Pre-IPO Studies, Restricted Stock Studies, LEAPS, Put Options Which Will You Rely On?

While the Courts have generally accepted discounts for lack of marketability (DLOM) for interests in privately held businesses, the challenge for the business appraiser in determining an accurate and defensible DLOM is selecting empirical evidence on which to base the amount of the discount. There are several forces at play regarding empirical evidence:

  1. If the appraiser's report is to be introduced in court, the evidence presented must include the facts or data on which the expert witness' reports and opinions are based.i
  2. What evidence is available from which relevant conclusions that can be drawn and used as the basis for the appraiser's opinion and, in part, for the valuation report?
  3. What conclusions can be drawn from the evidence chosen by the appraiser?
  4. What challenges can be offered to the evidence chosen and the conclusions drawn by the appraiser?

Pre-IPO Studies

Pre-IPO studies, as the Court summarized in McCordii" the private-market price of shares sold before a company goes public with the public-market price obtained in the initial public offering (IPO) of the shares or shortly thereafter."

Pre-IPO studies were first used in the Tax Court in 1985 in Galloiii, according to Shannon Prattiv, who had been retained by the petitioner. Such studies have been introduced, discussed, and followed or challenged in numerous cases, including McCordv, Greenvi, Mandelbaumvii, and Davisviii, to name a few. (For more on how the courts have responded to pre-IPO studies and other issues regarding the DLOM, see our Discussion on DLOM, "What Did the Courts Really Say?") Expert witnesses have developed their own pre-IPO studies or relied on one or more of the numerous published studies. We will not list the various published pre-IPO studies. Those interested can find listings in Valuing a Businessix and similar publications.

Support for Pre-IPO Studies

Most support for the use of pre-IPO studies will be found in academic articles and in testimony and reports by expert witnesses who developed or cited such studies. In a number of cases, authors have found validation of pre-IPO studies (and other empirical evidence) in statements by the courts. This can be misleading to the casual reader. For example, Pratt's Valuing a Businessx contains a sub-heading "Okerlund v. United States Approves Pre-IPO Studies." In Okerlund, both parties introduced both pre-IPO studies and restricted stock studies in support of their discounts for lack of marketability. Rather than placing a judicial imprimatur on pre-IPO studies, the court simply noted, "The Court finds Dr. Pratt's analysis of the appropriate discount for lack of marketability more persuasive than that of the government's expert."xi The careful reader will note that when the court indicates its preference for any empirical evidence, as it did in Okerlund and Davisxiii, it most often does so for its applicability to the facts of the case, rather than any over-all preference for one type of evidence over another.

Challenges to Pre-IPO Studies

One of the most quoted commentaries on pre-IPO studies was the article by Dr. Bajaj et al, "Firm Value and Marketability Discounts in 2001xiii. The authors challenged the pre-IPO studies approach as follows:

They concluded that "...the IPO approach likely generates inflated estimates of the marketability discount."

In McCordxiv , Dr. Bajaj again challenged the use of pre-IPO studies on the bases "...that buyers of shares prior to the IPO are likely to be insiders who provide services to the firm and who are compensated, at least in part, by a bargain price"; adding, "...that a pre-IPO purchaser demands compensation for bearing the risk that the IPO will not occur or will occur at a lower price than expected"; and concluding, " is of limited use in estimating the value of closely held firms."

Saliba and Chungxvi suggested that appraisers determine if the subject company could meet minimum listing requirements, and that if not, pre-IPO market discounts would not be accurate. They also believed that directly linking post-IPO return data to pre-IPO marketability data is erroneous, suggesting that, "Inserted between the mathematical steps should be a quantified Initial Public Offering (IPO) Discount" due to the IPO date "pricing phenomenon." Paglia and Harjotoxvii stated that, "Finally, it is unknown if the results of this study are applicable to typical private companies since most of these businesses never go public."

Published pre-IPO studies, especially, come under attack for their growing irrelevance to current valuations. The last of the Willamette Management Association studies covered a study period of 1991-1993, while the study period for the last of the Emory studies was 1997-2000xviii. How many will argue that today's security markets bear much resemblance to that of the 1990s? In addition, as Saliba and Chung notedxix in 1998, after the first drop in the Rule 144 holding period "...prior research regarding marketability discounts based on restricted stocks may be questioned as to its relevancy", and now that a subsequent reduction of the Rule 144 holding period has been made by the SEC, how relevant will any studies be that were made prior to 2008?

Restricted Stock Studies

One of the major early federal court cases that featured restricted stock studies is Jung in 1993, when Roger Grabowski reviewed six published restricted stock studies in his report and testimony for the taxpayer.

Support for Restricted Stock Studies

Again, a number of academic articles and expert witnesses have endorsed the use of restricted stock studies in determining a discount for lack of marketability.

