Leslie M. Marx University of Rochester
Contract Renegotiation for Venture Capital Projects
Xxxxxx X. Xxxx University of Rochester
March 1999
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1 Fntroduction
This paper examines the contracting problem faced by entrepreneurs and venture capitalists hen negotiating the financing arrangements for venture capital projects. Venture capital projects are typically financed ith a mixture of debt and equity. This paper examines the strategic behavior of venture capitalists and entrepreneurs
hen venture capital projects are financed in this ay.
The most common security used in venture capital financing is convertible pre- ferred stock. Although convertible preferred equity typically specifies a fixed con- version rate and dividend, these terms may be, and often are, renegotiated once the project is under ay. Some venture capital financing does not involve explicit dividend requirements, but requires fixed payments through contracts that require interest payments or a repayment of the initial investment. Any contract that re- quires a fixed payment to the venture capitalist before allo ing the remaining payoffs to be shared proportionally bet een the venture capitalist and the entrepreneur falls
ithin the scope of this study.
F present a principal-agent model in hich a venture capitalist and entrepreneur enter a contractual relationship, hich can (and in some states ill) be renegotiated after information is revealed about the initial progress of the project. F sho that, in equilibrium, hen renegotiation occurs, it results either in the forgiveness of part of the entrepreneur's debt obligation or a reduction in the debt obligation together ith an increase in the equity share of the venture capitalist. The results of the model fit
ell ith the stylized facts of venture capital financing.
Ft is typical for the behavior of venture capitalists and entrepreneurs to vary based
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on the level of success or failure of their projects. When a project proceeds as hoped, the venture capitalist remains distant and allo s the entrepreneur to make decisions for the project on his o n. Ff a project is not quite on target, there may be some renegotiation of the initial contract, typically in the direction of increasing the venture capitalist's proportional share in the project and decreasing required fixed payments. Although cash-flo constraints are a major reason for this type of renegotiation, the model developed in this paper sho s that this type of renegotiation can be expected for strategic reasons even in the absence of interim cash-flo constraints. Finally,
hen a project is going badly, the venture capitalist may step in and take over control of the project. The venture capitalist may do this herself or hire someone else to take over the decision making for the project.
As part of the financing arrangement, venture capitalists usually obtain inside management rights. These may include the right to appoint one or more directors or to serve as an officer of the company.2 Xxxxxxx (1997) sho s that, in a sample of fifty convertible preferred equity venture investments, contracts usually explicitly allocate control rights to the venture capitalist, including giving them enough board seats to control the board of directors. Xxxxxxx (1990, p.508) states that,
Venture capitalists sit on boards of directors, help recruit and compensate key individuals, ork ith suppliers and customers, help establish tactics and strategy, play a major role in raising capital, and help structure trans- actions such as mergers and acquisitions. They often assume more direct control by changing management and are sometimes xxxxxx to take over day-to-day operations themselves.
Xxxxx (1986, pp.8-9) comments on the relationship saying, “The matter of control has become one of the crucial ’sticking points' bet een entrepreneurs and venture capitalists. The entrepreneur ants to maintain the independence of his company
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free of outside control. But to get the vital initial capital to finance the venture, they usually must compromise their independence some hat.“ When things are proceeding reasonably ell in the underlying business, arrangements bet een venture capitalists and entrepreneurs allo each to advance the interest of the other merely by follo ing their o n self interests. But hen things go badly, the interests of the t o parties diverge.
As an illustration of the kinds of contracts that are used and the frequency and types of renegotiation, consider a sample of fifteen venture-backed companies that held FPOs during Iune-September 1997. These firms all achieved some measure of success since they all reached the point of holding a public offering, but the public nature of the prospectuses allo s us to obtain information on the firms' financing arrangements. All fifteen firms ere financed ith a mixture of debt and equity.e Seven of the firms had, prior to their FPO, renegotiated some feature of their financing, including: the conversion of payables to preferred stock or convertible preferred stock, the forgiveness of debt, and the aiver of debt compliance provisions. Four of the firms issued common or preferred stock or stock options in exchange for services or equipment. There ere no instances revealed in the prospectuses of the conversion of equity to debt or the reduction of the venture capitalists' equity shares in the projects.
Similar renegotiations (conversions of notes to equity and forgiveness of debt) are found in the investments of a large Texas venture capital fund that agreed to share its investment history from 1993-1996. Fn addition to successful investments, the investment history for the Texas fund also contains information on failed investments.
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During 1993–1996, the company rote off three of its thirty-eight investments as complete failures and disposed of its interest in t o investments at a loss. Again, although there ere conversions of debt to equity and the forgiveness of debt, there
ere no instances of the conversion of equity to debt or the reduction of the venture capitalists' equity shares in the projects.
Fn Section 2, F describe some related literature. Fn Section 3, F describe a model of venture capital contracting. Fn Section 4, F present the analysis of the model and a characterization of the equilibrium behavior of the venture capitalist and en- trepreneur. Section 5 concludes.
2 Related literature
A number of authors develop models of venture capital contracting.D Authors such as Xxxx, Xxxxxxx, and Xxxxxx (1990) study a ealthy entrepreneur's decision hether to involve an outside investor. Xx Xxxx, et al. (1990), the entrepreneur can finance his project ith his o n funds (or a fully collateralized loan) or sell out completely to an outside investor. Fn this paper, in contrast, the decision to involve an outside investor is not modeled, but rather is assumed to be necessary, and a range of financing arrangements are considered, including risky debt, equity, and mixtures of the t o.
Another general category of papers examines the circumstances that determine
hen a project that requires multiple rounds of investment should be continued and
hen it should be terminated. Kxamples of research on this topic include Admati and Pfleiderer (1991), Xxxxxx (1991), and Xxxxx (1994). Xxxxxx and Pfleiderer (1991) conclude that pure equity financing should be used, xxxx Xxxxxx (1991) concludes that the optimal contract is a complex financial arrangement similar to convertible preferred equity but has no conversion in equilibrium.
