the investment needs of portfolio companies for reputation reasons (Kaplan and Schoar (2005)). To get around such covenant or have it waived is rare, except for funds in emerging market economies (Lerner (2004)).

When the partnership agreement induces syndication of later financing rounds, venture capitalists are better off holding common equity, convertible preferred shares, or convertible debt in our model instead of straight debt. We show that with syndicated debt financing the initial venture capitalist does not hold up the entrepreneur ex post but he would set the face value of his debt higher ex ante in order to extract as much upside as possible. This creates a debt overhang, which translates into higher continuation thresholds and lower NPVs. Syndicated debt financing forces the original venture capitalist to capture the upside ex ante because (unlike the monopolist debt financier) he would receive no upside ex post. This contrasts with the case of common equity, convertible preferred stock or convertible debt financing where the venture capitalist shares in the upside of the project ex post. In practice venture capitalists receive common or convertible preferred shares or convertible debt in exchange of their effort andfinancial investment.

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financing and syndication in venture capital contracts. By demonstrating that ex ante com-mitment to later stage syndication of venture capital investments alleviates the hold up problem of staged financing, our theory highlights how venture capital term sheets and partnership agreements complement each other. Kaplan and Str¨omberg (2003) provides a detailed empirical analysis of term sheets and Gompers and Lerner (1996) of partnership agreements. We believe that more empirical studies are needed for understanding the link-ages of term sheets and partnership agreements within and across funds.

Our theory presents a new explanation for syndicate financing of later stage invest-ment. In our model commitment to syndication of later rounds of financing protects the entrepreneur from ex post hold up by incumbent investors and thereby encourages ex ante and ex post effort provision. Previous explanations for syndication of venture capital invest-ments in the literature include information gathering and pooling (Sah and Stiglitz(1986), Gompers and Lerner (2002) and Cassamatta and Haritchabalet (2004)), risk aversion (Wil-son (1968)) and tacit collusion between venture capitalists (Pichler and Wilhelm (2001)).

Our paper is related to the literature on stagedfinancing. In Bergemann and Hege (1998) and N¨oldeke and Schmidt (1998), staging allows the venture capitalist to learn the startup’s value and thereby induce the entrepreneur’s effort. In Neher (1999) and Landier(2002), the venture capitalist’s ability to deny financing at each stage forces the entrepreneur to exert higher effort and prevents her from diverting cash flows. In Hellman and Puri (2002) stagedfinancing adds value by contributing to the early professionalization of venture-backed start-ups. Chemla, Habib and Lyngquist (2006) studies the role of anti-dilution provisions, tag-along and drag-along rights in staged investments and how they increase incentives. Bienz (2005) contrasts the use of staged financing and round financing in venture capital investments. In this paper we provide a rationale for the combined use of staged financing and syndication of later stages of investments in venture capital contracts.

The closest to our research is Cornelli and Yosha (2003). In this article the authors highlight a different drawback of staged financing: short-term incentives to “window dress” entrepreneurial projects. Cornelli and Yosha argues that staged financing induces the en-trepreneur to focus on the immediate hurdle of the next stage and thereby creates adverse incentives to improve the interim prospects of the project. Their model demonstrates that the combined use of stagedfinancing and convertible securities in venture capital term sheets alleviates entrepreneurial shortermism. In our model stagedfinancing gives rise to a holdup problem. We show how an ex ante commitment to syndicate financing of later stage invest-ments, induced by common covenants in venture capital partnership agreements can alleviate the holdup problem of staged financing.

In a related paper by Admati and Pfleiderer (1994) the initial venture capitalist wants to bring in outside investors at the second stage and aims to design a contract that facili-tates truthful revelation. The authors show that a fixed fraction investment participation contract makes the venture capitalist indifferent between truth-telling and lying and there-fore implements truthful information revelation. In our model ex post the initial venture capitalist strictly prefers not to bring in outside investors at the second stage but ex ante he is better off if he can credibly commit to do so. We show that the fixed fraction rule does not induce truthful information revelation in our model where the terms of financing affect the entrepreneur’s effort. In our model the fixed fraction rule leads the incumbent venture

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capitalist to over-report the start-up’s value: the higher the price paid by the new investors, the more the entrepreneur’s existing shares are worth and the harder she works. The incum-bent venture capitalist captures part of the gain from her extra effort. A participation rule in which incumbent venture capitalist’s fractional investment participation increases as the reported value increases combined with incentive compensation in which entrepreneur’s own-ership share increases for high values of the project1 alleviates the asymmetric information

problem for a range of parameter values.

We use computational methods to investigate the multiple market imperfections inherent in the entrepreneur-venture capitalist relationship. While we are not aware of any other com-putational model of venture capital contracts, comcom-putational models have been frequently used to understand the tradeoff theory of capital structure and the risk-shifting incentives created by debtfinancing (Mello and Parsons (1992), Leland (1994, 1998), Boyd and Smith (1994), Parrino and Weisbach (1999), Robe (1999, 2001) Parrino, Poteshman and Weisbach (2002), Noe, Repullo and Wang (2003) and Ju, Parrino, Poteshman and Weisbach (2004)). In a venture capital setting the advantage of a computational model is two-fold. First, the use of a computational model gives us the freedom to study the entrepreneur-venture cap-italist relationship in its complexity without having to worry about finding a closed-form solution. Secondly, the computational model allows us to quantify the costs and benefits of venture capital provisions and the associated tradeoffs. We believe that in the context of the entrepreneur - venture capitalist relationship computational models can provide valuable insights by quantifying the value of complexfinancial contracts in the face of multiple market imperfections.

The rest of this paper is organized as follows. Section 2 provides an overview of relevant venture capital practice. Section 3 presents thefirst-best case. Section 4 compares the staged

financing and full upfrontfinancing of a project by a monopolist venture capitalist. Section 5 covers the case of staged financing with syndication of later stage investment. Section 6 discusses how the degree of the hold-up problem is affected by the type of financing used. Section 7 sums up conclusions and points out questions for further research.

2

Basics of venture capital contracting practice

Venture capital funds are created for a fixed term, typically ten years. They are formed as limited partnerships. The venture capital firm serves as the general partner and wealthy individuals, families and university endowments are the limited partners. The funds invest in entrepreneurial companies and distribute returns to their limited partners as they harvest their investments.

