Reprinted from Mercer Capital’s – Vol. 13, No. 1, 2001.

We believe the Quantitative Marketability Discount Model (QMDM) gained a significant amount of currency in a United States Tax Court decision – Janda v. Commissioner.1  As discussed below, although the Court took issue with the assumptions made in the use of the QMDM, it obviously carefully studied the model, and threw out the opposition’s use of the same old studies with little comment.

This is a synopsis of what we now know. The primary themes from this case are:

  1. The Court threw out using benchmark analysis for determining marketability discounts.
  2. The Court carefully examined the QMDM, but disagreed with some of the assumptions used and, as a result, disagreed with the marketability discount implied by the model. Other than that, the principal criticism was that the facts of the case as input into the QMDM resulted in too large a marketability discount.
  3. A modification of the assumptions used by the expert for the taxpayer, input into the QMDM, results in an implied marketability discount that reconciles with the Court’s opinion. It also proves that “slight” changes don’t result in “dramatic” differences in the marketability discount.
  4. We are increasingly comfortable that the QMDM meets the challenges presented by Daubert because of the model’s predictive power.2

Findings of Fact

In Janda, the Court decided as to the value of minority interests in the common stock of St. Edward Management Co. transferred by Mr. and Mrs. Janda to their children. In 1992, St. Edward Management Co. was a small bank holding company in an agricultural community in Nebraska, and both Mr. and Mrs. Janda were employed by the bank as president and vice president, respectively. The unadjusted book value of the bank was listed at $4,518,000, and the holding company, which owned 94.6% of the bank, had 130,000 shares issued and outstanding. In November, 1992, the Jandas each made gifts representing approximately 5.27% interests in the Company to their children.

The Experts and Their Reports

The Jandas presented a valuation report prepared by Mr. Gary Wahlgren. The IRS presented a report prepared by Mr. Phillip J. Schneider. At trial, Mr. Schneider agreed to Mr. Wahlgren’s conclusion of value on a marketable, minority interest basis of $46.24 per share, or a total value based on 130,000 shares issued and outstanding of about $6,011,000. The disagreement was over the marketability discount. Mr. Wahlgren used the QMDM and opined to a 65.77% discount, while Mr. Schneider relied upon the typical benchmark analysis and opined to a 20% marketability discount.

Mr. Wahlgren determined the applicable marketability discount using inputs to the QMDM as follows:

  • Growth In Value of 9.12%, based upon the historical ROE of the bank (13.54%) adjusted by dividing it by a factor of 1.4853 to take into account the difference between fair market value on a marketable, minority interest basis and the historical book value of the bank.
  • Dividend Yield of 0%. The bank apparently did not pay a dividend and did not intend to in the foreseeable future.
  • Holding Period of 10 Years. Mr. Wahlgren reasoned that the Company would not be sold within ten years because the Janda family intended to continue to operate it for at least that long.
  • Required Holding Period Return of 21.47%. This appears to have been determined using a build-up method similar to that described in Quantifying Marketability Discounts.

A quick check of our own templates confirms that these inputs imply a discount of 65.77%, as was used by Mr. Wahlgren.

Mr. Schneider opined to a 20% marketability discount based upon the following factors identified in his report:

  • The asset type held
  • The time horizon until liquidation
  • Distribution of cash flow
  • Earned Cash Flow (after debt service)
  • Information Availability
  • Transfer Costs and/or requirements
  • Liquidity factors:
    • Is the company large enough to be public?
    • Is there a pool of potentially interested buyers?
    • Is there a right of first refusal?

Mr. Schneider then quoted the restricted stock studies and pre-IPO studies listed in Shannon Pratt’s “Valuing A Business”, and a few court cases.3  In other words, Mr. Schneider used the usual benchmark studies. He then stated that he believed that “a bank would be a highly marketable business and that the stock would be highly marketable.” Based upon this, Mr. Schneider concluded that a 20% marketability discount was appropriate.

Echoing Daubert, lawyers for the IRS also asserted that “there is no evidence that appraisal professionals generally view the QMDM model as an acceptable method for computing marketability discounts.” We do not agree.