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The model of Xxxxxxxx (1998) sho s that an entrepreneur may voluntarily re- linquish control rights over his project to the venture capitalist hen the venture capitalist must be given incentives to engage in costly search for a ne CKO for the project. Other papers that describe ho venture capitalists retain control rights over projects include Xxxxxxxxxx (1988), Xxxxxxx (1990), Xxxxxxx (1995), and Xxxxxx (1995).
Another category of papers compare payoffs and control outcomes under different types of contracts, but do not attempt to characterize the optimal contract, e.g., Xxxxxxx (1993), Bergl¨of (1994), and Xxxxxxxx and Xxxxx (1997). The model of Berglo¨f (1994) sho s that debt and equity are complementary in an environment in hich control issues are important. Both Xxxxxxx (1993) and Berglo¨f (1994) sho that contracts more complicated that simple debt or equity are preferred. Xxxxxxxx and Xxxxx (1997) sho that, in an environment ith staged financing, convertible debt is better than a mixture of debt and equity because it reduces the entrepreneur's incentives to focus his effort on the short-term success of the project. Fn this paper, F consider only one round of financing. Xx Xxxx (1998), a contract involving both debt and equity components, is sho n to obtain the first best in a model ith one round of financing since the debt level can be chosen to balance the venture capitalist's ability to intervene in the project against the entrepreneur's desire for control over the project. Fn contrast, this paper takes as given the use of financing that is a mixture of debt and equity, and examines the implications of this type of contract for efficiency and for the incentives and behavior of the venture capitalist and entrepreneur.
3 Model
Fn this section, F present a model of venture capital contracting. The model has three periods, t = 0, 1, 2 as sho n in the timeline belo . The entrepreneur, ho is either a good type or a bad type, contracts ith the venture capitalist in order to obtain
investment capital for his project. During the initial contracting period, the venture capitalist cannot observe the entrepreneur's type. The entrepreneur and venture capitalist contract over three elements: (i) the initial investment by the venture capitalist, (ii) the sharing rule for the final return of the project, and (iii) the venture capitalist's control over the project. An initial investment of I is required. The sharing rule must respect the entrepreneur's ealth constraint, i.e. must not specify a payment to the venture capitalist that is greater than the project's return. And the venture capitalist's right to exert control over the project must be all or nothing, although, hen the venture capitalist is granted the right to intervene, she need not exercise that right.
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At t = 0, the entrepreneur makes a contract offer to the venture capitalist, hich the venture capitalist must accept or reject. The contract specifies the venture capi- talist's control rights and the share of the profits that the venture capitalist receives in exchange for her initial investment in the project of I.
At t = 1, information about the potential success of the project becomes available.
This information, referred to as the state, is observed by the entrepreneur and the venture capitalist but is nonverifiable. The state is denoted by w and is assumed to be an element of the real interval ▲, hich has finite lo er bound w. Ff w > w , then w is a “better“ state than w in the sense that returns in state w first-order stochastically dominate returns in state w . For a good entrepreneur, F assume a probability distribution for w ith full support, finite first moment, and no mass points. For a bad entrepreneur, F assume the state is w ith probability one. Other than the different distributions over states, good and bad entrepreneurs are identical.
After the state is revealed, the contract can be renegotiated. Fn the renegotiation phase, the venture capitalist makes a take-it-or-leave-it offer to the entrepreneur. Ff the venture capitalist's offer is rejected, she may still choose unilaterally to make changes in the terms of the contract that “favor“ the entrepreneur, such as forgiving part or all of the entrepreneur's debt obligation or giving up some of her equity share in the project.
After renegotiation is concluded, a venture capitalist ith control rights can choose to intervene in the project at cost s ≥ 0 to herself. A venture capitalist ithout control rights may not intervene. Ff the venture capitalist intervenes, then the venture
capitalist chooses the strategy herself. F assume that the entrepreneur, or the venture capitalist if she is in control, can choose a standard strategy, hich e can think of as the one that maximizes the expected payoff of the project, or a risky strategy, xxxx has lo er expected payoff and increases the probability of both the orst and the best outcomes for the project. The entrepreneur's choice of strategy is not observable.
At t = 2, the project's payoff is realized. Ff the standard strategy as used, the project's payoff is dra n from the cumulative distribution function J (· | w). Ff the risky strategy as used, the project's payoff is dra n from the cumulative distribution
function G(· | w). Distributions J (· | w) and G(· | w) are assumed to be absolutely continuous and to have continuous density functions ƒ(·| w) and g(·| w), respectively. The support of both ƒ(· | w) and g(· | w) is [0, y¯(w)], here y¯(w) is increasing in w. This assumption implies that there is al ays positive probability of lo returns and
that, given the state, the risky and standard strategies produce returns in the same range.
The assumption that the risky strategy is al ays suboptimal, in that it generates lo er expected return in every state, is formalized in Assumption 1.
Assumption 1 For all w c ▲,
, +7E/ yg(y | w)dy < , +7E/ yƒ(y | w)dy.
f f
The assumption that the risky strategy places higher eight on the orst and best outcomes relative to the standard strategy is captured by Assumption 2 and illus- trated in Figure 1.
)(⋅_ω)
*(⋅_ω)
ω \
\
Figure 1: Judsk ri J (y | w) dqg G(y | w) dv ixqfwlrqv ri y.
Assumption 2 For all w c ▲, there enists y/ c (0, y¯(w)) sush that G(y | w) > J (y |
w) if and only if 0 < y < y/ .
Finally, in Assumption 3, F assume that the project's expected payoff under the standard strategy exceeds the required initial investment. And, so that it is not efficient for venture capitalists to finance bad entrepreneurs, F assume that the ex- pected return for bad entrepreneurs, even under the standard strategy, is less than the required initial investment.
Assumption 3 E
k, l
+7E/ yƒ(y | w)dy
≥ I and
, +7E/ yƒ(y | w)dy < I.
