Annex 1: Cost-benefit analysis for vulnerability reduction in the context of uncertainty

The degree of risk and uncertainty differs in different elements of a large project, and may also vary over time. An important task for the planner is to identify areas of sensitivity and to describe them clearly, so that any decision is made with an understanding of how reliable the basic information is. Sensitivity analysis consists of testing the effects of variations in selected costs and benefit variables on the project’s rate of return or net present value.

Cost-benefit analysis for development projects in the context of uncertainty is the subject of a number of guidelines produced by development institutions. (See for example, World Bank Central Project’s Note 2.02, “Risk and Sensitivity Analysis in the Economic Analysis of Projects.”)

According to different forecasts or estimates of future events, the projected net present value of a project can vary over a wide range. Under some conditions a probability value can be assigned to a given outcome. A value known as the expected value of the net present value of the project takes into account the entire range of possible present values of net benefits from the project. It is calculated by weighing all possibilities with their corresponding relative frequencies or probabilities, and summing to give an average figure.

For example, if the net present value can take values of +$20 million with a probability of 0.7 and -$80 million with a probability of 0.3, then the expected NPV of the project is (0.7 × 20) + (-0.3 × 80), or -$10 million. (Projects with a negative NPV will normally be rejected). Sensitivity analysis involves testing how changes in selected cost and benefit variables affect a project’s net present value. It helps to identify what, in most cases, will be a small number of variables - changes which cause the greatest variation in the net present value. These are the factors which usually need the most detailed investigation and where management effort to prevent negative impacts will probably be most influential. A basic requirement is to identify those values of the variables at which the net present value of the project becomes zero (so-called “switching values”). The technique is theoretically fairly straightforward, but complicated in practice by correlation among variables, and the need to take variation in clusters of variables into account.

Individual variables can be assigned probability distributions for their values. With appropriate statistical advice, samples from these probability distributions, fed into the sensitivity analysis process, can sometimes be used to generate a sample of net present values which approximates the true probability distribution of the net present values. It is then possible to give some estimate of the percentage of outcomes in which the net present value will be unacceptable.