Valuating the capital structure under incomplete information

  • Received June 4, 2023;
    Accepted July 5, 2023;
    Published July 18, 2023
  • Author(s)
  • DOI
    http://dx.doi.org/10.21511/imfi.20(3).2023.05
  • Article Info
    Volume 20 2023, Issue #3, pp. 48-67
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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.

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    • Figure 1. Market value is convex in mean cash flow
    • Figure 2. Leverage ratio declines over mean log cash flow
    • Figure 3. Posterior volatility declines over age
    • Figure 4. Cash flow volatility is inversely related to leverage ratios
    • Figure 5. Leverage ratio varies over age without learning
    • Figure 6. Leverage ratio varies over age with learning
    • Conceptualization
      Dong Meng Ren, Yunmin Chen, Alex Maynard
    • Data curation
      Dong Meng Ren
    • Formal Analysis
      Dong Meng Ren, Alex Maynard
    • Funding acquisition
      Dong Meng Ren, Sergiy Pysarenko
    • Methodology
      Dong Meng Ren
    • Software
      Dong Meng Ren, Yunmin Chen
    • Visualization
      Dong Meng Ren
    • Writing – original draft
      Dong Meng Ren
    • Investigation
      Yunmin Chen, Alex Maynard, Sergiy Pysarenko
    • Validation
      Yunmin Chen, Alex Maynard, Sergiy Pysarenko
    • Writing – review & editing
      Yunmin Chen, Alex Maynard, Sergiy Pysarenko
    • Supervision
      Alex Maynard
    • Resources
      Sergiy Pysarenko