# **Project evaluation under uncertainty**

_INFRISK_ draws on recent developments in the literature on project evaluation under uncertainty6 to generate _probability distributions_ for key decision variables, such as a project's net present value (NPV), internal rate of return (IRR), or a project's capacity to service its debt on time during the life of the project. Such distributions are then used in assessing a project's economic viability, which is taken as the key criterion in project selection. Thus, judgement on the economic viability of a project is not based solely on a single "best estimate" of a project's metrics, i.e. net present value or debt service capacity, but also on the possible ranges of such variables and the likelihood of their occurrence within given ranges (see Box 1).

_INFRISK_ is capable of handling several sources of uncertainty and risk bearing on a project's economic viability. Such risks, for example, could be associated with the _revenue stream_ (tariff rate, demand forecast for electricity in a power project, or traffic volume forecast in a toll road project), _operations and maintenance costs,_ and _construction cost._ The user has the option of choosing the key risk variable or variables upon which to focus, depending on the specific features of the infrastructure project at hand and the questions being addressed.

For a particular risk variable of interest, the program first generates a stream of probability distributions for each year of a project's life through a Monte Carlo simulation technique, the methodology for which is well known and is described in Box 2 and Annex 1. Typically, the relevant risk variable in a project, i.e. demand forecast, costs, and tariffs can be quantified in terms of both single best-guess estimates as well as a range of estimates over the life of a project or the early years in a project's life. Using such information, a suitable probability distribution is assigned to each risk variable within a specified range. Care must be taken to ensure that such _a priori_ assigned probability distributions are consistent with the economic/statistical time series characteristics of relevant risk variables. For instance, exchange rates are known to obey a log-normal distribution, while revenue from a toll-road project is likely to exhibit an asymmetric probability distribution profile, such as a Beta distribution. _INFRISK_ offers the flexibility of incorporating four classes of probability distributions (uniformn, normal, lognormal, and beta) which provide a broad menu of probabilistic representation of relevant economic variables in an infrastructure project.

Specification of uncertainty through time may affect a project's cash flows and is also an important issue in project valuation. The pattern according to which uncertainty is resolved over time clearly varies from project to project, and requires careful consideration. For most infrastructure projects, the nature of risk changes fundamentally as the project reaches completion and is ready for operation. For this reason, _INFRISK_ explicitly recognizes the two main phases of project development and project operation. To specify how risk evolves over time, we focus on the variance of a given risk variable.

> **6** The literature on project appraisal under uncertainty goes back to Hertz (1964, 1979) and work done at The World Bank in the early 1 970s (Pouliquen, 1970, World Bank, 1970). Subsequent contributions include Hertz and Thomas (1983), and most recently, the application of real option-theoretic models to project valuation. See also Paddock, Siegel and Smith (1988); as well as Copeland and Keenan (1998).

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