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316 CHAPTER 8 Cash Flow Estimation and Risk Analysis

the combination of a high sales price, low production costs, high first year sales, and a

strong growth rate in future sales will result in a very high NPV, $146 million. However,

if things turn out badly, then the NPV would be $37 million. The graphs show a very

wide range of possibilities, indicating that this is indeed a very risky proj-

ect. If the bad conditions materialize, this will not bankrupt the company—this is just

one project for a large company. Still, losing $37 million would certainly not help the

stock price or the career of the project’s manager.

The scenario probabilities and NPVs constitute a probability distribution of re-

turns like those we dealt with in Chapter 3, except that the returns are measured in

dollars instead of percentages (rates of return). The expected NPV (in thousands of

dollars) is $30,135:^8

0.25($146,180) 0.50($5,809) 0.25($37,257)


$30,135.

Expected NPV
 a

n

i
 1

Pi(NPVi)

(^8) Note that the expected NPV, $30,135, is notthe same as the base-case NPV, $5,809 (in thousands). This is
because the two uncertain variables, sales volume and sales price, are multiplied together to obtain dollar
sales, and this process causes the NPV distribution to be skewed to the right. A big number times another
big number produces a very big number, which, in turn, causes the average, or expected value, to increase.
TABLE 8-4 Scenario Analysis (Dollars in Thousands)
Sales Unit Variable Growth
Scenario Probability Price Sales Costs Rate NPV
Best case 25% $3.90 26,000 $1.47 30% $146,180
Base case 50 3.00 20,000 2.10 0 5,809
Worst case 25 2.10 14,000 2.73  30 (37,257)
Expected NPV
$30,135
Standard deviation
$69,267
Coefficient of variation
Standard deviation/Expected NPV
2.30
Note: The scenario analysis calculations were performed in the Excel model, Ch 08 Tool Kit.xls.
Probability Graph
Probability
(%)
50
25
(37,257) 0
5,809
30,135
Most likely Mean of distribution = Expected value
146,180
NPV ($)
See Ch 08 Tool Kit.xlsfor
a scenario analysis using Ex-
cel’sScenario Manager.

Cash Flow Estimation and Risk Analysis 315