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Monte Carlo simulation 181
Of course, for a simple problem like this we could obtain the required
probability distribution by calculation. For example, we could use a
probability tree to represent the six combinations of inflows and outflows
and then calculate the probability of each combination occurring.
However, since most practical problems are more complex than this we
will use the example to illustrate the simulation approach. The fact that
we can calculate the probabilities exactly for this problem will have the
advantage of enabling us to assess the reliability of estimates which are
derived from simulation.
In order to carry out our simulation of the company’s cash flows
we will make use of random numbers. These are numbers which are
produced in a manner analogous to those that would be generated by
spinning a roulette wheel (hence the name Monte Carlo simulation).
Each number in a specified range (e.g. 00–99) is given an equal chance
of being generated at any one time. In practical simulations, random
numbers are normally produced by a computer, although, strictly speaking,
most computers generate what are referred to as pseudo-random
numbers, because the numbers only have the appearance of being random.
If you had access to the computer program which is being used
to produce the numbers and the initial value (or seed) then you would
be able to predict exactly the series of numbers which was about to
be generated.
Before we can start our simulation we need to assign random numbers
to the different cash flows so that, once a particular random number has
been generated, we can determine the cash flow which it implies. In this
example we will be using the hundred random numbers between 00
and 99. For the cash inflow distribution we therefore assign the random
numbers 00 to 29 (30 numbers in all) to an inflow of $50 000 which has a
30% probability of occurring. Thus the probability of a number between
00 and 29 being generated mirrors exactly the probability of the $50 000
cash inflow occurring. Similarly, we assign the next 40 random numbers:
30 to 69 to a cash inflow of $60 000, and so on, until all 100 numbers have
been allocated.
Cash inflow
($)
Probability
(%)
Random
numbers
50 000 30 00–29
60 000 40 30–69
70 000 30 70–99
The process is repeated for the cash outflow distribution and the allocations
are shown below.