Proposition 3 states that the inancial participation of the entrepreneur can enhance the value of the project if the initial investment needed is large. The intuition is that there is a maximal amount of outside inancing (I*) that can be raised while maintaining incentives for both agents to exert efort. As stated in Corollary 1, each extra dollar ofoutside inancing above I* afects negatively the entrepreneurs efort and reduces the projects value. The reason is the following. Increasing outside inancing raises the share of the inal income left to outside investors. This, in turn, destroys the entrepreneurs incentives to work. If the entrepreneur is wealthy enough, investing his own resources into the project reduces the amount of outside capital to be raised and preserves the entrepreneurs own incentives. The projects value consequently increases. If the level of investment is below I*, it can be entirely inanced by outside capital, for outside inancing ofsets the expected income left to the venture capitalist for incentive reasons. In that case, the NPV is maximal without the entrepreneurs inancial participation.

The assumption of the model that no agent is wealth constrained is clearly an important one. The above result states that the entrepreneurs participation is eicient for some values of the parameters. It is likely though that some entrepreneurs have no cash to invest in their irm. I turn to the case where this assumption is relaxed. Suppose that the entrepreneur has no personal wealth. Proposition 3 shows that for those projects requiring a low initial outlay, the entrepreneurs wealth constraint has no bite. It can, however, be detrimental to the projects value if the initial investment required is large. Proposition 4 sheds light on the impact of the entrepreneurs wealth constraint.

Proposition 4: The maximal amount of outside financing (Imax) that the entrepreneur can raise under moral hazard is strictly lower than the maximal level of investment, such that the project is profitable in the frst best I)

Proposition 4 relects the inancial constraints faced by the entrepreneur because of moral-hazard problems. If the project requires an initial investment larger than Imax but lower than I, it is, by assumption, potentially profitable.

However, if the entrepreneur has no personal wealth to invest, he is rationed on the capital market and cannot implement his project. if the level of outside inancing that must be raised is above Imax, too large a share of proits must be left to the investors so that they recoup their investment. This, in turn, destroys the entrepreneurs incentives to exert efort and leads to a negative NPV project: Capital suppliers cannot recover the opportunity cost of their investment and refuse to invest.

The first part of Proposition 3 along with Proposition 4 illustrates the impact of agency costs on the firms investment policy as well as the role of net worth or cash lows in mitigating these costs, as documented by Fazzari, Hubbard, and Peterson (1988), Gilchrist and Himmelberg (1995), or Lamont (1997). Raising external capital is expensive. it dilutes the entrepreneurs stake in the irm and discourages efort. This lowers the irms value and reduces investment. However, Proposition 2 as well as the last part of Proposition 3 unveils another aspect of the role of external inance. in the speciic venture capital setting, raising external capital is value enhancing, since it guarantees the involvement of the venture capitalist. Contrary to the traditional agency view of corporate finance,12 projects financed by external capital can be more proitable than pure internally inanced projects.

The above results delineate two types of situations. in the irst one, projects should be entirely inanced by external venture capital. This ensures that a sui-cient level of efort a is exerted by the venture capitalist. This case arises when the initial investment is lower than I*. Note that I* increases with (Ru - Rd)2. When I is small compared to (Ru - Rd)2, projects exhibit high expected profitability. in the opposite case, projects with lower expected proitability beneit from the inancial contribution of the entrepreneur. For those projects, the relation between the level of investment of the entrepreneur and the proitability of the project is expected to be positive.

This model explains why the joint provision of advice and money is so often observed in the case ofstart-ups. Although business expertise is not the exclusive property of VCs, it may sometimes be the only way for an entrepreneur to obtain eicient advice. The next section investigates which inancial claims purchased by venture capitalists optimally cope with the double-sided moral-hazard problem studied here.

III. Optimal Financial Contracts between Venture Capitalists and

Entrepreneurs

The previous section established the optimality of the venture capitalists financial participation in the entrepreneurs project. This section aims at deining which inancial claims will be optimally held by venture capitalists in response to their inancial investment. The objective is to determine which inancial claims will provide powerful incentives for both the venture capitalist and the entrepreneur. i restrict the analysis to the case where the only outside investor

12 Surveys of this numerous literature include Harris and Raviv (1991) or Allen and Winton (1995).

is the VC. Such a restriction is harmless from an eiciency point of view. The presence of a pure inancier along with the VC in the contract with the entrepreneur is irrelevant to the levels of effort exerted.13 The following proposition states which financial claims are optimally issued, depending on the level of outside inancing.

Proposition 5: There exists a threshold AyC, strictly lower than I*, such that

When AyC < AyC, the optimal contract can be implemented by giving common stocks to the VC and preferred stocks to the entrepreneur.

When AyC>AyC, the optimal contract can be implemented by giving preferred stocks or convertible bonds to the VC and common stocks to the entrepreneur

Recall that I* is the maximal amount of outside inancing that can be raised while inducing optimal eforts for both agents. Proposition 5 states that within the optimal range of outside inancing, incentive problems can be solved using different instruments. Two regimes arise. When the amount of outside financing is small, the VCs expected income is small, too. She must then be given higher-powered incentives to be induced to work. In that case, the entrepreneur is given preferred stocks that grant him a higher dividend than common stocks if the bad state of nature is realized. If the good state of nature is realized, the income is high enough so that common and preferred stocks give the same return. As a consequence, the VC who owns only common stocks is proportionally better remunerated in state Ru than in state Rd, which gives her more powerful incentives to exert efort. When the amount of outside inancing is large, the VC must be pledged a large share of proits in order to recoup her investment. As there is little left for the entrepreneur, he is less prone to make an efort, and needs a higher-powered incentive scheme. When the VC is given convertible bonds or preferred stocks, she captures most of the income in state Rd. The common stocks held by the entrepreneur are only valuable in the good state of nature. The entrepreneur intensifies his effort to increase the probability of state Ru occurring.

The speciic venture capital setting studied here provides a rationale for the use ofconvertible and equity-like claims as the optimal source ofoutside inance. These results contribute to the literature on the optimal capital structure of irms. The main insight is that outside equity, or equity-like claims, provide proper incentives to active investors such as venture capitalists. This is consistent with the empirical observation that convertible claims (bonds or preferred stocks) are extensively used in VC inancing, as evidenced by Sahlman (1988, 1990) or Kaplan and Stromberg (2000).

These two regimes are also related to the findings of Fenn, Liang, and Prowse (1998). They compare empirically the financial claims used by business angels and venture capitalists. In their sample of 107 U.S. firms of high-tech sectors (medical

13 This is true when the inancial contract of the pure inancier cannot decrease with the inal outcome of the project. otherwise it could improve incentives as mentioned in footnote 10.