## Monte Carlo Simulation

Every business faces a future fraught with uncertainty, which makes planning for tomorrow inherently difficult. A great plan for one possible future might perform horribly in another. That’s why the ability to assess the likelihoods of various outcomes is so essential to your business planning process that it can make or break your company. Monte Carlo simulation is one way to do just this.

Unlike traditional approaches to modeling the future, Monte Carlo simulation tells your decision makers not just what might happen in each course of action, but how likely it is to happen – exactly what they need to make the right business decisions. Let’s first step back.

## Low, Medium, High Scenarios- Monte Carlo Simulation

Most companies take a traditional approach to account for uncertainty. This is sometimes called the three-point estimation technique, or three-point estimate. Using this method, planners prepare three scenarios for how their plans will perform: Low, Medium and High. The Low and High scenarios represent the worst-case and best-case scenarios of how the plan will perform. Low is when everything goes wrong. For example, revenues are the lowest possible while costs are the highest. High is when everything goes right, and the reverse is true.

The Medium scenario is supposed to reflect something in the middle, or what some assume mistakenly assume is most likely. In this case, not everything goes right, but not everything goes wrong. Question is: does that mean everything just goes okay? Or does it mean that some things go right and other things go wrong? Or does it mean something else altogether? It’s never clear, especially to the decision makers who are presented with this scenario, and that clouds the evaluation and decision-making process.

Fact is, three-point estimation is inherently flawed from the start. It doesn’t reveal the probability of outcomes. It doesn’t factor the interdependence of inputs in the modeling process. And it doesn’t consider the potentially hundreds or thousands of possible outcomes – just three. These and other deficiencies can drive gravely inaccurate readings and interpretations.

## There’s More to the Story

Effective decision making requires an understanding of risks and trade-offs. But it is exceedingly difficult to evaluate various scenarios when decision makers have no sense of how likely each is to occur. How likely is the Low scenario? 10%? 5%? 0%? Imagine if the Low scenario has the potential to lose the company millions of Dollars. A decision maker might decide to make a very expensive investment to avoid the Low scenario. However, if the decision-maker knew that the Low scenario had a 0.00001% chance of occurring (i.e. essentially no chance at all), would he or she still make the same investment decision? Maybe, maybe not. Problem is, he or she doesn’t have that information, not with traditional modeling. The same concept applies to the High scenario. Worse yet is the Medium scenario, which most decision makers naturally assume is the ‘most likely’ scenario, when it often doesn’t represent that at all.

While people like the Low-Medium-High paradigm because it’s simple, it’s too simple to be useful. Decision makers need to understand the relationship between outcomes and the associated likelihoods of those outcomes. Only then can they make smart decisions.

## Monte Carlo Simulation

Monte Carlo simulation is a superior alternative to Low-Medium-High scenario analysis. Imagine you have thousands of analysts, each analyzing thousands of scenarios for how your plan will perform, and then aggregating their results to tell you the likelihoods of each possible outcome. Better yet, imagine you don’t have to pay for these thousands of analysts, who give you their results in a split second. This is Monte Carlo simulation.

Just like the Low-Medium-High approach, Monte Carlo simulation begins with you building a mathematical or financial model for your plan. Just like the Low-Medium-High approach, you insert placeholders into the model for all of your sources of uncertainty. These placeholders are variables in your model that can pertain to costs, sales revenues, or whatever it is you’re modeling. So far, it’s the same level of effort. Now here’s the difference. With Monte Carlo simulation, you substitute the static, single-point value in each placeholder with a whole range of values – a probability distribution – for each placeholder. If you are not familiar, probability distributions are just a special way of describing uncertainty. A really simple example is the probability distribution of a coin toss – 50% heads and 50% tails.

There are plenty of Monte Carlo simulation tools on the market (Vanguard Software has several of its own) to help you build the model for your plan and assign probability distributions to all of the variables, or sources of uncertainty, in your model. If you have data, these tools can analyze the data and tell you which probability distribution to use. If you don’t have data, many let you pick from a series of pictures with different shapes and sizes which makes the process really easy. One simple distribution that people like to use is the Triangular distribution because it only needs your Low, Medium, and High estimates for the source of uncertainty.

The Triangle distribution’s underlying math (which you would never need to know) figures everything else out for you. Note that I am okay using a Low-Medium-High approach here but not for the entire outcome of a plan because we are modeling uncertainty at a much more granular level and the Monte Carlo simulation will analyze thousands of scenarios and not just three.

## Not Just What Might Happen, But How likely

Once you have finished building your model, the Monte Carlo simulation prepares thousands of scenarios, calculates the outcome and the likelihood that each one occurs, and then aggregates the results. These days, most tools return results in less than one second.

The output of the Monte Carlo simulation can answer a variety of questions about your plan. Let’s take the example of one of Vanguard Software’s aerospace customers. The company runs Monte Carlo simulations to predict their total internal costs to manage 20-year support and maintenance contracts for its customers. This company can answer questions such as:

- What is the likelihood that our internal cost to manage this potential contract will be between $50million and $75million? Between $75million and $100million? Etc. (Note: These increments are my choice as Monte Carlo simulation can give you likelihoods for any value range.)
- What is the likelihood that we will lose money on this contract?
- What are sources of uncertainty contributing most to our total cost?
- Can we remove or reduce those sources of uncertainty so that we have a better estimate of our total cost?

And the list of questions goes on and on. Armed with this type of information, this company can make much smarter decisions about how much to bid on these contracts, how to manage parts, staff, facilities, etc. once they win the contracts, and much more.

Another Vanguard customer in the pharmaceutical industry uses Monte Carlo simulation to model how its multi-billion Dollar R&D pipeline will perform over a 10-20 year time horizon. They can better plan for where to invest in their pipeline, plan cash and resource needs, understand long-term revenue potential, etc.

## Next Steps

Many companies don’t use Monte Carlo simulation for one of two reasons. First, they don’t even know about it. We’ve solved that issue with this post. Second, they think their decisions makers won’t understand it. I take issue with this. I have never met a decision maker who didn’t want to know the outcomes likelihoods of their plan. If you think I’m wrong, in your next meeting I dare you to ask any of your decision makers: “Do you want to know how likely it is that your plan will be successful?” They will never say no. (But if they do, you should immediately find a new company!)

** About Vanguard Software**Vanguard Software introduced its first product for decision support analysis in 1995. Today, companies across every major industry and more than 60 countries rely on Vanguard Software’s Integrated Business Planning (IBP), forecasting and advanced analytic cloud platform. Vanguard Software is based in Cary, North Carolina.

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