What it calculates

Monte Carlo simulation runs a model thousands of times with inputs drawn at random from probability distributions instead of fixed point estimates. The output is a distribution of results, which lets you state the probability of an outcome rather than a single number that is certain to be wrong.

How it is calculated

Assign each uncertain input a distribution: normal where variation is symmetric, triangular where you have a low, likely and high estimate, lognormal for quantities that cannot go negative. Draw one random value from each per iteration, compute the model, record the result, and repeat several thousand times. The collected results form the output distribution, from which you read the mean, the percentiles and the probability of falling below any threshold. Correlations between inputs must be specified, or the simulation will assume they move independently when they do not.

How to read the result

Read the percentiles, not the mean. The P10 to P90 band is the honest range, and the probability of a negative NPV is usually the single most decision-relevant number. Beware of false precision: the output distribution is only as good as the input distributions, and those are usually estimates themselves. The value of the exercise is often less in the numbers than in forcing an explicit statement of how uncertain each assumption really is.

Worked example

Ten thousand iterations of a project NPV with revenue growth drawn normally at 8% plus or minus 3%, and margin triangular between 18%, 22% and 25%, might produce a mean NPV of 12,400,000, a P10 of 4,100,000, a P90 of 21,600,000 and an 11% probability of a negative NPV.

Common questions

How many iterations are needed?

Usually 5,000 to 10,000 for stable percentiles in a typical financial model. More iterations narrow the sampling error on the estimate, but they do nothing to fix a wrong distribution - accuracy comes from the inputs, not from the iteration count.

Which distribution should each input use?

Triangular where you have expert estimates of low, most likely and high, because it needs no more information than that. Normal for symmetric measurement-style variation. Lognormal for values bounded at zero such as prices or volumes, since a normal distribution would generate impossible negatives.

Why do correlations matter?

Because independent draws understate risk. If revenue growth and margin both fall in a downturn, treating them as independent makes the joint bad case far rarer in the simulation than in reality, and the left tail of the distribution ends up too thin.