Budgeting Models and System Simulation: A Dynamic Approach

Abstract: The goal of the present paper is to create a mathematical cash budgeting model capable of providing information on the liquidity state of a company, as well as its assets and liabilities, in a dynamical perspective. The aim of this innovative tool is to originate a new class of models able to adapt to the ever-changing planning and control requirements that come from the most different economic subjects, with special regard both to the firm liquidity dynamics issues and to the IT developments. In order to create such a model, the authors have decided to move from the logical structure inherent in double entry bookkeeping practices, as well as in the financial statement and the balance sheet accounts relationships, trying to provide a mathematical formalization for them. In greater detail, this work wants to show how, upon choosing a set of accounting items suitable for the researcher purposes, bookkeeping procedures and the relationships between the aforementioned items can be described through the use of difference equations. This mathematical description will allow us to model the dynamics of the cash flow budget and at the same time the dynamics of the entire balance sheet. After choosing a set of accounting items convenient for the scope of our presentation, an example of cash flow budget is displayed together with another important feature of the present model: its closed form mathematical solution after n-periods. This solution gives us information about the financial statement as well as the whole balance sheet of an enterprise after n-periods, proving this mathematical formalization to be a possible useful tool not only to simulate the firm budget but for the most different economic and financial purposes. Moreover, this model allows the researcher and the firm management to conduct easily tests on company policies in order to obtain a deeper knowledge of the firm economic processes.