### What’s a Monte Carlo Simulation

Monte Carlo simulation (also known as the Monte Carlo method) is an incredibly powerful probabilistic modeling technique used in the evaluation of risks and uncertainty. It does this by carrying out repeated random sampling and substituting a range of values for each specified variable to produce a range of outputs, rather than one precise result.

### Applications of the Monte Carlo Method

The Monte Carlo method was first used by scientists working on the Manhattan Project during World War II to study the effect of neutron diffusion when an atomic bomb explodes. Since then, its applications have extended into many other fields including business and finance.

To better understand the application of the method in a business context, consider a recent engagement we had with a commercial real estate developer. The developer was looking to build multiple warehouses for lease and a private lender was willing to extend him with a variable mortgage to pursue the project. Since future interest rate movements are difficult to predict, he wanted to first assess the impact that changes in the borrowing rate would have on the project’s cash flows before responding to the offer. To assess this risk, we used Monte Carlo simulation to model the project’s returns under a variety of interest rate scenarios. We first ran the simulation using the developer’s forecasts and determined that the probability of the project not yielding sufficient returns to the developer was higher than we were comfortable with and that the current cost structure didn’t provide enough margin of safety to safeguard against rate fluctuations. Hence, we went back to optimize the cost structure and helped the developer negotiate for more favorable terms. Ultimately, we were able to settle on a term sheet that provided enough cushion for the developer and meaningful returns for the lender.

Since clients have found this type of analysis highly useful, we wanted to share how a Monte Carlo simulation works in greater detail. We are going to do this with the help of a model we built in Python to forecast Canadian Tire’s interest coverage ratio for the next quarter (Q3 2018). ### Interest Coverage Defined

Interest coverage ratio measures a company’s ability to pay interest expense using its operating income or EBIT (Earnings Before Interest and Taxes). A ratio of less than 1 means the company will not be able to cover its interest obligations and could raise concerns about its solvency. A healthy ratio generally above 2.5x.

The formula for coverage ratio is: EBIT/Interest Expense

### Model Objectives

1) To obtain a range of CT’s Q3 2018 interest coverage ratio.

2) To determine the probability of CT’s coverage ratio falling below 1.0x.

### Key Assumptions

2) CT’s Q3 2018 interest expense is expected to be the same as Q2 2018.

### Model Inputs

The normal distribution is parameterized by its mean and standard deviation. Therefore, we need to figure out CT’s average EBIT growth and its standard deviation, which we have produced in Exhibit 1. The inputs we need are:

1) Current EBIT: 298.3 (from Q3 2017 since we are working with year-over-year growth)

2) Average EBIT Growth YoY: 0.07 (from the average of Q3 of 2017, 2016, 2015, 2014, 2013)

3) EBIT Growth YoY Deviation: 0.099

4) Last quarter interest expense: 35.6 (from Q2 2018)

5) Minimum coverage ratio desired: 1

6) Number of times to run simulation: 10000 Exhibit 1: Canadian Tire’s Quarterly EBIT

### Computation

Here is what happens behind the scene in the model. After we feed the inputs, the model will first start the calculation by coming up with 10,000 different EBIT growth rates for Q3 2018 using the mean and standard deviation that we provided. It will then apply these growth rates to last year’s Q3 EBIT figure to forecast the next year’s quarter.

To obtain the coverage ratio, the model will divide the computed EBIT figures by the next quarter’s interest expense (which he have assumed to be the same as the Q2 2018, a reasonable assumption as interest expenses are generally fixed unless the capital structure changes materially). This will give us 10,000 different interest coverage ratios.

The model will then count the number of ratios that are below the minimum desired coverage ratio (which is 1) and simply divide this number with 10,000 to compute the probability. Finally, it will plot each ratio’s frequency on a histogram to display the probability density function.

### Model Outputs

There are 3 key outputs that we want to pay attention to:

1) The highest and lowest interest coverage ratios.

2) The mean interest coverage ratio.

3) The probability of observing the ratio drop below 1.

The outputs will vary slightly with each simulation, but at the time of writing this article, we observe the following outputs. Over 10,000 trials the computed lowest, mean, and highest EBIT growth rates were -29.35%, 7.02% and 42.86%. Correspondingly, the interest coverage ratios were 5.92, 8.97, and 11.97., respectively. Thus, there is zero probability that the ratio will fall below 1.00. This is great news.

### Stress Testing the Model

Since CT is a market leader in the consumer staples sector, we would expect its operating income to be fairly stable from one period to another. This would suggest that its EBIT growth rate standard deviation would be fairly low. However, to stress test the model we are going to up the standard deviation from 9.9% to 20.0% while keeping all the other inputs the same. This is the result we observed. We now see that over 10,000 trials, the lowest EBIT growth rate is -76.52%, which imputes a coverage ratio of 1.97, a significant drop from 5.92. Nevertheless, the ratio is still positive. Again, this is good news.

### Conclusion

Despite doubling the standard deviation, Canadian Tire is still able to generate a positive interest coverage ratio. This suggests that the company is financially strong and is capable of meeting its debt obligations even if it experiences significant downward pressure on its operating income. 