Bayesian Networks …make zero-probability point estimates obsolete…empower factfinders to estimate values based on available evidence SEPTEMBER/OCTOBER 2019 PRSRT STD U.S. POSTAGE PAID SAL T LAKE CITY , UT PERMIT NO. 6563Association News The Association News contains valuable information about the Association and its members. The Association News is free for members and non-members alike. The Value Examiner® The Value Examiner is an independent, professional development journal dedicated to the exploration of value and its ramifications for consultants. It is the singular source of timely, technical, in-depth articles written for consultants by practitioners and academics at the top of their respective fields. QuickRead® Readers of the weekly QuickRead will come to appreciate it as a primary source for current news and information highlights in areas of interest to the financial consultant, and for immediate use in their practice. 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Build Your Reputation Authoring Articles for the Industry's Publishing Juggernaut NACVA stands alone from other professional valuation organizations in its commitment to publishing. Write an Article, Earn CPE, and Gain Recognition Many of these publications give authors the opportunity to get published, earn valuable CPE credit, and share their expertise with their peers. To learn more on this opportunity, ValExPubAd S-O18.indd 110/11/18 1:44 PMA PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES on the cover in this issue … t h e v a l u e e x a m i n e r SEPTEMBER | OCTOBER 2019 3 20 22 Bayesian Networks …make zero-probability point estimates obsolete…empower factfinders to estimate values based on available evidence SEPTEMBER/OCTOBER 20196 A CANDID OBSERVATION OF THE CANNABIS INDUSTRY By William K. Fowler, CVA, ABAR, MAFF In the past few years, several states have legalized cannabis sales, and by doing so, created a huge new industry. The cannabis industry has created opportunities for business valuators to expand their expertise and services. This article shares some insights the author gained by observing some early valuation practices for this new industry. LETTERS TO THE EDITOR In the July/August Issue of The Value Examiner, two articles generated interest from readers. In this issue, Roger Grabowski, FASA, Managing Director, Duff & Phelps LLC CFE, CVA, AIAF The full rebuttal to "Vasicek and Blume Betas: Back to the Future," (Parts I II on the NACVA website. Association News The Association News contains valuable information about the Association and its members. The Association News is free for members and non-members alike. The Value Examiner® The Value Examiner is an independent, professional development journal dedicated to the exploration of value and its ramifications for consultants. It is the singular source of timely, technical, in-depth articles written for consultants by practitioners and academics at the top of their respective fields. QuickRead® Readers of the weekly QuickRead will come to appreciate it as a primary source for current news and information highlights in areas of interest to the financial consultant, and for immediate use in their practice. Journal of Forensic and Investigative Accounting (JFIA) The JFIA is an open access journal showcasing articles which focus on creative and innovative studies employing research methodologies; improve forensic accounting research skills, tools, and techniques; and stimulate discussion and experimentation in instructional means in the fields of forensic accounting and fraud. Around the Valuation World® The Around the Valuation World webcast is the next generation method of obtaining the latest updates, news, trends, and activity occurring in the rapidly evolving business valuation and financial forensics profession. Each month, a team of industry experts cover the profession’s leading publications and deliver an online summary of all you need to know. To learn more about these publications and how to subscribe, visit www.NACVA.com/ publications or call Member/Client Services at (800) 677-2009. Build Your Reputation Authoring Articles for the Industry's Publishing Juggernaut NACVA stands alone from other professional valuation organizations in its commitment to publishing. Write an Article, Earn CPE, and Gain Recognition Many of these publications give authors the opportunity to get published, earn valuable CPE credit, and share their expertise with their peers. To learn more on this opportunity, visit www.NACVA.com/article. ValExPubAd S-O18.indd 110/11/18 1:44 PM By Kurt S. Schulzke, JD, CPA, CFE Experts often use linear regression in dispute resolution settings. Part I of this two-part article