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200 Applying simulation to decision problems
Table 7.5 – Calculating the NPVs for the Alpha and Beta machines
Time of
cash flow
Cash
inflow
($)
Cash
outflow
($)
Net cash
flow
($)
Present
value
factor
Discounted
cash flow
($)
(a) Alpha machine
Now 0 30 000 −30 000 1.0000 −30 000
Year 1 14 000 2 000 12 000 0.9091 10 909
Year 2 15 000 4 000 11 000 0.8264 9 090
Year 3 15 000 6 000 9 000 0.7513 6 762
Year 4 14 000 7 000 7 000 0.6830 4 781
Net present value (NPV) = $1 542
(b) Beta machine
Now 0 30 000 −30 000 1.0000 −30 000
Year 1 8 000 4 000 4 000 0.9091 3 636
Year 2 13 000 4 000 9 000 0.8264 7 438
Year 3 15 000 5 000 10 000 0.7513 7 513
Year 4 21 500 5 000 16 500 0.6830 11 270
Net present value (NPV) = −$143
turn out to be near $14 000 then our estimated NPV would have been
very misleading.
Clearly, the approach would be more realistic if we could incorporate
our uncertainty about the cash flows into the analysis. The result would
be a probability distribution for the NPV which would indicate the range
within which it would be likely to lie and the probability of it having
particular values. From this we could assess the chances of the project
producing a negative NPV or the probability that the NPV from one
project will exceed that of a competing project. In the section which
follows we will show how simulation can be used to extend the NPV
approach so that we can explicitly take into account the uncertainty
associated with an investment project.
Using simulation
Let us first consider the application of simulation to the Alpha machine.
It was thought that the following factors would affect the return on
this investment: