Court Opinion

ID: 4601537
Source: CourtListenerOpinion
Date Created: 2020-11-20 19:27:48.98197+00
Date Added: 2024-06-11T07:52:30.642365
License: Public Domain

ESTATE OF BESSIE I. MUELLER, DECEASED, JOHN S. MUELLER, PERSONAL REPRESENTATIVE, Petitioner, v. COMMISSIONER OF INTERNAL REVENUE, RespondentEstate of Mueller v. CommissionerDocket No. 2733-90United States Tax CourtT.C. Memo 1992-284; 1992 Tax Ct. Memo LEXIS 310; 63 T.C.M. (CCH) 3027; May 18, 1992, Filed *310  An appropriate order will be issued.  Decedent's gross estate included 7.5 percent of the outstanding shares of M Co., a privately held corporation.  Three days prior to decedent's death, M's board of directors apparently approved M's acceptance of an offer of a cash merger of M with I Corp., but the directors' vote may not have conformed to M's bylaws. The defect in the directors' vote was cured by another vote 11 days after decedent's death, and the merger was consummated 67 days after decedent's death.  Respondent determined that the value of the shares included in the gross estate was the amount paid for the shares in the merger, $ 2,150 per share, the same as the offer price outstanding on the valuation date. Held, under the facts of this case, a modified arbitrage analysis, rather than traditional analysis of fundamentals, is the preferable method for valuing the shares, inasmuch as the corporation was the subject of a takeover bid on the valuation date. Factors considered included the possibilities as of the date of decedent's death that a shareholder lawsuit would cause I Corp. to withdraw from the merger or that M's shareholders would vote against the merger, as well*311  as the time value of money.  Value of the shares held to be $ 1,700 per share. Held further, respondent's expert's report and testimony were result-oriented and biased, substantially diminishing their weight.  However, respondent's expert's comments on petitioner's experts' reports and testimony were helpful to the trier of fact.  Respondent's expert's report and testimony were admissible over petitioner's objection that respondent's expert had an impermissible conflict of interest by reason of having agreed to provide litigation support services to respondent in this case.  Stevan Uzelac, Michael A. Indenbaum, and Paul L. Winter, for petitioner. Thomas M. Rath, for respondent.  BEGHEBEGHEMEMORANDUM FINDINGS OF FACT AND OPINION BEGHE, Judge.  Respondent determined a deficiency of $ 1,985,624 in petitioner's Federal estate tax.  The sole issue for decision is the date-of-death fair market value of the 8,924 shares of common stock of the Mueller Co. (the Company) included in the gross estate of Bessie I. Mueller (decedent). FINDINGS OF FACT Some of the facts have been stipulated and are so found.  We incorporate the stipulation of facts with attached exhibits.  Unless otherwise*312  noted, all section references are to the Internal Revenue Code in effect on decedent's date of death, and all Rule references are to the Tax Court Rules of Practice & Procedure. John S. Mueller, the personal representative of the estate of Bessie I. Mueller, resided in Naples, Florida, at the time the petition in this case was filed. Bessie I. Mueller, a resident of Port Huron, Michigan, died March 24, 1986, 3 days after the board of directors of the family-owned Mueller Co. apparently approved the cash merger of the Company with an acquisition vehicle to be organized by a Middle East-backed investment bank.  Her gross estate included 8,924 common shares of the Company, or 7.5 percent of those outstanding. 1 On May 30, 1986, 67 days after decedent's death, the merger was consummated, essentially on the terms presented at the March 21, 1986, directors' meeting, and all shareholders of the Company received $ 2,150 per share for their stock. *313  The estate valued the shares at $ 1,505 per share on the Federal estate tax return, but did not provide any appraisal documentation with the return.  Respondent determined that the fair market value of the shares was $ 2,150 per share, the price received by all shareholders of the Company in the merger. At trial, respondent's expert opined that the fair market value of the shares was $ 2,007 per share. One of petitioner's two experts opined that the shares had a value of $ 1,527 per share. The other opined that the value of the shares was between $ 1,400 and $ 1,700 per share, most likely the average of these two extremes, or $ 1,550. History of the CompanyIn 1857, Hieronymus Mueller founded the Mueller Co. as a sole proprietorship when he opened a gunsmith shop in Decatur, Illinois.  In 1871, Mueller was appointed the Decatur city plumber.  The following year he invented the Mueller tapping machine, which enabled gas and water pipes to be tapped while the pipes were under full pressure.  This invention is still used throughout the world.  The tapping machine was followed in 1882 by Mueller's water pressure regulator, which permitted the main water line pressure to be*314  increased to fight fires without damaging the soft lead pipes used in home plumbing at that time. In 1885, Mueller converted the business to a partnership with one of his sons and began large-scale manufacturing operations.  By 1896, the business had been converted to a corporation, with Hieronymus Mueller owning one-third of the stock, and each of his six sons owning one-ninth.  In 1900, Hieronymus Mueller died and his son Henry was named president.  Two years later, Henry's brother Adolph succeeded Henry. Adolph and his descendants tried to keep the Company's stock in the Mueller family.  In 1915, 5 years after Henry's death, Adolph bought all the shares of Henry's widow and sold them to his four remaining brothers and one sister, Leda Mueller Cruikshank, on the condition that they not sell or encumber them without family approval.  In 1929, however, the Cruikshank family disregarded this condition and offered their Mueller Co. shares to the public.  The Mueller family and the Company bought 84 percent of the shares offered, and the balance found its way into outside hands.  