We have sold over 2,700 copies of Quantifying Marketability Discounts. The QMDM has been written up in all major valuation publications. We have spoken to hundreds, if not thousands, of professionals in the appraisal community via dozens of speeches and seminars. We have used the model in thousands of appraisals. We have received hundreds of phone calls, emails, and other communications from valuation practitioners outside of Mercer Capital who use the QMDM regularly. And, yes, we have even been engaged by the Internal Revenue Service to perform valuations on their behalf using the QMDM (none of which have made it to the point of being a matter of public record).

The Court noted the IRS objection, but neither agreed nor disagreed with it. We have no interpretation regarding the inclusion of the comment in the opinion, but we are confident that the QMDM meets the challenges of Daubert.4

The Court’s Ruling

The Tax Court Memorandum demonstrated that the Court thoroughly studied and it appears well understood the QMDM. While the Court did not accept Mr. Wahlgren’s 65.77% discount, the Court criticized the assumptions used, not the QMDM. Citing Weinberg, the Court noted that “slight variations in the assumptions used in the QMDM model produce dramatic difference in results” and that the “effectiveness of this model therefore depends on the reliability of the data input into the model.”5

We, of course, couldn’t agree more – at least with the second comment. The model is effective when the inputs to the model are reasonable. Unreasonable inputs produce unreasonable results, just as is the case with a discounted cash flow model, a single period capitalization model, a capitalization model using publicly traded companies, etc.

However, we disagree that “slight variations in the assumptions” result in “dramatic difference[s]” in the implied marketability discount. The comment in Weinberg cannot be substantiated. Having used the QMDM in literally thousands of appraisals, we can attest that, as a valuation model, it is less sensitive than single period capitalization models or discounted cash flow models or most other valuation models. At the end of this article, we modify Mr. Wahlgren’s assumptions to reconcile with the Court’s opinion. Clearly, the change in the conclusion is proportionate to the change in the assumptions. “Slight” changes in assumptions used in the QMDM do not produce “dramatic” differences in the marketability discount.

The Court questioned whether or not it was proper to use an adjusted historical ROE to imply growth in value. It noted that Mr. Wahlgren’s build-up of the required holding period return deviated from the method discussed in Quantifying Marketability Discounts in that it didn’t include adjustments for shareholder specific risks. It did not seem to take issue with the assumed 0% dividend yield or the ten-year expected holding period.

In summary, the Court wrote “we find Mr. Wahlgren’s application of the QMDM model…not helpful in our determination of the marketability discount.” Unfortunately, the Court went on to say “we have grave doubts about the reliability of the QMDM model to produce reasonable discounts, given the generated discount of over 65%.” Obviously we would prefer this last section not be written, but we note that the argument is principally with the inputs and the level of discount reached. If by “reasonable discounts” the Court means 35% to 45%, then we are puzzled.

In the case, the Court characterizes Mr. Schneider’s use of benchmark analysis as subjective and irrelevant to the facts of the case.

“We believe that he [Mr. Schneider] merely made a subjective judgment as to the marketability discount without considering appropriate comparisons. Mr. Schneider looked at only generalized studies which did not differentiate marketability discounts for particular industries. Further, although he stated that each case should be evaluated in terms of its own facts and circumstances, Mr. Schneider seems to rely on opinions by this court to describe different factual scenarios from the instant cases and generalized statistics regarding marketability discounts previously allowed by the Court. Finally, Mr. Schneider has failed to fully explain why he believes that bank stocks are more marketable than other types of stock. We therefore are unable to accept his recommendation.”

Yet, the Court appears to be asking for a model that is results-oriented, and that would end up with a marketability discount in the range of 35% to 45%. If benchmark analysis is no good, and a marketability discount should be fact-based, then Mr. Wahlgren’s analysis should win the day hands-down. If Mr. Wahlgren’s inputs to the model were reasonable, then a 65.77% marketability discount would also be reasonable. It must be the case that the Court just disagreed with Mr. Wahlgren’s interpretation of the facts, and therefore also disagreed with the inputs to the QMDM and the resulting marketability discount.

In the end, the Court split the baby, and declared a 40% combined minority interest and marketability discount. It did not differentiate as to what portion was attributable to the minority interest discount and what portion was attributable to the marketability discount.


We are excited that the Court appears to have carefully studied and understands the QMDM. The Court also appears to have not accepted Mr. Wahlgren’s conclusion based upon the inputs used in the model which produced a 65.77% marketability discount.