illuminates linear regression principles and pitfalls in the context of an actual case and offers related practice pointers. Part II demonstrates the use of Bayesian networks for a more transparent and user-friendly estimation of damages and firm value. While Bayesian networks have so far seen scant action in court, their user-friendliness and technical and aesthetic superiority point to their usefulness as evidence in dispute resolution. ESTIMATING ECONOMIC DAMAGES WITH LINEAR REGRESSION AND BAYESIAN NETWORKS (PART I OF III) LEGAL INSIGHTS VALUING A PAINTING FOR ESTATE TAX PURPOSES: ESTATE OF KOLLSMAN V. COMMISSIONER By Kevin A. Diehl, JD, CPA These days, many estates’ holdings include valuable paintings. As each picture is unique, valuation questions become prominent. Estate of Kollsman v. Commissioner, T.C. Memo 2017-40 (2017), is an instructive case about how not to value a painting properly for estate tax purposes. As such, it indirectly informs of how properly to value a painting. 24 departmentsA PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES EDITORIAL STAFF CEO & Publisher: Parnell Black Senior Editor: Nancy J. McCarthy Editor: Daniel Shiffrin, JD Associate Editor: Lynne Johnson EDITORIAL BOARD Chairman: Lari B. Masten, MSA, CPA, ABV, CFF, CVA, ABAR, MAFF Past Chairman: Michael Goldman, MBA, CPA, CVA, CFE, CFF 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 Rod P. Burkert, CPA, CVA Lorenzo Carver, MS, MBA, CVA Wolfgang Essler, CVA (Germany) Richard W. Goeldner II, ASA, CBA, CVA Judith Heim O’Dell, CPA, CVA Andrew M. Malec, PhD Danny A. Pannese, MST, CPA, ABV, CVA, CSEP Kevin Papa, CPA, CVA, ABV Donald Price, CVA, ASA Angela Sadang, MBA, CFA, ASA Keith Sellers, CPA, ABV Richard Trafford, MSc, FAIA, FCT, CVA, CFE, MAFF, PGCLTHE, FHEA (U.K.) Sarah von Helfenstein, MBA, CVA Todd Zigrang, MBA, MHA, FACHE, ASA The Value Examiner® is a publication of: National Association of Certified Valuators and Analysts® (NACVA®) 5217 South State Street, Suite 400 Salt Lake City, UT 84107 Tel: (801) 486-0600, Fax: (801) 486-7500 E-mail: ANNUAL SUBSCRIPTION United States—$215 International—$255 U.S. Funds Free to accredited university libraries The Value Examiner® 4 SEPTEMBER | OCTOBER 2019 t h e v a l u e e x a m i n e r departments SUBMISSION DATES Issue Submission Dates Publish Dates Jan./Feb. Dec. 15 Mar. 1, 2020 Mar./Apr. Feb. 15 May 1, 2020 May/Jun. Apr. 15 Jul. 1, 2020 ALL SUBMISSIONS The Value Examiner is devoted to current, articulate, concise, and practical articles in business valuation, litigation consulting, fraud deterrence, matrimonial litigation support, mergers and acquisitions, exit planning, and building enterprise value. Articles submitted for publication should range from 500 to 3,000 words. Case studies and best practices are always welcome. SUBMISSION STANDARDS All articles should be thoroughly edited and proofread. Submit manuscript by e-mail (in standard word processing format) to Nancy Include a brief biography to place at the end of the article and a color photo of the author. See authors’ guidelines and benefits pdf. The Value Examiner accepts some reprinted articles, if accompanied by appropriate reprint permission. 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: Production: Mills Publishing, Inc.; President: Dan Miller; Art Director/Production Manager: Jackie Medina; Magazine Designer: Jackie Medina; Graphic Designers: Ken Magleby, Katie Steckler, Patrick Witmer; Advertising Representatives: Paula Bell, Dan Miller, Paul Nicholas, Chad Saunders Administrative Assistant: Caleb Deane. Mills Publishing, Inc., 772 East 3300 South, Suite 200, Salt Lake City, Utah 84106, (801) 467-9419. Inquiries concerning advertising should be directed to Mills Publishing, Inc. Copyright 2019. For more information please visit millspub.com. PRACTICE MANAGEMENT PRACTICING SOLO: TRISCH GARTHOEFFNER By Rod P. Burkert, CPA, CVA The author interviews sole practitioner, Trisch Garthoeffner, ABV, CVA, MAFF, EA, from Naples, Florida. 35 43 HEALTHCARE INSIGHTS ASCs AND OFFICE-BASED LABORATORIES: VALUATION DISTINCTIONS AND CONSIDERATIONS PART I: DISTINCTIONS Todd A. Zigrang, MBA, MHA, FACHE, CVA, ASA, and Jessica L. Bailey- Wheaton, Esq. Until approximately forty years ago, if a patient required surgery, he or she went to a hospital for the procedure. Since the 1970s, however, the outpatient servic- es industry has grown at a steady pace. This article discusses how the American Medical Association’s 1971 adoption of a resolution endorsing the concept of outpatient surgery changed that landscape. ACADEMIC REVIEW ACADEMIC RESEARCH BRIEFS: AN OVERVIEW OF THE LITERATURE ON THE CANNABIS INDUSTRY By Peter L. Lohrey, PhD, CVA, CDBV The purpose of this column is to provide the readers of The Value Examiner, summaries of contemporary research in valuation and forensic accounting. The manuscripts covered are selected from numerous academic research outlets that include relevant topical coverage of valuation and related forensic accounting issues. The objective is to illustrate the core of this novel research while increasing awareness among the community of the subject matter. 