Continuity or Liquidation in Situations of Ambiguity: Fuzzy Binomial Model to Valuate Leveraged Firms

Abstract

This paper proposes a fuzzy binomial valuation model to estimate leveraged firm value while
conditioning its continuity or liquidation in cash flow generation after taxes to attend debt
payments. It includes two triangular fuzzy variables. Thus, we incorporate ambiguity in the
firm valuation process characterized by uncertainty in projections of both growth and
financial costs. Our proposed model is presented, developed, and exemplified through a case
which results complement both the DCF (under the adjusted present value) and the traditional
real option binomial method. This occurs because, in one hand, DCF method assumes
decisions’ irreversibility and operating firms’ situation. On the other hand, traditional
binomial model weakens previous restrictions but does not incorporate ambiguous variables
in the analysis. Hence, fuzzy logic applied to option models allows us to complement
probabilistic valuation approach working on a frame of possibilities.