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JULY/AUGUST 2026IN THIS ISSUE... Practice Management NACVA Offers Guidance on Retainer Agreements In a recent Advisory Brief, NACVA provides practitioners with non- authoritative guidance on the proper use, structure, and ethical implications of retainer agreements. COLUMNS & DEPARTMENTS Academic Review Academic Research Briefs By Philipp Schaberl This column provides readers with summaries of contemporary research in valuation and forensic accounting. In this issue, our contributor reviews “Accounting Basis and Verification: Survey Evidence from U.S. Private Firms,” by Andrew C. Call, Bradley Hendricks, Eva Labro, and Andrew G. Sutherland. The authors’ study helps answer the question: How do U.S. private companies actually make their financial reporting choices, and why? The findings carry significant practical relevance for valuation professionals. ON THE COVER Feature Article Exchange Option Models for DLOM: An Empirical Test Using the Stout Restricted Stock Study Database By Ashok Abbott Some commentators have questioned the credibility of restricted stock studies for estimating discounts for lack of marketability (DLOM). The author agrees that a simple mean or median of historical discounts is an insufficient measure for future DLOMs. Nevertheless, these transactions are helpful in identifying the underlying drivers of observed discounts. Using 700 transactions from the Stout Restricted Stock Study, the author tested exchange option models against observed placement discounts. The results show a strong convergence between observed discounts and model estimates—a convergence that holds across all regulatory regimes—and validates that volatility and the total liquidation period are the primary drivers of DLOMs. The study establishes exchange option models as a credible framework for marketability discount analysis. Utilizing readily available volatility and liquidity inputs, these models allow practitioners to derive credible, market- based DLOMs—even when a perfectly matched sample is unavailable. ON THE COVER 16 21 4 Production and Design: Chris Peterson, Creative Director, Digital Paint Booth, DigitalPaintBooth.com Inquiries concerning advertising should be directed to NACVA1@NACVA.com The Value Examiner 2SUBMISSION DATES Issue Submission Date Publish Date Jan./Feb. Oct. 19 Feb. 1, 2027 Mar./Apr. Dec. 17 Apr. 1, 2027 SUBMISSION STANDARDS The Value Examiner is devoted to current, articulate, concise, and practical articles on business valuation, litigation consulting, fraud deterrence, matrimonial litigation support, mergers and acquisitions, practice management, exit planning, and building enterprise value. Articles submitted for publication should range from 1,500 to 6,000 words. Manuscripts should be submitted via the Scholastica professional journal management platform. For more information, or to submit an article, please visit: https:// www.nacva.com/tveauthors. By clicking on the “Submit via Scholastica” button, you can view detailed editorial and submission guidelines. If you have questions, please contact Dan Shiffrin, Editor, at DanS1@NACVA.com, or Lynne Johnson, Associate Editor, at LynneJ1@NACVA.com. PEER REVIEW Articles designated as “Feature Articles” in the table of contents have undergone double-blind peer review by at least two qualified reviewers, either members of the editorial board or, in some cases, invited guest reviewers with expertise in the subject matter. REPRINTS Material in The Value Examiner may not be reproduced without express written permission. Article reprints are available; call NACVA at (800) 677-2009 and/or visit the website: www.NACVA.com. © 2026 NACVA. All rights reserved. NACVA members (except Affiliate members) are automatically provided a subscription to The Value Examiner with membership. If you do not want to receive this publication, upon request, we will reduce your annual dues by $25. EDITORIAL STAFF CEO & Publisher: Parnell Black, MBA, CPA, CVA Editor: Daniel Shiffrin, JD Associate Editor: Lynne Johnson EDITORIAL BOARD Chair: Michael D. Pakter, CPA, CFF, CGMA, CFE, CVA, MAFF, CA, CIRA, CDBV Past Chair: Lari B. Masten, MSA, CPA, ABV, CFF, CVA, ABAR, MAFF Ashok Abbott, MBA, PhD John E. Barrett Jr., MBA, CPA, ABV, CVA, CBA Gary W. Baum, MBA, CPA, CVA Neil J. Beaton, CPA, ABV, CFF, CFA, ASA Janae Castell, CVA, MAFF Michael Goldman, MBA, CPA, CVA, CFE, CFF Richard Gray, CPA, CVA, ABV, ASA Dorothy Haraminac, MBA, CFE, MAFF, CCI, PI Hubert Klein, CPA, ABV, CVA, CFE, CFF Z. Christopher Mercer, FASA, CFA, ABAR Michael J. Molder, JD, CPA, CFE, CVA, MAFF Judith H. O’Dell, CPA, CVA Danny A. Pannese, MST, CPA, ABV, CVA, CSEP Kevin A. Papa, CPA, CVA, ABV, CVGA Pasquale Rafanelli, CPA, ABV, CVA, CBA, MAFF, ASA, CFE, CDFA, AEP Sridhar Ramamoorti, PhD, ACA, CPA, CITP, CFF, CGMA, CIA, CFE, CFSA, CGAP, CGFM, CRMA, CRP, CVA, FCPA, MAFF Philipp D. Schaberl, PhD Keith Sellers, DBA, CPA, ABV William W. Thomsen, MBA, CFA, ASA