In response to the Cruikshank episode, in 1929 Adolph organized a family voting trust with a 10-year term, *315  which was renewed for additional 10-year terms in 1939 and 1949.  All shareholder branches of the family, except the Henry Mueller branch, joined the trust, comprising 52 percent of the outstanding shares. Adolph continued as president until 1939, when his son, William Everett Mueller, succeeded him.  William Everett Mueller died in 1947 as the last Mueller to be president of the Company.  The Company then sought outside managers and adopted a policy of not hiring family members as new managers, in the belief that family member managers would receive special treatment not necessarily in the interest of family member shareholders. Also, the four remaining shareholder branches of the family became adversarial.  The result was that during the period 1953-57, an executive committee of outside directors assumed total management control of the Company.  A change in Illinois law in 1957 forbidding such arrangements ended the executive committee's control.  The emphasis on outside management continued, however, and in 1968 the last Mueller retired as an officer of the Company. In 1977, Harlan White, an outsider who had served as president of the Company since 1972, unexpectedly announced*316  his resignation.  The board appointed an executive search committee, and after a year's search the committee recommended and the board accepted Edward D. Powers, a professional manager, to replace White as president and chief executive officer.  Until 1 year before Powers joined the Company, he had been head of one of the Company's major competitors, the valve division of International Telephone & Telegraph.  Powers is currently chairman and chief executive officer of Burnham Service Co., a transportation, warehousing, and distribution firm owned by Investcorp, the Middle East-backed firm that eventually acquired Mueller Co.  From approximately 1985 to 1991 he was a member of the board of the Federal Reserve Bank of Chicago, and he currently serves on the boards of directors of Schneider National, Little Rapids Paper Co., and Burnham Service Co. At about the time Powers became the Company's chief executive, the shareholders began to amend the bylaws of the Company, changing the size and structure of the board of directors. The board was reduced from 12 to 7 members, 4 of whom were "family-designated directors", each representing a surviving shareholder branch of the Mueller family. *317 Illinois law requires cumulative voting for directors, unless the articles of incorporation otherwise provide.  Ill. Ann. Stat. ch. 32, par. 7.40(a) (Smith-Hurd 1985).  The Company's bylaws also provided for cumulative voting.  Inasmuch as each branch of the family held approximately one quarter of the stock, each branch could cumulate its votes and perpetuate its representation on the board.  In 1979, the shareholders amended the bylaws to require that three family-designated directors be present to constitute a quorum (family quorum), and that three family-designated directors assent to any board action (family veto).  After these changes, the family-designated directors were decedent's son John S. Mueller, Adolph Mueller II, Philip M. Mueller, and A.E. Staley III.  Powers, chairman Robert V. Krikorian, and corporate counsel Dudley J. Godfrey were the nonfamily directors. In 1982, the board unanimously resolved to submit to the shareholders a recapitalization plan whose objective was to freeze the bulk of the then-current value of the Company's stock for estate tax purposes.  The plan was opposed by John A. Schluter, a member of the Adolph Mueller branch of the family.  Schluter*318  and other members of the Schluter/Adolph Mueller branch of the family believed their branch did not face estate valuation problems and did not see any other need for the proposed recapitalization.  Some directors believed the Schluter family planned to take over the Company by purchasing stock from estates that needed money to pay death taxes.  The recapitalization plan was defeated because less than the required two-thirds of the Company's outstanding shares were voted in favor of the plan.  Schluter was instrumental in blocking the recapitalization. Lines of BusinessIn its early years, the Company had a number of lines of business, from sporting goods to munitions.  The Company fabricated one of the earliest automobiles in the United States, and held patents on some of the earliest designs for automobile radiators, spark plugs, and variable speed transmissions.  Hieronymus Mueller was experimenting with high-test gasoline when a spark from his pipe ignited some fuel.  After he died from burns suffered in the fire, the Company got out of the automobile business and sold its automotive patents. The "flow control" products -- the tapping machine and the pressure regulator*319  -- became the core of the Company's business.  These products evolved into lines of valves and fire hydrants, manufactured in the United States and Canada.  The Company's products are used exclusively in large water supply systems.  A foray into porcelain bathroom fixtures was abandoned in 1933, and the Company stopped all manufacturing of household plumbing products with the advent of World War II. The Company is a longtime member of the American Water Works Association (AWWA), the standard-setting organization for municipal flow control products.  In 1986, Mueller Co. products satisfied AWWA's standards, and many municipalities required contractors to use Mueller Co. products. The core business was vulnerable to economic cycles.  Management knew it could expect about $ 100 in revenue and $ 40 in pretax profits per housing start, so the Company's revenues and profits were reduced when housing starts declined.  Powers convinced the board of directors to authorize a diversifying acquisition program.  In the period 1982-84, the Company acquired six firms in an effort to diversify its product lines.  The companies acquired were: YearFirm acquiredProduct1982Judd ValveHigh-pressure oil field valves1982Leopold Co.Municipal water filters1982Superior StainlessStainless steel valves and fittings forsanitary use1984Valley PumpSubmersible, jet, and turbine pumps forspecial applications.  