/ f f
As mentioned in the introduction, F take the contract form as fixed. F focus on contracts that can be characterized as a mixture of debt and equity financing, hich
is typical of venture capital financing. F define a mined debt−equity sharing rule ith
dividend v ≥ 0 and share c [0, 1] by s(y | v, ) Ξ min{y, v + (y — v)}. A mixed debt-equity sharing rule, sho n in Figure 2, can also be xxxxxx as
,
? y, y < v
s(y | v, ) = ,
v + (y — v), y ≥ v,
so it can be vie ed as a fixed dividend payment v in conjunction ith a proportional sharing rule for returns in excess of the dividend. Ff = 0, then the mixed debt-equity sharing rule is actually a debt sharing rule, and if v = 0 and c [0, 1], then it is an
equity sharing rule.
VORSH γ
VORSH
V(⋅_Y γ )
\
Y
Figure 2: Judsk ri pl{hg ghew0htxlw| vkdulqj uxoh s(y | v, ) dv d ixqfwlrq ri y.
Since a mixed debt-equity sharing rule is concave, a venture capitalist ho re- ceives payment s(y | v, ) hen a project's profit is y is risk averse. Similarly, an
entrepreneur xx receives payment y — s(y | v, ) hen a project's profit is y is risk
loving.
Fn a model such as this one, in hich returns are available in only one period, a mixed debt-equity sharing rule captures the basic characteristics of convertible
preferred equity financing. With returns possible only at t = 2, the decision to allo dividends to accrue and decisions on the timing of conversion can be ignored. One can vie v as the level of accrued dividends at t = 2. When the project's return at t = 2 is less than the level of accrued dividends, the holder of preferred shares has priority and receives all of the project's returns. When the project's return is greater than the accrued dividends, the investor receives the accrued dividends and converts her preferred stock into the fraction of the common stock in the venture, hich has value (y — v).
4 Results
Fn this section, F first examine the players' choices of the standard or risky strategy, then the renegotiation and intervention stage, and finally the entrepreneur's initial contract offer. The propositions characterize a perfect Bayesian equilibrium of the game. F focus on the equilibrium that involves the least amount of renegotiation, i.e., F focus on the equilibrium that involves forgiveness of contract terms by the venture capitalist only hen that makes her strictly better off and that, hen renegotiation occurs, involves the smallest possible changes to the terms of the contract.
5tandard and Rishy 5trategies
Ff, after the state is revealed, the venture capitalist intervenes, then the venture capitalist chooses bet een the standard and risky strategies. The venture capitalist is assumed to maximize her expected payoff. The venture capitalist's payoff under a mixed debt-equity contract ith dividend v and share , conditional on the standard
strategy, is
,
,
? +7E/ yƒ(y | w)dy, if v ≥ y¯(w)
v(w, v, | s) Ξ ,
f
,
yƒ(y | w)dy +
, +7E/ (v + (y — v))ƒ(y | w)dy, other ise,
f
and the venture capitalist's payoff conditional on the risky strategy is
, ,
?
v(w, v, | r) Ξ
+7E/ yg(y | w)dy, if v ≥ y¯(w)
f
, , yg(y | w)dy + , +7E/ (v + (y — v))g(y | w)dy, other ise.
f
Given these payoff functions, the venture capitalist is risk averse, and so al ays prefers the standard strategy. More formally, by Assumption 1, the standard strategy has higher expected payoff, and by Assumption 2, the risky strategy is riskier in the sense of second-order stochastic dominance. Then the concavity of the venture capitalist's payoff function implies that the venture capitalist has higher expected payoff under the standard strategy.
Ff, after the state is revealed, the venture capitalist chooses not to intervene, then the entrepreneur decides hether to pursue the risky strategy or the standard strategy. The entrepreneur chooses the strategy that gives him the higher expected return. F assume the entrepreneur chooses the standard strategy if he is indifferent bet een the t o strategies. The entrepreneur's payoff conditional on the standard
strategy, s, is
u(w, v, | s) Ξ
,
? 0, if v ≥ y¯(w)
,
, (1 — )
+7E/ (y — v)ƒ(y | w)dy, other ise,
and the entrepreneur's payoff conditional on the risky strategy, r, is
,
? 0, if v ≥ y¯(w)
u(w, v, | r) Ξ
, (1 — ) ,
+7E/ (y — v)g(y | w)dy, other ise.
The entrepreneur chooses the risky strategy if u(w, v, | r) > u(w, v, | s). Whether this inequality holds is independent of , so the entrepreneur's decision does
not depend on the share . The entrepreneur's choice of risky or standard strategy depends only on the fixed component of the sharing rule. By Assumption 1, hen the dividend is zero, the standard strategy gives the entrepreneur greater expected payoff than the risky strategy, so the entrepreneur al ays prefers the standard strategy
hen the project is financed entirely ith equity. But if the contract has some debt component, then the entrepreneur may prefer the risky strategy.
Define the dividend vr(w) to be the largest dividend such that the entrepreneur still prefers the standard strategy in state w :S
vr(w) Ξ max{v c [0, y¯(w)] | u(w, v, | r) ≤ u(w, v, | s)}. (1)
The s in vr is mnemonic for standard strategy since vr is the maximal dividend such that the entrepreneur chooses the standard strategy. Figure 3 sho s the en- trepreneur's expected payoffs for the standard and risky strategies as a function of the dividend v, holding fixed the state w and the share . The dividend vr is the div- idend such that for smaller dividends, the entrepreneur prefers the standard strategy and for larger dividends the entrepreneur prefers the risky strategy.
u(ω, v, γ|s)
u(ω, v, γ|r )
v V (ω) v
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As mentioned before, the entrepreneur's choice does not depend on , so vr also does not depend on . And, hen the dividend is zero, the entrepreneur is risk neutral ith respect to the project's returns, and so the entrepreneur strictly prefers the standard strategy, implying that vr(w) > 0. For all dividends less than vr, the entrepreneur chooses the standard strategy, and for dividends greater than vr, the entrepreneur chooses the risky strategy.
Lemma 1 states a property of vr, that for all w c ▲, vr(w) is less than the point at
hich the distributions J and G intersect, y/, hich is assumed to be strictly less than y¯(w) (see Figure 1). To see the intuition for this result, note that the entrepreneur's payoff depends only on project returns that are above the dividend, and, conditional on profits being greater than y/, the risky strategy results in higher expected profit (the cdf for G is belo the cdf for J for y > y/). Thus, for any dividend greater than y/, the entrepreneur prefers the risky strategy, and so vr(w) cannot be greater than y/.