Todd Zigrang, MBA, MHA, FACHE, CVA, ASA, ABV The Value Examiner ® is a publication of: National Association of Certified Valuators and Analysts ® (NACVA ® ) 1218 East 7800 South, Suite 301 | Sandy, UT 84094 Tel: (801) 486-0600, Fax: (801) 486-7500 E-mail: NACVA1@NACVA.com Healthcare Insights Urgent Care Centers: Finding Value in the Continuum of Care (Part II of II) By Todd A. Zigrang and Jessica L. Bailey-Wheaton Urgent care centers (UCCs) occupy a distinct niche in the continuum of care, positioned between the primary care physician’s office and the hospital emergency department in terms of acuity and cost. Part II of this two-part series explores the regulatory and technical environments currently shaping the valuation of UCCs, as well as the relevant value drivers and risk factors that valuation analysts should weigh when analyzing an investment in a UCC or portfolio of UCCs. Legal Insights Courtside View: Valuation and Financial Forensics Perspectives from the Bench By Michael J. Molder Courtside View highlights recent decisions by federal and state courts addressing significant valuation, financial forensics, and expert witnessing issues. In this issue, the author reviews two recent federal court decisions that illustrate the evidentiary and procedural hurdles facing lost-profits experts: Arch & Eng, LLC v. Gator Flower Mound (E.D. Tex. February 5, 2026) and Lyu v. Freightstar Expedited, LLC (D. Kan. January 23, 2026). 28 36 July | August 2026 3By Ashok Abbott Exchange Option Models for DLOM: An Empirical Test Using the Stout Restricted Stock Study Database 4 The Value Examiner Feature ArticleThe Value Examiner recently published a five-part series titled “Déjà Vu: Revisiting the Restricted Stock and Pre- IPO Studies,” by Z. Christopher Mercer. 1 This series is well written. It provides a comprehensive review of the previously published restricted stock studies and raises pertinent issues regarding the use of those studies to develop estimates for an applicable discount for lack of marketability (DLOM). Parts IV and V present a detailed analysis of the Stout Restricted Stock Study, concluding in Part V with a rather bold assertion: “This Déjà Vu series has attempted to illustrate and prove that these often dated and noncomparable studies cannot be used to develop credible discounts for lack of marketability … .” The Déjà Vu series advances two sets of arguments in support of this assertion, which may be described as the “sample selection argument” and the “lack-of-analysis argument.” The sample selection argument is based on the premise that any comparison between a subject block and the data contained in the restricted stock studies is invalid for the following reasons: 1. The reported transactions come from different time periods, with different regulatory restrictions on transfers. 2. Market conditions—including required rates of return, liquidity, and volatility—change over time. 3. The issuers for the subject block and for the transactions contained in the databases may have very dissimilar operating characteristics. The lack-of-analysis argument is based on the failure to: 1. Perform an independent discounted cash flow analysis of the restricted stock’s expected future income stream; 2. Account for the dividends expected to be received on the restricted stock; and 3. Estimate the terminal value of the restricted stock cash flows. While I agree that a simple mean or median of historical discounts is an insufficient measure for future DLOMs, a summary rejection of restricted stock data is questionable. These transactions are helpful in identifying the underlying drivers of observed discounts. Furthermore, the lack-of- analysis argument is difficult to sustain: Restricted stock 1 The series appeared in the July/August 2024, September/October 2024, November/December 2024, January/February 2025, and March/April 2025 issues. 2 Securities and Exchange Commission (SEC) Rule 144 establishes holding periods and other conditions for the sale of restricted stock in the public market without SEC registration. 3 This very pertinent point was raised by one of the anonymous reviewers. The lapse of the restriction period allows the issuer/holder to initiate the legal process of removing the restrictive legend from the stock to make it transferable. The liquidation process for the block can start only after the restriction is removed. The estimation period for the delayed liquidation consists of the regulatory restraint period plus the time required to dribble out the block without exerting excess price pressure. cash flows are identical to those of unrestricted stock, and a terminal value analysis is untenable because the restricted status is transitory. The trading restrictions expire at the end of the Rule 144 period. 2 At this point, the stock does not morph into an unrestricted liquid asset automatically. 