In venture capital practice the partnership agreement defines the relationship between the venture capitalist and its limited partners and the term sheet governs the relationship between the venture capitalist and the portfolio companies. In the entrepreneur - venture capital relationship entrepreneurs contribute ideas, plans, human capital and effort, and venture capitalists contribute experience, expertise, contacts and most of the money. Their joint participation creates an effort provision problem. First, the venture capitalist has to

1In their sample of detailed venture capital contracts Kaplan and Str¨omberg documented that the

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share financial payoffs with the entrepreneur in order to secure her commitment and effort. Thus he may not be willing to participate even if the startup has positive overall NPV. Second, the entrepreneur will underinvest in effort if she has to share her marginal value added with the investor.

2.1

Sweat equity

The entrepreneur invests even when she puts up none of the financing. She contributes her effort and absorbs part of the firm’s business risk. The difference between her salary and her outside compensation is an opportunity cost. Specialization of her human capital to the new firm also creates an opportunity cost if the firm fails.2

In practice the entrepreneur receives shares in exchange for these investments. These shares may not vest immediately, and they are illiquid unless and until the firm is sold or goes public.3 The venture capitalist frequently requires the entrepreneur to sign a contract

that precludes work for a competitor. The entrepreneur therefore has a strong incentive to stick with the firm and make it successful.

2.2

Staged

financing and control

A venture capital financed startup is a compound call option. Financing and investment are made in stages. The stages match up with business milestones, such as a demonstration of technology or a successful product introduction. At each stage the project is valued and new shares are issued in exchange for the new investment. The shares are identified by the round of financing as Series A, Series B, Series C, etc.

Staged financing gives the incumbent venture capitalist effective control over access to

financing.4 Although financing is conditional on milestones, in practice their completion

does not guarantee continuation of investment. Even if all milestones are surpassed, a project may be shut down if a competing product proves better. Similarly, a project may be allowed to continue even if not all milestones have met. Hence, completion of milestones is not necessarily verifiable for a third party, and the terms of refinancing are ultimately decided by the incumbent venture capitalist. In practice, the incumbent venture capitalist’s decision not to participate is usually a decision to shut down thefirm since his refusal in the second or later rounds of financing would deter other potential investors from investing.5

The benefit of stagedfinancing is the option to shut down non-performing projects early.

2This opportunity cost is reduced if new ventures are developed as divisions of largerfirms. See Gromb

and Scharfstein (2003) and Gompers, Lerner and Scharfstein (2003).

3Employees are granted options that vest gradually as employment continues and the startup survives.

Founders typically receive shares, not options. The entrepreneur’s shares are fully vested, but additional shares may be granted later. See Kaplan and Str¨omberg (2003).

4Previous theoretical papers argue that the venture capitalist’s right to decide on investment (Aghion

and Bolton (1992)) and to replace the entrepreneur (Fluck (1998), Hellman (1998), Myers (2000)) play an important role in enforcing financial contracts between investors and entrepreneurs. The entrepreneur’s option to reacquire control and realize value in an initial public offering is a key incentive offered by the venture capitalist in Black and Gilson (1998), Myers (2000) and Aghion, Bolton and Tirole (2001).

5The role of the monopolistfinancier was investigated in Rajan (1992), Petersen and Rajan (1994) and

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The decision to continue or shut down a project cannot be left to the entrepreneur, who is usually happy to continue investing someone else’s money as long as there is any chance of success. The venture capitalist is better equipped to decide whether to exercise each stage of the compound call option.

Staged financing is not without costs, however. The venture capitalist’s option to shut down the project is a double-edged sword. On the one hand, staging blocks the entrepreneur’s incentive to continue negative net present value projects. On the other hand, it allows the venture capitalist to use the threat of shutdown to hold up the entrepreneur when valuing the project at the next stage. The lower is the value estimate in the second round, the more shares the venture capitalist gets in that round (or at the conversion of Series B shares) and the more he can dilute the entrepreneur’s stake. This is what we call the hold up problem of staged financing. Ex post the threat of the hold up benefits the venture capitalist. Ex ante both parties are worse off as anticipated dilution feeds back into the entrepreneur’s incentives and effort and reduces overall value. This value loss constitutes the hold up costs of staged financing.6

In practice venture capital investors usually buy convertible preferred shares at each round of financing (Series A preferred, Series B preferred, etc.). The number of shares investors receive in exchange of their investment in a given round is determined by the valuation of the project at that round. The shares convert to common stock if the firm is sold or taken public.7 If thefirm is shut down, the investors have a senior claim on any remaining assets.

Ordinary debt financing is rarely used.

The incumbent venture capitalist’s control decreases with the number of successfully completed financing rounds (Kaplan and Str¨omberg (2003)). Nevertheless, the incumbent venture capitalist typically regains control if the firm’s progress turns unsatisfactory.

2.3

Syndication of later-stage

financing

In practice later-stage financing usually comes from a syndicate of incumbent and new venture-capital investors. Partnership agreements between venture capital firms and their limited partners commit venture funds to syndicate later stages of their investments by requiring the fund to limit its investment to a small percentage of the fund (typically 5 per-cent) or by specifying the maximum dollar value of an investment round (Sahlman (1990), Lerner (2005)). In practice, the incumbent venture capitalist always co-invests with the new investors.

Previous literature offered various explanations for syndication of venture capital invest-ments. Syndication is one way to gather additional information about a startup’s value — see, for example, Gompers and Lerner (2002, Ch. 9) and Sah and Stiglitz (1986). Wilson (1968) attributes syndication to venture capitalists’ risk aversion. Syndication may also reflect tacit collusion: early investors syndicate later rounds of financing, and the syndication partners

6Stagedfinancing also induces entrepreneurial short-termism. Since the entrepreneur’s immediate goal is

to surpass the next stage, stagedfinancing gives rise to incentives to window-dress the project. See Cornelli and Yosha (2003).

7The use of convertible securities in venture capital is analyzed in Green (1984), Bergl¨of (1994), Kalay

and Zender (1997), Repullo and Suarez (1998), Cornelli and Yosha (2003), Schmidt (2003) and Winton and Yerramilli (2003).

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return the favor when they develop promising startups (Pichler and Wilhelm (2001)). In Cassamatta and Haritchabalet (2004), venture capitalists acquire different skills and expe-rience and syndication pools their expertise. We offer a different rationale: syndication can protect the entrepreneur from ex post holdup by investors and thereby encourage effort. A commitment to syndicate finance later stages of venture capital investments alleviates the holdup problem of staged financing by assuring the entrepreneur more favorable terms in the later rounds of financing. This encourages effort in all periods, which increases overall value.

