Monte Carlo Simulation

What is Monte Carlo Simulation?

Monte Carlo Simulation is stochastic technique–meaning it uses random numbers and probabilities to solve problems. It is a procedure commonly used by Fortune 500 companies to analyze and model the uncertainties surrounding multiple investment options. Since the appraisal process, like investment options, is inherently based on uncertain inputs, a stochastic process which articulates the probabilities attached to those uncertain inputs is a more realistic and honest reflection of the appraisal process and the appraisal conclusion. For instance, this type of stochastic modeling can be used for the purpose of estimating the probability of multiple outcomes within an appraisal or financial forecast to predict what conditions might be like under different situations.

How Does Monte Carlo Simulation Work?

Monte Carlo methods randomly select values, based on probable assumptions to create probability distributions [e.g. the classic bell curve, pareato, log normal, chi square, uniform, logistic distributions, exponential, etc.], which articulate both the probability of a single value and its accompanying probable range or spread.

In a Monte Carlo simulation, many random trials are generated from the inputted assumptions. Each time a random trial is generated, it forms one possible scenario or solution. Together, they give a range of possible solutions to the problem, some of which are more probable than others. When repeated 50,000 or more times, a probability distribution is developed which illustrates a more realistic and honest estimated representation to the problem.

Does it Contribute to an Appraisal?

Without running multiple examples a spreadsheet model can only reveal a single solution or outcome. The weakness of a single outcome is that it is colored by the subjective biases of an appraiser, hazards being arbitrary, deceptive, indefensible, and ultimately is opaque in its failure to illustrate the implicit risks and range of probable outcomes. However, a Monte Carlo model, which inputs probabilities with many thousand simulations, automatically analyzes the effect of varying inputs on outputs of the modeled system and both articulates the uncertainties and mitigates biases.

How Much Does it Add to the Cost of an Appraisal?

For all but the more complex of appraisals, incorporating Monte Carlo Simulation into an appraisal should not raise the cost of the appraisal, yet the benefits over appraisals lacking this type of analysis are substantial. Despite the superior benefits of transparency which Monte Carlo Analysis provides, the vast majority of appraisers do not implement this procedure. For more on Monte Carlo Simulation or to request a business or real estate appraisal which incorporates Monte Carlo Simulation, contact us at

Alternatively Stated:

Monte Carlo Simulation Models are computer generated models designed to imitate real-life situations. They are like other models (subjective or mathematical), but superior in that they explicitly incorporate uncertainty into the model.

Simulation models are extremely useful for determining how sensitive a system is to changes in operating conditions or other uncertainties. For example, one might simulate a company’s sales and profit projections. Once the simulation model has been developed, one can then run it by asking a number of what-if questions. For example, what-if the growth rate ranged between 5 and 7% annually, or what if cost of sales fluctuated between 25% and 40% of sales? What then will happen to profits?

Simulation models are quite similar to static or deterministic (fixed) spreadsheet models, except for a very important difference, which is that simulation models use random numbers to drive the whole process. Each time the spreadsheet recalculates, all of the random numbers change. This gives one the ability to model the logical process once and then use the recalculation feature repeatedly to generate many different scenarios. By collecting the data from these scenarios, one sees which outputs are most likely and one sees which outputs are the best or worst case scenarios.

Alternatively stated, Monte Carlo Simulation is a method used to iteratively evaluate a fixed or deterministic model using sets of random numbers as inputs. By incorporating random numbers, one essentially turns the deterministic (fixed) model into a stochastic (probabilistic) model, the goal of which is to determine how random variation, lack of knowledge, or error effects the sensitivity, performance, or reliability of the system that is being modeled.

This is why Monte Carlo Simulation is an excellent tool for evaluating probable or expected future events and pro forma investment opportunities where:

1) One knows there is uncertainty in one’s inputs since a pro forma is by definition an estimation of performance.
2) One knows that the Monte Carlo Simulation will calculate “answers” that with reasonable accuracy represents the input data.
3) The calculated uncertainty of the “answers” will reflect the uncertainty of the input data.
4) The modeled uncertainty of the pro forma better informs and helps one understand the risks, or range of probable outcomes, of the proposed investment.

Therefore, Monte Carlo Simulation is superior to subjective or seat of the pants speculation to describe the probabilities and range of risks a business investment or a company’s future sales, profits or value will be, given a well studied and intelligent evaluation of the data inputs.