27 I Want to Sell My Business I Need Estate Planning I'm Getting a Divorce Certified Valuation Analyst I'm Missing Out My Partnership is Dissolving Co-Sponsored by the National Association of Certified Valuators and Analysts® (NACVA®) Visit www.theCTI.com/BVTC or Call (800) 677-2009 Early registration discounts available. Dates and locations subject to change. Consultants' Training Institute® Business Valuation Certification and Training October 21–26, 2019 . . . . . . . . . . . . . . . . . . . . . . . . Las Vegas, NV October 28–November 2, 2019 . . . . . . . . . . . . . . New Orleans, LA November 11–16, 2019 . . . . . . . . . . . . . . . . . . . . . . . . Houston, TX November 18–23, 2019 . . . . . . . . . . . . . . . . . . . . . . San Diego, CA December 9–14, 2019 . . . . . . . . . . . . . . . . . . . . Ft . Lauderdale, FL January 27–February 1, 2020 . . . . . . . . . . . . . . Salt Lake City, UT Live online broadcasts from select locations are also available, plus live online webcasts. BVTCad VE-SpetOct.indd 19/13/19 12:38 PMI Want to Sell My Business I Need Estate Planning I'm Getting a Divorce Certified Valuation Analyst I'm Missing Out My Partnership is Dissolving Co-Sponsored by the National Association of Certified Valuators and Analysts® (NACVA®) Visit Early registration discounts available. Dates and locations subject to change. Consultants' Training Institute® Business Valuation Certification and Training October 21–26, 2019 . . . . . . . . . . . . . . . . . . . . . . . . Las Vegas, NV October 28–November 2, 2019 . . . . . . . . . . . . . . New Orleans, LA November 11–16, 2019 . . . . . . . . . . . . . . . . . . . . . . . . Houston, TX November 18–23, 2019 . . . . . . . . . . . . . . . . . . . . . . San Diego, CA December 9–14, 2019 . . . . . . . . . . . . . . . . . . . . Ft . Lauderdale, FL January 27–February 1, 2020 . . . . . . . . . . . . . . Salt Lake City, UT Live online broadcasts from select locations are also available, plus live online webcasts. BVTCad VE-SpetOct.indd 19/13/19 12:38 PMA PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES 6 SEPTEMBER | OCTOBER 2019 t h e v a l u e e x a m i n e r VALUATION /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// Estimating Economic Damages with Linear Regression and Bayesian Networks (Part I of II) Kurt S. Schulzke, JD, CPA, CFE Experts often use linear regression in dispute resolution settings. Part I of this two-part article illuminates linear regression principles and pitfalls in the context of an actual case and offers related practice pointers. Part II demonstrates the use of Bayesian networks for a more transparent and user-friendly estimation of damages and firm value. While Bayesian networks have so far seen scant action in court, their user-friendliness and technical and aesthetic superiority point to their usefulness as evidence in dispute resolution.1 CASE BACKGROUND A transportation company (Plaintiff) alleged that a much larger transportation company (Defendant) breached their contract by dropping Plaintiff from Defendant’s government-contracted air transport team, thereby depriving Plaintiff of profits from April 2008 through September 2009. Central to the jury’s verdict was the Plaintiff’s estimate of avoided contract costs. Plaintiff’s damages expert (Damages Expert) used the data in Table 1 and Figure 1 to estimate costs with a “simple” linear regression in which contract cost was the “Y” and revenue was the (only) “X.” TABLE 1: PLAINTIFF’S ACTUAL MILITARY CONTRACT COSTS AND REVENUES (1998–2007) ($ MILLIONS) FIGURE 1: ACTUAL REVENUES VS. COSTS (1998–2007) 1. See, e.g., Safari Club Int’l v. Salazar, 709 F.3d 1, 13 (D.C. Cir. 2013) (rejecting a challenge to a Bayesian network model confirming other evidence of polar bear population trends); In re Testosterone Replacement Therapy Prods. Liab. Litig. Coordinated Pretrial Proceedings, 2017 U.S. Dist. LEXIS 69399, 1008-1010 (N.D. Ill., 2017) (rejecting a challenge to a Bayesian analysis because it omitted mention of a ninety-five percent confidence interval and debunking the notion that frequentist “confidence intervals can simply be interpreted in a Bayesian way”); People v. Belle, 16 N.Y.S.3d 793 (Supreme Court of New York, Bronx County, 2015), aff’d on appeal, People v. Belle, 2017 N.Y. App. Div. LEXIS 