3

The Model of the First-Best Case

The entrepreneur possesses a startup investment opportunity that requires her effort, x0 and

x1 at date 0 and date 1 and fixed amounts of financial investments, I0 and I1. Effort x

is defined on the interval [0,) and I0 and I1 are fixed. Firm value depends on the state

of nature and the effort exerted. If both date-0 and date-1 investments are made, then the startup continues to date 2, and thefirm is sold or taken public and thefinal value is realized. We value the startup as a real option. The underlying asset is the potential market value of the firm, which is assumed to be lognormally distributed. Full realization of potential value requires maximum effort from the entrepreneur at dates 0 and 1. The entrepreneur’s actual effort is costly, so her optimal effort depends on her expected share of the value of the firm at date 2.

The total payoff at date 2, P, is stochastic and depends on the entrepreneur’s effort at time 0 and time 1, x0 and x1, and on V2, the potential value of the firm at date 2. Effort

affects the payoff multiplicatively through the effort functions f0(x0) and f1(x1):

P =f0f1V2 (1)

Effort generates positive but decreasing returns, that is, f(0) = 0, f > 0 and f < 0. The entrepreneur bears the costs of her effort, g0(x0) and g1(x1). The effort cost function is

strictly increasing and convex, that is,g(0) 0,g >0 and g >0.

The potential value V2 is the sole source of uncertainty. We define the expected value

E1(V2) at date 1 as V1 and expected value E0(V2) at date 0 as V0. The expected payoffs at

dates 0 and 1, assuming that the firm will survive until date 2, are:

E1(P) =E1(f0f1V2) =f0f1E1(V2) =f0f1V1

E0(P) =E0(E1(P)) =f0E0(f1V1|V0)

(2) where E0(f1V1|V0) is an integral that accounts for the dependence of f1 on V1. We assume

risk-neutrality and a risk-free interest rate of zero. We use lognormal probability distributions for V1 and V2, with standard deviationσ per period.

We define the effort function f and the effort cost function g as

ft = 1−e−θfxt

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for t = 0,1. The effort function f asymptotes to 1, so we interpret V1 and V2 as maximum

attainable values asx→ ∞. The degree of concavity and convexity of f and g depends on

θf and θg. The effort functions are plotted in Figure 1 for several values of θf and θg.

In the first-best case, the entrepreneur supplies all of the money, I0+I1, and owns the

firm. The entrepreneur maximizes NPV net of her costs of effort. If she decides to invest, she expends the optimal efforts x0 and x1.

The entrepreneur has a compound real call option. The exercise price at date 1 is endogenous, however, because it includes the cost of effort, and effort depends on the realized potential value f0V1. Since we use the lognormal, our solutions will resemble the

Black-Scholes formula, with extra terms capturing the cost of effort.

We now derive the first-best investment strategy, solving backwards. Details of this and subsequent derivations are in the Appendix. By date 1, the entrepreneur’s date-0 effort and investment are sunk. Her date-1 NPV is

N P V1M = max[0,maxx

1 (f0f1(x1)V1−g1(x1)−I1)] (4)

The first-order condition for effort is f0V1 =

g1

f1, which determines optimal effort x1 and the

benefit and cost of effort, f1(x1) and g1(x1).

Define the strike value V1 such that N P V1M(V1) = 0. The entrepreneur exercises her

option to invest at date 1 when V1 > V1 and N P V1M >0. This strike value is similar to

the strike price of a traded option, except that the strike value has to cover the cost of the entrepreneur’s effortg1(x1) as well as the investment I1.

At date 0, the entrepreneur anticipates her choice of effort and continuation decision at date 1. She determines the effort level x0 that maximizesN P V0, the difference between the

expected NPV at date 1 and the immediate investmentI0 and cost of effort x0.

N P V0M = max[0,maxx

0 (E0(N P V

M

1 (x0))−g0(x0)−I0)]

E0(N P V1M(x0)) depends on x0 in two ways. First, increasing effort at date 0 increases f0,

and thus increases the value of the startup when it is in the money at date 1. Second, increasing effort at date 0 decreases the strike value V1 for investment at date 1 and makes

it more likely that the startup will continue.

The tradeoff between effort cost and startup value is illustrated in Figure 2. The top payoff line is the date-1 NPV for a call option with no cost of effort. In this case the value would be V1 and the strike price I1. The lower payoff line shows the net NPV when the

entrepreneur exerts less than the maximum effort at date 0 (f0 <1). N P V1 is close to linear

inV1, but the slope and the level ofN P V1 are reduced by the cost of effort. We have added

a lognormal distribution to show the probability weights assigned to these NPVs. The two horizontal lines are the date-0financial investment I0 and the full cost I0+g0 of investment

and effort.

We calculate E0(N P V1) by integrating from V1(x0). Since N P V1M(x0, V1(x0)) = 0, the

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E0(N P V1M(x0)) = g0(x0). From (4) we obtain E0(N P V1M(x0)) =f0 ⎡ ⎢ ⎣ ∞ V1(x0) Π(V)V dV 1 1 +θr θ− θr 1+θr r +θ 1 1+θr r f − θr 1+θr 0 ∞ V1(x0) Π(V)V 1 1+θr dV ⎤ ⎥ ⎦ (5) where Π(V) is the lognormal density and θr =θf/θg.

We solve for x0 analytically, using properties of the lognormal distribution. Then we

evaluateN P VM

0 (x0) = E0(N P V1M(x0))−g0−I0. When N P V0M(x0)>0, the entrepreneur

invests and the firm is up and running.

Table 1 includes typical outcomes from our first-best numerical results. Start with the

first two lines of Panel A, which report Black-Scholes and first-best results when potential value is V0 = E0(V2) = 150 and required investments are I0, I1 = 50, 50. The standard

deviation is σ = 0.4 per period. The effort parameters are θf = 1.8 and θg = 0.6, so the

value added by effort is high relative to the cost. Thus the option to invest in the startup should be well in the money, even after the costs of effort are deducted.

If the costs of effort were zero, first-best NPV could be calculated from the Black-Scholes formula, with a date-1 strike price of V = 50. But when the cost of effort is introduced, V

increases and NPV declines. First-best NPV is 37.90, less than the Black-Scholes NPV by 12.13. The difference reflects the cost of effort and the increase in strike value toV = 55.35.8

Panel B presents typical outcomes for higher standard deviation of σ = 0.8. Panels C and D assume lower investment at date 0 and higher investment at date 1 (I0, I1 = 10, 90).

NPV increases for higher standard deviations and when more investment can be deferred. The first-best initial effort decreases in these cases, though not dramatically. Panels E and F assume θf = 0.6, so that effort is less effective, and also back-loaded investment (again,

I0,I1 = 10, 90).9 First-best effort actually increases, compared to panels C and D, but NPV

declines dramatically.

