*Discussion Issues and Derivations*

*Are we double counting risk when we do what-if analysis? *

Consider the following scenario. You have computed the net present value of a project, using projected cash flows and a risk-adjusted discount rate, and the net present value is positive. You proceed to do sensitivity analysis on the NPV, changing the variables, and discover the NPV turns negative fairly frequently. You therefore reject the project. There are two primary problems with sensitivity analyses:

a. It can be argued here that risk has been considered twice, once in the discount rate and again in the sensitivity analysis. If the risk assessment in the discount rate is correct, a project with a positive net present value is a good project, no matter what the sensitivity analysis concludes.

b. There is another problem with sensitivity analysis. The only risk that should be considered in investment analysis is market risk or non-diversifiable risk. In most "what-if" analysis, the variables that get analyzed are firm-specific variables, which at the margin are diversifiable.
*What is the best way to use sensitivity analysis?*

Sensitivity analysis is most useful when you have to choose between projects or alternatives. When two projects rank fairly equally on a primary measure (NPV, IRR), an argument can be made that the project that is less sensitive to changes in the assumptions should be chosen.

*Probability Distributions in Simulation: The Practical Questions *

There are a number of choices here, ranging from discrete probability distributions (probabilities are assigned to specific outcomes), to continuous distributions (the normal or exponential distribution). In making this choice, the following factors should be considered:

a. the range of feasible outcomes for the variable; (e.g., the revenues cannot be less than zero, ruling out any distribution that requires the variable to take on large negative values, such as the normal distribution).

b. the experience of the company on this variable, with similar projects in the past. Data on a variable, such as operating margins on past projects, may be plotted to see what distribution best fits the data; statistical techniques exist that check for this fit.

While no distribution will provide a perfect fit, the distribution that best fits the data should be used.

It is far easier to estimate probability distributions for projects, when firms have analyzed similar projects in the past.