The value of a block of stock is influenced by many characteristics, including the level of control (or lack thereof) and the degree of marketability (ability to liquidate). The fair market value of shares in a firm can be expressed as: a control interest level; a minority, marketable interest level (for example, a freely traded stock market value); or a minority, non-marketable interest level (for example, the value of closely held shares). Many business appraisers apply, and business advisors are used to seeing (or hoping for), discounts for lack of marketability of 30 percent, 40 percent, or higher. In several recent Tax Court cases, valuation experts for the Internal Revenue Service, citing both old and new studies, have argued for lack of marketability discounts in the teens. What is happening?

Some professionals feel the discount for lack of marketability (DLOM) for minority interests in privately held companies is declining. I believe the IRS is splitting hairs and DLOMs in the 30 percent-plus range are still appropriate — if properly defended.


The goal of business valuations prepared for estate- and gift-tax purposes often is to determine the fair market value1 of a minority interest in a privately held company. Several valuation methods result in what business appraisers call “a minority, marketable value.” This is the cash value a minority shareholder would receive if he sold his interest into the liquidity of the public markets. Obviously, a privately held company does not enjoy the liquidity of a public market for its shares. Instead, appraisers drop down to what they call a “minority, non-marketable value,” by applying a DLOM. So in its truest sense, a DLOM is a means of equalizing a publicly traded minority interest with a privately held minority interest. This principle was explained in Central Trust Co. v. U.S.: “It seems clear…that an unlisted closely-held stock of a corporation in which trading is infrequent and which therefore lacks marketability, is less attractive than a similar stock which is listed on an exchange and has ready access to the investing public.”2

The challenge in developing the value of a non-marketable interest is determining the appropriate DLOM to subtract from the value of a similar marketable interest, given the particular facts and circumstances. Two sets of ad hoc studies, restricted stock studies and pre-initial public offering (IPO) studies, provide benchmarks for establishing DLOMs. By examining transactions in the shares of public companies, these studies offer direct market evidence to gauge the impact that the absence of marketability has on shares of privately held businesses.

To raise capital, public companies can issue new stock (registered and restricted shares) in the private placement market. One reason companies pursue a private placement is the relative ease of negotiating with a few sophisticated investors versus the hurdles created by a public offering. Restricted stock is the term used to describe shares of publicly traded companies that are not registered with the Securities and Exchange Commission and cannot be sold into the public market. Because of applicable disclosure requirements, buyers report to the SEC the (lower) price at which they purchased the restricted stock and the then-current market price of the unrestricted stock. The ability of researchers to compare these two prices forms the basis of the restricted stock studies and their collective premise: Price discounts received for restricted stock must be due solely to its impaired marketability because restricted stock participates in dividends, voting and all other rights enjoyed by the holders of unrestricted stock. Different researchers have conducted at least 12 restricted stock studies since 1966. Discounts crept up from approximately 26 percent in the mid-1960s to a high of 45 percent in the late 1970s and early 1980s; they then declined to less than 25 percent after 1990. (See “Restricted Stock Studies,” page 58.)

Notably, significant DLOMs are observed across all time periods, even considering the relative certainty that restricted stock will eventually trade on an open market once the restrictions expire. So, appraisers believe these observed discounts understate the DLOM for minority shares in privately held companies that, in all likelihood, will never enjoy such liquidity. Studies conducted after 1990 exhibit a trend of lower discounts. This pattern is a result of two factors that improved the liquidity of restricted stock. First, a Rule 144 amendment in 1990 allowed qualified institutional investors to trade unregistered securities among themselves without filing registration statements, creating a limited market for restricted stock. Second, effective April 29, 1997, the holding period for restricted stock was shortened from two years to one year. For these reasons, most appraisers rely on the pre-1990 studies, whose results reflect liquidity conditions more closely resembling (although still far from) the plight of privately held shares.

The pre-IPO studies observe transactions in privately held companies that eventually completed an IPO. When companies register for an IPO, they are required to disclose all transactions in their stock and options for three years prior to the offering. The pre-IPO studies compare the public offering price to prices of qualifying transactions in which stock or options were purchased by insiders for periods ranging from 90 days to three years before the IPO. The percentage discount from the offering price is considered a proxy for the DLOM.