Renamed MuellerPump1984Tri-Canada, Inc.Stainless steel valves and fittings forsanitary use.  Merged into SuperiorStainless to form TCI-Superior1984LFE B.V.Large vacuum-process castings.  Locatedin Northern Ireland.  Renamed MuellerFlow Products B.V.*320  In 1985, the Company also acquired Canada Valve, Inc., another water and gas valve maker.  In 1986, the Company had 9 wholly owned subsidiaries and 18 manufacturing facilities in the United States, Canada, and the United Kingdom. After the acquisition program, and on the valuation date, the Company was a world leader in production of flow control products, processing systems, and pumps for water and natural gas distribution, fire protection, oil and natural gas production, domestic water supply, farm irrigation, and food, beverage, and pharmaceutical processing.  The Company was also the largest manufacturer of fire hydrants in the world. Even after the diversification program, 90 percent of the Company's earnings still came from the core business.  The core business is capital intensive, requiring foundries costing tens of millions of dollars.  In addition, the foundries create environmentally dangerous wastes.  The Company's relative lack of diversification, capital intensiveness, and environmental risks tended to reduce its value. Despite these vulnerabilities, the Company was doing well financially by the mid-1980's.  Under an incentive program created in 1985, in which *321  the Company's return on equity was compared to 30 "peer group" public companies, the Company's return on equity would have ranked as follows: YearRankReturn on Equity198028th4.41 percent198118th9.27 percent198223d2.83 percent19832d18.28 percent19843d22.56 percent19852d22.61 percentIn addition, the Company posted record sales and earnings in 5 of the 7 years ending with 1985.  In 1981, the Company reported record sales and earnings, despite the lowest number of housing starts in 30 years.  Dividends steadily increased from a low of $ 13 a share in 1975 to $ 32.25 a share in 1985, when the Company earned $ 18.3 million on $ 277.2 million in sales: SalesEarningsDividendsYear($ mil)($ mil)($ /share)1974$  90.5$  4.8$ 17.75197572.83.313.00197679.51.416.75197797.63.116.501978117.53.518.001979127.15.619.501980121.42.719.751981142.25.721.201982130.61.822.201983176.811.527.901984212.216.030.001985277.218.332.25The Buyout TransactionIn October or November 1985, Powers told the Company's board of directors that Amsted Industries had expressed*322  some interest in acquiring the Company, but had later decided on a different course of action.  The board discussed the possibility of selling the Company.  In November, the board voted to form a search committee to interview investment bankers.  Philip M. Mueller appeared to oppose selling the Company and voted against the resolution.  While Adolph Mueller II was in favor of selling the Company, the rest of his branch of the family, including Schluter, appeared to be against selling.  John Mueller was not present at the meeting. Powers sent letters to several Wall Street investment banking firms, including Morgan Stanley & Co.The search committee interviewed four firms.  At a special meeting of the board in December 1985, the directors unanimously chose Morgan Stanley to find a buyer for the Company.  Morgan Stanley's representative, Frank Sica, told the board that the Company could bring more than $ 2,000 per share. Powers and John Mueller both thought that estimate was optimistic in light of the business' cyclical nature, capital intensiveness, and environmental risks. At the December 1985 meeting, Adolph Mueller II retired as a director of the Company.  At the board's January*323  1986 meeting, Schluter replaced Adolph Mueller II as the Adolph Mueller branch's family designated director. Also at the December 1985 meeting, the board approved a special stock appreciation rights plan (takeover rights plan) whose stated purpose was to: provide additional incentive to those employees of Mueller Co. and its subsidiaries whose decisions and services are considered to have a significant impact upon the profits of the Company and to encourage those employees to remain as employees throughout and to cooperate with any change in control of the Company.The takeover rights plan provided that on retirement each of the 11 participants would receive in cash the equivalent of the per share book value of the stock times the number of rights granted to him.  If, however, the Company underwent a change in control, then the plan would pay the equivalent of the sales price per share times the number of each participant's rights.  These rights were to expire on December 31, 1988.  Thus, management had substantial incentive to have the Company acquired at a premium over book value prior to the end of 1988, both under the takeover rights plan and under other stock appreciation*324  rights plans in which members of management had become vested.  For example, upon consummation of the merger, Powers received approximately $ 4.8 million with respect to his 2,250 rights, of which 1,200 were granted under the takeover rights plan.  But because management did not own any stock, it could not participate in the shareholder vote on a takeover proposal. On February 21, 1986, the board of directors approved an amendment to the fee agreement with Morgan Stanley.  The original agreement compensated Morgan Stanley at a rate of 0.75 percent of the first $ 240 million paid for the Company and 3 percent of any amount more than $ 240 million, plus expenses.  The amendment provided that Morgan Stanley would receive an amount equal to 0.75 percent of the purchase price up to $ 240 million, 3 percent of the purchase price between $ 240 million and $ 260 million, and 5 percent of the purchase price greater than $ 260 million, plus expenses.  