The Quantitative Marketability Discount Model’s (QMDM) 20th Anniversary

The Quantitative Marketability Discount Model (QMDM) is now 20 years old. We at Mercer Capital developed the model during the early 1990s and were using it in appraisals beginning in about 1994.

I officially introduced the QMDM at a speech at the joint American Society of Appraisers/Canadian Institute of Chartered Business Valuators Conference in San Diego in late 1994.

As I remember, I was a much younger man at the time…


However, the appraisal world had to wait (with eager anticipation?!) another three years for the publication of my book, Quantifying Marketability Discounts. I spoke at and gave a seminar following the ASA Business Valuation Conference in 1997 in San Francisco, introducing both the new book and the methodology to business appraisers in a comprehensive way for the first time.

The Quantitative Marketability Discount Model is still around and kicking some 20 years later. Appraisers ignore the QMDM or similar discounted cash flow methods for developing marketability discounts at their peril.


There are five things to remember about the QMDM as we begin a short journey about its 20 year history:

  1. Value = f (Expected Cash Flow, Risk and Growth). This basic theory is true whether we are looking at the value of an entire business or of an interest in that business.
  2. The QMDM conforms with basic valuation theory. It is a shareholder level discounted cash flow method under the income approach to valuation.
  3. Real investors think along the lines of the QMDM, which was designed to mirror such thinking.
  4. There is no “black box.” The QMDM is memorialized in an Excel spreadsheet, but all of its math is basic and accessible.
  5. The QMDM / Shareholder Level DCF complies with Uniform Standards of Appraisal Practice (USPAP), the American Society of Appraisers Business Valuation Standards, and all other business valuation standards.

So, here we go…

My First Marketability Discount

The first time I applied a marketability discount in an appraisal was in 1979 when I signed my first gift tax appraisal. I really didn’t know what I was doing, and merely mimicked the few other appraisals I could find.

I referenced a couple of restricted stock studies and concluded, guess what? The appropriate marketability discount was, of course, 35%.

Restricted stock studies examined transactions in shares of public companies that issued “restricted” stock (under SEC Rule 144), which restricted marketability for a period of two years and then allowed for a slow dribbling of stock following the period of restriction.

The idea of using restricted stock discounts for restricted, i.e., nonmarketable shares (for a period), as evidence for appraisals of illiquid minority interests in private companies was intuitively appealing. If restricted shares of public companies were discounted, on average, say 35%, then shares of doggy private companies should be discounted at least by that much and probably more – or so the logic went.

Questions re Restricted Stock and Pre-IPO Studies

As the years passed, I became increasingly uncomfortable with the “conventional wisdom” that all marketability discounts were in the range of 35%, plus or minus a bit.

First, I knew how I thought about investing personally, and that process had nothing to do with restricted stock studies. Then, we did drastic things like obtaining and reading all of the then-available restricted stock studies. What we learned was that while the averages of the studies tended to be in the vicinity of 35% (or 45%), the ranges of observations in the studies was wide, indeed.

Suffice it to say that I was not satisfied with the conventional wisdom regarding marketability discounts. And I was no less satisfied when other studies, called pre-IPO studies, came to be published.

Discounted Cash Flow and Illiquid Interests

The discounted cash flow model came into vogue in the appraisal profession during the latter 1980s and 1990s. Business value was defined in terms of the present value of all future benefits to be derived from a business (into the indefinite future) discounted to the present at a discount rate reflective of the risks associated with receiving the expected cash flows.

At some point, I recognized that if the value of a business was based on its expected cash flows, risks and growth, then there was a corollary definition for the valuation of an interest in a business. That definition was, in today’s terms:

The value of an (illiquid, minority) interest in a business is the present value of the expected cash flows to be derived from the interest (which are derivative of the cash flows of the business itself) over the expected holding period of the interest, and discounted to the present at a discount rate reflective of the risks associated with the receipt of the cash flows to the interest.

The Ever-Present Levels of Value

We began by forecasting cash flows for interests, but quickly realized that those cash flows are viewed in relationship to the enterprise value of the business from which they are derived. This meant that in developing the QMDM, we had to think in terms of two values:

  • The marketable minority interest value of the business. This was before the distinction we now make between marketable minority value and financial control value. This set the “as if freely traded” value of a business and the context within which to look at the value of an interest in it. This value is based on the expected cash flows of the enterprise, normalized as discussed here.
  • The nonmarketable minority interest value of the interest. This value is the present value of all expected dividends or distributions from the business over the expected holding period of the investment, including an estimate of the terminal value of the investment, which would normally relate to a terminal event in which the business is sold.

The difference between the concluded marketable minority interest value and the nonmarketable minority interest value is the marketability discount implied by the economics of the investment – expressed in percentage terms.

Let me make this clear. The marketability discount is not some magical or mysterious “discount” that is applied to get to a nonmarketable minority value. Rather, the marketability discount is the difference in two values.

