Valuating the capital structure under incomplete information

Abstract

Can higher uncertainty increase the valuation (market-to-book value) of young firms compared to more established ones? As the current market shows higher levels of uncertainty about companies’ expected cash flows and changes in firm value, the question of the fundamental convex relationship between the two becomes more relevant. This paper aims to study how cash flow uncertainty affects the capital structure/leverage of a firm over time. A simple Bayesian learning framework is employed to assess leverage ratios in the presence of parameter uncertainty about expected cash flow. This study provides an analytical solution for leverage as a function of firm age and explores the implications using numerical results. The model links market leverage with expected cash flow volatility and firm age. Young firms face uncertainty about their expected cash flows and hence their firm value. Managers continuously update their evaluation of leverage ratios when they observe realized cash flow until firms reach maturity. Therefore, the paper provides a novel explanation of why the leverage ratio for many start-ups increases over time: the resolution of uncertainty decreases upside shock expectations as the firm ages. This result is useful both for academics, who can test the formulas derived in this paper for various industries, countries, and conditions, and for practitioners, who can use them to calibrate algorithmic trading models when linking uncertainty and firm valuation.

Keywords

• Bayesian learning
• cash flow
• leverage ratio
• life cycle
• parameter uncertainty