, -" -- - -. -326 UNCERTAINTY INFUTURE EVENTS, There are models of risk and return that can allow us to choose between Projects F, 3, 2, 7,
and 6; but those models are beyond what.is coveredhere.Simulation
Simulation is a more advanced approach to considering risk in engineering economy prob-
lems. As such, the followingdiscussionfocuses on what it is. As the examples show,spread-
sheet functions and add-in packages make simulation easier to use for economic analysis.
Economic simulation uses random sampling from the probability distributions of one
or more variables to analyze an economic model for many iterations. For each iteration, all
variables with a probability distribution are randomly sampled. These values are used to
calculate the PW, IRR, or EUAC.Then the results of all iterations are combined to create a
probability distribution for the PW, IRR, or EUAC..
Simulation can be done by hand, using a table of random numbers-if there are only
a few random variables and iterations. However,results are more reliable as the number of
iterations increases, so in practice this is usually computerized. This can be done in Excel
using the RANDO function to generate random numbers, as shown in Example 10-15.
Because we were analyzingeach possible outcome,the probability distributions earlier
in this chapter (and in the end-of-chapter problems) used two or three discrete outcomes.
This limited the number of combinations that we needed to consider. Simulation makes it
easy to use continuous probability distributions like the uniform, normal, exponential, log
normal, binomial, and triangular.Examples 10-15and 10-16use the normal and the discrete
uniform distributions..ShipM4U is considering installing a new, more accurate scale, which will reduce the errorjn
computingpostagechargesandsave$250ayear.Thescale'susefullifeisbelievedtobe uniformly
distributed over 12, 13, 14, 15,and 16 years. The initialcost of the scale is estimated to be normally
distributed with a mean of $1500 and a standard deviation of $150.
Use Excel to simulate 25 random samples of the problem and compute the rate of return for
each sample. Construct a graph of rate of return versus frequency of occurrence.SOLUTIONI
.
t
This problem is simple enough to construct a table with each iteration's values of the life and
the first cost. From these values and the annual savings of $250, the IRR for eacb iteration can
be calculated using the RATE function. These are shown in Figure 10-8. The IRR values. are
summarized in a relative frequency diagram in Figure 10-9.~.. ,'" - .--'. -«:;11 _ _. ""
(Note: Each time Excel recaJ,cul<Itesthe spreadsheet, different values for all tlie ranaoIIl
numbers are generated. Thus the results depend on the set of random numbers, and your results
will be different if you create this spreadsheet.)in ..c_ c: 'Ii = :r::::r:::I::~!: ~ I:!: == == .....- -- - - --- --- ..---
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