# Calibrated Estimates

Calibrated estimates is a  helpful forecasting technique. Forecasting is the critical appraisal challenge because the value of a firm is directly related to the future expected economic benefits to the buyer. The more accurate the forecast of these benefits, the more accurate the assessment of value. Once we agree on the fairness principles guiding a negotiation of an equity, we are left with the challenge of forecasting future economic benefits. To the degree we can accurately predict future revenue streams and discretionary earnings (DE), we can accurately assess value.

A forecast of DE is by definition a prediction of the future and all such predictions are uncertain. Even if we have a very good understanding of how things work most of the time and lots of data about the past, chance or random events lead to a degree of uncertainty about the future. This variation and uncertainty implies:

1. Exact precision as to future levels of DE is not obtainable by any intellectually honest method of prediction.

2. Since the value of goodwill and the equity of a firm rely upon the forecast of future DE no precise exact number for an equity value is obtainable by any intellectually honest method of appraisal.

Does the inability of an appraisal method to offer a precise equity value make that method invalid or unhelpful? I think a surprising number of people would agree. Why? Well, obviously you can’t sell a business, stipulate a property division, or tax a gift of equity shares utilizing a range of values.1 You have to utilize precise values. The answer to this dilemma is to establish a reasonable range of forecast values utilizing computer simulation techniques and then simply choose the mid-point of this range.

A second reason why people might reject an appraisal method that relies on ranges rather than precise values is that we are predisposed to prefer certainty to uncertainty. Some people think that if a method cannot offer exact precision, then it cannot offer anything worthwhile. But knowing that some quantity of interest lies within a certain range of values is not equivalent to knowing nothing. For example, we might not know precisely the percentage of customers who will be retained after an equity transfer but knowing it will probably be closer to 50 or 60% than to 10% is useful information in helping a motivated and qualified buyer decide how much to pay for the firm’s equity.

A third reason to reject imprecise methods is the lack of awareness or outright fear of the mathematics of uncertainty and variance. The mathematics of uncertainty and variance is better known as probability theory and statistics. Probabilistic concepts underpin computer simulation techniques. While some of the mathematics is intuitive and within reach of most people with at least some modest training, much of the mathematics is not that intuitive and not so easily understood. This fear and distrust of statistical thinking is widespread in our society.

## The Key Drivers of Discretionary Earnings (DE)

In order to provide a reasonably accurate forecast of DE, and hence the equity of the firm, three critical rates that must be estimated:

1.     The transfer rate.

2.     The attrition rate.

3.     The DE per customer per year.

The transfer rate is simply the percentage of existing customers, clients or patients (CCPs) who would be willing to patronize the firm at least once after an equity transfer. The attrition rate is the rate at which the firm will lose CCPs that have patronized the firm at least once after the equity exchange. The DE per CCP per year is the amount the owner should realize net of all non-discretionary fixed and direct expenses divided by the total number of customers.

To my knowledge there are at this time no broad-based sector studies on the transfer rates following an equity transfer. Nor are there broad-based sector studies of attrition. Estimating DE per customer per year does not require reliance on data bases however. Instead this measure can be developed by analyzing prior income statements combined with a census of the firm’s CCP base.

Surprisingly (or perhaps not) most smaller firms may not have a precise record of just how many CCPs they regularly serve. The appraiser may have to work backwards to obtain a realistic estimate of this figure. If you know the accurate total annual gross revenue and have a reasonable idea of the average frequency of patronization and the typical revenue per patronization, you can develop a reasonable estimate of the number of CCPs.

## Why is Critical Data Missing?

As just noted there are no reliable databases for transfer and attrition rates. These are key variables needed in developing the forecasts of DE.  This sparse data problem haunts appraisal practice. Why is the data sparse?

Most of the data we seek would be quite useful to individual potential sellers and buyers of subject companies (SCs). Unfortunately, individual SC owners have neither the resources nor the motivation to collect it. Consider, for example, transfer rates. It would be very useful for buyers to have empirical data on transfer rates experienced during past equity exchanges. But what incentive do buyers really have to collect the data once they have acquired an SC? Not much, really. This data would be no more than a historical curiosity not worth the effort to collect for such owners. So they usually do not. A similar situation prevails for attrition rates. Again, for existing owners collecting such data seems like a historical exercise with little operational benefit to them.

