Question

Suppose that implementing an idea requires 50 thousand dollars, and your start-up then suc- ceeds with probability p, generating 150 thousand dollars in revenue (for a net gain of 100 thousand dollars), or fails with probability 1 − p (for a net loss of 50 thousand dollars). The success of each idea is independent of every other. What is the condition on p that you need to satisfy to secure the venture capitalist’s funding?

Answer 1

When this information is verifiable –that is, it can be materialized in objective performance indicators or milestones– it is possible to design a fully contingent financing contract. This contract explicitly determines the conditions for the continuation of the venture on to the expansion stage as well as the final sharing of its success return between the entrepreneur and the venture capitalist. We have found that the optimal contract assigns the venture capitalist a share that is independent from the venture’s success return and, hence, can be interpreted as a straight equity claim. The size of such share is increasing in both the relative importance of the managerial contribution of the venture capitalist and the size of the investments for which he has to be compensated. Interestingly, there is a range of profitability states in which the expansion investment occurs despite the fact that the venture capitalist’s continuation pay off is negative. In this sense, the contract exhibits some cross - subsidization from high to low profitability states.When the interim information is not verifiable –that is, no relevant milestones can be found– the previous type of arrangement is not feasible. In particular, under stage financing the funds for each investment round are raised as they are needed. In this case, the cross-subsidization that characterizes contingent financing is no longer possible and the continuation on to the expansion stage is solely determined by the venture capitalist’s ex-post participation constraint. Yet the security design problem is not trivial, as the financing of the start-up investment requires pledging a share of the success return which will condition the resolution of the incentive problems present at the expansion stage. Such initial claim will be renegotiated at the expansion stage,giving raise to the final sharing of the venture’s success return. We have shown that the design of the optimal initial claim is directed to make this sharing as close as possible to a constant. In fact, for low profitability states, the sole funding of the expansion investment will already require too large a share and, hence, the optimal initial claim must avoid further distortions by giving nothing to the venture capitalist.At higher profitability states, the final constant share is implementable through an initial claim that is increasing in the venture’s success return.Thus, the initial contract is associated with a non-linear claim that, as we have explained, resembles the pay off structure of a sequence of warrants with increasing strike prices.