The amendment also provided that if a deal was not consummated, Morgan Stanley would to be entitled to a $ 3 million "breakup fee". The Company had instructed Morgan Stanley not to make a public announcement of the Company's desire to be acquired. *325 Morgan Stanley instead used its extensive network of business contacts and approached 43 companies it thought would make suitable buyers. Nonetheless, the fact that the Company was seeking a buyer became known in the corporate community, and a number of unsolicited bidders contacted Morgan Stanley, although none of them made an acceptable bid. By February 21, 1986, 16 companies were examining the proposal and 5 had expressed interest.  Four interested firms -- British Tire & Rubber (BTR), Kohlberg, Kravis & Roberts (KKR), Georgetown Industries, Inc., and Investcorp -- visited Mueller Co. offices and facilities to conduct due diligence investigations.  Of these four firms, Investcorp devoted the most resources to its investigation of the Company.  Investcorp sent representatives two separate times; the second time 12-14 Investcorp representatives spent 3 days at the Company.  KKR bid $ 235 million to $ 240 million, and BTR bid between $ 220 million and $ 250 million, but the initial bids from Georgetown and Investcorp were the highest. Prior to March 20, 1986, the Company simultaneously negotiated with Investcorp and Georgetown at the offices of Morgan Stanley in New York.  Georgetown*326  ultimately bid $ 270 million.  Georgetown's negotiator, former Secretary of the Treasury William Miller, claimed that Georgetown represented the Kuwaiti Investment Authority, a fund operated by the Government of Kuwait.  Powers demanded proof of an agency relationship.  The negotiations adjourned for a day, but when Miller did not provide an authorization letter from the Kuwaitis, Powers broke off talks with Miller and instead negotiated directly with the president and chief executive officer of Investcorp, Nemir A. Kirdar. Investcorp refers to itself as a "publicly held investment bank" based in Bahrain, but from the evidence available to us, an important aspect of its operations is to take long-term, controlling positions in companies in which it acquires equity and debt interests.  Investcorp had acquired other American companies prior to 1986, such as Tiffany's, Bertram-Trojan Yachts, and A&W Brands, but the Company was Investcorp's biggest acquisition until that time and its first occasion to finance an acquisition with money raised in the U.S. public capital markets. Investcorp's highest bid had been $ 260 million, but because Sica and Powers expected problems with Schluter*327  if management recommended an offer less than the highest one, Powers pressed Kirdar to increase Investcorp's bid. Kirdar agreed to match Georgetown's $ 270 million offer.  After expenses and incentive payments to management, the offer promised to net shareholders $ 2,150 a share.  The Investcorp offer also provided for allowing Mueller Co. management to acquire 150,000 shares (of 1 million fully diluted shares) of the surviving corporation's stock on favorable financing terms.  In addition, management was to receive an option to purchase an additional 90,000 shares, and an employee stock ownership plan was to receive an option on 60,000 shares. Investcorp's offer was to be held open only until the Mueller Co. board's March 21, 1986, meeting.  Thus, the offer was to terminate by its own terms if not accepted by that date.  In addition, completion of the deal was to be conditioned on the following: . that the warranties each of the parties had made to each other were true, including warranties regarding the nature and ownership of patents and know-how, . that each party would perform its obligations under the acquisition agreement, . that the parties would each receive*328  opinion letters from counsel stating that the other party was legally empowered to complete the transaction, . that the transaction be approved, or the time for objection expire, under the Hart-Scott-Rodino Antitrust Improvements Act and the Canadian Foreign Investment Review Act, . that no lawsuit seeking to halt the transaction be filed, . that key employees (including Powers) sign 5-year employment contracts with the Company, and . that a registration statement or private placement memorandum for the financing of the transaction become effective.If any of these conditions was not satisfied or waived, the agreement could have been terminated.  The agreement also could have been terminated by mutual consent, by failure to win shareholder approval, or by either party without cause after July 31, 1986, if the transaction had not closed. Investcorp secured financing commitments on March 20, 1986.  On that date, Merrill, Lynch, Pierce, Fenner & Smith agreed to place or sell $ 125 million in senior subordinated debentures and issued its "highly confident" letter that it could place $ 60 million of 10-year senior secured notes.  Investcorp told Merrill Lynch it would*329  not ask Merrill Lynch to raise the money unless Investcorp had $ 66 million in other funds to invest in the deal. The Mueller Co. board of directors met on March 21, 1986.  All directors but John Mueller were present, constituting a quorum.  Although Schluter said he believed the price was fair, he was the only director present at the meeting who did not vote to recommend the Investcorp deal to shareholders. Dudley Godfrey, a board member and the Company's counsel, telephoned John Mueller during the board meeting to obtain his views.  Godfrey told the board that John Mueller said he did not wish to stand in the way of a deal, but was personally opposed to selling the Company.  However, John Mueller could not be heard by the entire board and did not believe that he was casting his vote by phone.  Thus, only two family-designated directors clearly recorded yes votes at the meeting. Three days later, on March 24, 1986, decedent died.  At the time of her death, the estate of her other son, Robert, was undergoing a Federal estate tax audit.  Robert Mueller's estate included Mueller Co. shares. At the time of decedent's death, Powers was pessimistic that the deal would go through.  *330  He believed that only the Staley branch of the family could be counted on to vote in favor of the deal.  