3 Restricted securities carry a restrictive legend and cannot be freely resold until the mandated conditions under Rule 144 are met upon completion of the restriction period and a legal opinion confirming compliance is obtained and filed with the transfer agent. Trading can commence only after completing the legal process for removal of the restrictive legend from the previously restricted stock. A terminal value can only be determined for the unrestricted stock, provided the company is expected to remain a going concern. I respectfully disagree with the summary conclusions presented in the Déjà Vu series. Restricted stock placements provide a unique opportunity to observe actual market prices for the restricted and unrestricted versions of a stock at the same point in time. The transactions involve publicly listed companies for which a substantial amount of financial disclosure is mandatory and publicly available, including the total number of shares outstanding, daily trading volumes, return volatilities, block sizes, and the period of trading restriction. A direct comparison of prices between the two variants provides strong empirical evidence for estimating the DLOM applicable to the restricted stock. This article argues that the limitations of sample selection can be addressed using exchange option models. By accounting for the “total delay” (the regulatory period plus the time required to liquidate a block), these models provide a robust, empirical framework for estimating DLOM. Methodology and Data Methodology This article analyzes the Stout Restricted Stock Study database (2023 version) and compares reported placement discounts with corresponding discounts estimated via exchange option models. The results, presented below, suggest that the estimated discounts and observed discounts converge within a very narrow band. 5 July | August 2026 A Professional Development Journal for the Consulting DisciplinesRestricted securities consist of shares acquired in unregistered, private offerings—often conducted pursuant to Regulation D—which are exempt from the SEC’s registration requirements. Resales of these shares are governed by the Securities Act’s safe harbor rule (Rule 144), which permits public resales if specified conditions are satisfied. The safe harbor rule seeks to balance the need for investor protection with the goal of reducing the cost of raising capital. Restricted securities, acquired under Rule 144, require a “seasoning period” before they can be resold. In step with increasing market participation and liquidity, Rule 144 resale holding periods for restricted securities—including those acquired in Regulation D placements—were shortened in two major regulatory shifts. April 1997 amendments reduced the Rule 144 holding period from two years to one year. February 2008 amendments further shortened the holding period for restricted securities of reporting issuers from one year to six months, and simplified resale conditions, particularly for nonaffiliates. The holding period for restricted securities of nonreporting issuers remains one year. Sales by affiliates remain subject to applicable Rule 144 conditions, including volume limits, manner-of-sale requirements, and Form 144 filing requirements. My analysis accounts for the three principal Rule 144 holding-period regimes: • Pre-April 29, 1997: Two-year holding period • April 29, 1997, through February 14, 2008: One-year holding period for nonaffiliates (no change for affiliates) • Post-February 14, 2008: Six-month holding period for reporting issuers (no change for nonreporting issuers) Exchange Option Models Following is a brief description of the three classes of exchange option models used in this analysis. These models are widely known and employed in business valuation practice. 1. Margrabe exchange option • Payout at maturity = one unrestricted share • This model is appropriate for arm’s-length transactions between a hypothetical buyer and a hypothetical seller where both have access to all public information. 2. Lookback exchange option (Longstaff model) • Payout at maturity = highest price achieved for one unrestricted share during the life of the option • This model is appropriate when the seller has access to public and private information, and the buyer has access only to public information (e.g., an owner/insider selling to an outsider). The buyer believes that the seller will sell at the most advantageous time and therefore demands a higher discount to compensate for potential adverse selection. 