Intermediate Financial Management (with Thomson One)

Figure 13-2
a. Sales Price
Probability Density Probability Density
Probability Density Probability Density
0
462 • Part 3 Project Valuation
Probability Distributions Used in the Monte Carlo Simulation
0 1.50 2.00 2.50 3.50 4.00 4.50
0
0
3.00 1.50 2.00 2.50 3.00
Sales Price ($ x thousands)
b. Variable Cost
c. Year 1 Unit Sales d. Unit Sales Growth Rate
Year 1 Unit Sales (thousands)
Variable Cost per Unit ($ x thousands)
15 20 25 30 35 –50 –40 –30 –20 –10 0 10 20 30 40 50
Unit Sales Growth Rate (%)
project is clearly risky. The standard deviation of $22,643 indicates that losses
could easily occur, and this is consistent with this wide range of possible outcomes.
9 The coefficient of variation is 1.63, which is large compared with most of
RIC’s other projects. Table 13-6 also reports a median NPV of $10,607, which
means that half the time the project will have an NPV greater than $10,607. The
table also reports that 72.8 percent of the time we would expect the project to
have a positive NPV.
A picture is worth a thousand words, and Figure 13-3 shows the probability
distribution of the outcomes. Note that the distribution of outcomes is skewed to
the right. As the figure shows, the potential downside losses are not as large as the
9 Note that the standard deviation of NPV in the simulation is much smaller than the standard deviation in the scenario
analysis. In the scenario analysis, we assumed that all of the poor outcomes would occur together in the worst-case scenario,
and all of the positive outcomes would occur together in the best-case scenario. In other words, we implicitly
assumed that all of the risky variables were perfectly positively correlated. In the simulation, we assumed that the variables
were independent, with the exception of the correlation between unit sales and growth. The independence of variables
in the simulation reduces the range of outcomes. For example, in the simulation, sometimes the sales price is high,
but the sales growth is low. In the scenario analysis, a high sales price is always coupled with high growth. Because the
scenario analysis’s assumption of perfect correlation is unlikely, simulation may provide a better estimate of project risk.
However, if the standard deviations and correlations used as inputs in the simulation are not estimated accurately, then
the simulation output will likewise be inaccurate.