Three firms have essentially conducted all the pre-IPO studies.3 In one form or another, these studies have occurred every year since 1975, and the range of the observed mean discounts is 27 percent to 73 percent. As one would expect, the observed discounts were higher the further the transaction occurred from the IPO date, as more time creates more uncertainty that an IPO will occur. Over time, a benchmark DLOM of 35 percent has emerged for the restricted stock studies and 45 percent for the pre-IPO studies. It is to be expected that the restricted stock discounts are lower than the pre-IPO discounts. There is a known, active market for restricted stock once the restrictions expire, whereas there is only the prospect of such a market at the time of the pre-IPO transactions. This begs the question: How much more should the DLOM be for minority interests of privately held stock, which have no expectation of ever trading on a public market?


Business valuation is an evolving discipline. The body of knowledge is expanding rapidly, and attacks on the DLOM have come from several sources.

Karen Wruck's 1989 paper4 was presented to show the effect on firm value when capital is raised via private placements or public offerings; it had nothing to do with DLOMs. Nonetheless, in the course of her analysis of 73 private placements made between July 1, 1979 and Dec. 31, 1985, Wruck noted that the median offering price for unregistered shares was 12.2 percent less than the freely traded stock market price one day before the announcement and 1.8 percent less for registered shares.5 (See “Wruck's Results,” p. 59).

Today, Wruck's study is cited as the pioneering evidence that privately placed stock not subject to resale restrictions is also discounted by the marketplace. This implies that not all of the DLOM can be due purely to illiquidity and suggests the difference in discounts may be a better gauge for the DLOM. This is obviously a far cry from the 35 percent to 45 percent conventional wisdom.

In 1993, Michael Hertzel and Richard Smith published a paper that built on Wruck's work.6 This paper has drawn attention among appraisers and the IRS for the authors' analyses and interpretations of DLOMs observed in private placements.

The Hertzel/Smith study relies on a sample of 106 private placement transactions from Jan. 1, 1980 through May 31, 1987, of which 88 were for registered shares and 18 were for unregistered shares. The mean and median discounts for all 106 transactions, calculated using stock prices ten trading days after the announcement date, were 20.14 percent and 13.25 percent, respectively.7 They also found an additional discount of 13.5 percent for the 18 placements of restricted shares.8 While the range in observed discounts was not stated in the study, it appears the discounts varied from less than 10 percent for large companies (market value greater than $75 million) to approximately 35 percent for small companies (market value less than $25 million).9

This range is consistent with the pre-1990 restricted stock studies. But rather than accept that their observed discounts were due solely to the illiquidity of the privately placed shares, Hertzel and Smith analyzed the discounts to determine what other factors may influence their size. Ultimately, Hertzel and Smith argue that what they call “information asymmetry” is crucial to understanding the magnitude of discounts. That is, in addition to illiquidity issues, private placement discounts stem from costs incurred by private investors to initially gather and evaluate information about the company as well as de facto compensation for expert advice and monitoring results after the placement. Also, because the prospects of smaller firms are more difficult to assess and monitor than larger firms, it is logical that larger discounts are associated with smaller firms.

Hertzel and Smith conclude that the additional 13.5 percent discount they observed for restricted shares may compensate an investor for the resale restrictions. However, they speculate that even this amount is too high, because an issuing firm facing such a large reduction in proceeds from the placement of restricted stock would surely have a strong financial incentive to register the shares prior to placement to lower the cost.

Josh Koeplin, Atulya Sarin and Alan C. Shapiro's 2000 paper re-labels the DLOM a “private company discount [that] is more comprehensive in that it captures the valuation consequences for firms that continue to remain private.”10 While this concept is never fully developed, the authors echo Hertzel and Smith's information asymmetry sentiments: “…the private placement discount might represent, at least in part, compensation for due diligence by an informed investor, leading to valuable equity financing for a firm with few other alternatives. Also, private placement investors usually commit to be active monitors and provide valuable advisory services.”11 Koeplin, Sarin, and Shapiro estimated DLOMs for private companies by using an acquisitions approach. Their data sample consisted of 192 U.S. and foreign acquisitions of private companies between 1984 and 1998, excluding financial institutions and regulated utilities. For each acquisition, they identified the acquisition of a proxy public company in the same country, in the same year and in the same industry. They then calculated each firm's enterprise value as a multiple of earnings before interest (EBIT), earnings before interest, taxes, depreciation and amortization (EBITDA), book value, and sales. The private company discount was measured as:

1 — (Private Company Multiple/ Public Company Multiple.12))

They consider the discounts based on EBIT and EBITDA multiples to be “statistically and economically significant.”13 (See “Koeplin Study,” p. 60.)