Figure 3 plots first-best NPV for a wide range of standard deviations and effort parame-ters. Due to exponential function choice, only θr =θf/θg, the ratio of the effort parameters,

matters, so that ratio is used on the bottom-left axis. The ratio is θr = 3 in Panels A to

D of Table 1 and θr = 1.0 in Panels E and F. In Figure 3, θr is varied from 1/11 to 11.

The startup becomes worthwhile, with first-best N P V 0, for θr slightly below 1.0. NPV

increases rapidly for higher values ofθr, then flattens out. NPV also increases with standard

deviation, especially when most investment can be deferred to date 1.

8The eort parameters in Panel A of Table 1 are θ

f = 1.8 and θg = 0.6. Date 0 effort is x0 = 2.4, so f0= 0.99 andg0= 4.59. Of course the date 0 effort is sunk by date 1. From (4),f1∗= 0.978 andg∗1= 3.58.

The breakeven value levelV = 55.35 is determined by 0.99×0.978×55.353.58 =I1= 50. 9We do not include panels for equal investment (I

0,I1= 50, 50) andθf = 0.6, because NPVs are negative

in all cases where outside venture-capitalfinancing is required. A startup with these parameters could not befinanced.

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4

Monopoly Financing and Staged Investment

In this section we formalize the hold-up problem of staged financing. For the analysis of the venture backed startup we assume that the entrepreneur has no wealth (except for the project) and approaches the venture capitalist for financing. We further assume that the project cannot start or continue without the entrepreneur. The entrepreneur’s effort func-tions are the same as before. We treat the venture capitalist’s effort as a{0,1} variable. In effect we assume that if the venture capitalist decides to invest, he will exert the appropriate effort and the cost of his effort is rolled into the required investment at date 0 and date 1. The venture capitalist has a specialized knowledge in the field and acts as a monopolist in the initial stage of financing.

If the investment at date 1 is not made, or if the entrepreneur refuses to participate, the startup is shut down and liquidated. We assume for simplicity that date-1 liquidation value is zero. (It is typically small for high-tech startups.) This assumption simplifies our analysis offinancing. We can treat all convertible preferred shares as if they were common since these shares have value only if converted.

At 0 the venture capitalist and the entrepreneur negotiate the terms of the date-0 financing and the venture capitalist receives series A shares in proportion to his date 0 investment. At date 1 the terms of the new round offinancing are decided and if the project continues the venture capitalist receives his series B shares in proportion to the ratio of the project’s reported value and his date 1 investment. The entrepreneur’s effort and the project value are non-verifiable for a third party such as a court.

Staged financing gives the venture capitalist monopoly power at the date-1 negotiation with the entrepreneur since his refusal to participate in the second round deters other in-vestors from investing and shuts down the firm. Because of his monopoly power, the initial venture capitalist can dictate terms of financing at both date 0 and date 1, subject to the entrepreneur’s participation constraints. He will not exploit all his bargaining power be-cause of the feedback to the entrepreneur’s effort. The timeline of the financing process is as follows:

−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−→

t=0 t=1 t=2

V0 known V1 realized V2 realized

αC

0 is set αC1 is set P =f0f1V2

I0,x∗0 invested if N P V0M ≥0 I1,x∗1 invested if N P V1M ≥0

and N P V0C ≥0 and N P V1C ≥0

First, the entrepreneur (M) goes to the initial venture capitalist (C) to raise startup

financing. The venture capitalist and the entrepreneur negotiates the terms of the date 0

financing and if the venture capitalist is willing to invest, he receives shares in proportion to his date 0 investment. We denote the venture capitalist’s and the entrepreneur’s stakes in the company after the date-0 financing round by αM0 and αC0, respectively. At date 1, V1 is

observed and the venture capitalist and the entrepreneur negotiates the terms of the second round of financing. If the project is shut down at date 1, its liquidation value is zero. We denote by αC1, and αM1 , respectively the venture capitalist and the entrepreneur’s stakes in

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the firm after both rounds of financing is completed. The terms of financing are fixed after date 1. We assume that the entrepreneur’s shares cannot be diluted between dates 1 and 2.

4.1

E

ort and investment at date 1

At date 1 the venture capitalist and the entrepreneur negotiate the second stage offinancing. Both the entrepreneur and the venture capitalist decides whether or not to continue with the project. There are two derivative claims on one underlying asset. Both must be exercised in order for the project to proceed.

At date 1 the entrepreneur decides whether to exercise her option to continue, based on her strike price, the cost of optimal effort g1(x1). But first the parties observe V1 and

venture capitalist sets the terms of the date-1 financing and chooses whether to put up the

financial investment I1. We can focus on the venture capitalist’s decision if we incorporate

the entrepreneur’s response into the venture capitalist’s optimization problem.

The equation for the entrepreneur’s NPV is similar to Eq. (4), except that the second-period investment I1 drops out andfirm value is multiplied by the entrepreneur’s share αM1 .

Recall that αC

1, and αM1 stand for the venture capitalist’s and the entrepreneur’s stakes in

the firm after both rounds offinancing is completed.

N P V1M(αC1) = max[0,maxx

1 (α

M

1 f0f1(x1)V1−g1(x1))] (6)

At date-1 the venture capitalist decides on the terms of the second round of financing. The upper bound on the venture capitalist’s stake after both rounds offinancing are completed is obtained by setting the entrepreneur’s NPV from the project to zero, i.e. N P VM

1 (αC1) = 0.

This defines αC1(max) and αM1 (min). When αM1 (min)≥ αM1 , the entrepreneur will not

par-ticipate.10 The venture capitalist chooses the terms of the date-1financing so that his stake

after the two rounds, αC

1 maximize his date-1 NPV, subject to his and the entrepreneur’s

participation constraints. This constrained maximization problem represents the hold-up problem of staged financing.

N P V1C = max ⎡ ⎣0, max αC 1∈(0,αC1(max)] αC1f0f1(x1)V1−I1 ⎤ ⎦ (7)

If the entrepreneur’s participation constraint is binding, the venture capitalist sets the

financing terms at αC1(max). Otherwise, he accepts a lesser share. In most of our

exper-iments, VC1, the venture capitalist’s strike value for the staged financing case falls in the region αC

1 ∈ 0,αC1(max) where the entrepreneur’s NPV is positive. In these cases the

venture capitalist is better off by taking a smaller share αC

1 <αC1(max) in order to give the

entrepreneur stronger incentives. Nevertheless, those incentives are weaker than first-best, because αM1 (x0)<1, which decreases the expected payoff by reducing x1.

