Optimal equity split under unobservable investments

This paper examines the optimal equity split between a penniless entrepreneur (E) and a deep-pocketed venture capitalist (V) cooperating in a two-stage investment project. The first-stage investment explores project profitability, and the final success probability is a function of V's unobservable investment amount, E's and V's private effort like the Cobb-Douglas production function. We show that if project profitability is good enough, the optimal equity split and the welfare loss rate arising from moral hazard are explicitly determined by the project inputs' output elasticities, independent of project profitability and inputs' costs. If project profitability is not contractible, we propose a new renegotiation mechanism. The renegotiation is profitable only when V's participation constraint is not met. We identify the thresholds determining whether E should abandon the project, whether E should go ahead without any changes, and whether E should increase V's equity or roll back cash to V. We show that the initial wealth transferred from V to E can be appropriated upon renegotiation to realize a Pareto improvement; our model provides a novel explanation why internal financing is preferred.