Lemma 1 For all w c ▲, vr(w) ≤ y/ < y¯(w).
Proof. Suppose vr(w) > y/. Then by Assumption 2,
∫ +7E/
[G(y | w) — J (y | w)] dy < 0,
r E/
but, using the definition of u and integrating by parts, this implies that
u(w, vr(w), | r) > u(w, vr(w), | s),
hich violates the definition of vr(w). This contradiction implies that vr(w) ≤ y/,
and Assumption 2 implies y/ < y¯(w).
Renegotiation and interuention
Fn state w, the venture capitalist is xxxxxx to reduce the fixed payment to vr(w) to avoid having the entrepreneur choose the risky strategy if and only if that change
increases the venture capitalist's expected utility, i.e., if and only if v(w, vr(w), | s)
is greater than the payoff the venture capitalist ould get other ise. Ff the venture capitalist has control rights, then the venture capitalist is xxxxxx to reduce the fixed payment to vr(w) if and only if
v(w, vr(w), | s) > max {v(w, v, | r), v(w, v, | s) — s} .
Ff the venture capitalist does not have control rights, then the venture capitalist is
xxxxxx to reduce the fixed payment to vr(w) if and only if
v(w, vr(w), | s) > v(w, v, | r).
The venture capitalist ill not al ays be xxxxxx to forgive dividends in order to give the entrepreneur the incentive to choose the standard strategy. Ff the state is such that vr(w) is much less than v, then the venture capitalist may not be xxxxxx to reduce the dividend from v to vr(w) just to give the entrepreneur the incentive to choose the standard strategy.
S
When the venture capitalist has control rights, let vs (w, ) be the maximum divi-
?
dend such that the venture capitalist is xxxxxx to forgive dividends do n to vr(w) to avoid having the entrepreneur choose the risky strategy hen the state is w and the share is . When the venture capitalist does not have control rights, let vs (w, ) be
similarly defined:.
i v v
yf +$> , pd{iy 5 ^y +$,> | +$,` m +$> y +$,> m v, pd{ i +$> y> m u,> +$> y> m v, fjj> +5,
dqg
i v v
yq+$> , pd{ iy 5 ^y +$,> | +$,` m +$> y +$,> m v, +$> y> m u,j = +6,
The ƒ in vs is mnemonic for forgive since vs is the maximum dividend such that the venture capitalist is xxxxxx to unilaterally forgive part of the entrepreneur's dividend obligation.
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By construction, given state w and share , the venture capitalist prefers to forgive
dividends do n to vr(w) rather than continue ith the original contract if and only if v ≤ vs (w, ) or v ≤ vs (w, ), depending on hether the venture capitalist has
S ?
S
control rights or not. Ff v > vs (w, ), then the venture capitalist prefers to continue
?
ith the original contract and either let the entrepreneur choose the risky strategy or intervene and implement the standard strategy. Ff the venture capitalist does not have control rights and v > vs (w, ), then the venture capitalist prefers to continue
ith the original contract and let the entrepreneur choose the risky strategy.
u
Figure 4 sho s the venture capitalist's payoff as a function of v, holding fixed the state w and share . The figure sho s that for dividends bet een vr(w) and vs (w, ), the venture capitalist prefers to forgive dividends do n to vr(w) rather than continue
ith the original contract since v(w, v, | r) < v(w, vr(w), | s). Fn Figure 4, the
S
?
cost of intervention, s, is sufficiently large that the venture capitalist prefers to let the entrepreneur choose the risky strategy rather than intervene, so the dividend vs (w, ) as ell as the dividend vs (w, ) are determined by the intersection of v(w, v, | r)
and v(w, vr(w), | s). Ff the cost of intervention ere sufficiently small, the venture
S
capitalist ould prefer to intervene rather than let the entrepreneur choose the risky strategy, and so vs (w, ) ould be determined by the intersection of v(w, v, | s) — s
and v(w, vr(w), | s).
u
Ff v > vs (w, ), the venture capitalist is not xxxxxx to forgive dividends so as to in- duce the entrepreneur to choose the standard strategy because the amount that ould have to be forgiven is so large that doing so ould decrease the venture capitalist's expected payoff. Ho ever, renegotiation of the contract is possible. Fn renegotiation, the venture capitalist offers a ne contract that has dividend vr(w), hich is less than the dividend in the original contract, and a share that is greater than the share in the original contract.
When the venture capitalist has control rights, there are t o cases to consider. First, if v(w, v, | r) ≥ max {v(w, v, | s) — s, v(w, vr(w), | s)} , then the en-
π(ω, v, γ| s)
π(ω, v, γ|r )
π(ω, v V ( ω),
γ| s)
π(ω, v, γ| s)− c
v V (ω)
Y
•
v I (ω, γ)
Figure 4: Yhqwxuh fdslwdolvw*v sd|r dv d ixqfwlrq ri v, kroglqj {hg wkh vwdwh w dqg vkduh
.
trepreneur accepts any renegotiation offer that gives him payoff at least u(w, v, | r),
since this is the payoff the entrepreneur gets if he rejects the renegotiation offer. We define o to be the share that leaves the entrepreneur indifferent bet een accepting and rejecting the renegotiation offer, i.e., o(w, v, ) satisfies
u(w, vr(w), o(w, v, ) | s) = u(w, v, | r).
Second, if v(w, v, | s) — s > max {v(w, v, | r), v(w, vr(w), | s)} , then the en- trepreneur accepts any renegotiation offer that gives him payoff at least u(w, v, | s), since this is the payoff the entrepreneur gets if he rejects the renegotiation offer. (Ff
the entrepreneur rejected the offer, the venture capitalist ould intervene and choose the standard strategy.) So (w, v, ) satisfies
u(w, vr(w), (w, v, ) | s) = u(w, v, | s).
The r in o is mnemonic for the share the is acceptable rather than choosing the
“r“isky strategy, and the i in is mnemonic for the share the is acceptable rather than facing “i“ntervention. Note that F assume that the venture capitalist does not intervene hen she is indifferent bet een intervening and not.
