Assigning Correlations among Project Components

After the analyst has identified all the relevant variables and specified their probability distributions, the next step is to make some judgments about the covariances among the different variables. Failure to specify covariances and to take them into account may lead to large errors in judging risk. For example, in a pioneering study on the use of risk analysis, Pouliquen  noted that the risk of project failure was estimated at about 15 percent when two important variables—labor productivity and port capacity—were treated as independent, and at about 40 percent when their positive correlation was introduced into the analysis.

Analysts may need to treat variables jointly if they are statistically dependent. In such a case they should specify, in principle, the multivariate joint distributions involved. Specification of multivariate distributions can be extremely complex, but to resort to comprehensive descriptions of statistical polygons, dependence is seldom necessary in applied project work. Rather, pragmatic methods are readily available for imposing arbitrary levels of statistical dependence. Analysts usually do this by specifying a rank correlation coefficient for each designated pair of variables. The individual variables can be of any specified type, and many different types are available in commercial software: normal, triangular, beta, exponential, and the like, as well as arbitrary continuous and discrete distributions. The final step consists of putting it all together—estimating the expected NPV and its attendant probability distribution, which includes the probability that the project’s NPV is negative.

The results of the analysis can be reported in condensed form through summary statistical measures such as the expected NPV and its coefficient of variation. Analysts will also naturally wish to examine the complete probability distribution of project performance, for example, by depicting graphically the complete CDFs for the project’s NPV   Analysts can read one key measure—the probability that the project’s NPV is less than zero—directly from such CDFs. An illustration of such an analysis based on a hypothetical example using a spreadsheet-based program follows.

A Hypothetical Example: Advantages of Estimating Expected NPV and Assessing Risk

The Caneland Republic is typical of several efficient producers and exporters of cane sugar in that because sugar makes up about 35 percent of exports, it is a major source of foreign exchange. Because the price of sugar fluctuates considerably, however, earnings from sugar exports are unstable, which contributes to significant macroeconomic fluctuations. Gross value of sugar production constitutes about 10 percent of GDP, but this is varies considerably, from 27 percent in 1974 to 4 percent in 1978. GDP and sugar prices are highly correlated. For a recent 21-year period, there is a simple correlation of 0.32 between the residuals from constant  growth rate trends of real GDP and sugar output valued at the real international price. This valuation ignores domestic sugar pricing and the price realized on privileged sales to the United States and other importers.

The hypothetical project involves a major new sugar estate and associated infrastructure of mills, roads, and other handling facilities. When the project is fully on stream, farmers will harvest an additional 30,000 hectares of cane annually. When processed, the farmers will have to sell the sugar on the international market, within the limits agreed under the International Sugar Agreement.