Enterprise Debts Analysis Using a Mathematical Model of Production, Considering the Deficit of Current Assets

Abstract

In this paper, we present the results of investigation of the production model that extends Houthakker—Johansen approach of distribution of capacities over technologies and takes into account financial characteristics of manufacturer that works in conditions of current assets deficit and Poisson process of demand arrivals. The model is formalized in form of Bellman equation. The solution of Bellman equation defines the value of a company in dependence on parameters of manufacturing process and economic environment (interest rates, price, cost, etc.). The closed form expression for the solution of Bellman equation and calculation of average characteristics of production activity in model terms allow developing the methodology of calculation and analysis of company’s value that bases on official company reporting data and economic environment parameters. The developed method we apply to compute and analyze the economic conditions of functioning of FCA Company (Fiat Chrysler Automobiles, Italy). We calculate average debt in terms of the model and analyze the dynamic of average debt of FCA. We present the results of modified model investigation that reflects the crisis management strategy of business owner and takes into account the debt load and how it affects the company’s value. The condition of uniqueness for the solution of Bellman equation in modified model is identification of coefficient of debt accounting due to the bankruptcy procedure. In terms of the model, we calculate a closed form of critical debt value that corresponds to the bankruptcy bound.