When the venture capitalist does not have control rights, the entrepreneur accepts any renegotiation offer that gives him payoff at least u(w, v, | r), since this is the payoff the entrepreneur ould get if he rejected the renegotiation offer. So the
same share o from above leaves the entrepreneur indifferent bet een accepting and rejecting the renegotiation offer in this case.
As sho n in Lemma 2, the shares o and are ell defined, leave the entrepreneur indifferent bet een accepting the renegotiation offer and not, and leave the venture capitalist at least as ell off as if she did not make the renegotiation offer. The proof of Lemma 2 is given in the Appendix.
Lemma 2 There enist funstions o, : ▲ × Rn × [0, 1] → [0, 1] sush that for all
w c ▲, c [0, 1],
S
?
(i) if v ≥ vs (w, ) and v(w, v, | r) ≥ max {v(w, v, | s) — s, v(w, vr(w), | s)} or if v ≥ vs (w, ), then u(w, vr(w), o(w, v, ) | s) = u(w, v, | r) and
v(w, vr(w), o(w, v, ) | s) ≥ u(w, v, | r); and
S
(ii) if v ≥ vs (w, ) and v(w, v, | s) — s > max {v(w, v, | r), v(w, vr(w), | s)} ,
then u(w, vr(w), (w, v, ) | s) = u(w, v, | s) and
v(w, vr(w), (w, v, ) | s) ≥ v(w, v, | s).
S
Lemma 2 implies that it is al ays possible for the venture capitalist and en- trepreneur to renegotiate out of a situation in hich the venture capitalist ould intervene or the entrepreneur ould choose the risky strategy. Ff v ≥ vs (w, ) and
v(w, v, | s) — s > max {v(w, v, | r), v(w, vr(w), | s)} ,
then the venture capitalist ould intervene in the absence of renegotiation. Fn this case, the entrepreneur must be offered a contract that gives him payoff at least u(w, v, | s). This leaves a payoff of v(w, v, | s) for the venture capitalist, and
this is at least as large as the payoff she ould get if she intervened in the project,
S
v(w, v, | s) — s. Ff either v ≥ vs (w, ) and
v(w, v, | r) ≥ max {v(w, v, | s) — s, v(w, vr(w), | s)}
?
or v ≥ vs (w, ), then the entrepreneur must be offered a contract that gives him payoff at least u(w, v, | r). Assuming the standard strategy is chosen, this leaves a payoff of v(w, v, | s) + u(w, v, | s) — u(w, v, | r) for the venture capitalist, and this is at least as large as the payoff she ould get if she intervened in the
project, v(w, v, | s) — s, or allo ed the entrepreneur to choose the risky strategy,
v(w, v, | r).
We can no characterize the subgame perfect equilibrium starting from the xxxx- gotiation stage. Before doing that, it ill be useful to define t o partitions of the state space, one for the case in hich the venture capitalist has control rights, and one for the case in hich she does not. For the case in hich the venture capitalist has control rights, a partition is
▲ (v) Ξ {w c ▲ | v ≤ vr(w)},
▲2(v, ) Ξ {w c ▲ | vr(w) < v < vs (w, )},
S , S ,
? s @
S
▲ (v, ) Ξ
and
S
▲e(v, ) Ξ
w c ▲
,
,
?
w c ▲
,
vS (w, ) ≤ v and
,
v(w, v, | r) ≥ max {v(w, v, | s) — s, v(w, vr(w), | s)} ,
,
S
vs (w, ) ≤ v and @
.
v(w, v, | s) — s > max {v(w, v, | r), v(w, vr(w), | s)} ,
For the case in hich the venture capitalist does not have control rights, a partition
is ▲ (v) together ith
▲2 (v, ) Ξ {w c ▲ | vr(w) < v < vs (w, )}, and
?
?
▲ (v, ) Ξ
?
}
?
w c ▲ | vs (w, ) ≤ v .
Given the earlier assumptions that ▲ is a real interval and that J (·| w) and G(·| w) first-order stochastically dominate J (·| w ) and G(·| w ), respectively, hen w > w ,
then the sets ▲ are real intervals or the union of real intervals.
We can no define the subgame perfect strategies starting from period t = 1, given the initial sharing rule and allocation of control rights. Proposition 1 im- plies that, hen the venture capitalist has control rights, an equilibrium outcome
starting from t = 1 is that there is no renegotiation if v ≤ vr(w), dividends are
S
S
?
forgiven do n to vr(w) if vr(w) < v < vs (w, ), and the sharing rule is changed to s(· | vr(w), o(w, v, )) or s(· | vr(w), (w, v, )) if vs (w, ) ≤ v. When the venture capitalist does not have control rights, there is no renegotiation if v ≤ vr(w), div- idends are forgiven do n to vr(w) if vr(w) < v < vs (w, ), and the sharing rule is
?
changed to s(· | vr(w), o(w, v, )) if vs (w, ) ≤ v. These ne sharing rules are pre- ferred (at least eakly) by both the venture capitalist and the entrepreneur to the old
sharing rule, and there is no sharing rule that gives higher expected payoff to both.
Proposition 1 Let w c ▲, v ≥ 0, and c [0, 1] be giuen. The follouing strategies are subgame perfest for the subgame starting at t = 1 :
S
S
S
Renegotiation with control rights: If w c ▲ (v) ∪ ▲2(v, ), the uenture sapitalist mahes no renegotiation offer; if w c ▲ (v, ), the uenture sapitalist proposes a neu sharing rule uith diuidend vr(w) and share o(w, v, ); and if w c ▲e(v, ), the uenture sapitalist proposes a neu sharing rule uith diuidend vr(w) and share (w, v, ). If
w c ▲ (v) ∪ ▲e(v, ), w c ▲2(v, ), or w c ▲ (v, ), the entrepreneur assepts a
S S S
renegotiation offer if and only if it giues him enpested payoff at least u(w, v, | s), u(w, vr(w), | s), or u(w, v, | r), respestiuely.
?
?
?
?