Koeplin, Sarin, and Shapiro hypothesize that their work evidences an upper bound on the private company discount, because selling company key managers may get value consideration in the form of employment contracts rather than higher shares prices: “To the extent that these employment contracts entail above-market compensation, the observed private company valuations will be less than the fair market valuations, which should include any excess value associated with these contracts.”14

John Kania, an IRS economist, generally champions Wruck, Hertzel and Smith.15 Kania argues for a multiple causal factor model to explain the marketability discount and specifically summarizes Hertzel and Smith's findings as:

Total Marketability Discount = a function of (lack of marketability discount + other information causal factors).16

Kania leaves no doubt about the importance of Hertzel and Smith's findings. He says: “The discovery that observed marketability discounts are not entirely due to illiquidity, [sic] clearly set the pace for all future research.”17 Although Kania says his opinions are his own and do not necessarily represent the positions of the IRS, we all should assume that they probably are, as the IRS has followed this logic in recent litigation.

Kania also agrees with Hertzel and Smith's conclusion that restrictions on resale (and the additional 13.5 percent discount found on restricted stock) would not be important to long-term institutional investors, for example insurance companies and pension funds: “Investors in stock with expected long holding periods typically have a high tolerance for illiquidity and are more interested in long-term gain,”18 Kania states. The insinuation is that such investors do not expect or require a large DLOM, but no evidence is offered for this supposition.

Mukesh Bajaj, David J. Denis, Stephen P. Ferris and Atulya Sarin critically review the old restricted stock and pre-IPO studies, but the bulk of their 2001 paper19 is devoted to a new restricted stock study that uses more recent private placements and advanced statistical analysis to examine the DLOM. They assert that the restricted stock approach and Koeplin's acquisition analysis yield the best estimates of the DLOM. However, these researchers believe both of these methods rely on old data and don't consider other determinants that may explain the magnitude of previously observed DLOMs (for instance, the size of the private placement issue, earnings volatility and degree of financial distress).

Bajaj's most strident argument is: “It is often the case that private equity investors commit to provide the issuing firm with advice and oversight following the private placement of equity. Moreover, these investors often commit to providing capital in the future, provided that the issuing firm meets a set of predetermined goals for financial performance. Consequently, at least a portion of the price discount observed in private equity placements might reflect compensation to these investors for future services rendered, rather than compensation for the lack of marketability.”20

Bajaj's restricted stock study includes a sample of 88 private placement transactions completed between Jan. 1, 1990 and Dec. 31, 1995. (See “Bajaj Study,” page 61, for a summary of Bajaj's observed discounts.) The transactions had the following attributes, and the Bajaj group believes the latter two imply high informational asymmetries about the companies that would increase DLOMs:

  • 46 of the placements (52 percent) occurred in two years, 1992 and 1993.

  • 49 of the placements (56 percent) are in five industry groups that tend to be technology-driven.

  • 72 of the placements (82 percent) were made by firms traded in the OTC market.21

The Bajaj group computed discounts using the stock price 10 days after the private placement announcement date.22

Of course, discounts are expected for the unregistered issues. But as in the Wruck and Hertzel and Smith studies, registered issues also were placed at discounts despite their marketability. Bajaj asserts: “Clearly, the discounts on private placement are being generated, at least in part, by factors that are distinct from the marketability of theses issues…. Since the most visible difference between the two types of issues is in their marketability, it is tempting to infer that at least this differential discount of 14.09 percent is a reflection of the marketability discount.”23 Bajaj, however, believes that even the 14.09 percent differential is too high a cost for just liquidity concerns. Falling back on Hertzel and Smith's information asymmetry hypothesis Bajaj isolated three explanatory factors for a private placement discount other than liquidity:

  • Fraction of total shares offered in placement (discount increases as shares placed increases).

  • Business risk (discount increases as volatility of firm's daily returns increases).

