Optimal contracting with effort and misvaluation

Abstract

We propose a new continuous time contracting model, where the project value process can only be observed with noise, and there are two sources of moral hazard: effort and misvaluation. We consider an economic scenario where principal and agent can alter the fundamental value of the firm through misvaluation, thus increasing the price estimated by the market. In doing so, the latter uses a level of effort and misvaluation that he believes the agent will apply. We specialize the framework to analyze in detail two cases, namely when the market can only correctly anticipate the effort, and when it can correctly anticipate both. In the first case, we find that it is optimal for the principal to induce the agent to misvalue the firm. Using calculus of variation techniques, we recover the optimal pay-per-performance sensitivity (PPS) of the contract, optimal effort and misvaluation action, as the solution of a second order ordinary differential equation. In the second case, we find that it is not in the interest of the principal and agent to fool the market through misvaluation.