Renegotiation without control rights: If w c ▲ (v)∪▲2 (v, ), the uenture sapital− ist mahes no renegotiation offer; and if w c ▲ (v, ), the uenture sapitalist proposes a neu sharing rule uith diuidend vr(w) and share o(w, v, ). If w c ▲ (v), w c ▲2 (v, ), or w c ▲ (v, ), the entrepreneur assepts a renegotiation offer if and only if it giues him enpested payoff at least u(w, v, | s), u(w, vr(w), | s), or u(w, v, | r), respes− tiuely.
Forgiveness and intervention: 5uppose that after renegotiation, the sontrast has diuidend vˆ and share ˆ. If the uenture sapitalist has sontrol rights, she forgiues diui−
dends to vr(w) if and only if w c ▲2(vˆ, ˆ) and interuenes if and only if w c ▲e(vˆ, ˆ).
S S
If the uenture sapitalist does not haue sontrol rights, she forgiues diuidends to vr(w)
?
if and only if w c ▲2 (vˆ, ˆ).
Strateg) choice: 5uppose that after any forgiueness or interuention, the sontrast in plase has diuidend v . If the uenture sapitalist interuened, she shooses the standard strategy. If the uenture sapitalist did not interuene, the entrepreneur shooses the standard strategy if and only if w c ▲ (v ).
Proof of Proposition 1. By earlier arguments using Assumptions 1 and 2, the ven- ture capitalist's choice of the standard strategy is subgame perfect. By the definition of vr(w), the entrepreneur's strategy choice is subgame perfect. By the definitions of
vr(w), ▲ , ▲ , for j c {2, 3, 4}, and ▲ , for j c {2, 3}, the forgiveness and intervention
S ?
strategies are subgame perfect. Using those definitions again, the definitions of o,
, and Lemma 2, the venture capitalist's strategy for renegotiation offers and the entrepreneur's strategy for accepting renegotiation offers are subgame perfect.
Interuention
By intervening, the venture capitalist prevents the entrepreneur from using the risky strategy, and thus precludes negotiation, but intervening also imposes costs on the venture capitalist. Since F assume the entrepreneur is indifferent bet een the
original and the renegotiated contract, all gains to the change in strategy achieved through renegotiation are captured by the venture capitalist. Thus, the venture capitalist al ays prefers the renegotiated contract over intervention. Ho ever, in reality e do observe instances in hich venture capitalists intervene in venture capital projects, install ne management, and even remove the founding entrepreneur. Ff the model of this paper ere modified to allo the entrepreneur to have some bargaining po er in renegotiation, then in some states the venture capitalist ould prefer to intervene rather than renegotiate. This suggests that e should expect increases in the entrepreneur's bargaining po er to increase the likelihood of intervention by the venture capitalist. The addition to the model of frictions such as costly renegotiation
ould also result in intervention by the venture capitalist in some states.
The addition of costly renegotiation or bargaining po er for the entrepreneur in renegotiations also implies that some efficient projects ill not receive financing, since either the choice of the risky strategy by the entrepreneur or costly intervention by the venture capitalist ill be unavoidable in some states, reducing the ex-ante expected payoff of some projects belo the required initial investment.
Initial sontrast shoise
To determine the equilibrium initial contract, F define the venture capitalist's ex-ante break-even constraint, taking into account the subgame perfect equilibrium strategies starting in period t = 1 given in Proposition 1, but assuming a good entrepreneur. With control rights, the constraint is
I ≤ Pr [w c ▲ (v)] E/ [v(w, v, | s) | ▲ (v)]
+ Pr [w c ▲2(v, )] E/ [v(w, vr(w), | s) | ▲2(v, )]
S S (4)
+ Pr [w c ▲ (v, )] E/ [v(w, vr(w), o(w, v, ) | s) | ▲ (v, )]
S S
+ Pr [w c ▲e(v, )] E/ [v(w, vr(w), (w, v, ) | s) | ▲e(v, )] ,
S S
and ithout control rights it is
I ≤ Pr [w c ▲ (v)] E/ [v(w, v, | s) | ▲ (v)]
+ Pr [w c ▲2 (v, )] E/ [v(w, vr(w), | s) | ▲2 (v, )]
(5)
? ?
+ Pr [w c ▲ (v, )] E/ [v(w, vr(w), o(w, v, ) | s) | ▲ (v, )] .
? ?
Let v¯S and v¯? be the smallest dividend levels such that the venture capitalist's break-even constraints (4) and (5), respectively, hold ith equality hen = 0.H For v c [0, v¯ ], e can define W(v) to be the share such that the sharing rule
S S
S
s(·| v, W(v)) satisfies the venture capitalist's ex-ante break-even constraint (4) ith
equality, and for v c [0, v¯?], e can define (v) to be the share such that the sharing
W
?
?
rule s(· | v, W (v)) satisfies the venture capitalist's ex-ante break-even constraint (5)
ith equality. By the follo ing lemma, the shares W(v) and W (v) are ell defined
S ?
(asterisks denote equilibrium values). The proof is in the Appendix.
Lemma 3 For j c {s, n}, there enists W : [0, v¯ ] → [0, 1], sush that for all v c [0, v¯ ],
the sharing rule uith diuidend v and share W(v) is feasible and satis es the uenture sapitalist’s en−ante breah−euen sonstraint (e) if j = s or (5) if j = n uith equality.
F no complete the statement of the equilibrium.
