A propos of my previous post on valuing notes receivable, yesterday I participated in a conference call with my American Business Appraisers National Network colleagues on that very subject. One theme of the discussion was the uncertainty (for example, of estimating the discount rate for notes with missed payments and uncertain prospects for future payments) and necessity for due diligence and subjectivity to mitigate that. Another theme was the various technical means of developing the discount rate (using a build-up approach with a risk-free rate or a corporate rate, or using various databases on bond prices and yields).

Underlying the whole discussion was a fundamental concept: appraised value is a range under any standard of value. The central appraisal task is to estimate, express, and support value either as a point estimate (as in tax valuations) or as a range estimate (in transactions).

The challenge appraisers confront is that we cannot estimate value with full confidence. This can arise because of lack of data (no or too few guidelines), imperfect data (unaudited financials), inconsistent data (guidelines with a wide range of indicated pricing multiples), uncertain assumptions (the company-specific equity cash flow discount rate), conflicting premises (going concern versus liquidation), and / or inconsistent results (different value indications derived from different approaches and methods).

Appraised (estimated) value is thus inherently uncertain.

This poses two problems. First, it is easy for appraisers to forget this. If we rush into our calculations without consideration of the underlying uncertainties, we may come up with a value that is wide of the mark. We find out about this when the IRS challenges our results, when we are cross-examined, or otherwise challenged. Second, others may not realize how uncertain our estimates are. A value conclusion of $36,814 looks very precise, when in fact there could be great uncertainty associated with it.

If we apply just one method and set of assumptions, we have an “inside out” perspective on value. To use an archery analogy, we are shooting rather blindly at the target, assuming we will hit the bull’s-eye. Sometimes this can be done with ease and high confidence. For example, it does not take much work to value marketable public securities.

If, however, the securities are held in a FLP and we have to appraise the LOMD for a limited interest, the inside out approach is highly risky. If we blithely select a LOMD, we may miss the bull’s-eye, let alone the entire target, by a considerable amount. This is why professional standards require us to support our conclusions. In any event, we will probably not be very confident of our blithe LOMD guess.

Enter the “outside in” perspective on value. We start by asking a basic question: what is the maximum and minimum possible LOMD? (Gee, let me think…ummm)…100% to 0%!

That might seem dumb and obvious, but look what we have accomplished: we narrowed the range of possible LOMDs from -∞ to +∞ with 100% confidence. (That is why we earn the big bucks!) In the archery analogy, we have clearly separated the target (0% to 100% LOMD) from the vacant space around it. Next, we employ as many methods, data sets, and assumptions (with reasonable ranges) as we can to develop reasonable ranges for the LOMD. We do not have perfect confidence about any of them, but we certainly have a fair amount. Next, we combine the ranges, albeit with some subjective judgment, to narrow the ultimate range even more. We then select a final value from somewhere in the range, again subjectively. Each step of narrowing the range involved logic and (increasing amounts of subjective) judgment, but the result is something we can be confident above, much more so that our confidence with our inside out blithe guess.

When I teach valuation, I illustrate the inside out and outside in perspectives with a class exercise. Using only information they previously knew and information they can obtain by looking out the window (but not going outside, and without a thermometer), estimate the current outside temperature (in Fahrenheit).

With a pure inside out perspective, most students guess the temperature and are relatively unconfident about their guesses. In addition, they have no support for them other than “judgment” (in appraisal reports, this is often stated as “in my professional opinion”).

With a pure outside in perspective, students often make better and more confident guesses (estimates). For example, as this is written (September in Cleveland), I look outside and see the sun shining, no ice or snow on the ground, and people walking around dressed in long-sleeve shirts and light jackets, but not winter coats or gloves. The first cut at the temperature estimate is that it is not freezing so the temperature is above 32 degrees. The temperature almost never exceeds 100 degrees here, so my first estimate of the temperature range, which has very high confidence, is 32 to 100 degrees. The second cut is that, based on what people are wearing, the temperature is probably above 45 degrees (no winter garb) and below 65 degrees (jackets and long sleeves). I am fairly confident of this refined range of 45 to 65 degrees. If I have to be more specific, I will estimate (guess with subjectivity) a 55 degree temperature, but be willing to concede that, say, 50 or 50 is equally probable (reasonable).

To summarize, the inside out perspective – a blithe guess using one (or no) method might be tempting at first because it seems reasonable, but we have little confidence in it because of lack of empirical and logical support, and lack of disclosure of a reasoned, reasonable range. The outside in perspective, by contrast, progressively limits the range, first with facts and logic, and second with subjective judgment. The result is much more strongly defensible than that of the inside out approach.

Do you see the valuation analogy with respect to the LOMD? Value (the estimated LOMD) is a range. The scientific part of appraisal is narrowing the range with (case) facts and (sound appraisal methodology) logic. The artistic part is narrowing it further and selecting a point estimate (conclusion) with common sense, informed judgment, and reasonability…the considerations enumerated in Revenue Ruling 59-60.