# A Quirk with Third Appraisers in Buy-Sell Agreement Valuation Processes

The role of the third appraiser is always to bring resolution to buy-sell agreement valuation processes.  The question is how the third appraiser’s conclusion will be used to bring pricing resolution.  There are a few ways:

• Regardless of the conclusions of the first two appraisers, the third appraiser’s conclusion can be determinative for the process.
• The third appraiser’s conclusion can be averaged with the conclusions of the first two appraisers to yield the conclusion for the process.
• The third appraiser’s conclusion can be averaged with the conclusion of the first two appraisers closest to it.

The first two solutions are fairly straightforward and understandable.  The third solution, however, creates an unintended consequence that has caused problems for a number of buy-sell agreement valuation processes.  Call this consequence a “quirk” that I’ve never seen anyone talk about or write about. Consider the following figure.

In the figure above, assume that Appraiser 1 has reached a conclusion of fair market value for a buy-sell agreement valuation process of \$100 per share.  Appraiser 2 reached a conclusion of \$200 per share.  The differences are not always this dramatic (although sometimes they are), but they show up well on the figure. The principles are the same with smaller differences.

In the appraisal process, the third appraiser is designated as the reconciler.  Their conclusion will be averaged with the closest of the conclusions of the other two appraisers.  The italicized words sound simple and logical; however, they mask important dynamics and implications for the third appraiser and for all parties to similar agreements.  Let’s look at the potential outcomes for the third appraiser and for the parties.  The third appraisers is the  green-dashed line above, and the implied final prices are reflected by the solid line.  Now assume the following about the third appraiser’s conclusion.

• Appraiser 3 concludes \$100 per share, agreeing with Appraiser 1. The conclusion is averaged with that of Appraiser 1 and the final price is \$100 per share. See this at the lower left of the figure above.
• Appraiser 3 concludes up to \$149 per share. At \$149 per share, the final price is \$124.50 per share (the average of \$100 and \$149).  Note that the final price is a simple average of the conclusions of Appraisers 1 and 3 up until a price of \$149 per share is reached (actually \$149.99 per share at the extreme).
• Alternatively, Appraiser 3 concludes \$200 per share, agreeing with Appraiser 2. The conclusion is averaged with that of Appraiser 2 and the final price is \$200 per share.  See this at the upper right of the figure above.
• Appraiser 3 concludes down to \$151 per share. At \$151 per share, the final price is \$175.50 per share (the average of \$200 and \$151).  The final price is the simple average of the conclusions of Appraisers 2 and 3 down until a price of \$151 per share is reached (actually \$150.01 per share at the extreme).

The undiscussed dynamics of this “logical and simple” averaging process is that a \$2.00 per share swing in the third appraiser’s conclusion (from \$149 per share to \$151 per share) creates a 41% change in the final price. That small \$2 per share change results in an increase in the final price by \$50.00 per share, or from \$124.50 per share to \$174.50 per share.  The percentages are different but the result is the same if the change is from \$151 per share to \$149 per share.

Left unstated in all similar agreements I have seen, what happens if Appraiser 3’s conclusion is \$150.00 per share? It is equally close to the \$100.00 per share and \$200 per share conclusions of both Appraiser 1 and Appraiser 2, respectively.  Presumably the parties could agree to average all three conclusions and conclude the process at \$150.00 per share.

This kind of valuation process places a great deal of pressure on the third appraiser.  Assume that his conclusion is honing in on \$140 per share.  That would yield a final price of \$120 per share (average of \$100 and \$140).  However, a small change in one assumption could push the conclusion up 9% to \$152 per share, which would yield a final price of \$176 per share (average of \$100 and \$152), or 47% higher than at the lower potential conclusion.  Rest assured, Appraisers 1 and 2 and their clients become aware of the math behind the figure above and will be lobbying with the third appraiser to reach a conclusion above \$150 per share (midpoint) or below it based on their respective points of view.

Consider a couple of other alternatives for the third appraiser as reconciler.

• Appraisers 1 and 2 set the range. If the third appraiser reached a conclusion of, say, \$60 per share, or \$40 per share below the \$100 per share conclusion of Appraiser 1, the average would be \$80 per share, or outside the range of Appraisers 1 and 2 and below it.  Similarly, if the third appraiser reached a conclusion above \$240 per share, the final price would be outside the range and above it.  For this reason, many agreements state that, regardless of the conclusion of the third appraiser, the conclusions of Appraisers 1 and 2 will set the range for the final price.
• All three appraisal conclusions are averaged. Occasionally, an agreement will state that the final price will be the average of all three appraisers.  This option is most often not considered because it is thought to provide undue influence on the final price of an outlier conclusion from Appraiser 1 or 2 on the low or the high side.

The role of the third appraiser is always to bring the valuation process to conclusion. With the third appraiser as the reconciler, the third appraiser is not necessary in most valuation processes if the first two reach similar conclusions (say, within 10% of each other). The third appraiser is brought in to resolve larger differences and to cause the process to reach a conclusion by reconciling with one or both of the first two appraisals.

This quirk exists in numerous buy-sell agreements “out there” in the world.  It generally goes unrecognized until an agreement is triggered.  Then, it becomes painfully obvious to the parties that they have a ticking time bomb on their hands.

There has to be a better way to resolve buy-sell agreement pricing.  And there is.  One such process is found in my book, Buy-Sell Agreements for Closely Held and Family Business Owners (available for purchase).  It is called the Single Appraiser, Select Now and Value Now process.

I hope you are all staying well and safe during these pandemic times.  Until next time, be well.

Chris

Please note: I reserve the right to delete comments that are offensive or off-topic.