## 12 Oct Monte Carlo Analysis – Why and How it is Used

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Modeling a business can be simple. Given assumptions for revenue growth, fixed and variable expenses, and typical balance sheet ranges, the metrics of interest such as discretionary cash flow to shareholders, change in business value, and need for capital can be derived in a relatively straightforward manner. Risks to the business or the effect of rapid growth can usually be simulated through scenario testing. There are those situations, however, where the sheer number of variables, their interplay, and their unpredictability, requires that a more robust method be used. That is where the Monte Carlo analysis shines.

In situations where there are multiple interacting degrees of freedom which influence an outcome, the Monte Carlo analysis is often the best tool to get a handle on the probable outcomes of a certain course of action.

Here is an example of a situation where a Monte Carlo analysis is appropriate:

Example

- The company is a manufacturer with two commodity inputs each with highly variable but independent prices.
- The industry is highly competitive with significant price pressure, and the company can only increase prices due to the cost of inputs once a year, leading to a one-year lag in price adjustments.
- How large of a line of credit should the company have to ensure that it does not run into a capital crunch?

A static model of the company indicates that they should have no concerns about their available line of credit. Existing debt is being repaid quickly given current input prices and unit sales growth.

However, if we discover after further discussion that input prices are very volatile, a Monte Carlo analysis tells a different story. In the example, the CFO informs us of the following:

- The cost of Input 1 is currently at its long-term average of $35 per unit but historically varies in a normal distribution with a standard deviation of $15 per unit.
- Likewise, the cost of Input 2 is at its average of $60 per unit but varies with a standard deviation of $10 per unit.

The analysis indicates that over 10,000 iterations (50,000 samples, since we’re looking at 5 years per iteration), significant borrowing against the line of credit is often required.

In 37% of the iterations, no credit line is needed. In 15% of the iterations, a balance of $0-$1 million is required. The cumulative % of iterations is shown by the orange line and represents the percentage of iterations where the needed line of credit was less than the amount shown.

The CFO might decide, after reviewing this analysis, that a line of $7 million would accommodate 95% of the likely future capital needs, giving the company a cushion to weather short-term capital crunches while minimizing commitment fees.

Alternate Assumptions

The CFO may decide, on reflection, that the restriction on adjusting product pricing changes to once a year is too conservative, and that their actual experience is that price changes lag an average of half a year after input cost changes. With this adjustment, the credit line need is reduced significantly.

Under these revised assumptions, the CFO discovers that 95% of the iterations require a line of less than $3 million.

Conclusion

In most cases, a detailed Monte Carlo analysis of a company’s financials is unneeded overkill. However, there are certain situations where inputs are highly variable, such as commodity prices or investment returns, where a combination of factors lends itself to analysis using the method. Monte Carlo analysis can prove an invaluable tool in a complex situation.