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In a recent publication by the Institute of Business Appraisers, Business Appraisal Practice: 2016 Second Quarter, there was discussion over the topic of Monte Carlo simulation and its application to the valuation world. The survey conducted by Toby Tatum, MBA, CBA, CVA, MAFF, editor of Business Appraisal Practice, showed that 34.55% of surveyors had never heard of Monte Carlo simulation or if they had, knew little about it. Along with this, of those that actually knew about it, 27.78% had never used it in a business valuation. Within this article, and the many others within the publication, there is plenty of discussion about the validity and usefulness of its application. The articles discuss both practical application to standard valuation engagements, as well as, the method’s interpretation within a court of law. While the peer-reviewed journal brought forth conversation on an extremely important topic, it is unfortunate that this essential technique is not considered standard within the valuation industry today.
Monte Carlo simulation (Monte Carlo Method), at its most basic level, is a computerized technique used to assess risk and probability. When given specific parameters and inputs, the simulation outputs a range of possible outcomes, at given probabilities. Essentially, the algorithm runs though the inputted parameters (or previously simulated), and comes up with a solution. Since, there is a range of values that come from various probabilities, the final value could fall within a range of possible outcomes. Monte Carlo Method runs through these potential outcomes 1,000, 10,000, 100,000, or 1,000,000 million times. It plots all of them into a chart that allows the user to see the probability of each possibility. This may seem pretty complicated, and some of the nuances of it are, but at its fundamental basis it is simple. To better explain this, observe a simple example: Let’s say you have a dice, and you roll that dice 10 times. The results you get are posted below.
Given these rolls, is it fair to assume that one has ten percent probability of being rolled, two has a zero percent, and three has a thirty percent chance? Obviously, not. Any person with a basic concept of probability knows that each side of the dice has the same probability of being rolled (16.67%). Yet, if an individual wanted to prove that experimentally, he or she would have to spend weeks at a time rolling the dice and recording the results until the results display this reality. The Monte Carlo simulation, on the other hand, can roll the dice one million times in just a couple minutes.
While this example significantly oversimplifies what a Monte Carlo simulation does, it provides a good basis for understanding the following discussion on the importance of the simulation on business valuation.
Despite the business valuation community’s movement towards increased acceptance of the method, the publication represents an industry that often falls behind when pushing for advancements in thought and methodology. Monte Carlo simulation has been around since the 1930s, and well documented studies of its methodology have existed since the 1960s. Yet, the business valuation community has been excruciatingly slow in accepting its practicality to their profession. The reality is, a business’s value (excluding a liquidation) is based on its future ability to produce returns. Key word: future. A business that made ten million in sales last year is worth no more than the sum of its parts if it has no potential for generating cash flows in the future. Those past earnings are not indicative of future earnings. Monte Carlo simulation excels in this world of future probabilities, which is the world in which every business exists.
So what is inherently wrong about not using the Monte Carlo Method in a business valuation? If professionally certified valuators have done without it in the past, why is it so important now? These are the questions that are certain to come to mind. Luckily, they are very easy questions to answer. Without it, business valuations rely too heavily on assumptions. Take for example, one of the most crucial components of a valuation: discount and capitalization rates. Minute changes in the determined discount rate can cause the valuation to fluctuate greatly. The example below for calculating net cash flow to equity will clearly demonstrate this.
The above comes out to a difference of $1,904,236 with the value of the first estimation coming in 34.7% higher than the second estimation. Given the way the valuation industry works today, two valuators could very reasonably give each of these valuation conclusions, and they could both technically be “correct.” As long as the valuation professional can support his estimations the end result is deemed valid and acceptable. So essentially, what a valuation comes down to by today’s current standards is that an individual’s own personal judgement is more valid than another’s.
The idea that future growth rates, rates of return, and other risk factors in the future can be determined to be a specific value for a specific investor in a specific purchase opportunity makes complete sense. In this specific circumstance what is important is what the investor thinks the value will be in the future. His determination of these values it what makes him believe the business is value generation opportunity. Yet, this should be seen as only a specific instance in which exact values are estimated and used for a final determination of value. When it comes to a valuation under the terms of fair market value, this should not be seen as a legitimate practice, and for good reason.
IRS Ruling 59 – 60 states the definition of fair market value to be, “The price at which property would change hands between a willing buyer and a willing seller, when the former is not under compulsion to buy and the latter is not under any compulsion to sell, both parties having reasonable knowledge of relevant facts.” The IRS interpretation is exactly what it should be, it as an explanation of a hypothetical transaction between hypothetical parties. The transaction and parties involved are assumed to be the most generic examples available, and as such a fair market value assumption should not be based on an individual preconceived notion of what the future will hold. Simply put, just because an analyst is thinking the market will demand higher future equity risk premium returns and places a rate of return of seven percent, does not mean that figure is the most likely outcome. In reality, there is a range of values of which there is a given likelihood of occurrence. The analyst could still choose the equity risk premium of seven percent, but using a Monte Carlo simulation will show that given outcome is twenty percent over the median value, and in reality, there is only a ten percent change that the actual realized equity risk premium will be that high. The Monte Carlo simulation forces the valuator to put his estimates in to check, and helps to prevent his or her own bias from influencing the end result.