Figure 4 plots values of αC

1 as a function of V1 when I0 =I1 = 50, σ = 0.4,θf = 1.8, and

θg = 0.6, the same parameters used in Panel A of Table 1. The optimal shareα1C is less than

the maximum shareαC1(max) = 1−αM1 (min) for allV1 ≥V

C

, the venture capitalist’s strike

10Whenf

0 is small orV1is low, αM1 (min) may be greater than 1, so that continuation is impossible even

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value at date 1. Notice that the venture capitalist’s optimum share increases as the project becomes more valuable, with a corresponding decline in the entrepreneur’s share. This is typical in all of our experiments of the monopolist venture capital case. This implication of the monopolist venture capitalist case is contrary to the evidence in Kaplan and Str¨omberg (2003), who find that entrepreneurs gain an increasing fraction of payoffs as and if the firm succeeds. This suggests that in venture capital practice staged financing must be combined with other contractual provisions to assure the entrepreneur more favorable terms in later rounds of investment. We will explore such provisions in Section 5 of this paper.

Assuming the αC

1(max) constraint does not bind, we computeV

C

1 by looking for the pair

VC1,αC

1 (V

C

1) that setsN P V1C equal to zero. Investment occurs if V1 > V

C

1. The derivations

of the results is shown in Appendix 8.1.2.

4.2

E

ort and exercise at date 0

In the first round of staged financing, the entrepreneur anticipates the venture capitalist’s date-1 decision in her choice of x0. As in the first-best case, higher effort at t = 0 lowers

the threshold for investment att= 1 (makes it more likely that both the entrepreneur’s and venture capitalist’s options are in the money) and increases the value of the project when the option is in the money.

The entrepreneur’s date 0 value is

N P V0M = max[0,max

x0 (E0(N P V

M

1 (x0))−g0(x0))] (8)

with the first-order condition

E0(N P V1M(x0)) =Π(V1)N P V1M(f0, V1)V1+g0(x0) (9)

Here there are no closed-form solutions. We solve the first-order condition and deter-mine x∗0 numerically. Given x∗0, and assuming that the entrepreneur wants to go ahead

(N P VM

0 (x∗0)>0), the venture capitalist invests if:

N P V0C = max[0, E0(N P V1C(x0))−I0]>0 (10)

Thus two options must be exercised at date 0 in order to launch the startup. The entrepreneur picks x∗0 to maximize the value of her option to continue at date 1, and then

determines whether this value exceeds her current strike price, the immediate cost of effort

g∗

0. The venture capitalist values his option to invest I1 at date 1, taking the entrepreneur’s

immediate and future effort into account, and then decides whether to investI0. Derivations

of these results are presented in Appendix 8.1.2.

We compare the case of staged financing by the monopolist venture capitalist against two benchmarks: thefirst best and a hypothetical date-0 and date-1 competitive financing. Relative to these two benchmarks there is a substantial value loss when staged financing is provided by a monopolist venture capitalist. The venture capitalist’s ability to dictate the terms of date-1financing reduces the entrepreneur’s effort at date 0 as well as date 1, reducing value and increasing the venture capitalist’s breakeven point VC1. A typical comparison of stagedfinancing by a monopolist venture capitalist and the first-best case is shown in Panel

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A of Table 1. When the terms of staged financing are dictated by a monopolist venture capitalist the entrepreneur’s initial effort falls by about 50 percent from the first-best level and the date-1 strike value VC1 increases by almost 30 percent. The entrepreneur’s NPV drops by more than 90 percent. Overall NPV drops by more than half. Similar value losses occur in panels B to F. In Panel E, a startup with first-best NPV of 10.98 cannot be

financed in the monopoly case. NPV would be negative for both the entrepreneur and the initial venture capitalist. This raises the question whether stagedfinancing by a monopolist venture capitalist adds value relative to full upfront financing. We compare these two cases in the next subsection.

4.3

Comparison of investment with and without staged

financing

Does staged financing dominate the alternative of full upfront financing in venture capital contracts? Do the benefits of staged financing outweigh its costs? The benefits of staging are embodied in the efficient continuation decisions it implements. The cost is the hold up problem of staged financing. When full upfront financing is provided, then the hold-up problem will not arise. This is the benefit of full upfront financing. The cost of full upfront

financing is that continuation decisions by the entrepreneur will be inefficient. Which of these two problems are more severe will determine whether or not stagedfinancing actually adds value.

In this section we compare staged financing and full upfront financing by a monopolist venture capitalist. When the project is fullyfinanced is upfront, the entrepreneur and venture capitalist bargain only once at date 0 over the terms of the financing, αM and αC. These

terms are thenfixed for dates 1 and 2. The entrepreneur calculates her NPV at date 1 just as in the monopoly case with staging, but her stake is predetermined. She ignores the financial investment I1 and continues at date 1 so long as her NPV exceeds her cost of effort, g1(x1).

The venture capitalist retains monopoly power over financing at date 0, but loses all his bargaining power at date 1. He setsαC to maximize his NPV at date 0, taking into account the effects of his choice on the entrepreneur’s effort at dates 0 and 1. His maximization problem is identical in appearance to Eq. (10) but the values ofx∗

0, x∗1 and αC are different.

The entrepreneur’s date-0 maximization problem closely resembles Eq. (8) except for the choices ofx∗

1andαC. If both parties’ participation constraints are met at date 0 (N P V0C ≥0

and N P VM

0 ≥ 0), the startup is launched. The solutions to the full upfront financing case

are presented in Subsection 8.1.3. of the Appendix.

Table 1 and Figures 5, 6, 9 and 10 illustrate the numerical results. Panel A of Table 1 shows a typical scenario. For a wide range of parameter values the hold up cost is so severe that it overhelms the option-like benefits of staged financing. Here the value loss from the holdup problem actually exceeds the cost of inefficient continuation in the no-staging case. The NPV to the entrepreneur more than doubles in the full upfrontfinancing case compared to the staged investment, and overall NPV increases from 16.47 to 26.89. It is as if the “side-effects” of the “medication” (the hold up costs of stagedfinancing) are more “deadly” than the “disease” (inefficient investment decisions) it meant to “treat”.

Figures 5 and 6 compare the NPVs for the entrepreneur and monopolist venture capitalist with and without staging against effort returns and the standard deviation of the project returns. Figure 5 assumes equal investment in both periods (I0, I1 = 50, 50). Here NPV

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is higher without staging, except at extremely high standard deviations. Figure 6 assumes back-loaded investment (I0,I1= 10, 90), which adds to option value and the value of staging.

In Figure 6, full upfront financing still dominates staged financing for a range of parameter values but this range is much smaller and there is a downward shift in the breakeven between staging and full upfrontfinancing relative to Figure 5 with respect to the standard deviation of project returns.

