Mercer’s Musings #2: Using Restricted Stock Studies to Support Marketability Discounts

Mercer’s Musings #1 addressed the topic of compliance with USPAP and the Internal Revenue Service.

This second musing addresses the use of restricted stock studies to support marketability discounts in gift and estate tax appraisals prepared for the Internal Revenue Service (or for anyone, for that matter).  This musing is addressed to all appraisers, regardless of which valuation credential(s) they hold.  Chapter 8 of Business Valuation: An Integrated Theory Third Edition (by Mercer and Harms) (“Integrated Theory 3”) contains a detailed discussion regarding restricted stock transactions.  I’ll try to be brief but effective in this musing.

Restricted Stock Transactions

Figure 8.1 from Integrated Theory 3 defines and illustrates a Restricted Stock Discount (RSD) for a hypothetical public company issuing restricted shares in a private offering.

The exhibit is fairly basic and illustrates a single, hypothetical restricted stock transaction involving a publicly traded company that issued restricted stock on a given date.  What do we know based on this restricted stock transaction?

  • The restricted stock transaction occurred at $15.00 per share.
  • PubliCo’s unrestricted shares sold at $20.00 per share at the time of the transaction.
  • The restricted stock transaction occurred at a price that was $5.00 per share lower than the freely trading shares ($20.00 – $15.00).
  • The restricted stock transaction was 25% lower than the price of PubliCo’s otherwise identical but freely trading shares.
  • PubliCo’s unrestricted shares closed at a price $5.00 per share higher than the restricted stock transaction price.
  • PubliCo’s unrestricted shares closed at a 33.3% premium to the restricted stock transaction price.

These facts are all we know about this restricted stock transaction.  There is absolutely no economic information in this or any restricted stock transaction.  An RSD simply measures the difference between two prices.  RSDs are not value drivers like EBITDA, gross profit, number of cases, or any other value drivers.

If there is no economic information in a single restricted stock transaction, how much economic information is there in an average of 30, 50, 400 restricted stock discounts in the tired and old restricted stock studies?  The answer, of course, is none.

Restricted Stock Studies

There are perhaps 20 or more restricted stock studies of one kind or another.  Sixteen of the most prominent studies are summarized in the following figure, which is based on Exhibit 8.15 of Integrated Theory 3.

The figure highlights six studies at the top.  Note the range of averages and medians.  These studies, based on restricted stock transactions occurring up through 1982, or more than forty years ago, were the basis for what I call a long-lasting “appraisers’ folly” regarding restricted stock discounts.  These six studies and their bare statistics created the myth that restricted stock discounts “tended” to be in the broad range of 25% to 45% and in the narrower range of 35% to 45%. And more than a few appraisers use these stale and tired studies to guess at marketability discounts in 2024.  Nevertheless, most appraisers have never read the studies, which are referenced in Exhibit 8.15 of Integrated Theory 3.

The total number of restricted stock transactions noted in the figure above is 1,647, not accounting for transactions that were examined in multiple studies.  About 80% of all transactions in the studies occurred between 1966 and 2006, or going on twenty years ago.  Only about 275 transactions have been examined since 2006.  Both the studies and the transactions are “old and cold.”  The pricing and discounts of these ancient studies have nothing to do with private company valuation in 2024.

Restricted stock analysis is a very weak form of guideline public company analysis.  What would you (or a court) say if I created a guideline public company group for a valuation as of December 31, 2023, consisting of companies that existed twenty years ago, and based my analysis on multiples calculated as of December 31, 2003?  Even assuming almost perfect “comparability” of the group with my subject company, you would call me crazy — or worse.  The pricing and multiples from 2003 have no bearing on the value of my private company in 2023.

It has been argued that restricted stock discount analysis is a method “accepted” by the IRS and the Tax Court that has been used for years.  Whether such analysis is “accepted” or not, the old data has no relevance for valuations occurring at the present.  If you disagree with this rather strong statement, feel free to comment on this blog with your rationale for such relevance.

If there is no economic evidence in one restricted stock transaction, there is none in the 1,647 transactions summarized in the figure above.

