Liquidity Management with Decreasing-returns-to-scale and Secured Credit Line

TL;DR

This paper studies how cash-constrained firms with access to collateralized debt can optimize dividend and investment policies, considering decreasing returns to scale and performance-sensitive interest rates, using advanced control methods.

Contribution

It introduces a bi-dimensional singular control model incorporating collateralized debt and derives qualitative properties and explicit solutions in special cases.

Findings

Collateralized debt increases investment capacity.

Optimal policies depend on decreasing returns to scale.

Explicit solutions are obtained in specific scenarios.

Abstract

This paper examines the dividend and investment policies of a cash constrained firm that has access to costly external funding. We depart from the literature by allowing the firm to issue collateralized debt to increase its investment in productive assets resulting in a performance sensitive interest rate on debt. We formulate this problem as a bi-dimensional singular control problem and use both a viscosity solution approch and a verification technique to get qualitative properties of the value function. We further solve quasi-explicitly the control problem in two special cases.