He believed that the Adolph Mueller/Schluter branch and Philip M. Mueller opposed the deal.  Powers saw John Mueller, the representative of decedent's branch, as wavering. Powers also was concerned about a defect in the March 21 meeting.  John Mueller had not been "present" and could not have voted at that meeting under Illinois law because he could not hear and be heard by all directors simultaneously.  Ill. Ann. Stat. ch. 32, par. 8.15(d) (Smith-Hurd 1985).  The family veto provision of the Mueller Co. bylaws ostensibly required yes votes from three family-designated directors, and only two valid family yes votes were recorded at the meeting.  The Company's local attorney had advised Powers in October 1985 that the family veto provision violated Illinois law and would be struck down if challenged in court, but the family veto provision had been respected by the board, 2 and Powers believed litigation on the point was inevitable and would threaten the merger. The threat was real because Investcorp had a reputation for shying away from hostile deals. *331  The doubts about the March 21 vote were cleared up at an April 4, 1986, special meeting of the board.  By telephone conference call, the board ratified the vote of March 21.  John Mueller voted yes, and the other directors voted the same way they had voted at the prior meeting.  Schluter proposed that the board merely send the Investcorp deal to shareholders for their vote, but not recommend that shareholders vote in favor of the transaction.  Schluter's motion was not seconded.  Schluter also reminded the directors that they could be sued for breach of their fiduciary duty to shareholders and that the Company did not have directors and officers liability insurance.  The minutes of the April 4 meeting show that the debt offerings were then expected to close on June 18, with the merger closing to occur immediately thereafter. Schluter continued to threaten legal action to block the sale.  Schluter's attorneys assailed the proxy statement as failing to disclose all material facts and accused the board of failing to discharge its fiduciary duty to shareholders. Schluter's attorneys tried to convince the Company to delay mailing the proxy statement, but the Company mailed it anyway. *332  The proxy statement included a favorable fairness opinion from Morgan Stanley. The directors met informally, on April 15, 1986, to discuss Schluter's criticisms, but took no action.  The Company's attorney responded to Schluter's charges on April 16.  Schluter's attorney replied that Schluter did not seek to block the merger, but only obtain the best price.  However, it seemed to Powers that Schluter was willing to block the sale.  On April 16, the Company retained special litigation counsel to prepare for the possibility of a lawsuit by Schluter. During this period, Powers and other members of management tried to persuade shareholders to vote in favor of the merger. Powers and other members of management had attended decedent's funeral and had used the occasion to try to convince members of her branch of the family to vote for the merger. On March 30, 1986, Powers wrote a letter to Milton Bush, coadministrator of decedent's estate, emphasizing the cyclical nature of the Company's business.  In the letter, Powers relayed management's projection that housing starts would level off, with adverse effects on the Company's earnings. Powers also believed that the merger fever of the*333  mid-1980's was at its height.  Powers noted that AWWA, the nationwide standard-setting organization, might approve the design of low-cost European valves, resulting in greater competition for the Company in the municipal water distribution market, the Company's core business, and that the Company might be required to use lightweight ductile iron, used in European valves, rather than cast iron, the material of which Mueller Co. valves were made.  This change would have required $ 30-40 million in capital improvements.  Powers made similar arguments to the other branches of the Mueller family, but was certain only that the Staley branch would vote in favor of the transaction. Although John Mueller had voted at the April 4 meeting in favor of recommending the Investcorp deal to shareholders, he had not decided prior to the middle of that month how he would vote the 15,196.1 shares he controlled as trustee.  The decedent, who knew she would die soon, had told John Mueller during the first week of March that she opposed the sale.  About 2 weeks after his mother's death, John Mueller received a letter from a friend and investment adviser, Samuel R. MacArthur of MacArthur & Co., outlining*334  several alternative courses of action, including a public offering or recapitalization of the Company.  However, MacArthur concluded by advising John Mueller to vote for the sale. On April 10 management made an informal presentation to shareholders in an effort to convince them to vote for the merger. Schluter told shareholders that he and other Mueller Co. shareholders wished to take the Company private by matching or exceeding the Investcorp offer.  But Schluter had no financing commitment, and Powers and other members of management said they would not work for Schluter.  Powers also argued that the Company and the board of directors had a commitment to Investcorp under a "best efforts" clause in the merger agreement. Another issue raised at the April 10 meeting was the disposition of family memorabilia and land used by the family but owned by the Company.  John Mueller suggested that the Company donate the land, known as Mueller Heights, and some cash to a college in Decatur to establish a museum, and said he would feel better about selling the family company if the family heritage in Decatur were preserved.  Investcorp agreed to John Mueller's proposal. By April 14, John Mueller*335  had decided to vote for the sale.  On April 14, 28 shareholders, including John Mueller, entered into a voting agreement naming John Mueller, Philip M. Mueller, and Staley as voting shareholders. By the time of the shareholder meeting, the voting agreement covered more than 60,000 shares of the 119,468.83 shares outstanding. On May 1, 1986, the day before the annual shareholder meeting, the directors held a special meeting.  