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Solution
1314.74 The table, calculator, and spreadsheet values indicate that for the projects to
be acceptable, they must have annual cash inflows of at least $1,315. Given this
breakeven level of cash inflows, the risk of each project could be assessed by
determining the probability that the project’s cash inflows will equal or exceed
this breakeven level. The various statistical techniques that would determine that
probability are covered in more advanced courses.1 For now, we can simply
assume that such a statistical analysis results in the following:
Probability of CFA
Probability of CFB $1,315 → 100%
$1,315 → 165% Because project A is certain (100% probability) to have a positive net present
value, whereas there is only a 65% chance that project B will have a positive
NPV, project A is less risky than project B. Of course, the expected level of
annual cash inflow and NPV associated with each project must be evaluated in
view of the firm’s risk preference before the preferred project is selected.
The example clearly identifies risk as it is related to the chance that a project
is acceptable, but it does not address the issue of cash flow variability. Even
though project B has a greater chance of loss than project A, it might result in
higher potential NPVs. Recall from Chapters 5 through 7 that it is the combination of risk and return that determines value. Similarly, the worth of a capital
expenditure and its impact on the firm’s value must be viewed in light of both
risk and return. The analyst must therefore consider the variability of cash
inflows and NPVs to assess project risk and return fully. Sensitivity and Scenario Analysis
Two approaches for dealing with project risk to capture the variability of cash
inflows and NPVs are sensitivity analysis and scenario analysis. As noted in
Chapter 5, sensitivity analysis is a behavioral approach that uses several possi- 1. Normal distributions are commonly used to develop the concept of the probability of success—that is, of a project
having a po...

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