376 Part 4 Investing in Long-Term Assets: Capital Budgeting
12-5 MEASURING STAND!ALONE RISK
A project’s stand-alone risk re! ects uncertainty about its cash! ows. The required
investment, unit sales, sales prices, and operating costs shown in Table 12-1 for
Project S are subject to uncertainty. First-year sales were projected at 537 units
(actually, 537,000; but we shortened it to 537 to streamline the analysis) to be sold
at a price of $10 per unit. However, unit sales would almost certainly be somewhat
higher or lower than 537, and the price would probably turn out to be different
from the projected $10 per unit. Similarly, the other variables would probably dif-
fer from their indicated values. Indeed, all the inputs are expected values, and actual
values can vary from expected values.
Three techniques are used to assess stand-alone risk: (1) sensitivity analysis,
(2) scenario analysis, and (3) Monte Carlo simulation. We discuss them in the fol-
lowing sections.12-5a Sensitivity Analysis
Intuitively, we know that a change in a key input variable such as units sold or
sales price will cause the NPV to change. Sensitivity analysis measures the percent-
age change in NPV that results from a given percentage change in an input, other variables
held at their expected values. This is by far the most commonly used type of risk
analysis, and it is used by most " rms. It begins with a base-case situation, where the
project’s NPV is found using the base-case value for each input variable. Here’s a
list of the key inputs for Project S:- Equipment cost
- Required working capital
- Unit sales
- Sales price
- Variable cost per unit
- Fixed operating costs
- Tax rate
- WACC
The data we used in Table 12-1 were the most likely, or base-case, values; and the
resulting NPV, $78.82, is the base-case NPV. It’s easy to imagine changes in the
inputs, and those changes would result in different NPVs.
When senior managers review capital budgeting studies, they are interested
in the base-case NPV, but they always go on to ask the " nancial analyst a series
of “what if” questions: What if unit sales turn out to be 25% below the base case
level? What if market conditions force us to price the product at $9, not $10?
What if variable costs are higher than we forecasted? Sensitivity analysis is
designed to provide answers to such questions. Each variable is increased or
decreased from its expected value, holding other variables constant at their base-
case levels. Then the NPV is calculated using the changed input. Finally, the re-
sulting set of NPVs is plotted to show how sensitive NPV is to changes in each
variable.
Figure 12-1 shows Project S’s sensitivity graph for six key variables. The
table below the graph gives the NPVs based on different values of the inputs,
and those NPVs were then plotted to make the graph. Figure 12-1 shows that
as unit sales and price increase, the project’s NPV increases, whereas the oppo-
site is true for the other four input variables. An increase in variable costs, " xed
costs, equipment costs, and WACC lowers the project’s NPV. The ranges shown
at the bottom of the table and the slopes of the lines in the graph indicate how
sensitive NPV is to changes in each input. When the data are plotted in
Sensitivity Analysis
Percentage change in NPV
resulting from a given
percentage change in an
input variable, other
things held constant.Sensitivity Analysis
Percentage change in NPV
resulting from a given
percentage change in an
input variable, other
things held constant.Base-Case NPV
The NPV when sales and
other input variables are
set equal to their most
likely (or base-case)
values.Base-Case NPV
The NPV when sales and
other input variables are
set equal to their most
likely (or base-case)
values.