Bargaining, size, and return in venture capital funds

Abstract

The terms of an investment by venture capitalists are the result of cooperative bargaining between the project originators (owners or entrepreneurs) and the financiers. This study examines conditions under which bargains can be consummated, the nature of the bargains, and the way in which bargains are both influenced by venture fund size and also contribute to a theory of fund size. As much as possible, the theory of fund size and earnings is related to required rate of return concepts, with the objective of explaining relative variations in the value of venture capital funds, and of incorporating such investments within the general body of finance theory. The most basic form of contract is a simple bilateral bargain between owners and fund managers, with the shares of financing and earnings as the bargaining variables. Agency and other considerations can be factored into the resulting project value to be financed and partitioned. An Edgeworth box construction is used to establish the efficient (Pareto optimal) set as the contract curve. The two endpoints of the contract curve correspond respectively to the monopoly solution, where there is one fund and many owners, and to the competitive solution. The Nash bargaining solution of game theory can also be exhibited within this framework, although we are careful to remain agnostic about whether or not this constitutes the only or even the best solution. A first requirement is that some basis for agreement exists so that mutually beneficial bargains can actually be struck. Conditions most favorable to existence arise where (1) owners who cannot properly diversify their own investments are more risk-averse or else suffer from some other financing impediment; or (2) owners are more optimistic than fund managers on the prospects for the project. Fund size, operating via the cost of capital, can also affect the existence of solutions. Given that contracting is mutually beneficial, the precise terms depend upon the relative bargaining power of funds versus owners. This may depend upon required rates of return. It also depends upon market structure—the environment may be more conducive to monopoly surplus if search impediments exist for owners, as they might for technological projects or if the market is in an early stage of development. Bargains are often asymmetric, wherein the fund derives a higher share of earnings than pro-rata with its share of financing. Fund size and bargaining power are related especially where fund investors or managers rely on the fund for portfolio, or internal, diversification as opposed to external diversification, in which they invest extensively in other assets. With internal diversification, the fund's cost of capital is size-dependent, in terms of the number of projects on the books. Larger funds acquire bargaining power via a lower cost of capital, leading to higher rates of actual returns and therefore higher fund value. Such effects are not present where investors have external diversification. Because fund returns are generally asymmetric, arising from the significant risk of project failures, it is sometimes thought that the asymmetry constitutes a factor to be priced. As the asymmetry is size-dependent, this would make the cost of capital size dependent as well. However, it turns out that the asymmetry is not in fact priced and that standard CAPM arguments continue to hold. Thus, for external diversification, fund size is mainly a matter of economies of scale in administration, evaluation, and monitoring. In all cases, fund size can be described in terms of equality at the margin between required and available rates of return, and we describe the influences that impinge on both schedules. Generally speaking, the kinds of bargains actually observed, as well as the rates of return and variations therein across funds and over time, are all consistent with predicted bargaining features. They appear also to be consistent with basic finance theory, suggesting that “special” features, such as failure to maximize the expected utility of monetary returns, are not really needed.