Simulation

Simulation is a modelling technique that shows the effect of more than one variable changing at the same time.

It is often used in capital investment appraisal, particularly to model the impact of uncertainty.

Method

The Monte Carlo simulation method uses random numbers and probability statistics. It can include all random events that might affect the success or failure of a proposed project - for example, changes in material prices, labour rates, market size, selling price, investment costs or inflation.

The model identifies key variables in a decision : costs and revenues, say.

Random numbers are then assigned to each variable in a proportion in accordance with the underlying probability distribution.

For example, if the most likely outcomes are thought to have a 50% probability, optimistic outcomes a 30% probability and pessimistic outcomes a 20% probability, then random numbers, representing those attributes, can be assigned to costs and revenues in those proportions.

A computer is then used to repeat the decision many times and give management a view of the likely range and level of outcomes. Depending on the management's attitude to risk, a more informed decision can then be taken.

This helps to model what is essentially a one-off decision using many possible repetitions. It is only of any real value, however, if the underlying probability distribution can be estimated with some degree of confidence.

Illustration

The MP Organisation is an independent film production company. It has a number of potential films that it is considering producing, one of which is the subject of a management meeting next week. The film which has been code named CA45 is a thriller based on a novel by a well respected author.

The expected revenues from the film have been estimated as follows:there is a

• 30% chance it may generate total sales of $254,000;
• 50%chance sales may reach $318,000 and
• 20% chance they may reach $382,000.

Expected costs (advertising, promotion and marketing) have also been estimated as follows: there is a

• 20% chance they will reach approximately $248,000;
• 60% chance they may get to $260,000 and
• 20 %chance of totalling $272,000.

In a Monte Carlo simulation, these revenues and costs could have random numbers assigned to them as follows:

A computer could then generate 20-digit random numbers such as 98125602386617556398.

These would then be matched to the random numbers assigned to each probability and values assigned to 'Sales Revenues' and 'Costs' based on this.

The random numbers generated give 5 possible outcomes in our example:

Note that simulation has not generated a decision, but has given management more information.

Making a decision

Suppose a  business is choosing between two projects, project A and project B.

It uses simulation to generate a distribution of profits for each project as follows.

Which project should the business invest in?

• Project A has a lower average profit but is also less risky (less variability of possible profits).
• Project B has a higher average profit but is also more risky (more variability of possible profits).
• There is no correct answer. All simulation will do is give the business the above results. It will not tell the business which is the better project.
• If the business is willing to take on risk, they may prefer project B since it has the higher average return.
• However, if the business would prefer to minimise its exposure to risk, it would take on project A. This has a lower risk but also a lower average return.

Drawbacks of simulation

There are major drawbacks of simulation:

• It is not a technique for making a decision, only for obtaining more information about the possible outcomes.
• Models can become extremely complex.
• The time and costs involved in their construction can be more than is gained from the improved decisions.
• Probability distributions may be difficult to formulate.

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Tags:	simulation;Monte Carlo