The table below displays the Build-up Method, a common technique for calculating discount and capitalization rates, and shows how rates can easily be influenced by individual perceptions and outlooks.
Examining the two valuators and their conclusion of after-tax net cash flow capitalization rate, you can see how having slightly different conclusions as to the effect of certain risk factors greatly affects the final rate, and ultimately the value. Yet, each value could be deemed acceptable under current valuation standards. Looking at each individual piece of the valuation, it can be seen how each could be justified.
Risk-free rate for example was determined to be two different acceptable values by each of the valuators. Valuator number one determined the risk free rate to be the 20-year government bond yield rate, a fairly widely accepted risk free proxy for the valuation community. Valuator two choose the 30-year risk-free rate, which could also be justified by the valuator. Since the valuator is estimating the business to continue on indefinitely into the future, it could be said that the 30-year time horizon better reflects this assumption.
The equity risk premium differs widely for both professionals in the example, and again, both can be considered reasonable under current standards. For number one, the equity risk premium was determined to be 5.40% through Duff Phelps1. With Duff Phelps as a reliable data source, it is hard to rebuke as a quality estimation of equity risk premium. For valuator number two, equity risk premium was estimated at 7.00%. This valuator cites several sources and reasoning factors for their conclusion. Citing sources from both NYU Stern School of Business, as well as, Federal Reserve economic forecasts to support his conclusions(2). Utilizing these sources portrays a slightly riskier outlook for equity markets, and thus justifies the valuators inclusion of a higher equity risk premium.
In order to keep this sample company as generic as possible, there is no industry premium included by either valuator. Although, in a real life example, the industry premium could vary widely depending on the valuator’s assessment of the industry risk. Instead, the next risk category of the build-up method is size premium. There have been many studies on this topic, with a very wide range of conclusions from which valuators can draw upon. Even using a single source, the size premium can differ greatly. Take for example Ibbotson’s SBBI: Valuation Edition. Valuator one utilizes the smallest decile of companies which stands at 6.20%, and valuator two utilizes the sub section of 10, 10b, that puts the size premium at 9.78%3. Depending on the reasoning, each could be justified. Valuation professional number two believes that since the company falls within this market cap range, that is the proper premium to use. Valuator one on the other hand, believes that the fluctuations in small company market caps is too inconsistent to utilize the broken down subsections, so the use of the general category premium is the one that makes sense.
The next important risk premium comes from company specific risk, this category is subject to possibly the most subjective opinion, and can vary by much wider margins than is displayed in this particular situation. Looking at the company’s financials, relative performance, trends, management, structure, facilities, and so on, gives the valuator an idea of what specific company risk value to assess. Based on all of these given factors the first professional assessed the factor of 6.10%, while the second valuator assessed the value of 6.40%.
The last factor, long-term sustainable growth rate, is subtracted off in order to convert the after-tax net cash flow discount rate to after-tax cash flow capitalization rate (for next year). For this estimation, both valuators choose a fairly common estimate of 3.00%, a reasonable sustainable rate of return that could be expected of most successful companies.
With the build-up method finally completed, and after completing an adjustment for the current year, the after tax capitalization rate for the current year is determined. This rate is then used to calculate the net cash flow to equity for the current year. As can be seen in the beginning of the paper, these two capitalization rates lead to drastically different conclusions of value. A $1.9 million difference at that, and with nothing inherently wrong with either of the valuators approaches. To further illustrate the point, these calculations do not include any difference that can arise from other discounts and premiums, specifically, the discount for lack of marketability and discount for lack of control. These two factors can combine for discounts as high as thirty, forty, or even fifty percent. When this factor comes into play, it is easy to see how valuations can differ by extreme margins.
With this being the reality of the business valuation profession, it leads to a question: How can business valuations become more reliable? The answer is simple, through mathematically sound techniques, such as Monte Carlo simulation. Monte Carlo simulation, among other statistical methods forces the valuator to put his estimations within ranges and probabilities that can be clearly displayed and read. It allows the individual who uses the valuation to better trust the results, it allows other valuation professionals to more capably critique the calculations involved, and it allows the courts to put more faith and confidence into the conclusions reached.
The valuation profession is built on be objectivity, and in the journey to becoming more objective, the business valuator must put aside his or her ego, and take steps to advance the profession and its credibility. Monte Carlo simulation may just be the next best step.
1 Not the actual Duff Phelps figure for equity risk premiums.
2 Not the actual figures for the NYU Stern School of Business.
3 Not the actual Ibbotson cost of capital figures.
Sources: Business Appraisal Practice: 2016 Second Quarter, “Opinion Survey”, Toby Tatum Rev. Rul. 59-60, 1959-1 CB 237 -- IRC Sec. 2031