We cannot comment at length on Mr. Wahlgren’s report because we have not seen it, and we do not disagree with his analysis at this point because we have no basis to do so. However, we can infer a few things from the memorandum and postulate our own analysis. Mr. Wahlgren valued the Company at a multiple of reported and adjusted book value. Then, in his QMDM analysis, he derived an expected growth in value by adjusting the historical ROE by his multiple of book. This could be considered inconsistent unless an investor expected a contraction in the valuation multiples. Instead, the market value of an entity appraised at a multiple of book value will increase at the same rate as ROE if the multiples don’t change.

In the case of St. Edward Management Company, Mr. Wahlgren capitalized reported and adjusted book values to arrive at a controlling interest value of $51.38 per share. He then applied a 10% minority interest discount to arrive at a marketable, minority interest value of $46.24, or about 1.4 times book value of $32.88 per share. If historical ROE was 13.54% and it was reasonable to expect that to continue, in ten years book value would be $117.06 per share. Assuming no changes in the multiples (none was discussed in the memo), the bank would then be valued at $163.89 per share (1.4x book value). This implies an expected growth in value at the marketable, minority interest level of 13.54% – the same as ROE. Leaving the rest of his QMDM analysis intact, and changing the expected growth in value from 9.12% to 13.54%, the implied marketability discount drops from 65.77% to 49.09%.

One more adjustment. The 1990s saw rapid consolidation in community banks, and many investors might have expected a shorter holding period on the order of, say, five to ten years. With this change, the implied marketability discount is 29% to 49%, and the average is, you guessed it, 40%, exactly what the Court ruled (albeit on a combined minority interest/marketability discount basis).

Note that these adjustments are not “slight” changes in the marketability discount analysis. We have increased the expected growth in value by 40%, and have cut the holding period as much as in half. The result is an implied marketability discount about one-third lower. The change in the marketability discount is proportionate to the change in the assumptions. It is not a “dramatic” difference resulting from “slight changes.”

Anecdotal Evidence: The Predictive Power of the QMDM

In about 1990, Mercer Capital was called upon for advice regarding the value of minority interests in the stock of an attractive community bank. The closely held bank had excellent fundamentals. However, it paid no significant dividends, and the Chairman and controlling shareholder of the bank had publicly declared over and over again that the bank would not be sold until he died and not even then if he could arrange it. What stunned our client was that they had bids for the stock, at that time, for about 20% of book value. How, they asked us, could that be? The answer, of course, can be derived using the QMDM. We didn’t have the model at the time, but in retrospect it seems clear to us that the investment prospects of even an attractive closely held bank with limited liquidity prospects would result in a very, very large marketability discount. And that discount was imbedded in the bid for the minority interests in the bank at 20% of book value. This is what Mr. Wahlgren was trying to explain in his valuation, and what we will continue to do in our analyses until we see something better.

Final Thoughts

Winston Churchill once commented, “It has been said that democracy is the worst form of government except all those other forms ….”

The controversy about the QMDM may be much the same thing. On balance, the Court disagreed with Mr. Wahlgren’s use of the QMDM and seemed to be uncomfortable with the size of the marketability discount his analysis implied. We were encouraged and gratified that the Court apparently spent significant time understanding the model and devoted so much of the written opinion to it. As for the alternative, the Court dismissed benchmark analysis as subjective and irrelevant with little comment.

At the same time the Court criticized the QMDM, it reiterated the call for a fact-based valuation discount methodology.


1 Janda v. Commissioner, T.C. Memo 2001-24.

2 Daubert v. Merrell Dow Pharmaceuticals, Inc. 113 S.Ct. 2786 (1993).

3 Pratt, Shannon P., Reilly, Robert F., and Schweihs, Robert P., Valuing a Business: The Analysis and Appraisal of Closely Held Companies, Fourth Edition, New York (McGraw Hill, 2000).

4 See our discussion of this in The E-Law Business Valuation Perspective 2000-10, “Rule 702, Daubert, Kuhmo Tire Co. and the Development of Marketability Discounts,” October 23, 2000.

5 Estate of Weinberg v. Commissioner, T.C. Memo. 2000-51.

Reprinted from Mercer Capital’s – Vol. 13, No. 1, 2001.