  • Financial distress (discount in-creases as Altman Z-Score decreases).24

After segregating the effect of these factors, Bajaj concludes that the portion of the private placement discount related solely to the illiquidity of unregistered shares is 7.23 percent.25


If the goal is to develop a DLOM for minority shares in a privately held company, there are both specific and general rebuttals to the propositions put forth by Wruck, Hertzel and Smith, and the Bajaj group. Specifically, they disregard these important considerations:

  • A firm's history of paying dividends and the amount of dividends. Is there a history of paying meaningful dividends so that shareholders receive a current return on investment? If not, a minority shareholder unable to unilaterally change corporate policy is stuck with the status quo, and this will seriously impair the marketability of a minority interest.

  • A shareholder's expected holding period for the stock. Absent the payment of dividends, the only way for a minority interest to receive a return is to wait until the control shareholders decide to sell or go public. This suggests a holding period of many years in excess of that embedded in any of the restricted stock and pre-IPO studies.

Another specific rebuttal applies to Koeplin's acquisitions approach. The unmentioned, underlying premise of his group's methodology is that someone had the ability to sell the privately held company in the first place. Clearly, a minority shareholder is not in this position. Thus, Koeplin's observed discounts may be appropriate for control interests, but they do not address DLOMs for minority interests.

Generally, the authors ignore that several of the restricted stock studies include sufficient detail to allow an appraiser to create nexus between their studies and specific variables of the company and interest being valued, including the following: trading market; revenues; earnings; earnings volatility; and interest size (dollar amount and percentage). By analyzing these selected attributes across several different studies, an appraiser would, in fact, account for factors that contribute to a DLOM that were separately identified by Hertzel, Smith and Bajaj.

Wruck also overlooked the use of qualitative analysis that the decision in Mandelbaum26 gave appraisers. Important elements in determining a DLOM also include an assessment of:

  • Costs associated with making a public offering: Are the public offering costs (both time and money) something the company can undertake and absorb?

  • Past or future stock redemptions: Does the company have a history of redeeming its shares and/or or does management have any plans to redeem shares in the near future?

  • Restrictions on transferability of stock: Is there an agreement restricting the transferability of the shares, and if so is there a mandatory redemption or simply a right of first refusal?

  • Put rights: Are there any rights to put the shares back to the company?

  • Existence of potential buyers: Is there any evidence of any potential buyers, or have any offers to buy ever been received?

  • Type of business: Does the firm have a business with specialized operations and/or regulatory compliance that would limit potential buyer interest and detract from its marketability?


I believe it comes down to semantics. All of the factors identified by the major studies' authors contribute to a DLOM for a minority interest. Whether some factors are identifiable as illiquidity, information asymmetry or compensation, it is the total discount that equalizes a minority interest in publicly traded stock with a minority interest in privately held stock. Perhaps the best summation comes from Bajaj himself: “When valuing a closely held operating company, a prospective buyer will take all elements of the marketability discount into account. Therefore, the fact that we can say that some of these discounts reflect information and monitoring cost is helpful in our understanding of economics of privately held companies, but it does not necessarily imply that only the narrowly construed notion of liquidity impairment is relevant. If a hypothetical buyer will incur information and monitoring-related costs, he will expect to be fairly compensated for such services in the form of a discount.”27

The fact that there is not a readily accessible market for privately held stock substantially increases the risks of ownership and reduces value, because it increases an investor's required rate of return. Thus, the required rate of return for a minority shareholder will generally be higher than the required rate of return for the entire business. So a sanity check for a DLOM for a minority interest is to recompute the implied required rate of return for that minority interest, and review it for reasonableness, given: (1)the background, prospects and financial condition of the business; (2)the general economic overview and specific industry outlook in which the business operates; and (3)other facts and circumstances that a knowledgeable buyer and seller would consider.

Determining a DLOM is a true blend of the art and science of business valuation. Academics should recognize that a DLOM may be an imprecise term if their intention is to only quantify liquidity. Practitioners must spend more time analyzing and defending the DLOM in their reports.

If ultimate vindication occurs in Tax Court, recognize that, in the past, the judges often were guilty of splitting the baby. Having now seen so many valuation issues, the courts are more educated, and their decisions today generally follow the better-reasoned expert analysis. As seen in Gross,28Heck,29McCord,30 and Lappo,31 all of which employed Bajaj's study, courts do not criticize the data, only how it is explained and applied. Unprepared appraisers, beware.


  1. As defined in Section 20.2031-1(b) of the Estate Tax Regulations and Section 25.2512-1 of the Gift Tax Regulations, fair market value is “the price at which property would change hands between a willing buyer and a willing seller when the former is not under any compulsion to buy and the latter is not under any compulsion to sell, both parties having reasonable knowledge of the relevant facts.”