Proposition 2 A perfest Bayesian equilibrium sonsists of the strategies in Propo− sition 1 together uith (i) beliefs for the uenture sapitalist that an offer somes from a good entrepreneur if and only if it offers sontrol rights to the uenture sapitalist and has diuidend at least y¯(w), and (ii) the follouing strategies: A good entrepreneur giues sontrol rights to the uenture sapitalist and offers a sharing rule uith diuidend
S
y¯(w) and share equal to W (y¯(w)) if
y¯(w) ≤ v¯S
and equal to xero otheruise. A bad
?
entrepreneur does not giue sontrol rights to the uenture sapitalist and offers a sharing rule uith diuidend xero and share W (0). The uenture sapitalist assepts an initial offer if and only if it insludes sontrol rights, has diuidend at least y¯(w), and satis es the breah−euen sonstraint (e).
f
;Jlyhq wkh frqwlqxlw| dvvxphg lq wkh prgho dqg Dvvxpswlrq 6/ lw lv fohdu wkdw y
dqg y q
h{lvw1
Proof. Proposition 1 establishes subgame perfection starting in period t = 1 for good and bad entrepreneurs. Fn equilibrium, the standard strategy is al ays chosen and the venture capitalist never intervenes, so a sharing rule that satisfies the venture capitalist's break-even constraint ith equality gives the entrepreneur the maximum
possible payoff. Ff y¯(w) ≤ v¯ , then, by the definition of W , the equilibrium contract
S S
satisfies the venture capitalist's break-even constraint (4) ith equality. By the first part of assumption 3, the entrepreneur has nonnegative expected payoff in this case.
Ff y¯(w) > v¯S, then, by the definition of v¯S, (4) is satisfied hen (v, ) = (y¯(w), 0).
Since y¯(w) is increasing in w, a good entrepreneur has nonnegative expected payoff under such a sharing rule. Thus, given the venture capitalist's acceptance strategy, the strategy for a good entrepreneur maximizes his expected payoff. Suppose a bad entrepreneur offers a sharing rule that satisfies the venture capitalist's acceptance criteria. Then the bad entrepreneur must offer a dividend greater than or equal to
S
y¯(w). By the definition of vs , for all c [0, 1], vs (w, ) ≤ y¯(w), so for all c [0, 1] and
v ≥ y¯(w), w c ▲ (v, )∪▲e(v, ). This implies that the bad entrepreneur's contract is
S S
al ays renegotiated. Since the entrepreneur has zero expected payoff in the absence of renegotiation, his disagreement payoff is zero and so he gets a payoff of zero in the renegotiated contract. Thus, it is payoff maximizing for a bad entrepreneur to offer a contract that is, in equilibrium, not accepted by the venture capitalist. Finally, given the venture capitalist's beliefs, her acceptance strategy maximizes her expected payoff, and given the strategies for the t o types of entrepreneur, the venture capitalist's beliefs are consistent.
As sho n in Proposition 2, a good entrepreneur can signal his type by offering control rights to the venture capitalist and proposing a sharing rule that has a positive dividend. The equilibrium dividend is sufficiently large that a bad entrepreneur has zero expected payoff under such a contract.b Fn this model there is no reason other
<Wkh dgglwlrq ri dq h ruw frvw eruqh e| wkh hqwuhsuhqhxu ru d uhtxluhphqw wkdw wkh hqwuhsuhqhxu
than signalling for an entrepreneur to offer control rights to the venture capitalist since intervention does not occur in equilibrium. Ho ever, hether the venture capitalist has control rights affects the entrepreneur's disagreement payoff in renegotiation and so does affect the renegotiation offer that is made in equilibrium. Fn some cases, i.e.,
S
hen y¯(w) ≤ v¯ , f the entrepreneur captures the differences in renegotiation outcomes
in the initial sharing rule, so that the venture capitalist's exante break-even constraint is satisfied ith equality.
The equilibrium contract described in Proposition 2 is efficient. Fn equilibrium, good entrepreneurs receive financing and bad entrepreneurs do not. Fn equilibrium, the venture capitalist never chooses to undertake costly intervention, and the en- trepreneur never chooses the inefficient risky strategy. Although F restrict the sharing rule proposed by the entrepreneur to be a mixed debt-equity sharing rule, Proposition 2 sho s that contracts of that form are sufficiently complex so as to achieve efficiency. Fn summary, in the equilibrium of Proposition 2, contracts are sometimes renegoti- ated (either one-sided forgiveness or t o-sided renegotiation) so that the entrepreneur has the incentive to choose the standard strategy. Renegotiation al ays prevents a situation in hich the entrepreneur has the incentive to choose the risky strategy. Kquilibrium renegotiation or forgiveness involves either no change, the reduction of the entrepreneur's debt obligation, or the reduction of debt together ith an increase in the venture capitalist's equity share. Although the renegotiation outcome described is not unique, e can think of it as the least-cost renegotiation in that it involves the
minimal adjustments to the contract terms.
3
lqyhvw vrph ri klv shuvrqdo zhdowk +dvvxphg wr eh }hur lq wkh prgho,/ zrxog uhvxow lq d qhjdwlyh h{shfwhg sd|r iru d edg hqwuhsuhqhxu zkr plplfv wkh htxloleulxp frqwudfw ri d jrrg hqwuhsuhqhxu1
$
43D vx flhqw frqglwlrq iru wklv lv wkdw H
kU | +$, |i+| m $,g|l ? L=
5 Conclusions
The analysis from the previous section allo s us to characterize the behavior of en- trepreneurs and venture capitalists hen projects are financed by mixtures of debt and equity. Some notable features of the equilibrium are as follo s: (i) renegotiation occurs if the state is revealed to be lo , (ii) renegotiation never leads to an increase in the dividend, (iii) renegotiation never leads to a decrease in the venture capital- ist's share, and (iv) renegotiation may affect only the dividend but never affects only the venture capitalist's share. These results are consistent ith observed behavior bet een venture capitalists and entrepreneurs. Furthermore, the results sho that mixed debt-equity contracts can achieve efficiency and that positive dividend levels can be used by an entrepreneur to effectively signal the expected profitability of his project.
Ft is interesting that, xxxx intervention by the venture capitalist does not occur on the equilibrium path, the threat of intervention is important in determining the entrepreneur's disagreement payoff in renegotiation, and thus the outcome of contract renegotiation. The addition of frictions to the model, such as costly renegotiation,
ould result in intervention by the venture capitalist in some states. Also, increases in the entrepreneur's bargaining po er in renegotiation ould result in intervention by the venture capitalist in some states. Kither of these changes to the model ould also result in some efficient projects not being financed.
Fn the model, good entrepreneurs use a combination of positive dividends and the granting of control rights to distinguish themselves from bad entrepreneurs. An extension of the model ould allo a greater role for control rights, so that giv- ing control rights to the venture capitalist ould serve as a stronger signal of the entrepreneur's quality.
