Value maximization under present-biased preferences

We examine a value-maximizing problem involving present-biased behavior, a prevalent and empirically observed psychological phenomenon, in a firm’s strategic decisions on earnings retention, payout, and capital injections. By modeling present-biased preferences using stochastic quasi-hyperbolic discounting, we frame the decision-making process as an intrapersonal game with sophisticated agents and seek equilibrium solutions. Our analysis within a spectrally positive Lévy framework confirms the solvability of the issue and yields closed-form solutions, showing that double-barrier strategies are Markov perfect equilibrium strategies. We find that present-biased agents adopt equilibrium strategies with lower retention levels and start dividend payouts earlier, resulting in a reduction in overall value compared to scenarios with exponential discounting. In addition, we address bailout optimality, specifying the necessary and sufficient conditions for it.