  2. Central Trust Co. v. United States, 305 F.2d 292 (Ct. Cl. 1962).

  3. The individuals and/or firms are: John Emory, president of Emory Business Valuation, LLC and formerly first vice president of Appraisal Services at Robert W. Baird & Company; Willamette Management Associates; and Brian Pearson of Valuation Advisors, LLC.

  4. Karen H. Wruck, “Equity Ownership Concentration and Firm Value: Evidence from Private Equity Financings,” Journal of Financial Economics, January 1989, pp. 3-28.

  5. Wruck, p. 17.

  6. Michael Hertzel and Richard L. Smith, “Market Discounts and Shareholder Gains for Placing Private Equity,” The Journal of Finance, June 1993, pp. 459-485.

  7. Hertzel and Smith, p. 470.

  8. Hertzel and Smith, p. 480.

  9. Kenneth W. Patton, “The Marketability Discount: Academic Research in Perspective-The Hertzel Smith Study,” Mercer Capital E-Law, Volume 2003-02, June 5, 2003, p 2.

  10. Josh Koeplin, Atulya Sarin and Alan C. Shapiro, “The Private Company Discount,” Journal of Applied Corporate Finance, Winter 2000, p. 96.

  11. Koeplin et al, p. 95.

  12. Koeplin et al,, p. 99.

  13. Koeplin et al, p. 99.

  14. Koeplin et al, p. 101.

  15. See, for example, John J. Kania, “Evolution of the Discount for Lack of Marketability,” Business Valuation Review, March 2001, pp. 11-18 and “Has Restricted Stock Data Become Irrelevant for Determining Marketability Discounts,” Business Valuation Review, June 2001, pp. 10-15.

  16. Kania, March 2001, p. 12.

  17. Kania, March 2001, p. 13.

  18. Kania, March 2001, p. 14.

  19. Mukesh Bajaj, David J. Denis, Stephen P. Ferris and Atulya Sarin, “Firm Value and Marketability Discounts,” The Journal of Corporation Law, Fall 2001, pp. 89-115.

  20. Bajaj et al, p. 98.

  21. Bajaj et al, p. 105.

  22. Bajaj et al, p. 107.

  23. Bajaj et al, p. 107.

  24. Bajaj et al, pp. 108-109.

  25. Bajaj et al, p. 113.

  26. Mandelbaum, T.C. Memo 1995-255 (June 12, 1995).

  27. Mukesh Bajaj, “A Response to Dr. Shannon Pratt's Critique of My Work on Marketability Discounts,” the full response of “Dr. Bajaj Responds to Dr. Pratt's February 2002 Editorial,” Shannon Pratt's Business Valuation Update, March 2002, pp. 12-13, which is available at

  28. Gross, T.C. Memo 1999-254 (July 29, 1999).

  29. Heck, T.C. Memo 2002-34 (Feb. 5, 2002).

  30. McCord, 120 T.C. 13 (May 14, 2003).

  31. Lappo, T.C. Memo 2003-258 (Sept. 3, 2003).


The market discounts both unregistered and registered shares

Unregistered shares 37 12.2% 13.5% -48.2% 95.0%
Registered shares 36 1.8 -4.1 -105.1 52.0
Difference 10.4 17.6
Source: Karen Wruck, 1989


Private companies sell at discounts relative to their publicly traded counterparts

Enterprise Value/EBIT 11.76x 8.58x 16.39x 12.47x 28.26% 30.62%
Enterprise Value/EBITDA 8.08 6.98 10.15 8.53 20.39 18.14
Enterprise Value/Book Value 2.35 1.85 2.86 1.73 17.81 -7.00
Enterprise Value/Sales 1.35 1.13 1.32 1.14 -2.28 0.79
Source: Josh Koeplin, Atulya Sarin and Alan C. Shapiro, 2000


Bajaj believes the 14.09 percent difference between registered and unregistered issues stems from more than just liquidity concerns

All issues 88 22.21% 20.67% -14.28% 68.00%
Unregistered issues 51 28.13 26.47 -7.14 68.00
Registered issues 37 14.04 9.85 -14.28 62.13
Difference 14.09 16.62
Source: Mukesh Bajaj, David J. Denis, Stehen P. Ferris and Atulya Sarin, 2001