## A Brief Guide to Engineering Financial Calculations: Uncertainty

Key Assumptions

Most of our calculations have been done with the assumption that the parameters are known. In reality, there is often a lot of uncertainty in our estimates, and no one really knows what interest rates will be a couple of years in the future. To deal with such uncertainty, analysts use probability distributions or other methods to describe the uncertainty. A simple way to describe uncertainty is to state the most likely value, and a number on either side that represents the “worst-case” value and the “best-case” value. Ideally these would bracket the risk associated with the uncertainty.

Calculations

For each parameter, choose a value for the most likely case, the worst case, and the best case.

*Best-Case/Worst-Case Scenarios*

Do the analysis first using the most likely values for the parameters. This gives the realistic result.

Repeat the analysis, assigning all the uncertain parameters their best-case values. This gives the optimistic result.

Repeat the analysis, assigning all the uncertain parameters their worst-case values. This gives the pessimistic result.

*Sensitivity Analysis*

Do the analysis first using the most likely values for the parameters. This gives the realistic result.

Repeat the analysis, but varying only one of the uncertain parameters. The set of results shows the sensitivity of the answer to variability of that particular parameter. Computing the variation of a particular parameter that would cause a decision to change yields the sensitivity of the decision to that parameter.

*Monte Carlo Analysis*

A more sophisticated uncertainty analysis uses not just three values for the range of a parameter, but a broader range in a probabilistic distribution. (The distribution can be a continuous function, or it can be a discrete set of values.) Monte Carlo analysis does the same analysis over and over, picking random variables from all of the probably distributions of the parameters. The result is a probabilistic representation of the result of the analysis.