A Modelization of Public–Private Partnerships with Failure Time

Abstract

A commissioning of public works (Maitrise d’ouvrage publique, namely MOP in French) is a system where the community has commissioned equipment (hospital, prison, etc.) for its own needs and to bear the cost, partly by self and partly by a loan from a bank. On another hand, public–private partnership (PPP) means that community agrees on a period (15–25 years) with the contractor and is billed rent. More or less it means “leasing” purchase, covering three parts: depreciation of equipment, maintenance costs, and financial costs. This new formula is based on an “ordonnance” of June 17, 2004, amended by the law of 28 July 2008 (see legifrance.gouv.fr), justified by the emergency of requested equipment construction or its complexity. Our aim is to study the advantages and disadvantages of the new PPP formula. Here is a particular case of a risk-neutral consortium. We discuss the advantages of outsourcing (“externalization”) in terms of model parameters and prove that externality is interesting only in case of large enough noise when we exclude the risk of bankruptcy. Indeed, this risk does not seem covered under current legislation. Finally, we study what could happen in case of failure penalties to be paid by the private consortium. In such a case, externality could be interesting in some context as high noise, high reference cost, short maturity, and high enough penalty.