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202 Applying simulation to decision problems
Random numbers were then used to sample a value from each distribution,
using the methods which we outlined earlier, and the NPV
was calculated for this set of values. For example, the first simulation
generated the following values:
Purchase costs = $30 000
Year 1 Revenue = $24 500 Maintenance costs = $2 150
Year 2 Revenue = $14 200 Maintenance costs = $3 820
Year 3 Revenue = $17 320 Maintenance costs = $4 340
Year 4 Revenue = $16 970 Maintenance costs = $9 090
Scrap value = $1 860
This led to an NPV of $8328. The process was then repeated until
500 simulations had been carried out. Figure 7.11 shows the resulting
probability distribution for the net present value. It can be seen that
the NPV could be between about −$20 000 and $36 000. Moreover,
although the expected (mean) NPV was $7364, there was roughly a 20%
probability that the NPV would be negative.
A similar simulation was carried out for the Beta machine and the
resulting distribution is also displayed in Figure 7.11. While this machine
has a higher probability (about 30%) of yielding a negative NPV, its
distribution is much tighter than that of the Alpha machine. For example,
in contrast to the Alpha machine, there is little chance of the NPV being
below −$5000.
−30
−20
Probability
0.7
0.5
0.1
−10 0 10 20
Net present value ($000)
Beta machine
Mean NPV = $1670
standard deviation
of NPV = $2885
Alpha machine
Mean NPV = $7364
standard deviation
of NPV = $10125
Figure 7.11 – Probability distributions for the NPVs of the Alpha and Beta machines
30
40
50