Model for the Value of a Business, Some Optimisation Problems in its Operating Procedures and the Valuation of its Debt

In this paper we present a model for the value of a firm based on observable variables and parameters: the annual turnover, the expenses, interest rates. This value is the solution of a parabolic partial differential equation. We show how the value of the company depends on its legal status such as its liability (i.e. whether it is a Limited Company or a sole trader/partnership). We give examples of how the operating procedures can be optimised (e.g. whether the firm should close down, relocate etc.). Finally, we show how the model can be used to value the debt issued by the firm.