Schluter again asked that the shareholder vote be postponed to allow him time to put together a leveraged buyout at $ 2,250 a share.  All the directors but Schluter voted against the request.  The following day, the board held another special meeting to discuss the issues raised at the previous meeting.  Schluter's attorney told the board that the proxy statement was incomplete and defective, that the board had a fiduciary responsibility to consider better offers, and that the board could recommend that the shareholders delay voting without violating the agreement with Investcorp.  Schluter's motion to postpone the shareholder vote was not seconded. At all times relevant to this case, the only class of Mueller Co. stock outstanding was common stock. Each share*336  of common stock was entitled to one vote.  There was no public market for the shares.  On March 21, 1986, decedent's date of death, the various branches of the family held Mueller Co. stock as follows: Name of GroupShares(percent)Group MembersSchluter30,567.67(25.59 %)Adolph Mueller II,John SchluterStaley30,100.00(25.19 %)A.E. Staley IIIDecedent's29,766.66(24.92 %)Bessie I. Mueller,John S. MuellerPhilip Mueller26,612.50(22.28 %)Philip M. MuellerOutsiders2,422.00(2.03 %)Total119,468.83For the most part, the family shares were held in trust, with family members acting as trustees.  Although John Schluter directly owned only 2.5 shares, he beneficially owned 18,971.33 shares, as to 10,800 of which he shared voting power.  No Mueller Co. stock was sold or exchanged between March 21 and May 2, 1986. On May 2, 1986, the Company's 183 shareholders held their annual meeting.  Proxies for their shares were held as follows: A.E. Staley III61,623.89Company management25,786.96John A. Schluter22,526.26No proxy9,530.72Unrepresented1.00Total119,468.83Schluter moved to postpone the meeting until June 10. *337  Powers told the shareholders that Investcorp had waived the conditions that a valid Securities and Exchange Commission registration statement become effective for the debt financing and that the proposed merger obtain favorable review under the Hart-Scott-Rodino Act and the Investment Canada Act (formerly known as the Canadian Foreign Investment Review Act).  Power also told the shareholders that financing for the deal was in place and the deal would close by May 30 because Merrill Lynch had agreed to make a "bridge loan" to Investcorp.  This type of financing, which was not yet generally used, allowed Investcorp to complete the deal before the public offering of senior subordinated debentures and senior secured notes.  Schluter's motion was defeated, 87,410.85 shares to 22,526.26 shares.  Shareholders then approved the Investcorp transaction, with 92,761.57 shares voting in favor and 26,706.26 shares abstaining. On May 14, the Federal Trade Commission and the Department of Justice granted early termination of the premerger notification period required by section 7A of the Clayton Act and section 803.10(b) of the Department of Justice premerger notification rules. On May 30, the*338  Company merged with Mueller Merger Corp., a subsidiary of Mueller Holdings Corp., an affiliate of Investcorp.  Mueller Co. shareholders received $ 2,150 for each of their shares.  Merrill Lynch provided a $ 177.9 million bridge loan, giving Investcorp until November 30, 1986, to raise the money in the public market.  With loans from Investcorp and affiliates, the Company's management acquired 150,000 of the 1 million fully diluted shares of Mueller Holdings.  Morgan Stanley received $ 2,675,000, plus expenses, as its fee. On July 1, 1986, the registration statement for the debt offering became effective and the notes and debentures were offered to the public.  The notes and debentures were delivered on July 10, raising $ 177.9 million. On July 8, 1986, the merger of the Company and Mueller Holdings Corp. was declared unreviewable under the Investment Canada Act. ULTIMATE FINDING OF FACT The March 24, 1986, value of the 8,924 common shares of the Mueller Co. includable in decedent's gross estate was $ 15,170,800, or $ 1,700 a share. OPINION The value of decedent's gross estate is the fair market value of property includable in the gross estate. Sec. 2031.  Fair market value *339  is defined as "the price at which the property would change hands between a willing buyer and a willing seller, neither being under any compulsion to buy or to sell and both having reasonable knowledge of relevant facts." United States v. Cartwright, 411 U.S. 546">411 U.S. 546, 551 (1973); Estate of Newhouse v. Commissioner, 94 T.C. 193">94 T.C. 193, 217 (1990); sec. 20.2031-1(b), Estate Tax Regs.  When the facts indicate that a lawsuit could impair the value of the property, we need not decide the probable outcome of the suit.  The only relevant consideration is the effect of the possibility of a suit on the market price for the shares on the valuation date. Estate of Newhouse v. Commissioner, supra at 232-233. Our task is to determine what a willing buyer would have paid a willing seller on the date of decedent's death for a 7.5-percent equity interest in the Mueller Co.  The question of fair market value is a question of fact.  Estate of Newhouse v. Commissioner, supra at 217; Estate of Gilford v. Commissioner, 88 T.C. 38">88 T.C. 38 (1987). Valuation issues are "inherently imprecise and capable of resolution*340  only by a Solomon-like pronouncement." Estate of Gilford v. Commissioner, supra at 50. However, we once again intone our warning to parties before this Court that we need not reconcile or average the opinions of the experts.  We may choose one approach over another, resulting in a windfall for one party and a disaster for the other.  