ACCA P4考試：Monte Carlo Simulation

Traditional sensitivity analysis can be used if one project variable changes independently of all others. However, some project variables may be interdependent (e.g. production volume and unit costs).

Simulation is a technique which allows more than one variable to change at the same time. The classic example of simulation is the "Monte Carlo" method which can be used to estimate not only a project's NPV but also its volatility.

Designing a Monte Carlo Simulation

An assessment of the volatility (or standard deviation) of the net present value of a project requires estimates of the distributions of the key input parameters and an assessment of the correlations between variables. Some of variables may be normally distributed (e.g. demand), but others may be assumed to have limit values and a most likely value (e.g. redundancy costs).

In its simplest form, Monte Carlo simulation assumes that the input variables are uncorrelated. More sophisticated modelling can, however, incorporate estimates of the correlation between variables.

Monte Carlo simulation then employs random numbers to select a specimen value for each variable in order to estimate a "trial value" for the project NPV. This is repeated a large number of times until a distribution of net present values emerges. This distribution will approximate a normal distribution.

Refinements such as the Latin Hypercube technique can reduce the likelihood of spurious results occurring through chance in the random number generation process.

Outputs From Monte Carlo Simulation

The output from the simulation will give the expected NPV for the project and a range of other statistics including the standard deviation of the output distribution.

In addition, the model can rank the significance of each variable in determining the project NPV.

Summary of Monte Carlo Simulation

1. Specify the major variables.

2. Specify the relationship between the variables.

3. Attach probability distributions (e.g. the normal distribution) to each variable and assign random numbers to reflect the distribution.

4. Simulate the environment by generating random numbers.

5. Record the outcome of each simulation.

6. Repeat simulation many times to obtain a frequency distribution of the NPV.

7. Determine the expected NPV and its standard deviation.