Figure 9 and 10 compares the net present value loss at date 0 relative to the first best for the staged financing and full upfront financing cases. The NPV loss is expressed as a percentage of total required investment and plotted against effort returns for representative values of standard deviations of project returns. For financing rounds of equal size the value loss is greater for staged investments than for full upfront financing in all of our cases (reported and not reported). When investment is back-loaded, then the NPV loss for projects with highly variable returns is higher in the full upfront financing case, for other projects the NPV loss is higher in the stagedfinancing case.

Thesefindings can be interpreted at least two ways. First, venture capitalists benefit from staged financing in practice because they only invest in projects with standard deviations above the breakeven values that we calculated. For these projects the benefits from im-proved continuation decisions always outweigh the hold up costs. This interpretation, while plausible, does not help to explain the co-existence of multiple provisions in venture capital contracts. The second interpretation offers such a rationale. According to this interpreta-tion, the benefits of staged financing outweigh the costs because venture capital contracts include provisions that are effective in dealing with the hold up problem of stagedfinancing. In the next section we will show how a particular covenant that is common in venture capital partnership agreements alleviates the hold up problem of stagedfinancing.

5

Syndication of Later-stage Investments

As we have demonstrated in the previous section staged financing may actually exacerbate the effort provision problem. Both parties may be better off if the venture capitalist could promise ex ante not to hold up the entrepreneur ex post. Such promise is not credible, however, since effort and potential value are non-contractible. A credible commitment not to hold up the entrepreneur is full upfront financing but this means giving up the option value of shutting down non-performing projects early.

Suppose that the initial venture capitalist can commit (explicitly or implicitly) to bring in a syndicate of new investors for the second round of financing. Assume that the syndicate is fully informed. Consider the limiting case in which only the syndicate participates in the series B financing. Obviously, these investors will have the same incentive to hold up the entrepreneur and dilute his shares in the series B round as the incumbent in the monopolist venture capitalist case. However, the syndicate’s presence in the series B financing changes the incumbent venture capitalist’s date-1 incentives. As a series A investor, the incumbent venture capitalist’s interest is now well aligned with the entrepreneur’s and therefore he is no longer inclined to holding the entrepreneur. In the limiting case, any change in the relative valuation of the series A and B rounds would hurt the incumbent venture capitalist at least as much as the entrepreneur (at least as much because the entrepreneur’s dilution has a

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negative feedback effect via her effort provision on the initial venture capitalist’s holding). When the initial venture capitalist co-invests with the syndicate, his interest is not per-fectly aligned with the entrepreneur’s. Nevertheless, his incentive to hold up the entrepreneur is reduced relative to the monopolist venture capitalist case. The degree of the hold up prob-lem will depend on how a unit change in the terms of the series Bfinancing affects the wealth of the incumbent venture capitalist. The larger is the syndicate’s stake in the series B fi -nancing the better off the entrepreneur. In the limiting case the initial venture capitalist sets the terms of the series B financing so that the syndicate’s participation constraint will be binding and the syndicate will receive zero NPV. When the initial venture capitalist and the syndicate co-invest at date 1, the syndicate may enjoy positive NPV but always strictly less than what the incumbent can guarantee himself in the monopolist venture capitalist case. Thus, syndication of later stages of investment serves as a mechanism that restrains the initial venture capitalist’s temptation to hold up the entrepreneur and alleviates the hold up problem of staged financing. Subsections 5.1, 5.2 and 5.3 present the mathematical arguments and derive the results.

Syndication of later stagefinancing is common practice. In later rounds the original ven-ture capitalist brings in other venven-ture capitalists that he worked with in the past, funds that specialize in later-stage investments, or occassionally, some of the original limited partners of his fund (Lerner (2004)). We suggest that syndication of later stage investments by venture capital funds is induced in practice by a covenant in partnership agreements between venture capital firms and their limited partners which prohibits funds from investing more than a small percentage (typically 5 percent) in any portfolio company (Sahlman (1990)). We view this covenant as a commitment device that assures that date-1 syndication is credible and fully anticipated by the entrepreneur ex ante.

The model of date-1 syndicate financing is as follows. At date 0 the entrepreneur an-ticipates that the incumbent venture capitalist will bring in a syndicate of other venture capitalists to take part in the series B financing. The incumbent venture capitalist will set the terms of date-1financing. The syndicate will own series B shares, the entrepreneur owns series A shares and the incumbent venture capitalist owns either series A shares or a combi-nation of series A and series B shares. We denote by αS

1 the fraction of the company owned

by the syndicate of new investors following the date-1 round offinancing. The notationsαM

1

and αC

1 stand for the fraction of the company owned by the entrepreneur and the original

venture capitalist following the series B investment. Note that αM

1 may differ from αM0 due

to the syndicate’s participation in the date-1 round and possible dilution or reverse dilution of the series B financing. Note also that αM

1 +α1C+αS1 = 1.

5.1

E

ort and investment at date 1

For a given shareαM

1 , the entrepreneur’s NPV and maximization problem at date 1 are the

same as in the monopoly case. We obtain x1,f1, g1, andN P V1M(αS1) exactly as in Eq. (6),

but withαM

1 =αM0 (1−α1S). For the limiting case in which only the syndicate participates in

the series B round of financing, the incumbent venture capitalist who maximizes his payoff

subject to the participation constraints of the entrepreneur and the syndicate will set the syndicate’s share αS

1 so that I1 =α1Sf0f1(x1)V1. Investment at date 1 occurs for V1 ≥ V

S

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We solve for the cutoff value of date-1 investment in the syndicate case, VS1 by finding the value of αS

1 that maximizes N P V1 subject to the syndicate’s participation constraint. The

derivations of the mathematical formulas are presented in Appendix 8.1.4.

Figure 7 plots ownership shares against value at date 1 for the date-1 syndicate financing case when (I0, I1) = (50,50), σ = 0.4, θf = 1.8 and θg = 0.6, the parameters in Panel A

of Table 1. The curve αM AX shows the syndicate’s maximum shares if the syndicate were

given free rein to maximize their NPV. The curve αF OC represents the syndicate’s shares if

the incumbent venture capitalist sets the terms of the date-1 financing by maximizing his NPV. As we can see on Figure 4, forV1 ≥V

S

1 the syndicate’s share declines as V1 increases.

The shares held by the entrepreneur and incumbent venture capitalist therefore increase as performance improves, consistent with the evidence in Kaplan and Str¨omberg (2003) and contrary to the pattern in the monopoly case.