6 Appendix
Proof of Lemma 2
S
(i) Suppose w c ▲, v ≥ 0, c [0, 1], and either v ≥ vs (w, ) and v(w, v, | r) ≥
?
max {v(w, v, | s) — s, v(w, vr(w), | s)} or v ≥ vs (w, ). F claim o is uniquely de-
fined by
u(w, vr(w), o (w, v, ) | s) = u(w, v, | r).
Using the definition of u and integrating by parts, this equality implies (suppressing the arguments of J, G, vr , and y¯):
+4 u+$> y> ,,
| yv
|
]
Ig|
v
y
@ +4 ,
#| plqiy> | j
]
|
plqiy>| j
Jg|$
= +9,
Since vr(w) < y¯(w) by Lemma 1, (6) uniquely defines o (w, v, ). One can easily sho that o (w, v, ) > , i.e., the decrease in dividend requires an increase in the share to keep the entrepreneur indifferent. To see that o (w, v, ) < 1, so that the share o is feasible, note that
| yv U| I g| +4 , | plqiy> | j U| Jg|
u +$> y> ,@
v
y
v
| yv U| I g|
plqiy>| j
? 4= +:,
y
To sho that v(w, vr(w), o (w, v, ) | s) ≥ v(w, v, | r), note that
v(w, vr(w), o (w, v, ) | s) — v(w, v, | r)
, r ,
= vr — J dy + oE? (w, v, ) y¯ — vr — +7 J dy
f r
f
—v + , 4 ?t c+7 Gdy —
, +7
y¯ — min{v, y¯}— , +7
4 ?t c+7
, +7
Gdy
= y¯ — min{v, y¯}—
4 ?t c+7 Gdy +
f [G — J ] dy
≥ 0,
here the first inequality uses the definition of v and integration by parts, the second equality uses (7), and the inequality uses Assumption 1.
S
(ii) Suppose w c ▲, v ≥ 0, c [0, 1], v ≥ vs (w, ), and v(w, v, | s) — s >
max {v(w, v, | r), v(w, vr(w), | s)} . F claim is uniquely defined by
u(w, vr(w), (w, v, ) | s) = u(w, v, | s).
Using the definition of u and integrating by parts, this equality implies (suppressing the arguments of J, G, vr, and y¯):
l
4 +$> y> ,
| yv
]yv
I g|
@ +4 ,
#| plqiy> | j
|
|
]plqiy>| j
I g|$
= +;,
Since vr(w) < y¯(w) by Lemma 1, (8) uniquely defines (w, v, ). One can easily sho
that (w, v, ) > , i.e., the decrease in dividend requires an increase in the share to
keep the entrepreneur indifferent. To see that (w, v, ) < 1, so that the share is feasible, note that
| yv U| I g| +4 , | plqiy> | j U| I g|
l+$> y> ,@
yv
yv
| yv U| I g|
plqiy>| j
? 4= +<,
To sho that v(w, vr(w), (w, v, ) | s) ≥ v(w, v, | s) — s, note that
v(w, vr(w), (w, v, ) | s) — v(w, v, | s) + s
, r , +7
= vr — J dy + (w, v, ) y¯ — vr — J dy
f r
f
4 ?t c+7
— min{v, y¯} + , 4 ?t c+7 J dy — y¯ — min{v, y¯}— , +7
J dy + s
= s
≥ 0,
here the first inequality uses the definition of v and integration by parts, the second equality uses (9), and the inequality uses the assumption that s ≥ 0.
Proof of Lemma 3. Let dividend v c [0, v¯ ] and c [0, 1] be given. When the break- even constraint is satisfied ith equality, the follo ing equation holds (suppressing
the arguments of the ▲&s and defining ▲e Ξ Ø):
Pr [w c ▲ ] E/
k, +7E/
?
l
k
,
(y — v)ƒ(y | w)dy | ▲
+ Pr
w c ▲2 E
l
+7E/ (y — vr(w))ƒ(y | w)dy | ▲2
/ k r E/ l
, , +7E/
= I — Pr [w c ▲ ] E yƒ(y | w)dy + vƒ(y | w)dy | ▲
/ f
— Pr
w c ▲2
k, r E/
E/
yƒ(y | w)dy +
, +7E/
l
vr(w)ƒ(y | w)dy | ▲2
(10)
k f r E/ l
, +7E/
— Pr c ▲ E s(y | vr(w), o(w, v, ))ƒ(y | w)dy | ▲
w / k f l
, +7E/
— Pr c ▲e E s(y | vr(w), (w, v, ))ƒ(y | w)dy | ▲e .
w / f
Given our assumptions about the probability distribution for w, both sides of (10) are continuous in . When = 0, the left-hand side is zero. When = 0, the right-hand side is zero if v = v¯ and strictly positive if v < v¯ (by the definition of v¯ and using Assumption 3). When = 1, o(w, v, ) = (w, v, ) = 1, so the left-hand side of
(10) is
Pr [w c ▲ ] E
k, l
+7E/ (y — v)ƒ(y | w)dy | ▲
/
+ Pr w c ▲2 E
k, l
+7E/ (y — vr(w))ƒ(y | w)dy | ▲2 .
(11)
and the right-hand side is
/ r E/
I — Pr [w c ▲ ] E/
k,
yƒ(y | w)dy +
, +7E/
l
l
vƒ(y | w)dy | ▲
,
k f
— 2 r E/
, +7E/ r 2
Pr w c ▲ E/ f yƒ(y | w)dy +
k
r E/ v (w)ƒ(y | w)dy | ▲
— Pr w c ▲ E/
, +7E/
l
yƒ(y | w)dy | ▲
(12a)
k f l
— Pr
, +7E/
w c ▲e E yƒ(y | w)dy | ▲e ,
/ f
, +7E/
Taking the difference of expression (11) minus expression (12a), e get E/ f yƒ(y |
w)dy — I hich is nonnegative by Assumption 3. Therefore, for all v c [0, v¯ ], there exists W(v) c [0, 1].
7 References
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