378 Part 4 Investing in Long-Term Assets: Capital Budgeting
the input variables would produce large changes in the NPV. Thus, sensitivity
analysis provides useful insights into a project’s risk.^612-5b Scenario Analysis
In sensitivity analysis, we change one variable at a time. However, it is useful to
know what would happen to the project’s NPV if all of the inputs turned out to be
better or worse than expected. Also, we can assign probabilities to the good, bad,
and most likely (or base-case) scenarios, then " nd the expected value and the stan-
dard deviation of the NPV. Scenario analysis allows for these extensions—it
allows us to change more than one variable at a time, and it incorporates the prob-
abilities of changes in the key variables.
In a scenario analysis, we begin with the base-case scenario, which uses the
most likely set of input values. We then ask marketing, engineering, and other
operating managers to specify a worst-case scenario (low unit sales, low sales
price, high variable costs, and so forth) and a best-case scenario. Often the best
and worst cases are de" ned as having a 25% probability of conditions being that
good or bad, with a 50% probability for the base-case conditions. Obviously, con-
ditions can take on many more than three values, but such a scenario setup is use-
ful to provide an idea about the project’s riskiness.
The best-case, base-case, and worst-case values for Project S are shown in
Figure 12-2, along with plots of the data. If the project is highly successful, the com-
bination of a high sales price, low production costs, and high unit sales will result
in a very high NPV, $7,450.38. However, if things turn out badly, the NPV will be a
negative $4,782.40. The graphs show the wide range of possibilities, suggesting that
this is a risky project. If the bad conditions materialize, the company will not go
bankrupt—this is just one project for a large company. Still, losing $4,782.40 (or
$4,782,400 since we are working in thousands) would hurt the stock price.
If we multiply each scenario’s probability by the NPV under that scenario and
then sum the products, we will have the project’s expected NPV, $706.40 as shown
in Figure 12-2. Note that the expected NPV differs from the base-case NPV. This is
not an error—mathematically, they are not equal. We also calculate the standard
deviation of the expected NPV; it is $5,028.94. When we divide the standard devia-
tion by the expected NPV, we get the coef" cient of variation, 7.12, which is a mea-
sure of stand-alone risk. The " rm’s average project has a coef" cient of variation of
about 2.0, so the CV of 7.12 indicates that this project is much riskier than most of
the " rm’s other projects.
Our " rm’s WACC is 10%, so that rate should be used to " nd the NPV of an
average-risk project. Project S is riskier than average, so a higher discount rate
should be used to " nd its NPV. There is no way to determine the “correct” dis-
count rate—this is a judgment call. However, some " rms increase the corporate
WACC when they evaluate projects deemed to be relatively risky and reduce it for
low-risk projects. When the NPV was recalculated using a 12.5% WACC, the base-
case NPV fell from $78.82 to $33.62; so the project still passed the NPV test.
Note that the base-case results are the same in our sensitivity and scenario
analyses; but in the scenario analysis, the worst case is much worse than in the sen-
sitivity analysis and the best case is much better. This is because in scenario analysis,
all of the variables are set at their best or worst levels, while in sensitivity analysis,
only one variable is adjusted and all the others are left at their base-case levels.Scenario Analysis
A risk analysis technique in
which “bad” and “good”
sets of financial
circumstances are
compared with a most
likely, or base-case,
situation.Scenario Analysis
A risk analysis technique in
which “bad” and “good”
sets of financial
circumstances are
compared with a most
likely, or base-case,
situation.
Base-Case Scenario
An analysis in which all of
the input variables are set
at their most likely values.Base-Case Scenario
An analysis in which all of
the input variables are set
at their most likely values.
Worst-Case Scenario
An analysis in which all of
the input variables are set
at their worst reasonably
forecasted values.Worst-Case Scenario
An analysis in which all of
the input variables are set
at their worst reasonably
forecasted values.
Best-Case Scenario
An analysis in which all of
the input variables are set
at their best reasonably
forecasted values.Best-Case Scenario
An analysis in which all of
the input variables are set
at their best reasonably
forecasted values.(^6) Sensitivity analysis is tedious using a regular calculator but easy using a spreadsheet. We used the chapter’s
Excel model to calculate the NPVs and to draw the graph in Figure 12-1. To conduct such an analysis by hand
would be quite time-consuming, and if the basic data were changed even slightly—say the cost of the
equipment was increased slightly—all of the calculations would have to be redone. With a spreadsheet, by
simply typing over the old input with the new one, the analysis changes instantaneously.