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# MQnomix® – MonteCarlo

The real estate direct investment problem can and should be solved by using appropriate modeling techniques under uncertainty. Such investments are rather challenging due to the sheer number of input variables, financial and operational, that can impact the profitability and, therefore, are extremely important for the decision making process.

For example, within an LTV setup, what price should an investor pay for a unit of real estate, given a  ROE target value of, say, 12%, corresponding to its 40-th percentile.

Moreover, what is the LTV as a result of getting the 40th percentile of ROE equal to 12%? In simple terms, what should be the Mortgage Value, in order for the ROE’s x%-percentile to equal the investor’s target value?

To answer the above question, investors should apply some advanced features of @Risk.

One other important problem the direct investors should solve, this time related to the operational burden, is the tenants turnover distribution over a certain period of time. Using Monte Carlo simulation in conjunction with certain assumptions, one can get (see below).

Some other examples of output variables, whose probability distributions are found based on Monte Carlo simulation algorithm, are:

Financial (excerpt):

Present Value of the ATCF

Property Debt Coverage Ratio

NOI (Net Operating Income)

Effective Gross Income

Note: a standard approach for @Risk -the Box Plot

Break-Even Occupancy Ratio

Note: obviously one can notice the steep slope around the 6th year. Why that?

Gross Income Multiplier – 1st year

Cash on Cash Return- 1st year

Note: The Cash-on-Cash return is rather meager in the 1-st year and onwards, until…it suddenly jumps upwards (see below)! Why that?!

Cash on Cash Return- 10 years

Note: The Cash-on-Cash over a 10-yr. period. In this graph we can see the sudden positive jump around the 6-th year. If we are asking ourselves why is that happening, the answer is Debt related…Using @Risk Monte Carlo simulation, we can have a pretty good idea of the Debt impact upon Cash-on-Cash returns and much more!

Operational (excerpt):

Percentage of weeks the RE unit is not rented

Note: the average value is around 4.8%, but the max. value can be as high as 12.3%. However, the percentiles of the distribution are more revealing, that’s why a probability distribution is so important!

Number of positive and negative Business Cycles

Note: the whiskers of the Negative Growth Cycles are more pronounced. When the input probability of getting a certain type of cycle is higher, the consecutive number of that respective cycle is bigger, resulting in the displayed behaviour.

Cash-on-Cash, 4-th year- Change in Output Mean

Cash-on-Cash, 7th year- Change in Output Mean

Notes: These last two graphs are the so-called Spider graphs and are part of the Sensitivity Analysis. They identify the rate of change in output value as the input changes. For example, in the Cash-on-Cash (Mean) Return spider graph for the 7-th year, if we consider changes in the input variable “Monthly Rent Value” (green line) from the 70-80-th percentile bin to the 80-90-th percentile bin, the Cash-on-Cash (mean) return changes,linearly, from approx. 4.90% to 4.95%. No big deal…, but still in line with our general expectations. The point is that the  steeper the curve, the higher the impact and vice-versa!

Everything described so far highlights the simpler aspects of a Real Estate Monte Carlo simulation model. There is a lot more to find out related to Monte Carlo Simulation Output Reports.

If you want to get a deeper understanding of how insightful modeling business decisions under uncertainty is, you can get in touch with us here

Investors should not forget the long-term nature of real estate direct investments. This means that various economic cycles, with their different underlying growth rates, can have a considerable impact upon all Output variables.

Other input variables considered in the model are interest and WACC rates and some other discretionary variables like the income tax rates.

A more in-depth view of the real estate direct investment model would also reveal variables such as:

the Matrix Migration between business Cycles (positive vs. negative growth cycles)

the Positive/Negative Cycle’s Growth Rates

the Increase/Decrease of Rental Durations, based on empirical evidence that recessions generate lower rental durations

the Increase/Decrease of Vacancy Durations, based on the same empirical evidence from above

the Maintenance Policy, which defines the time period when maintenance costs are considered in the model.

From our experience, modeling  the inherent uncertainty of a business is a milestone reached by every successful organization. If interested to move things towards this milestone, we can guide you through the whole process of decision modeling and make it a worthwhile experience for you and your organization.