One might expect the better financing terms in the date-1 syndicate case to decrease the strike value VS1 relative to V1 from the monopoly case. But the strike value is actually

higher in the syndicate case — for example, it is 84.9 in Figure 7 and 70.8 in Figure 4. The value realizations that fall in between correspond to projects that can continue only if the incumbent venture capitalist accepts a smaller share to provide additional incentives for the entrepreneur. In the monopolist venture capital case the incumbent voluntarily dilutes his shares at date 1 to move these projects forward. Since in the date-1 syndication case the incumbent venture capitalist cannot unilaterally reset his shares at the series B financing round, projects with low date-1 value realizations, V1 < V

S

1, will be shut down.

Thus the commitment to syndicate later-stage financing has two countervailing effects. On the one hand, there is a higher threshold for investment, so that marginal projects will be rejected more often. On the other hand, syndication provides better incentives for the entrepreneur, so that low values of f0V1 are less likely. Our numerical analysis shows that

the second effect outweighs the first and syndication of later stage investment always adds value.

5.2

Renegotiation at date 1

Of course, realizations of V1 ∈ [V1;V

S

1) could trigger renegotiation between the

incum-bent venture capitalist and the entrepreneur to reset the incumincum-bent’s share before syndicate

financing is sought. For example, the incumbent venture capitalist could provide bridge

financing on terms favorable to the entrepreneur, or the entrepreneur could be given addi-tional shares or options in a “down round” — a round of financing where new investors buy in at a price per share lower than in the previous round. As our numerical experiments for the syndicate case show, the gains from such renegotiation are small. For example, renegoti-ation gains would increase the NPVs reported in Table 1 by about 2% of the required total investment.11

11We approximate renegotiation gains (holdingαC∗

0 andx0constant) by solving for (1) the value realization

at which the venture capitalist will start to reduce his share; (2) the new strike value and (3) the integral of NPV changes over this range. Only a small portion of the renegotiation gains come from more efficient continuation decisions (VS1(R)< V1< V

S

1). Most of the gains can be attributed to better effort incentives

(higherx1) in the region where the project continues regardless (V1> V S

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While renegotiation adds value ex post by improving effort and preserving access to

financing, one might worry that the flexibility to reset shares at date 1 could distort the initial venture capitalist’s incentives ex ante. Fortunately, this problem does not arise in our model, since ex ante the incumbent venture capitalist would be better offif he could give up his bargaining power ex post.

5.3

E

ort and exercise at date 0

Here we compute the date-0financing terms set by the initial venture capitalist in anticipa-tion of the date-1 syndicate investment. At date 0, the venture capitalist chooses αC

0 and

the entrepreneur decides how much effort to exert. Given αC0, the entrepreneur chooses x0

to maximize:

N P V0M(αC0) = max[0,maxx

0 (E0(N P V

M

1 (x0(αC0),αC0)−g0(x0(αC0)))] (11)

The entrepreneur anticipates the syndicate’s share αS1 as a function of date-1 value V1. For

a given αC

0, date-1 syndicate financing will result in less dilution of her share than in the

monopoly case, so she provides higher effort att= 0 as well as at t= 1. We cannot express NPV or effort in closed form, so we compute them numerically.

The venture capitalist anticipates the entrepreneur’s reaction when he sets αC0. He must

restrict his search to αC0 ∈ 0,αC0(max) , where αC0(max) is determined by

E0(N P V1M(x0(α C 0(max)),α C 0(max))−g0(x0(α C 0(max)))) = 0 (12)

This constraint rarely binds, since at the margin there is almost always value added by leaving positive value to the entrepreneur. Thus αC∗

0 is determined by αC0 = arg max αC 0∈(0,αC0(max)] E0(N P V1C(x0(α C 0),α C 0))−I0 (13)

If N P V0C ≥ 0, investment proceeds. The derivations of these results are presented in

Ap-pendix 8.1.4.

Typical results for syndicate financing are shown in Table 1. Effort and value increase across the board, despite increases in the strike value VS1 from the monopoly case. We find that syndicate financing dominates monopoly financing with or without staged financing. Syndicatefinancing is better ex ante for the initial venture capitalist and also increases overall NPV. This is true for all parameter values, including values outside the range reported in Table 1.

Figures 9 and 10 compare value losses for the staged financing, no-staging and date-1 syndication cases over a wide range of the effort parameter θr. Value loss is defined as the

difference between NPV at date 0 and first-best NPV. Note that value losses may increase with standard deviation in the monopoly and syndication cases, at least for the region whereθr is about 1.0 and higher. It appears that increased uncertainty makes the incentive

problems worse, because more uncertainty can lead to lower initial effort. When overall NPV is near zero, the entrepreneur’s effort x0 increases rapidly with σ. The more uncertainty,

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the greater chance that the entrepreneur’s call option will be in the money and the greater the marginal reward to effort. But asθr increases and NPV rises, effort eventually declines

as σ increases, because the marginal impact of effort is less. Compare the bottom-left and bottom-right panels in Figure 9, for example. The effects of volatility on effort and value can also be seen in panels E and F of Table 1. In the syndicate case, the value loss in panel E, with σ = 0.4, is 10.98 - 1.55 = 9.43. In panel F, with σ = 0.8, value loss is 27.72 - 17.50 = 10.22. Initial effort falls from x0 = 3.05 in panel E to x0 = 2.80 in panel F.

Notice that the value losses increase rapidly with θr when θr is below 1.0, but the losses

are always less in the syndication case than in the monopoly cases. Thus, syndication of later-stage financing creates value. It does so by alleviating the hold up problem. When the later financing rounds are syndicated, then the incumbents share the benefits from granting the venture capitalist the option of shutting down non-performing projects early but they do not bear the associated hold up costs.

5.4

Syndication with asymmetric information

So far we have assumed that the incoming syndicate investors and the incumbent venture capitalist are equally informed. Now we consider asymmetric information between the in-cumbent and new investors.

Both the incumbent and entrepreneur want the syndicate to perceive a high valueV1. The

more optimistic the syndicate, the higher the ownership shares retained by the incumbent and entrepreneur. Increasing the entrepreneur’s share also increases her effort. Therefore, mere announcements of “great progress” or “high value” coming from the entrepreneur or incumbent are not credible.

Credibility may come from the incumbent’s fractional participation in date-1 financing. Suppose the incumbent invests βI1 and the outside syndicate the rest. What participation

fraction β is consistent with truthful revelation of V1? If we could hold the entrepreneur’s

effort constant, we could rely on Admati and Pfleiderer’s (1994) proof thatβ should befixed at the incumbent investor’s ownership share at date 0, that is, at αC0. This fixed-fraction

rule would remove any incentive for the incumbent to over-report V1. (The more he

over-reports, the more he has to overpay for his new shares. Whenβ =αC

0, the amount overpaid

cancels out any gain in the value of his existing shares.)12 The fixed-fraction rule would also insure optimal investment, since the incumbent’s share of date-1 investment exactly equals his share of thefinal payoffV2. Admati and Pfleiderer also show that no otherfinancing rule

or procedure works in their setting.

