informs ® doi 10.1287/deca.1050.0040 © 2005 INFORMS Traditional decision analysis methods can provide an intuitive approach to valuing projects with managerial flexibility or real options. The discrete-time approach to real-option valuation has typically been implemented in the finance literature using a binomial lattice framework. Instead, we use a binomial decision tree with risk-neutral probabilities to approximate the uncertainty associated with the changes in the value of a project over time. Both methods are based on the same principles, but we use dynamic programming to solve the binomial decision tree, thereby providing a computationally intensive but simpler and more intuitive solution. This approach also provides greater flexibility in the modeling of problems, including the ability to include multiple underlying uncertainties and concurrent options with complex payoff characteristics. Key words: decision analysis; real options; decision trees; binary approximation

The participation of private capital in public infrastructure investment projects has been sought by many governments who perceive this as a way to overcome budgetary constraints and foster economic growth. For some types of projects, this investment may require government participation in the form of project guarantees in order to reduce the risk to the private investor, and as a consequence, the government assumes a contingent liability which may have significant future budgetary impacts. We present a minimum traffic guarantee (MTG) real options model that differs from most of the literature in the field by using market data to determine stochastic project parameters. This model can be used to assess the value of these guarantees, allows the government to analyse the cost-benefit of each level of support, and proposes an alternative to limit the exposure of the government while still maintaining the benefits to the private investor. We apply this model to the projected 1000 mile long BR-163 toll road that will link the Brazilian Midwest to the Amazon River. We conclude that the use of public-private partnerships (PPP) with guarantees and caps on total government outlays can be modelled effectively using option pricing methods and can be a solution to attract private investment to high risk public infrastructure projects.Real options, infrastructure projects, toll roads, government guarantees, concessions,

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I n this note, we respond to Smith's (2005) discussion of the approach outlined in our paper (Brandão et al. 2005) on using traditional decision analysis methods to solve real-options problems. Our response addresses several areas where we largely agree with Smith, but have different views on modeling preferences or on the practicality of implementing alternative modeling approaches. We view the issue raised by Smith on the estimation of process volatility to be a valid concern and propose a modification to our method to address this problem.

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In this paper we seek to enhance the real options methodology developed by Copeland and Antikarov (2001) with traditional decision analysis tools to propose a discrete time method that allows the problem to be specified and solved with off the shelf decision analysis software. This method uses dynamic programming with an innovative algorithm to model the project's stochastic process and real options with decision trees. The method is computationally intense, but simpler and more intuitive than traditional methods, thus allowing for greater flexibility in the modeling of the problem.

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