7089 (N.Y. App. Div. 1st Dep’t, Oct. 10, 2017) (citing eight New York criminal cases in which Bayesian-based DNA analysis was “validated and approved by experts in the field”); Reference Manual on Scientific Evidence at 172 (noting that “Bayes’ rule is routine in cases involving parentage testing,” and that most courts admit Bayesian “probability of paternity” evidence “when the prior odds...are disclosed to the jury”). ObsYearActual RevActual Cost 11998128.5234008113.94 21999113.9648208106.86 32000185.4108919174.99 42001159.4876406155.82 52002176.201147177.12 62003276.37698257.45 72004302.6619754268.43 82005406.0856147315.13 92006342.5537673306.74 102007276.9183014 0 50 100 150 200 250 300 350 400 450 1998199920002001200220032004200520062007 Co ntr ac t Co st & Re ve nu e Year Plaintiff's Contract Revenues & Costs ($ millions) Actual RevenueActual Cost 274.8A PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES t h e v a l u e e x a m i n e r SEPTEMBER | OCTOBER 2019 7 Damages Expert chose linear regression, with 2008 contract revenues as the predictor, because he judged the available 2008 revenue information more reliable than the related cost information. R output equivalent to that produced by Damages Expert output appears in Table 2. TABLE 2: PLAINTIFF EXPERT’S FULL LINEAR REGRESSION OUTPUT PERFORMED IN R PLAINTIFF’S COSTS MODELED ON REVENUES (1998–2007) Table 2 coefficient estimates inform the cost formula in Equation 1:2 Cost = 30,502,004 + 0.779608851 x Revenue Equation 1 Lacking a systematic way to quantify uncertainty, Damages Expert picked $286,478,392—the transport team’s actual 2008 international contract revenue, $609,528,494,3 times Plaintiff’s historical forty-seven percent share thereof 4—over three alternatives,5 and estimated lost EBITDA as shown in Table 3.6 2. Table 2 replicates Damages Expert’s regression in R (car package). Rounding accounts for differences between Table 2 and Equation 1 (which Damages Expert generated in Excel). 3. For discussion purposes, the $609,528,494 was derived by dividing $286,478,392 by forty- seven percent. 4. Trial Transcript, p. 970. 5. The three were $260 to $470 million (a 2006 consultant’s projection of 2008 revenue, Trial Transcript p. 971); $339,288,621 (January 2008 Plaintiff budget projection, Damages Expert Report p. 58); $313 million (Plaintiff’s actual revenues of $156.5 million October 2007 and April 2008, annualized, Trial Transcript, p. 968). 6. Damages Expert Report pp. 67–70. The Report’s bottom line (and jury verdict) was $65,998,141. This is $143,239 less than the $66,141,650 shown in Table 3. This difference is due to math errors and/or rounding in calculating interest and depreciation add backs.8 SEPTEMBER | OCTOBER 2019 t h e v a l u e e x a m i n e r A PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES TABLE 3: PLAINTIFF’S ESTIMATE OF EIGHTEEN-MONTHS LOST EBITDA PER DAMAGES EXPERT REPORT In his report and deposition, Defendant’s rebuttal expert (Rebuttal Expert) faulted Table 3 because the underlying avoided cost model (a) treated revenue as the cause of costs instead of cost as the cause of revenue, (b) omitted essential variables, and (c) implied a forecasted cost range (a.k.a. “confidence interval”) that “covered” or included the $286 million point estimate of revenue, meaning that Plaintiff’s lost EBITDA might equal zero.7 The trial court denied Defendant’s motion to exclude Damages Expert’s opinion, and the jury awarded the Plaintiff sixty-six million dollars, matching Table 3’s bottom line. In an opinion written by one of the nation’s most sophisticated judges, the appeals court reversed the jury’s verdict and chastised counsel on both sides for what the court saw as seriously deficient direct and cross-examinations of an unnecessary and flawed regression analysis. In the following sections, we first outline the principles of linear regression and then explore apparent inconsistencies between these principles and opinions expressed in this case by the experts and the appellate court. As we shall see, the appellate court’s diatribe on the Plaintiff’s linear regression 7 Rebuttal Expert’s Declaration at 14–15. model was considerably more defective than the model itself. Its principal contribution is revealing the misunderstanding of regression among the deepest thinkers on the federal bench. For experts considering a regression analysis for courtroom use, this is a very important data point. LINEAR REGRESSION OVERVIEW Linear regression is a statistical tool for discovering mathematical relationships between so-called “predictor” variables and one or more continuous “target” variables.8 It relies on objective data and subjective expert judgments regarding—among many other things—the choice of the target and predictors. The primary output of linear regression is a line formula like Equation 1. A linear regression project typically follows a path like that shown in Figure 2 using statistics-tailored software like R or SAS. Excel, which Damages Expert used,9 is less sophisticated. 