Page 327 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

Table 10.5 Possible Combinations of Values for Three Parameters

From Table 10.5, it can be seen that Scenario 9 is the worst case and Scenario 19 is the best case. Either
of these two cases has a 1 in 27 (or 3.7%) chance of occurring. Based on this result, it is not very likely
that either of these scenarios would occur, and hence we should be careful in evaluating the scenario
analysis. This is indeed one of the main shortcomings of the scenario analysis [2]. In reviewing Table
10.5, a better measure of the expected profitability might be the weighted average of all 27 possible
outcomes. The idea of weighting results based on the likelihood of occurrence is the basis of the
probabilistic approach to quantifying risk that will be discussed shortly. However, before looking at that
method, it will be instructive to determine the sensitivity of the profitability of the project to changes in
important parameters. Sensitivity analysis is covered in the next section.

Sensitivity Analysis. To a great extent, the risk associated with the variability of a given parameter is
dependent on the effect that a change in that parameter has on the profitability criterion of interest. For the
sake of this discussion, the NPV will be used as the measure of profitability. However, this measure
could just as easily be the DCFROR, DPEP, or any other profitability criterion discussed in Section 10.2.
If it is assumed that the NPV is affected by n parameters (x , x , x , ..., x ), then the first-order sensitivity
1 2 3 n
to parameter x is given in mathematical terms by the following quantity:
1