Considering risk within net present value: calculations for government projects.

INTRODUCTION

Net present value (NPV) is a technique that is used to assess the viability of projects based on the projected receipts and disbursements over the projects' planning horizons. It can, however, become difficult to arrive at credible single point estimates for some of these cash flows. Increases in project complexity, increases in planning horizons, and the need to engage multiple subcontractors are all factors that increase the risk in developing an accurate NPV. One possible approach to address this problem is to incorporate the risks associated with each of these factors into the decision-making process to arrive at a project NPV.

There are several methods for dealing with uncertainty and risk in financial models. One of these methods is Monte Carlo simulation, which uses random sampling of input (independent) parameters to model uncertainty. Statistical analysis of the output of the simulation runs can then be used to formulate conclusions about the model (Taha 2003). Common statistics for Monte Carlo simulation include the mean, standard deviation, minimum, and maximum for all output (dependent) variables. Often enough runs are conducted such that the central limit theorem can be applied, normality assumed, and a confidence interval about the mean can be calculated. The inherent problem to this approach is that it can be hard to capture within a traditional simulation model the thought process associated with assessing risk, as opposed to collecting statistics that measure uncertainty. In many situations where risk is under consideration, decision-makers could simply want to determine an extreme value for an output, such as NPV, that can be incorporated when reducing the number of alternatives under consideration.

With real options, decision-makers approach a project by examining it in stages rather than as a whole. This analysis method rewards flexibility by allowing the decision-maker a "right, but not an obligation" to invest in real assets (Park 2007, p. 670). Essentially, one has the opportunity to react to potentially changing situations in the future, as events occur or more information is obtained, rather than act immediately. There are several advantages to this method for evaluating projects costs; however, Eschenbach, et al. (2009) point out that "far too often" ignoring the costs associated with delaying a project can result in a "near fatal flaw in most engineering economy analyses" (p. 3). Lewis et al. (2008) note that another problem with real options is that volatility of the option is not appropriately estimated. Given that many engineering projects cannot easily or practically be delayed, real options is not necessarily an appropriate decision tool (Eschenbach et al. 2007).

Another option for dealing with risk is to incorporate the concept of risk attitudes, which involves determining whether an individual or organization displays risk-seeking, risk-neutral, or risk-averse behavior (Clemen and Reilly 2001). Utility functions are generally used for describing these attitudes and involve equating dollars amounts to utility values. There are multiple techniques for assessing a utility function, but these are typically iterative and can be quite time consuming. Walls (2005) has developed a survey technique that is quite effective at measuring the risk tolerance for a group of managers, but the method is more appropriate for strategic investment decisions rather than for a specific project.

This article explores a methodology to address the risk in developing NPVs for complex aerospace projects. The method looks at an extreme (worst-case) scenario, which can be used in conjunction with simply examining the deterministic NPV or a method such as simulation using the mean and standard deviation to determine a confidence interval about the mean. Unlike real options, which assumes that there may be value in delaying a decision, this method quantifies risks over the life of the project without considering delaying the project. The inherent simplicity of this method makes it more suitable for examining the risks in a single project rather than multiple strategic investments within an organization. This method is meant to provide the decision-maker with additional information and quantifies the difference between the higher risks associated with projects still in the early phases of development compared to the lower risks of more mature projects. First, a test project, the need for and the current development status of a J-2X to support the new Ares I and Ares V launch systems, is discussed. Next, two approaches to modifying NPV, those by Davis (2002) and Ridlehoover (2004), are presented. Finally, a modified approach based on the work by Davis and Ridlehoover is presented and applied to the J-2X engine nozzle trade study. The article concludes with a summary of the conclusions drawn from this effort and the identification of further work that should be pursued.

This work contributes to existing decision analysis and engineering economy knowledge in the following ways: (1) expanding Ridlehoover's (2004) model to address a minimum cost situation such as those seen in government applications; (2) incorporating risks associated with life cycle stages separately from the subjective assessment of the uncertain parameters; and (3) providing a detailed matrix for assessing the risk level for various risk factors. The application presented addresses the risk in cost estimating for complex aerospace development projects.