8. Target variables are also known as “response,” “dependent,” or “Y” variables, while predictors are also “regressor,” “independent,” or “X” variables. 9. Plaintiff’s Response in Opposition to Defendant’s Motion in Limine (Plaintiff’s Response Memo), p. 21. Forecasted annual lost contract revenue $286,478,392 Forecasted avoided costs Intercept estimate $30,502,004 Rev coefficient 0.779608851 Multiplied by forecasted revenue $286,478,392 223,341,090 Total forecasted avoided costs (253,843,094) Forecasted net profit $32,635,298 Plus: Interest (1.3% x revenue) 3,724,219 Depreciation & Amortization (2.7% x revenue) 7,734,917 Lost EBITDA (12 months) $44,094,434 Multiplied by 18/12 1.5 Lost EBITDA (18 months) $66,141,650A PROFESSIONAL DEVELOPMENT JOURNAL for the CONSULTING DISCIPLINES t h e v a l u e e x a m i n e r SEPTEMBER | OCTOBER 2019 9 FIGURE 2: TYPICAL LINEAR REGRESSION PROCESS Each step requires expert judgment. For example, checking LINE assumptions, fit, and influence (Step 8) can all be performed in a variety of equally valid ways.10 As a result, regression-based testimony is likely to provoke vigorous cross-examination along the lines outlined below. FURTHER CONSIDERATION Causation and Correlation In rebutting Damages Expert’s Report, Rebuttal Expert wrote: [Damages Expert] posits a causal relationship, one in which costs are determined by revenues, that is backward. In standard mathematical and statistical methodology, the left-hand side (dependent) variable—[here Contract] Costs—is determined by, or caused by, the right-hand side (independent)... But economic theory tells us that, if anything, the reverse is the case, i.e., costs cause revenues…Costs are what we pay to employ inputs; revenues are what we receive from selling output. Since changing input levels cause changes in output, it follows that changes 10. See Robert Nau, Regression diagnostics: testing the assumptions of linear regression, evaluation and remediation); SLR Model psu.edu/stat501/node/275/ (last visited May 15, 2019). in costs cause changes in revenues, and not conversely.11 Here, Rebuttal Expert’s opinion is open to challenge in three directions. First, something causes businesses to change input levels: the expectation of future revenues. Even lemonade stands ramp up available inputs to meet expected demand. So even if causation mattered, Damages Expert could still be right. Second, causation does not matter. The Defendant’s team transport contract was a cost-plus deal with Revenue = Cost * 1.11, roughly speaking. Through simple algebraic rearrangement, this equates to Cost = Revenue/1.11. So, while Plaintiff could and sometimes did beat the team’s benchmark cost ratio, simple algebra was at the heart of the deal.12 The “=” symbol denotes association, not cause, a widely understood doctrine13 that has been acknowledged by damages experts and courts in other cases.14 Third, requiring that predictors cause targets is statistical heresy. While correlation that is discovered through regression may support a finding of causal relation after the regression is performed,15 no such finding is permissible before the regression analysis is complete16 except in statistical outposts like Bayesian networks or structural equation models. But finance and law are existentially dependent on 11. Rebuttal Expert Declaration p. 9. 12. Trial transcript at 943–944. 13. See generally Judea Pearl and Dana Mackenzie, The Book of Why (2018). 14. See AICPA, Forensic and Valuation Services Practice Aid, Attaining Reasonable Certainty in Economic Damages Calculations: Revenues, Costs, and Best Evidence at 48 (endorsing revenue or volume as a predictor of costs); Schneider (Europe) AG v. Scimed Life Sys., Inc., 852 F. Supp. 813, 847 (D. Minn. 1994), aff’d mem., 60 F.3d 839 (Fed. Cir. 1995) (adopting the plaintiff’s regression of costs on revenues in a patent infringement case). 15. Hume defined cause as an object that (a) precedes an effect, and (b) is so conjoined (i.e., correlated) with it, that (c) it “forms the impression” of the effect in the mind of the observer. C.M. Lorkowski, David Hume: Causation, Internet Encyclopedia of May 5, 2019). 16. See Pearl and Mackenzie at 68–69; RMSE at 323 (asserting that the “expert should be prepared to defend his or her [causal] assumption” based on case-specific behavior evidence because statistical tests for causality do not exist).Next >