314 CHAPTER 8 Cash Flow Estimation and Risk Analysis
assessing a project’s stand-alone risk: (1) sensitivity analysis, (2) scenario analysis, and
(3) Monte Carlo simulation.Sensitivity Analysis
Intuitively, we know that many of the variables that determine a project’s cash
flows could turn out to be different from the values used in the analysis. We also
know that a change in a key input variable, such as units sold, will cause the
NPV to change. Sensitivity analysisis a technique that indicates how much NPV
will change in response to a given change in an input variable, other things held
constant.
Sensitivity analysis begins with a base-casesituation, which is developed using the
expectedvalues for each input. To illustrate, consider the data given back in Table 8-3,
where projected cash flows for RIC’s computer project were shown. The values used
to develop the table, including unit sales, sales price, fixed costs, and variable costs, are
all most likely, or base-case, values, and the resulting $5.809 million NPV shown in
Table 8-3 is called the base-case NPV.Now we ask a series of “what if” questions:
“What if unit sales fall 15 percent below the most likely level?” “What if the sales price
per unit falls?” “What if variable costs are $2.50 per unit rather than the expected
$2.10?” Sensitivity analysis is designed to provide decision makers with answers to
questions such as these.
In a sensitivity analysis, each variable is changed by several percentage points
above and below the expected value, holding all other variables constant. Then a new
NPV is calculated using each of these values. Finally, the set of NPVs is plotted to
show how sensitive NPV is to changes in each variable. Figure 8-1 shows the com-
puter project’s sensitivity graphs for six of the input variables. The table below the
graph gives the NPVs that were used to construct the graph. The slopes of the lines in
the graph show how sensitive NPV is to changes in each of the inputs: the steeper the
slope, the more sensitive the NPV is to a change in the variable.From the figure and the
table, we see that the project’s NPV is very sensitive to changes in the sales price and
variable costs, fairly sensitive to changes in the growth rate and units sold, and not
very sensitive to changes in either fixed costs or the cost of capital.
If we were comparing two projects, the one with the steeper sensitivity lines would
be riskier, because for that project a relatively small error in estimating a variable such
as unit sales would produce a large error in the project’s expected NPV. Thus, sensi-
tivity analysis can provide useful insights into the riskiness of a project.
Before we move on, we should note that spreadsheet computer programs such as
Excelare ideally suited for sensitivity analysis. We used the Data Table feature in the
file Ch 08 Tool Kit.xls,on the textbook’s web site, to generate the table used for Fig-
ure 8-1. To conduct such an analysis by hand would be extremely time consuming.Scenario Analysis
Although sensitivity analysis is probably the most widely used risk analysis technique,
it does have limitations. For example, we saw earlier that the computer project’s NPV
is highly sensitive to changes in the sales price and the variable cost per unit. Those
sensitivities suggest that the project is risky. Suppose, however, that Home Depot or
Circuit City was anxious to get the new computer product and would sign a contract
to purchase 20,000 units per year for four years at $3,000 per unit. Moreover, suppose
Intel would agree to provide the principal component at a price that would ensure that
the variable cost per unit would not exceed $2,200. Under these conditions, there
would be a low probability of high or low sales prices and input costs, so the project
would not be at all risky in spite of its sensitivity to those variables.