Fixed-fraction financing does not induce truthful information revelation in our model, although a modified fixed-fractionfinancing works in some cases. The problem is the effect of the terms of date-1financing on the entrepreneur’s effort. Suppose the incumbent investor takes a fractionβ =αC

0 of date-1financing and then reports a value ˆV1that is higher than the

true value V1. If the report is credible, the new shares are over-priced. The incumbent does

not gain or lose from the mispricing, becauseβ =αC

0, but the entrepreneur gains on his old

12Thefixed-fraction rule would also remove any incentive to underreport. The more the incumbent

under-reports, the more he gains on the new shares. But the amount of profit made on the new shares is exactly offset by losses incurred on existing shares.

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shares at the syndicate’s expense. Since the entrepreneur’s ownership share is higher than it would be under a truthful report, she exerts more effort, firm value increases, and both the entrepreneur and incumbent are better off. Therefore the incumbent will over-report.

A modified fixed-fraction rule can work, however, provided that β is set above αC

0 and

effort is not too sensitive to changes in the entrepreneur’s NPV at date 1. The required difference between β and αC

0 depends on the responsiveness of the entrepreneur’s effort to

her ownership share. (For formal details see Appendix 8.2.) In many cases, a constantβ set a few percentage points above αC0 removes the incentive to overreport over a wide range of

V1 realizations. But this rule may break down as a general revelation mechanism in at least

three ways.

First, when V1 is low but exceeds V1, we find situations where the required β exceeds

1. This would make sense only if the new syndicate investors could short the company, so we must constrain β < 1. This outcome is common in our numerical results, because the incumbent’s initial share αC

0 is frequently above 85% - 90%, and in some of these cases the

entrepreneur’s effort is very sensitive to the value of her stake in the firm. There is not much room forβ to increase between these starting points and a maximum level strictly less than 1. When β hits the maximum, the modifiedfixed fraction rule fails to induce truthful revelation. This failure is less frequent if the entrepreneur has some personal wealth and can co-invest with the venture capitalist at date 0. The coinvestment reduces the venture capitalist’s ownership share and provides more room for β to increase to a maximum level strictly less than 1.

Second, the modified fixed fraction rule also fails when V1 falls just below V

C

1. In this

case the incumbent’s incentive to over-report becomes very strong, and only extremely high

βs can discipline the incumbent to tell the truth. This problemflows from the discontinuity of the entrepreneur’s effort at the strike value VC1. Here the limit of β as V1 approaches

VC1 from below is infinity and no fixed-fraction rule works. This problem can be solved, however, if the incumbent and the entrepreneur renegotiate their ownership shares when

V1 falls between the monopoly and syndicate strike values V

C

1 and V

S

1. If the incumbent

venture capitalist renegotiates, the lower strike value removes the discontinuity of effort. As the incumbent’s share declines, it is easier to find a β <1 that works.

The third problem arises at high levels of V1. Setting β > αC0 gives the incumbent

venture capitalist an incentive to under-report V1. The incumbent would gain more from

underpricing the new shares and buying them cheaply than he would lose from dilution of his existing stake. Revelation works only if this incentive is offset by the impact on the entrepreneur’s effort. But as V1 and ˆV1 increase, effort becomes higher and less sensitive to

the terms of financing. As effort tops out, the incentive to under-report takes over. This could be preventedlocally by allowingβto decrease with ˆV1, returning toβ=αC0 at very high

values. But then the almost-fixed fraction rule fails globally to induce truthful information revelation, because at lower V1 realizations he wants to over-report to these higher levels at

which β =αC

0.

One possible solution, not fully explored here, is to introduce more complex contracts that allow signalling along two dimensions. For example, the incentive for the incumbent venture capitalist to under-report at high levels ofV1 could be offset by an incentive contract

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that grants the entrepreneur extra shares if the incumbent reports very high project value. With this additional provision in place, it should be possible to allow β to decrease with

ˆ

V1, reaching β = αC0 at high values of V1. This could be one justification for contingent

share awards to entrepreneurs, as observed in Kaplan and Str¨omberg (2003). Alternatively, entrepreneurs could be granted a series of stock options with increasing exercise prices, so that their final ownership share increases at high values of V2.

Even if the modified fixed fraction rule fails, there may be other ways to convey V1.

Syndicate members could estimate V1 from conditions at date 0, the entrepreneur’s effort

functions and the entrepreneur’s and incumbent venture capitalist’s decision rules, given the anticipated terms of date-1 financing. But since syndicate members do not know the true value V1, their new financing is overpriced when V1 is low and underpriced when V1 is high

(Myers and Majluf (1984)). This leads to more effort whenV1 is low and less when it is high,

compared to the full-revelation case. Alternatively, the value of the incumbent investor’s reputation could generate truthful reports in a repeated game setting, for example. Since the syndicate usually includes other venture capitalists that the incumbent has worked with in the past and expects to work with in the future, truthful information revelation can arise as a tacit collusion equilibrium.

6

Debt

fi

nancing

This paper argues that staged financing alleviates the effort provision problem by trading it off for the hold-up problem. The hold-up problem arises independently from the type of financing used because staged financing gives disproportionate bargaining power to the series B investor against the entrepreneur. However, the degree of the hold-up problem may depend on the type of financing. After all, traditional agency models suggest that debt

financing calls forth maximum effort, because when debt is issued, the entrepreneur retains the maximum fraction of the value added at the margin by her effort. In our original model the entrepreneur and the venture capitalist receive equity shares, convertible preferred stock or convertible debt for their effort and financial investments. Because the project has no liquidation value at date 1, convertible preferred equity, convertible debt and common equity are equivalent but not straight debt.

In this section we revisit our original model and assume that the entrepreneur and the venture capitalist write straight debt contracts at date 0 and date 1. The face value of the debt equals the required investment. Of course, this debt faces a high probability of default, so the promised payoff, including interest, is well above face value. If the project’s date-2 value falls below its promised payoff, then the entrepreneur defaults and receives nothing. If there is any value in the project, it belongs to the venture capitalist. Above the promised payment, the entrepreneur receives the residual. Since debtfinancing converts the entrepreneur’s stake to a call option, our discussion of debt financing also applies if the entrepreneur receives no shares but only options.

Now consider the monopolist venture capitalist case, holding all aspects of the model constant, except that at date 0 and date 1 the venture capitalist and entrepreneur negotiate promised debt payoffs K0 and K1 where K1 denotes the total debt outstanding after the

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