3. Average price exchange option • Geometric average price exchange option (Ghaidarov model) º Payout at maturity = geometric average price achieved for one unrestricted share during the life of the option • Arithmetic average exchange option (Finnerty model) º Payout at maturity = arithmetic average price achieved for one unrestricted share during the life of the option The average price model is appropriate when both the seller and the buyer have access to public and private information, and there is no information asymmetry. This price averaging reduces effective volatility because averaging smooths price fluctuations. The buyer faces the least uncertainty and demands the lowest discount (e.g., stock compensation/incentives to officers/ managers). The arithmetic average approaches the geometric average as the frequency of averaging increases. Each of these models estimates the exchange ratio for the number of restricted shares to be exchanged for the option payout at the expiration of the restriction period. In contrast to the Black-Scholes options framework, there is no risk-free asset The average price model is appropriate when both the seller and the buyer have access to public and private information and there is no information asymmetry. 6 The Value Examiner Feature Articlein this analysis, and the exchange ratio estimation is based on the volatility of the lognormal returns for the assets and the duration of the period until liquidation (exercise of the option). The basic exchange option model, providing a measure of the exchange ratio between two assets when their future values are unknown, was introduced by William Margrabe (1978). 4 This exchange option model estimates the exchange ratio between two assets with uncertain future values, assuming equal access to public information for both parties. Margrabe simplified the analysis by designating one asset as the numeraire, or unit of account. In this context, treating the restricted asset as the numeraire implies that the unrestricted share price is expressed as a multiple of the restricted share’s price. As the restriction period approaches zero, the exchange ratio converges to one. Since the unrestricted share’s current price is observable, this relationship allows inference of the restricted share’s current, unobserved price during the period of restriction. The Margrabe model was closely followed by the floating strike lookback option analysis developed by Goldman, Sosin, and Gatto (1979). 5 This model accounts for defensive bidding by a buyer with imperfect information while trading with a better-informed seller. In 1987, Standish and Spaughton, working with the Bankers Trust London, developed the first commercially used pricing formula for arithmetic average price options linked to the price of crude oil contracts. The options were first offered by Bankers Trust Tokyo and came to be known as the Asian Average options. In academic finance literature, Kemna and Vorst (1990) 6 provided the first closed-form equation for estimating the value of the exchange option with a payout linked to the geometric average of asset prices. This analysis was extended to an arithmetic average price approximation by Turnbull and Wakeman (1991). 7 4 William Margrabe, “The Value of an Option to Exchange One Asset for Another,” Journal of Finance 33, no. 1 (March 1978): 177–186. 5 M. Barry Goldman, Howard B. Sosin, and Mary Ann Gatto, “Path Dependent Options: ‘Buy at the Low, Sell at the High,’” Journal of Finance 34, no. 5 (December 1979): 1111–27, https:// onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1979.tb00059.x. 6 A.G.Z. Kemna and A.C.F. Vorst, “A Pricing Method for Options Based on Average Asset Values,” Journal of Banking and Finance 14, no. 1 (March 1990): 113–29. 7 Stuart M. Turnbull and Lee MacDonald Wakeman, “A Quick Algorithm for Pricing European Average Options,” Journal of Financial and Quantitative Analysis 26, no. 3 (September 1991): 377–89, https://doi.org/10.2307/2331213. 8 Francis A. Longstaff, “How Much Can Marketability Affect Security Values?,” Journal of Finance 50, no. 5 (December 1995): 1767–74, https://www.anderson.ucla.edu/documents/areas/fac/ finance/2-95.pdf. 9 Francis A. Longstaff, “Optimal Portfolio Choice and the Valuation of Illiquid Securities,” Review of Financial Studies 14, no. 2 (April 2001): 407–31, https://doi.org/10.1093/rfs/14.2.407. 10 Ashok Abbott, “Discount for Lack of Liquidity: Understanding and Interpreting Option Models,” Business Valuation Review 28, no. 3 (2009): 144–48, https://doi.org/10.5791/0882-2875-28.3.144. 11 Stillian Ghaidarov, “The Use of Protective Put Options in Quantifying Marketability Discounts Applicable to Common and Preferred Interests,” Business Valuation Review 28, no. 2 (2009): 88–99, https://doi.org/10.5791/0882-2875-28.2.88. 12 John D. Finnerty, “An Average-Strike Put Option Model of the Marketability Discount,” The Journal of Derivatives 19, no. 4 (Summer 2012): 53–69, https://doi.org/10.3905/jod.2012.19.4.053. 