## Calibrated Estimates

As just noted many users of appraisal reports will be less than satisfied with anything other than opinions that provide an exact value of goodwill. The problem of course is that this expectation cannot be met. An appraiser specifying an exact value for goodwill is analogous to a meteorologist predicting exactly how much rainfall will accumulate in Boise, Idaho between January 1, 2017 and December 31, 2022. No self- respecting, credible or knowledgeable meteorologist would even attempt to provide such an exact prediction.

Assessing the value of an SC requires a forecast of future DE at least as uncertain as the exact amount of rainfall that will fall in Boise over the next five years; no self-respecting, credible and knowledgeable appraiser should attempt to provide an exact value of the SC’s total equity (unless of course the evidence weighs heavily in favor of an exact value of zero). What a credible, self-respecting and knowledgeable meteorologist can and will do is provide an estimate of the likely range of rainfall that will fall in Boise over a five-year period.

Specifying a range of course entails specifying a lower and upper bound. Appraisers have a simpler task than meteorologists in the sense that they know that the lowest bound for an SC’s equity is almost always zero whereas as dry as Boise might be, zero is not a credible lower bound for rainfall over a five- year period. Meteorologists will also likely have much more confidence in specifying upper and lower bounds than amounts falling between these extremes. A similar situation is faced by appraisers. We can be much more confident that a value will not be lower than or exceed a given amount than we can be that a value will be precisely some exact value within the upper and lower bound.  Douglas Hubbard’s remarks well summarize these observations:

“No matter how little experts think they know about a quantity, it always turns out that there are still values they know are absurd. The point at which a value ceases to be absurd and starts to become unlikely but somewhat plausible is the edge of their uncertainty about the quantity.” 2

Taking the meteorology analogy a bit further, forecasts such as the amount of expected rainfall are explicitly stated in terms of probability. Meteorologists make statements such as “there is a 40% chance of measurable rainfall tomorrow.” Meteorologists embrace probability theory in their science. Appraisers need to do the same.

In probability theory, when the events being forecast involve continuous variables such as rainfall, the specified probability associated with an exact forecast value is zero. So the assigned probability of precisely, say, 66.6 inches of rain falling in Boise between January 1, 2013 and December 31, 2018, is zero. Non-zero probability assignments can only be made on intervals or ranges.3

Doug Hubbard has described a useful method of developing reliable estimates of key variables in the absence of “hard” data known as “calibrated estimates”. To apply this method, individuals with experience and expertise in the relevant economic sector are asked to provide plausible ranges to key appraisal parameters. The basic idea is to have the expert estimate the lowest and highest values for a particular parameter. The estimate is calibrated by asking the expert to set the values so that they are 90% confident that the true value falls within the specified upper and lower bound. Hubbard has shown that experts can be trained to become more accurate over time in setting these 90% confidence intervals.4

Who should provide calibrated estimates? Who is educated or experienced enough? The general answer is someone who has had experience in the SC’s market sector. Even absent detailed and reliable records, owners and managers will have an educated intuition based on their past experience to provide plausible ranges for key appraisal parameters. In a specific appraisal engagement the owner manager or some non-owner long-standing employee is usually available to make reasonably reliable calibrated estimates.

It should be emphasized that even if “hard” data is available to estimate the key appraisal parameters, this “hard” data should be vetted for applicability to the SC. Almost all reported data that involves sampling will be subject to sampling error. Sampling error arises when a sample fails to fully represent the characteristics of the population. The owner manager of an SC or other key employees should be informed of the data and be asked to opine on its correspondence to the SC’s economic experience. Experienced, expert opinion should never be ignored even if “hard” data is available.

## References

1.  Of course, if an “earn out” is utilized in selling the business, no exact value is set at the time of sale. Click here for more on “earn out” sales.

2. Doug Hubbard, How to Measure Anything: Finding the Value of Intangibles in Business, John Wiley & Son, Hoboken, New Jersey, 2010Hubbard (2010) p. 64-65.

3. See John Kruschke’s discussion of the difficulty of assigning precise probabilities to continuous variables in his Doing Bayesean Data Analysis: A Tutorial with R and BUGS, Academic Press, Burlington, MA 2011 pp. 31-33.

4. Hubbard (2010) pp. 53-69.

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