Chapter 12 Cash Flow Estimation and Risk Analysis 37912-5c Monte Carlo Simulation
Monte Carlo simulation, so named because this type of analysis grew out of work
on the mathematics of casino gambling, is a sophisticated version of scenario
analysis. Here the project is analyzed under a large number of scenarios, or “runs.”
In the " rst run, the computer randomly picks a value for each variable—units sold,
sales price, variable costs per unit, and so forth. Those values are then used to cal-
culate an NPV, and that NPV is stored in the computer’s memory. Next, a second
set of input values is selected at random and a second NPV is calculated. This pro-
cess is repeated perhaps 1,000 times, generating 1,000 NPVs. The mean of the 1,000
NPVs is determined and used as a measure of the project’s expected pro" tability,
and the standard deviation (or perhaps the coef" cient of variation) of the NPVs is
used as a measure of risk.
Monte Carlo Simulation
A risk analysis technique in
which probable future
events are simulated on a
computer, generating
estimated rates of return
and risk indexes.Monte Carlo Simulation
A risk analysis technique in
which probable future
events are simulated on a
computer, generating
estimated rates of return
and risk indexes.Cash Flows Under Alternative ScenariosProb:
Best Case
Base Case
Worst Case25%
50%
25%-$750
-$1,000
-$1,250$2,685
$500
-$1,077$2,520
$400
-$1,119$2,390
$300
-$1,213$2,135
$100
-$1,343
Expected NPV
Standard Deviation (SD)
Coe$cient of Variation (CV) = Std Dev/Expected NPV7.50%
10.00%
12.50%$7,450.38
$78.82
-$4,782.40
$706.40
$5,028.94
7.120 1 2 3 4 WACC NPVPredicted Cash Flow for Each Year85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116117
118
119
120A B C D E F G H I050%25% 25%-$4,782.40 $7,450.38 NPVDiscrete Probabilities Probability-$4,782.40^0 $78.82 $7,450.38 NPVContinuous Probabilities Probability Density$78.82Scenario Analysis for Project S
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