13 Ashok Bhardwaj Abbott, “Cost of Illiquidity: Marketability and Liquidity Discounts in a Margrabe Exchange Option Framework,” Journal of Forensic Accounting Research 8, no. 1 (2023): 357–86, https://doi.org/10.2308/JFAR-2023-006. Longstaff (1995) 8 explored the potential relationship between the discounts for lack of liquidity and marketability, and the value of the floating strike lookback option. Longstaff (2001) 9 proposed a fully developed method for estimating the discount for lack of liquidity/marketability. The exchange ratio estimated in a Margrabe exchange option framework values the unrestricted stock as a multiple of the price of restricted stock. A critical component of this methodology is the conversion formula: DLOM = 1 − 1 exchange ratio Abbott (2009) 10 used this rationale to develop blockage/ DLOM discount models yielding the appropriate discounts for lack of liquidity/marketability. Ghaidarov (2009) 11 suggested application of a geometric average exchange option model for estimating the applicable DLOM. Finnerty (2012) proposed using an Asian arithmetic average model for DLOM. 12 Abbott (2023) 13 illustrates this procedure and presents a comparison of the DLOM discounts developed under each of the three approaches. The necessary conversion from the estimated exchange ratio to an equivalent discount has often been neglected in business valuation practice. This omission leads to severely inflated estimates of the applicable DLOM as the holding period and volatility increase. Abbott (2023) presents a comparison of the reported incorrect DLOM discounts (using the exchange option premium) and the correct equivalent DLOM discount approaches. The analysis presented in this article follows the DLOM discounts approach proposed in Longstaff (2001) and illustrated in Abbott (2023). 8 The Value Examiner Feature Article 8 The Value ExaminerData Inputs The data inputs for the analysis presented here are based on published data from the Stout Restricted Stock Study, 2023 version, and have not been independently verified for purposes of this article. The applicable Rule 144 restriction periods are based on reported transaction dates. In cases where a stock registration was submitted on or following the placement date and became effective before expiration of the Rule 144 restriction, the actual restriction period is used. The liquidation period (blockage) effect following expiration of the trading restriction, and the DLOM discounts, are calculated using the Abbott (2023) protocol described above. The overall sample covers three distinct regulatory regimes, reflecting the progressive shortening of the Rule 144 trading restriction. The Stout Restricted Stock Study dataset consists of 772 transactions, with 718 transactions reporting discounts and all the required data inputs. This dataset also contains 18 outlier transactions with extremely high volatility or exceptionally long liquidation periods that are influential in driving the discount means. Eliminating these 18 transactions yields a dataset with 700 transactions that is used for subsequent analysis. Table 1 summarizes this dataset. (Note: CL = confidence interval) The data distribution statistics indicate that the mean block size placed was 13.75%, the mean annualized volatility was 81.24%, and the mean Rule 144 restriction period was 299 days. Combined with a mean market- based liquidation period of 86 days, the mean total delay was 385 days. These characteristics support a mean observed discount of 20.31%. The estimated option model discount mean of 22.10% yields a small mean difference of 1.79% between the observed and estimated discounts. The narrow 95% confidence interval (1.33%–2.25%) indicates that in 95% of cases, the mean difference between the observed and estimated discounts lies between 1.33% and 2.25%. This supports the observation that there is a strong convergence between observed and estimated discounts. The following discussion describes the evolution of the Rule 144 regime and its impact on applicable DLOM measures. Robustness tests for the convergence of estimated and observed discounts, and the impact of registration rights on the applicable DLOM, are provided for comparison. Impact of Regulatory Regime As discussed above, three distinct regulatory periods are covered in the Stout data. During the pre-April 29, 1997, period, the Rule 144 restriction period was two years. This is followed by the April 29, 1997, through February 14, 2008, period, when the nonaffiliate sale period was reduced to one year (affiliate trading limits were unchanged). Post-February 14, 2008, the restriction period for reporting issuers was reduced further to six months. Nonreporting issuers are still subject to a one- year holding period. Table 1: Stout Restricted Stock Study Data After Removing Extreme Outliers (Total Sample Size = 700) VariableMedianMeanStd DevMinimumMaximumLower 95%Upper 95% CL for MeanCL for Mean Observed discount15.83%20.31%15.17%0.38%77.78%19.18%21.44% Option model discount18.58%22.10%13.73%1.09%88.70%21.08%23.12% Estimation difference1.51%1.79%6.17%–18.29%21.75%1.33%2.25% Block size10.93%13.75%12.22%0.10%95.27%12.85%14.66% Market value ($000s)91,003252,775694,1303,1378,635,945201,265304,285 Volatility (annualized std dev) 74.45%81.24%39.38%2.80%260.10%78.31%84.16% Liquidation days25862390411368104 Rule 144 restriction days25229916015543287311 9 July | August 2026 A Professional Development Journal for the Consulting DisciplinesNext >