A Hypothetical Valuation Situation

Let’s assume that all the restricted stock information available to an appraiser (or you) is contained in the figure above.  If you have more evidence not included above, feel free to use it.  Now assume the following example to determine marketability discounts for 10% interests in two companies that are identical except as noted in the figure below.  The valuation date is January 31, 2024.

Looking at the valuation characteristics of the Companies:

  • Company A and Company B have identical discount rates and long-term growth rates (and cap rates and price/earnings multiples).
  • They also have identical net (after-tax) earnings and, therefore, values at the marketable minority/financial control (MM/FC) level of value (Lines 1 to 6 above).

The hypothetical calls for the determination of appropriate marketability discounts for two 10% interests, one in Company A and the other in Company B.  Looking at the valuation characteristics of the two interests, we note:

  • They have identical values at the MM/FC level of value (Lines 7 and 8 above).
  • Company A’s annual dividend for the 10% interest is $100,000, which provides a 10% expected dividend yield based on the MM/FC value of the interest.  The dividend will be paid quarterly, so the mid-year discounting convention is assumed.
  • Company B’s annual dividend for the 10% interest is $30,000, which provides a 3% expected dividend yield.  This dividend is paid at the end of each year, so the end-of-year discounting convention is assumed (see these assumptions on Line 11).
  • The expected growth in value of Company A over the expected holding periods is 3% (Line 12), which is identical to the long-term expected growth in value for Company A (Line 2) [Line 1 (13%) minus Line 10 (10%), or (3%)], The expected growth in the dividend is 3%, or the same as the expected growth in value of Company A (Lines 12 and 13).
  • The expected growth in value for Company B over the expected holding periods is 9% (Line 13).  Given that the discount rate for Company B is 13% (Line 1) and that the expected dividend growth and growth in value for Company B is 9% (Lines 12 and 13),  we can assume that there are sufficient agency costs (e.g., excess owner compensation) to lower the overall base return for the interest from 13% (the discount rate for Company A is 13%) to 12% (for Company B).
  • Now assume that we desire to estimate marketability discounts for the two 10% interests assuming expected holding periods of five and ten years for each interest (Line 14).  Liquidity will occur at the end of each of the expected holding periods at the MM/FC level.
  • The hypothetical assumes that the appropriate required holding period return (i.e., the discount rate for the holding period) is 18% for the interest in Company A.  That represents a 5% premium to the discount rate for Company A itself.  This is because holding a 10% interest in business entails more risk than Company A itself.  Assume for purposes of the hypothetical that this 5% “holding period premium” is reasonable and supported by market evidence (including from the restricted stock studies above).
  • The assumed required holding period return for the interest in Company B is 19.5%, or 1.5% greater than the comparable interest in Company A. The investment in the 10% interest in Company B is a riskier investment than the comparable interest in Company A.  The annual dividend is much lower and, although expected growth is greater, the return on expected growth in value is deferred, leaving the greatest portion of return to the end of the expected holding period.  Think time value of money.

While Companies A and B are identical as noted above, the 10% interests in them represent two distinctly different investments.  The interest in Company A is a high cash flow and slow growth investment.  The interest in Company B is a more rapidly growing investment with a much smaller dividend yield (and modest agency costs).

Recall the guidance from USPAP Standards Rule  9-4(d) noted in Mercer Musing #1.

(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…

If any reader is able to articulate cogent reasons for the marketability discounts applicable to the 10% interests in Companies A and B for five and ten-year expected holding periods using only the information in the studies above, I will personally donate $1,000 to St. Jude Children’s Research Hospital in his or her honor.  Given the facts assumed in the hypothetical, appraisers cannot “analyze the effect on value, if any,” of the differing valuation characteristics of the two 10% interests using a qualitative analysis.  The hypothetical provides two different sets of cash flows, two different risk profiles, and two separate expected holding periods.  Think about the discounted cash flow method for companies.

What Does SSVS (VS 100) Say?

It has been said that holders of the ABV and CVA designations are not required to follow USPAP.  What are they required to do?  We examine SSVS issued by the AICPA:

Statement on Standards for Valuation Services (VS Section 100) issued by the AICPA states the following about the application of discounts (Paragraphs per Standards, emphasis added):


During the course of a valuation engagement, the valuation analyst should consider whether valuation adjustments (discounts or premiums) should be made to a pre-adjustment value. Examples of valuation adjustments for valuation of a business, business ownership interest, or security include a discount for lack of marketability or liquidity and a discount for lack of control. An example of a valuation adjustment for valuation of an intangible asset is obsolescence.