See Buffalo Tool & Die Manufacturing Co. v. Commissioner, 74 T.C. 441">74 T.C. 441, 452 (1980). We continue to believe that valuation disputes are better settled than litigated. Whatever the weaknesses of the litigation process in its application to valuation questions, we cannot simply "pick at random any number that happens to lie somewhere between the Commissioner's valuation and the taxpayer's." Akers v. Commissioner, 798 F.2d 894">798 F.2d 894, 897 (6th Cir. 1986), revg. T.C. Memo 1984-208">T.C. Memo. 1984-208. We therefore explain how we arrived at our valuation conclusion. Expert TestimonyWe heard expert testimony on the valuation issue, and we weigh that testimony in light of the experts' qualifications and other credible evidence. Estate of Newhouse v. Commissioner, supra at 217.*341  But we are not bound by the opinion of any expert, and we weigh expert testimony in the exercise of sound judgment. Helvering v. National Grocery Co., 304 U.S. 282">304 U.S. 282, 295 (1938); Estate of Newhouse v. Commissioner, supra at 217. All three experts and the parties agree that the relevant valuation standards are contained in sections 20.2031-1 (valuation of gross estate generally) and 20.2031-2 (valuation of stocks and bonds), Estate Tax Regs., and Rev. Rul. 59-60, 1 C.B. 237">1959-1 C.B. 237 (valuation of stock of closely held corporations).  Those standards emphasize that each case should be decided by reference to the facts and circumstances knowable on the valuation date: 3A sound valuation will be based upon all the relevant facts, but the elements of common sense, informed judgment and reasonableness must enter into the process of weighing those facts and determining their aggregate significance.  [ Rev. Rul. 59-60, 1 C.B. 237">1959-1 C.B. 237, sec. 3.01.]*342  Respondent's expert Respondent presented the expert's report of Willamette Management Associates, Inc., which was prepared under the "direct supervision" of Willamette's managing director, Dr. Shannon Pratt.  Kathryn Daly "managed" the report, with the assistance of Scott Beauchene.  Both Dr. Pratt and Ms. Daly signed the Willamette report. Dr. Pratt also testified on behalf of respondent.  Dr. Pratt has a doctorate degree in business administration and finance from Indiana University, and is a chartered financial analyst.  He is a member of the American Society of Appraisers and of several of the Society's committees, including the theory and techniques committee.  He is the author of the book Valuing a Business: Analysis and Appraisal of Closely Held Companies (2d ed. 1989).  His academic and professional accomplishments are disclosed by his curriculum vitae, attached to the Willamette report, and the record of his introductory testimony. Willamette appraised Mueller Co. stock using two methods.  First, Willamette figured the Company's "discounted effective merger price." Willamette surveyed various sources for public market takeovers between January 1985 and May 1986. *343 Willamette discarded transactions that were not friendly, leaving a universe of 80 transactions.  Willamette then noted that the Mueller Co.-Investcorp merger was consummated 67 days after the valuation date, so it examined the trading price of the stock of each of the target companies in its survey 67 days prior to the consummation of their respective mergers. The median discount was 3.4 percent.  Willamette discounted the Mueller Co. takeover price of $ 2,150 a share by 3.4 percent and determined that the discounted effective merger price of Mueller Co. shares on the valuation date was $ 2,077 a share. We are convinced Willamette made erroneous assumptions at nearly every step of this part of its analysis.  First, Willamette figured the discount by looking back 67 days, the exact time it took the transaction to close, even though the Mueller-Investcorp acquisition agreement contemplated an outside date almost 2 months later than what turned out to be the sale date, and there was no indication on the valuation date that the period would be shortened to 67 days.  On April 4, the deal was expected by management to close some time after June 18, at least 86 days after the March 24*344  valuation date. The announcement that the deal would close on May 30 was made at the shareholders meeting on May 2, after Investcorp secured the bridge loan commitment from Merrill Lynch.  At that time bridge loans were not widely used and the availability of such a loan could not have been foreseen on the valuation date. Respondent argues that 67 days was a reasonable period because it was the midpoint between the valuation date and the outside termination date.  In effect, respondent asks us to average two unreasonable assumptions and hope that we reach a reasonable result.  This we decline to do. The only legitimate use of hindsight is for the limited purpose of establishing what a reasonably well-informed investor might have believed on the valuation date. Estate of Gilford v. Commissioner, supra at 52. No reasonable investor would have believed that the Investcorp-Mueller Co. deal would close exactly 67 days after decedent's death.  As we stated in Estate of Newhouse v. Commissioner, 94 T.C at 231, "it would be error to postulate a certainty that did not exist." Common sense tells us that by shortening the "expected" time for the*345  merger to close, Willamette's hindsight approach reduced the amount of the discount from the Investcorp offer price necessary to reach the value on the valuation date, and consequently bolstered respondent's position. Another way Willamette reduced the discount was to limit its universe to "friendly" acquisitions in which the risk of deal failure was, in our view, lower than in the Company's case.  The apparent likelihood of shareholder objections required that acquisitions that were less than friendly be included in the sampling. Willamette also, of necessity, looked only at public market transactions.  We recognize that data on privately held companies is rarely available.  But we believe Willamette should have adjusted its discount to reflect the shares' lack of liquidity. Those who bought the stock of the target companies in Willamette's survey on speculation that the deals would go through could have liquidated their positions quickly if the deals cratered.  A potential purchaser of Mueller Co. shares would not have had that option, and would have demanded an additional discount for this risk.  