 # Using Risk Modelling and Monte Carlo Simulation in Cash Flow Valuation: Role and Benefits

Since 1989, I have been using risk modelling combined with Monte Carlo simulation to improve the robustness, transparency and accuracy of cash flow valuation models. This powerful approach is still underused for reasons that can be debated elsewhere. Here, I briefly summarise the key reasons that drive the improvement in the valuation when using such methods.

The key benefits and improvements are:

• To highlight biases in the input assumptions and in the calculated output value. Part of the risk modelling process is to determine (or estimate) the position of any specific numerical assumption (i.e. the base case) within its own possible range. For example, the base case assumption on the growth rate may be “reasonable” at first sight, but in fact may be overly optimistic or pessimistic when placed under the scrutiny that is required if determining the possible range of values for that input. In fact, as mentioned in the next point, it is generally impossible to have non-biased values.
• To calculate the average output. It is worth recalling that the core concept of value in economics is based on the average. In most cases, calculated outputs will not by default show the average. For example, if a model has its input values that are estimated as their most likely values, then the model’s output will generally show neither the average, nor even the most likely value (the “fallacy of the most likely” and the more general concept of the fallacy of the belief that input cases and output cases of a model are aligned are discussed extensively in my book Business Risk and Simulation Modelling.) The risk modelling process and the associated calculation of many scenarios during the simulation will help to establish the average value. Note that this point also highlights that non-risk-based approaches to modelling are generally inherently (or structurally biased): any quantity for which a single value must be used (as a base case) would in principle be selected at its most likely possible value, so that the resulting model will not show the average (nor even the most likely) of the output.
• To calculate the average when contingent cash flows are present. The most widely described forms of contingent cash flows are options (derivatives) and real options, but generally such cash flows are present in many contract forms and implicitly in any model with any non-linearity in its logic (e.g. IF or MAX functions). Whilst this point is in fact already covered by the above point (about the calculation of the average) it is worth noting that the application of contingent claim contracts is particularly important, since the accurate valuation of such a claim requires that many scenarios be considered, each of which is representative of the likelihood and magnitude of what may happen and its consequences for value.

To generate more insight by highlighting business value-drivers. The risk modelling process is a more logically robust and coherent one than is general Excel modelling, and in particular requires an understanding of risk drivers and hence of value drivers (in order to build a proper model which captures the risks). The extra insight generated is often useful to highlight or enhance thinking and establish a more robust and more accurate valuation.

The fact that risk-based approaches are not frequently used (indeed there is a high resistance to them from many valuation practitioners in my experience) is perhaps surprising but can be debated elsewhere.