This section should [formatting changed]

(a) identify each valuation adjustment considered and determined to be applicable, for example, discount for lack of marketability,

(b) describe the rationale for using the adjustment and the factors considered in selecting the amount or percentage used, and

(c) describe the pre-adjustment value to which the adjustment was applied (see paragraph .40).

Looking at the figure summarizing the restricted stock studies above, it would appear to be difficult or impossible to make a reasonable determination of the appropriate marketability discounts.  Following this guidance from SSVS, an appraiser could:

a. Identify the need for a marketability discount.

b. Describe a rationale for using a marketability discount.  For example, referencing a levels of value chart, the appraiser could say that the rationale for using the discount for lack of marketability is to recognize the difference in valuation characteristics between the pre-adjustment value ($10,000,000 for both companies at the marketable minority/financial control level of value) and the nonmarketable minority level of value, which is appropriate for an illiquid, minority interest of a business.  The appraiser would run into a problem, however, when trying to describe the “factors considered in selecting the amount or percentage used.”  There is no ability to do this from the data provided.

c.  As noted in b., describe the pre-adjustment value.

There is simply no information in the restricted stock studies (summary statistics or information on companies paying dividends) to enable an appraiser to satisfy the basic requirements of SSVS as quoted above.  Let me provide the following caveat.  I am not a CPA and do not hold the ABV designation.  Neither do I hold the CVA designation (I do hold the ABAR designation of the NACVA).  I have, however, studied and worked to develop the ASA Business Valuation Committee (as a member of the Valuation Standards Committee for nearly thirty years and as its Chair for several years) and the International Valuation Standards of the IVSC as a member of its Professional Board for a number of years.

The fact that appraisers have “guessed” at marketability discounts for decades using the filters above does not make such guessing correct or standards-compliant for the Internal Revenue Service or for any other purpose.

Determining the appropriate marketability discounts for 10% interests in Companies A and B must be, at least substantively, a quantitative exercise.  While the marketable minority/financial control values are equal and the companies have almost identical earnings and risk profiles, the subject interests have significantly different valuation characteristics and expected cash flows over the (assumed) five and ten year expected holding periods.  To the best of my knowledge and understanding, these differences cannot be realistically examined qualitatively.  Appropriate quantitative assumptions must, of course, be made; however, those assumptions must be made considering common sense, informed judgment, and reasonableness, the trilogy of considerations from RR 59-60.

ASA Business Valuation Standards

The ASA Business Valuation Standards provide fairly specific guidance on the application of premiums and discounts in “BVS-VII Valuation Premiums and Discounts.”

II. The concepts of discounts and premiums

C. A discount or premium is warranted when characteristics affecting the value of the subject
interest differ sufficiently from those inherent in the base value to which the discount or premium
is applied.

D. A discount or premium quantifies an adjustment to account for differences in characteristics
affecting the value of the subject interest relative to the base value to which it is compared.  (bold in original, italics added)

These ASA standards make clear that the reason that valuation discounts and premiums exist is to recognize the impact on value of “characteristics affecting the value of the subject interest”, which may vary between an illiquid minority interest and the equity value of the business as a whole.

An appraiser limited only to the information summarized above about restricted stock studies would, like an appraiser attempting to follow SSVS, not be able to meet the requirements of these basic standards.  At least that is my interpretation based on the quoted standards and the data limitations using restricted stock studies to determine marketability discounts.

What’s an Appraiser to Do?

Determining the appropriate marketability discounts for 10% interests in Companies A and B must be, at least substantively, a quantitative exercise.  Granted, appropriate assumptions must be made, but they must be made while remembering the trilogy of common sense, informed judgment, and reasonableness from RR 59-60.  We will address this basic quantitative derivation of marketability discounts for Companies A and B in Mercer Musings #3.  Feel free to comment, either on the blog post directly or on LinkedIn when the post is published there.

In the meantime, I hope you are well.



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

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