Unlike typical scenario or what-if analyses that allow you to analyze the impact of changing one input variable at a time, Monte Carlo simulation analyzes all possible combinations at once. In a typical scenario analysis, you manually calculate as many scenarios as you deem necessary. Monte Carlo simulation, on the other hand, calculates these scenarios automatically, based on your definition of simulation parameters. It allows you to run thousands of scenarios instead of the few in a typical what-if analysis.

Monte Carlo simulation was popularized by physicists in the 1950s at the dawn of the computer age and it got its name from the Monte Carlo Casino in Monaco. Games of chance played at a casino exhibit random behavior that is bound by the characteristics of the game. When rolling a die for example, you know that a number between 1 and 6 will come up, but you don't know which one.

Similarly, in a capital investment project you may know the range of possible financial outcomes, but you don't know exactly which one will materialize. Monte Carlo simulation allows you to model all potential scenarios driven by the uncertain variables. These scenarios are defined by the probability distributions and their simulation parameters.

Probability distributions

There are few probability distributions that are used frequently in the business world. Many times a normal distribution (also known as the bell curve) is a good representation of the business situation. The normal distribution is symmetrical around the mean with open tails on both ends (see left chart below). Each distribution is described through its distribution parameters and in the case of normal distribution these parameters are the mean and the standard deviation. The mean represents the center of distribution and the standard deviation is a measure of spread or variability. The smaller the standard deviation, the less variable the underlying metric is expected to be. In other words, the smaller the standard deviation, the higher the chance that the actual metric will be close to its mean.

Although normal distribution is very common in a business setting, there may be cases where other distributions may be more appropriate. For example, when modeling days payable outstanding (DPO) in a cash flow analysis, it may be more appropriate to set a fixed range of possible values of DPO and model same likelihood of occurrence across that range. In this case the uniform distribution should be used (see middle chart below). Its parameters are the minimum and the maximum, and the most likely value is usually between these two parameters. With a uniform distribution, all values of a metric have the same chance to be between the minimum and maximum values.

A distribution that is skewed to one side may be appropriate in other cases. Unit sales of new products in a ROI analysis, for example, most likely won't be negative. On the other hand, they may be much higher than the most likely estimates if the product is a hit. Hence, instead of a symmetrical distribution a skewed distribution could be used. The triangular distribution could be used and defined as skewed distribution. In this example, its minimum could be set at zero to avoid negative unit sales in the simulation. The parameters of a triangular distribution are minimum, mode, and maximum. The mode is the most common value. The triangular distribution can be symmetrical around the mode or can be skewed to the right or left of the mode. The chart below on the right shows a triangular distribution skewed to the right. The triangular distribution is closed on both ends with definitive minimum and maximum values.