  • The first value is at the marketable minority level (or now, financial control), which values the enterprise (MM-FC). Assume this value is $100
  • The second value is at the nonmarketable minority level (NMM). Assume this value is $75.

The marketability discount, or DLOM as some prefer, is therefore defined as:

1 – NMM/(MM-FC)

What is the marketability discount? It is 25% in the example above, of (1 – $75/$100).

Why does the marketability discount exist? Because there are differences between the expected cash flows, risks and growth of the enterprise and the derivative expected cash flows, risks and growth of the interest in the enterprise.

At its simplest, the QMDM was and is a shareholder level discounted cash flow model. The QMDM is still around and frequently used by business appraisers because its logic is sound and the model provides a superior way to estimate the value of illiquid minority interests than using restricted stock averages as benchmarks for the value of illiquidity or lack of marketability.

The First Application of the QMDM I Remember

One of the early times I used the QMDM was in an estate tax appraisal in the early 1990s. The estate was substantial, and was in litigation with the Internal Revenue Service when Mercer Capital was retained. The IRS retained the services of a firm that they used frequently at the time.

The facts pertaining to minority investments in the subject business were not favorable. The expected holding period was lengthy, and prospects for liquidity on a favorable basis were remote. The appraiser for the IRS concluded that the appropriate marketability discount was about 55%.

My concluded discount was 80%. The matter was headed to Tax Court. I was hopeful that the scheduled trial would occur, because it would have allowed me to explain the methodology at trial and would have provided good exposure for the then new QMDM.

However, in preparation for trial, we were provided with a copy of the opposing expert’s report to review. In doing so, we found a significant math error that, when fixed, placed that report’s conclusion right on top of mine. Needless to say, the matter settled at an 80% marketability discount and never went to trial.

Thompson v. Commissioner (72 T.C.M. 1036 (1996))

In 1994, Mercer Capital was retained by the Thompson family to provide valuations in anticipation of potential trial over the value of minority interests of T&S Hardwood Company, Inc. which were gifted in periods dating back to the late 1980s.

The gifts had been made based on appraisals by a CPA who capitalized average earnings, considered book value, and applied a 35% marketability discount. His concluded value was $113.52 per share. The Internal Revenue Service argued for a value of $240 per share, inclusive of a 20% marketability discount.

The relevant portion of the case pertaining to my valuations follows:

On or about February 16, 1994, Mr. Thompson hired attorney David Aughtry (hereinafter Mr. Aughtry) to represent Mr. Thompson and petitioner at trial. A valuation expert, Z. Christopher Mercer (hereinafter Mr. Mercer), of Mercer Capital Management, Inc., was in turn engaged by Mr. Aughtry to prepare an appraisal of the shares of the Company for use in the gift tax valuation cases of Mr. Thompson and petitioner.

Mr. Mercer prepared an appraisal report and submitted it to Mr. Thompson. Mr. Mercer’s fee was paid by the Company and charged as compensation to Mr. Thompson.8 Although Mr. Aughtry and Mr. Mercer were formally engaged by Mr. Thompson, it was understood that they would also represent petitioner’s interests in her separate gift tax case. Mr. Aughtry entered his appearance in petitioner’s case on March 15, 1994.

Petitioner provided a copy of the valuation report prepared by Mr. Mercer to respondent within the time required under Rule 143(f). Respondent, on the record at a hearing in Atlanta, Georgia, on April 22, 1994, accepted the per-share value of the Company stock as determined by Mr. Mercer, $124.50 for the year 1988, and lesser values for gifts in the 2 previous years. Respondent also conceded on the record that the addition to tax under section 6660 would not apply. It was agreed that the settlement would apply to both petitioner’s and Mr. Thompson’s case…

What is not clear from the above is that the Mercer Capital report used the QMDM to develop its marketability discount, which was, I recall, about 35%. This valuation was accepted by the Internal Revenue Service and the Court in the above memorandum decision.

By the time the QMDM was introduced at an international business valuation conference in 1994 and later published in Quantifying Marketability Discounts in 1997, we were confident that the model worked, provided reasonable estimates of marketability discounts, and could withstand scrutiny in litigation.

Written Exposure of the QMDM

I have written extensively about the QMDM. It is discussed in a number of books I have published, including the following:


The books have been around for a long time. It is impossible to suggest that the QMDM has not been exposed to peer review. All of the above books have been available and have been reviewed by numerous writers in a variety of valuation publications.

In addition to the books, I have written articles about the QMDM in many business appraisal publications. In this article, I’ll focus only on the articles I have written. Others professionals at Mercer Capital and elsewhere have also written numerous articles about the QMDM.


The QMDM has been exposed in all of the major valuation journals over the years. Again, others at Mercer Capital have also written articles about the QMDM. It has further been discussed in numerous articles published by other writers.

Educational Sessions re the QMDM

We have taught seminars regarding the QMDM to a number of groups, including law firms, CPA firms, and the Internal Revenue Service. I have given well more than 50 speeches and educational sessions to many groups over the years. Speeches have included:


Interestingly, the QMDM seems to be receiving renewed interest. I’m speaking on the topic again, and requests keep coming in.

