A Two-Factor Uncertainty Model to Determine the Optimal Contractual Penalty for a Build-Own-Transfer Project

47 Pages Posted: 19 May 2013 Last revised: 24 Jun 2013

See all articles by João Adelino Ribeiro

João Adelino Ribeiro

Universidade Autónoma de Lisboa Luís de Camões

Paulo Jorge Pereira

Universidade do Porto - Faculdade de Economia (FEP)

Elisio Brandao

Universidade do Porto - Faculdade de Economia (FEP)

Date Written: May 20, 2013

Abstract

Public-Private Partnerships (PPP) became one of the most common types of public procurement arrangements and Build-Own-Transfer (BOT) projects, awarded through adequate bidding competitions, have been increasingly promoted by governments and other public entities. The theoretical model herein proposed is based on a contractual framework where the government grants leeway to the private entity regarding the timing for project implementation. However, the government is aware that delaying the beginning of operations will lead to the emergence of social costs, i.e., the costs that result from the corresponding loss of social welfare. This fact should motivate the government to include a contractual penalty in case the private firm does not implement the project immediately. The government also recognizes that the private entity is more efficient in constructing the project facility. Considering both the existence of social costs and the private firm's greater efficiency, the model's outcome is the optimal value for the legal penalty the government should include in the contract form. A two-factor uncertainty approach is adopted, where the facility construction costs and the cash-flows to be generated by running the subsequent activities follow geometric Brownian motions that are possibly correlated. Adkins and Paxson ((2011)) quasi-analytical approach is followed since homogeneity of degree one can not be invoked in all of the model's boundary conditions. Sensitivity analysis reveals that variations both in the correlation coefficients and in the standard deviations have a strong impact on the optimal contractual penalty. Sensitivity analysis also demonstrates that there is a level of social costs above which the inclusion of a legal penalty is necessary and, similarly, that there is a level for the comparative efficiency above which the inclusion of a legal penalty is not justifiable. The analytical solution to determine each of these values is presented. Finally, the effects of including a non-optimal penalty value in the contract form, which result from overestimating or underestimating the selected bidder's real comparative efficiency are examined, using a numerical example. Results demonstrate that overestimating (underestimating) the selected bidder's real comparative efficiency leads to the inclusion of a below-optimal (above-optimal) value for the legal penalty in the contract and produces effects that the government would prefer to prevent.

Keywords: real options, two-factor uncertainty models, public-private partnerships, optimal contractual penalty

JEL Classification: G31, D81

Suggested Citation

Ribeiro, João Adelino and Pereira, Paulo and Brandão, Elísio Fernando Moreira, A Two-Factor Uncertainty Model to Determine the Optimal Contractual Penalty for a Build-Own-Transfer Project (May 20, 2013). Available at SSRN: https://ssrn.com/abstract=2266920 or http://dx.doi.org/10.2139/ssrn.2266920

João Adelino Ribeiro (Contact Author)

Universidade Autónoma de Lisboa Luís de Camões ( email )

Lisbon
Portugal

HOME PAGE: http://autonoma.pt

Paulo Pereira

Universidade do Porto - Faculdade de Economia (FEP) ( email )

Rua Roberto Frias
s/n
Porto, 4200-464
Portugal

Elísio Fernando Moreira Brandão

Universidade do Porto - Faculdade de Economia (FEP) ( email )

Rua Roberto Frias
s/n
Porto, 4200-464
Portugal

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