Let’s start with a pair of conflicting realities:
1. Value is a range.
Maybe it is a probability distribution (a range in which each value has a certain probability). Every so often it is a single number (usually when it is zero). Sophisticated techniques like scenario analysis, Monte Carlo simulation, option models, and statistical regression provide logically sound ways to incorporate probabilities and are heavily used in academic research. The problem with these methods is that the probabilities are unknown, requiring subjective inputs or proxies. Moreover, there is usually no way to condense the range or probability distribution to a single number. A mean, median, or mode (the most probable value) by itself says nothing about the uncertainty of the range.
2. Most appraisal assignments require that value be expressed as a single number.
This is obvious in tax, ESOP, and financial reporting assignments in which value has to be reported on a form as one number. In transactional and litigation assignments, ranges are permitted. In transactions, the parties use the range to negotiate a deal. In litigation, judges and juries have the job of concluding a single value number.
I don’t have any great insight to share with you as to resolving this conflict, except to say that we should be intellectually honest in recognizing that probability-based methods, although logically sound, are subject to challenge as to the probability assumptions. And we should be equally honest, and humble, about the fact that point estimates of value do not reflect their associated uncertainties.