The QMDM and Daubert

In today’s contentious and litigious environment, appraisers are being challenged regarding many aspects of their appraisals. Daubert and its progeny have raised the specter of challenges in which appraisers’ valuation methods can be potentially disqualified.

That should not happen with the QMDM, because the model clearly meets all of the Daubert factors.

QMDM Daubert

I have never been challenged under Daubert for using the QMDM. I am not aware of any other appraiser who has been challenged, or even successfully challenged for using the model. A successful challenge should not happen with the QMDM, because the model clearly meets all of the Daubert factors.

The QMDM and Business Appraisal Standards

In the last decade or so, two major business appraisal standards bodies have issued guidance regarding the valuation of illiquid minority interests of businesses. The guidance is illustrative of focus on well-known valuation discounts such as the minority interest discount and the marketability discount.

Standards Rule 9-4(d) of the USPAP has provided guidance regarding the valuation of illiquid minority interests since about 2006. SR 9-4(d) states, in part:

d) An appraiser must, when necessary for credible assignment results, analyze the effect on value, if any, of the extent to which the interest appraised contains elements of ownership control and is marketable and/or liquid.

Comment: An appraiser must analyze factors such as holding period, interim benefits, and the difficulty and cost of marketing the subject interest. Equity interests in a business enterprise are not necessarily worth the pro rata share of the business enterprise interest value as a whole. Also, the value of the business enterprise is not necessarily a direct mathematical extension of the value of the fractional interests. The degree of control, marketability and/or liquidity or lack thereof depends on a broad variety of facts and circumstances that must be analyzed when applicable. (emphasis added)

The American Society of Appraisers, through its ASA Business Valuation Standards, has issued certain procedural guidance regarding the valuation of illiquid minority interests. Procedural Guideline PG-2, Valuation of Partial Ownership Interests, suggests that the following items, among others, be considered when valuing minority interests.

  1. Provisions of organizational documents
  2. Applicable laws and regulations
  3. Ownership structure and configuration
  4. Access to reliable information re asset/entity
  5. Relevant pool of potential buyers
  6. Transactions in similar assets

These first six items are fairly standard qualitative factors for consideration. The next factors, however, get much more specific:

  1. Expected holding period of the investment
  2. Expected economic benefits to the interest

a. Expected interim dividends or distributions

b. Expected terminal cash flow at end of the expected holding period

c. Current value of enterprise [that’s the marketable minority/financial control value noted above] and expected growth rate in value of the enterprise over the expected holding period (considering distribution policy and effectiveness of expected reinvestment in entity)

  1. Required return for investments in the subject interest, including all appropriate risks of the interest in relationship to the enterprise.

Procedural Guidelines in the ASA Business Valuation Standards are not binding, but they do provide best practices guidance for business appraisers. Factors seven through nine above are quantitative factors that are best addressed in quantitative terms. Interestingly, the factors noted above are the key assumptions of the QMDM.

To bring home the point of standards compliance and the QMDM, we show the assumptions of the QMDM in light of the USPAP and ASA Business Valuation Standards above.


The table above references USPAP SR 9-4(d), but it should be clear that the QMDM clearly covers the guidance from PG-2 of the ASA Business Valuation Standards.


We began by noting that the Quantitative Marketability Discount Model is having its 20th anniversary this year. And we stated that readers should remember five things about the QMDM. We repeat those items now:

  1. Value = f (Expected Cash Flow, Risk and Growth). This basic theory is true whether we are looking at the value of an entire business or of an interest in that business. I hope this is clear at this point.
  2. The QMDM conforms with basic valuation theory. It is a shareholder level discounted cash flow method under the income approach to valuation. To critics of the QMDM, of which there remain, perhaps, a few, I say: “What part of discounted cash flow do you not understand?”
  3. Real investors think along the lines of the QMDM, which was designed to mirror such thinking. To be treated in the next post.
  4. There is no “black box.” The QMDM is memorialized in an Excel spreadsheet, but all of its math is basic and accessible. To be treated in the next post.
  5. The QMDM / Shareholder Level DCF complies with USPAP, the ASA Business Valuation Standards, and all other business valuation standards. I have not spent time discussing other methods, like comparisons with restricted stock studies, or the qualitative approach advocated by the AICPA, but it should be clear that these qualitative methods cannot address the quantitative guidance found in USPAP SR 9-4(d) or PG-2 of the ASA Business Valuation Standards.

Wrap-Up and Offer

The QMDM is available today in a product that is named The QMDM Companion. The QMDM Companion includes a pdf that explains the QMDM and its assumptions in detail, providing numerous examples to illustrate the concepts. It also includes the QMDM in Excel format, which is immediately available for your use.


The QMDM Companion is available for $125. You can purchase it not by clicking here.

Shortly, I’ll show how the QMDM works and prove that it is not a “black box.” We’ll also talk about how the QMDM conforms with the thinking of real, as well as hypothetical investors.

Until then, be well!


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

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