### 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.

### 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

1) CT’s EBIT growth follows a normal distribution (learn more about normal distribution here)

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.

### 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.