Challenges to Restricted Stock Studies

Tom Decosimo restated the objections in a 2008 presentation:

  1. The companies are public and therefore are fundamentally different from small private companies.
  2. The owners of restricted stock know there will be a market for shares in the future (see also Feder on this pointxxi).
  3. There is a known value for the marketable sharesxxii.

Also commenting on published studies, Paglia and Harjoto remarked, "The restricted stock studies utilize relatively small sample sizes, with most studies using fewer than 100 observations. These limited sample sizes make specific industry analysis challenging. Restricted stock studies may also include compensation for future services, such as providing capital in the future or advisory services. Perhaps most importantly, it is unknown if these discounts, which are derived from publicly traded company securities, apply to privately held companies."xxiii

Put Options

In 1993, David Chaffe suggested that the same logic that found a basis for DLOM in restricted stock studies could be applied to options to sell (put options), stating, "When provided with an option to sell, otherwise non-marketable shares are given marketability. Following this logic, the cost or price of the option to see (a put option) represents all (or a major portion) of the discount to be taken from the marketable price to price the non-marketable shares."xxiv

Support for Put Options

The put option methodology was applied as one of the methods in Litmanxxv. However, the court criticized the put option methodology, and ultimately sided with the taxpayer's expert for applying an analytical framework from the restricted stock studies to determine the appropriate discounts.

Challenges to Put Options

The concept of a put option acting as a proxy for the discount for marketability was challenged by Espen Robak: "The problem with this method is that the standard option pricing methodologies available provide no insight into the value of liquidity. Indeed, one of the assumptions behind the Black-Scholes model, the most widely used valuation model for options, is that the security can be continuously traded. When valuing a put option on a security with limited marketability, the most appropriate method is either to discount the underlying security for lack of liquidity (and then apply the Black-Scholes model with the adjusted input data), or to apply a marketability discount directly to the option value indication from the Black-Scholes formula. In fact, institutions active in the 'market' for private warrants purchase them at significant discounts to their calculated Black-Scholes values because of their illiquidity."xxvi


In 1990, the Chicago Board Options Exchange (CBOE), introduced a long-term option contract that permitted investors to purchase options with terms extending to three years. These contracts were referred to as Long-term Equity. In 2003, Robert Trout published a study of nine LEAPS for large companies with actively traded securities.xxvii

Support for LEAPS

Other studies tying DLOM to LEAPS were made by various authors. A review of these studies can be found in Travis Lance's (2007) review of these and other models for estimating DLOMxxviii.

Challenges to LEAPS

While there has been a good deal of interest in LEAPS studies as a means of estimating a DLOM, no significant challenge has been raised. To date, no published judicial opinion mentions LEAPS being used as evidence, and therefore, no serious challenge has been made to the use of a LEAPS study in determining DLOM.


Which to choose? Whichever type of study is chosen, the appraiser should keep in mind Robak's finding that up-to-date, first-hand studies are preferred by the court, contending that, "This continues a trend since McCormick, with the Court showing a preference for studies performed by the testifying expert..."xxix This same concept was emphasized by Judge David Laro: "Judges prefer 'real world' solutions to valuation issues. Although the definition of fair market value inherently involves a hypothetical buyer and seller, it is likely that judges will require the hypothetical buyer and seller to use terms and conditions which most closely relate to actual business standards utilized contemporaneously on the valuation date. Valuation experts will need to strive to convince the courts that their methods of valuation most accurately reflect market activity. Valuation principles may change over time to accurately reflect contemporaneous business standards. Therefore, there is some danger in relying upon past precedents as a means to provide standards for future decisions. Valuation is a vital and constantly changing process, and the experts who perform valuations will be sufficiently challenged to make sure that their standards are accurate, up to date, and persuasive."xxx

Perhaps the most important point for the appraiser in selecting or creating a study for determining a discount for lack of marketability to remember is that not only is the appraiser's report and testimony evidence in a court proceeding, but the data on which the appraiser relied is evidence as well. The Tax Court has repeatedly found the analysis and conclusions of appraisers to be unpersuasive, and has drawn its own conclusion from the data used by those appraisers. As the court noted in Silverman, "Finally, because valuation necessarily involves an approximation, the figure at which we arrive need not be directly traceable to specific testimony if it is within the range of values that may be properly derived from consideration of all the evidence."xxxi Thus, the appraiser should be careful that the data selected points clearly to the conclusion reached and is not susceptible to widely varying interpretations.

Finally the appraiser will choose and study empirical data carefully with an eye towards its relevance to the interests being valued and take into consideration all of the factors the courts have found to bear on the determination of the DLOM. (See more on this topic in the DLOM Discussion, "Defending Your DLOM")

The topics discussed herein are only a few of the many issues facing the appraiser in determining an appropriate DLOM for a business interest. Please see the other discussions in our DLOM Discussion articles. Also, please feel free to offer comments, criticisms, and suggestions about these discussions by contacting us at For more information on the Pluris DLOM Database, visit the Pluris DLOM Database product page.

iRules of Practice and Procedure, United States Tax Court, Title XIV, Rule 143 "Unless otherwise permitted by the Court upon timely request, any party who calls an expert witness shall cause that witness to prepare a written report for submission to the Court and to the opposing party. The report shall set forth the qualifications of RULE 144 (1/1/10) 95 the expert witness and shall state the witness's opinion and the facts or data on which that opinion is based. The report shall set forth in detail the reasons for the conclusion, and it will be marked as an exhibit, identified by the witness, and received in evidence as the direct testimony of the expert witness, unless the Court determines that the witness is not qualified as an expert." (emphasis by the editor)
iiCharles T. McCord, Jr. and Mary S. McCord v. Commissioner, 120 T.C. No 13 (2003)
iiiEstate of Mark S. Gallo v. Commissioner, 50 T.C.M. 470, 476 (1985);
ivPratt, Shannon (2005) The Market Approach to Valuing Businesses, Hoboken, NJ: John Wiley & Sons
vMcCord, op. cit.
viEstate of Mildred Green, Deceased, Thomas R. Green, Executor, Petitioner v. Commissioner of Internal Revenue, T.C. Memo. 2003-348
viiBernard Mandelbaum, et al., Petitioners v. Commissioner of Internal Revenue, Respondent T. C. Memo 1995 - 255
viiiEstate of Artemus D. Davis, Deceased, Robert D. Davis, Personal Representative, Petitioner, v. Commissioner of Internal Revenue, Respondent 110. T.C. 530, Filed June 30, 1998
ixPratt, op cit.
xPratt, Shannon Valuing A Business 5th Ed. (2008) New York: McGraw-Hill p 450
xiiiBajaj, Mukesh, Denis, David J, Ferris, Stephen P., & Sarin. Atulya (2001) Firm Value and Marketability Discounts Journal of Corporation Law, 27 89-115. [ed: for those interested, this paper is available online at]
xivMcCord, p 48
xvMcCord, p 48
xviSaliba, R. Gary and Chung, Jason K (1998) "When Linking Post IPO Return Data with Pre-IPO Marketability Discount Data Should Initial Public Offering (IPO) Discounts be Considered When Estimating Value at the Shareholder Level", Business Valuation Review Vol. 17, No. 4
xviiPaglia, John K. and Harjoto, Maretno (2010) "The Discount for Lack of Marketability in Privately Owned Companies: A Multiples Approach" Journal of Business Valuation and Economic Loss Analysis, Volume 5, Issue 1
xviiiPratt, Shannon, ibid
xixSaliba and Chung, ibid, 4
xxEstate of Mildred Herschede Jung, Deceased, Ruth J. Conway, Executrix, Petitioner v. Commissioner of Internal Revenue, Respondent 101 T.C. 412; 1993 101 T.C. No. 28
xxiFeder, Robert D. (1997) Valuation Strategies in Divorce 4th Ed., Hoboken, NJ: Wiley Law Publications
xxiiDecosimo, J. Thomas (2008) MSNA Business Valuation SIG Meeting;
xxiiiPaglia and Harjoto, op. cit. 4
xxivChaffe, David B. H. III "Option Pricing as a Proxy for Discount of Lack of Marketability in Private Company Valuations: A Working Paper", available at
xxvRobak, Espen. "Litman Audacity" Trusts & Estates, December 2007
xxviRobak, Espen and Hall, Lance (2001 ) "Bringing Sanity to Marketability Discounts: A New Data Source" Valuation Strategies, July/August 2001
xxviiTrout, Robert (2003) "Minimum Marketability Discounts," Business Valuation Review, September 2003, cited in Lance, Travis (2007) "The Use of Theoretical Models to Estimate the Discount for Lack of Marketability" Gift and Estate Tax Valuation Insights Autumn 2007
xxviiiLance, ibid
xxixRobak, Espen (2004) "The Current State of Marketability Discounts" ACTEC Journal 138
xxxLaro, David (2003) " Valuation Issues: A Perspective from a U.S. Tax Court Judge", 22ND ANNUAL ADVANCED BUSINESS VALUATION CONFERENCE CHICAGO, ILLINOIS
xxxiESTATE OF H.A. TRUE, JR., DECEASED, H.A. TRUE, III, PERSONAL REPRESENTATIVE, AND JEAN D. TRUE, ET AL.1, Petitioners v. COMMISSIONER OF INTERNAL REVENUE, Respondent T.C. Memo 2001-167 Docket Nos. 10940-97, 3408-98, 3409-98, Filed July 6, 2001, 171 (citing Silverman v. Commissioner, 538 F.2d 927, 933 (2d Cir. 1976), and Alvary v. United States, 302 F.2d 790, 795 (2d Cir. 1962).