Nonetheless, Willamette did not adjust for the Company's lack of liquidity in determining*346  an appropriate "discounted effective merger price." Willamette did adjust the second part of its analysis for lack of liquidity, but that discount applied only to the so-called buy-and-hold valuation. We also have concluded the amount of the discount was too small compared to the overall value reached by Willamette, amounting to just 5 percent (25 percent discount times 20 percent weighting) of the total value. Finally and most importantly, Willamette's hindsight method caused Willamette to use a skewed statistical sample.  The decedent died 3 days after the announcement of the proposed merger. Willamette, therefore, should have scoured its vast library 4 for similar tender offers for comparable companies, and looked at the price of target companies a few days after those announcements.  Instead, Willamette looked only at deals that actually closed (rather than all deals that were announced) and counted back 67 days. *347 Willamette's sample universe of mergers that actually closed is not representative of the universe of tender offers.  The sample was underinclusive because tender offers relating to deals that actually failed were not included.  Assume that investors make an educated guess about the likelihood that a deal that was announced 3 days ago will eventually go through.  If some potential investors are good predictors, they will be able to avoid investing in the stocks of targets that will not be acquired.  The price of those stocks would reflect this belief, resulting in a comparatively large discount from the offer price.  These large discounts (if they existed) were excluded from the Willamette analysis, inflating the supposed value of the Mueller Co. stock. If Willamette instead had looked at all comparable deals a few days after the deals were announced, as petitioner's expert Frederick J. Schroeder did, the potential for bias would have been eliminated.  We cannot be sure of the actual effect of Willamette's sampling mistake.  The correct sample and Willamette's sample might coincidentally point to the same result, but we cannot jump to that conclusion any more than we can decide *348  this case by rolling dice.  We conclude that Willamette's "discounted effective merger price" methodology is flawed not only because it relies on information (the exact day the deal would close) that could not have been known on the valuation date, but also because the methodology limited Willamette to an inappropriate sample. The second part of Willamette's analysis was an attempt to come up with the value of a minority long-term investment in the Company, on the assumption that some investor would have been willing to make such an investment on March 24, 1986.  Willamette chose three methods -- historical price-earnings multiple, historical price-cash flow multiple, and projected earnings and cash flow multiple.  In the case of the historical earnings calculations, Willamette multiplied the Company's 1985 earnings per share by the average price-earnings multiple of 11 "comparable" publicly traded firms.  Willamette then multiplied the Company's average earnings per share for 3 years, 1983-85, by the average multiple the comparable firms were trading at over their 1983-85 average earnings. Willamette weighted these values (70 percent 1985 earnings, 30 percent 1983-85 earnings) to*349  come up with a weighted average: MuellerPrice-PreliminaryEarningsEarningsIndicatedIndicated Per ShareMultipleValueWeightValue1985$ 135.67x15.7=$ 2,130x0.7 =$ 1,491Avg. 1983-85121.95x21.1=2,573x0.3 =772$ 2,263Willamette performed the same procedure for historical cash-flow multiples: MuellerPrice-PreliminaryCash FlowCash FlowIndicatedIndicated Per ShareMultipleValueWeightValue1985$ 212.90x9.4$ 2,001x0.7 =$ 1,401Avg. 1983-85187.6412.32,308x0.3 =692$ 2,093The same method was applied to 1986 projected earnings and cash-flow multiples, although the weighting was 50-50: MuellerPreliminaryFundamentalMarketIndicatedIndicatedPer ShareMultipleValueWeightValue'86 Earnings$ 193.80 x13.1 =$ 2,539 x0.5 =$ 1,270'86 Cash Flow363.76 x7.1 =2,583 x0.5 =1,291$ 2,561Willamette then took a weighted average of the weighted averages to reach an indicated fundamental value of $ 2,301 per share: ApproachValueWeightWeighted ValuePast Earnings$ 2,263 x0.4 =$ 905Past Cash Flow2,093 x0.3 =628Projected 19862,561 x0.3 =768$ 2,301*350  This number was discounted by 25 percent, to $ 1,726 per share, toreflect the lack of liquidity of Mueller Co. shares. We doubt any investor would have applied such an approach to value a minority interest in Mueller Co. on March 24, 1986.  There had been two very recent definitive offers for the company.  The offerors had developed well-informed opinions on the value of the Company, and the management of the Company had a substantial incentive to maximize the price offered, as did the Company's investment bankers. 5 We believe that those offers, not the mathematical manipulation of the Company's financial results, were the best evidence of the proper starting point for arriving at the Company's value. *351  Even if the Georgetown and Investcorp offers did not truly represent the Company's date-of-death value, Willamette's calculations are not a good alternative.  Willamette, in its analysis of the Company's fundamentals, used only the most recent 3 full years prior to the Investcorp deal, 1983-85, all banner years.  The year Willamette used twice, 1985, was the all-time record year for the Company.  Willamette excluded 1981 and 1982 on the ground that they were recession years and might result in a "misleading" valuation. Willamette failed to explain why Mueller Co., a firm that rises and falls on economic cycles, should be analyzed only by reference to good years and not bad years.  We think it would have been more appropriate to value a firm such as Mueller Co. by factoring in results from an entire business cycle, and not just a few good years. Rev. Rul. 59-60 recommends that appraisers refer to income statements covering a period of 5 years or more. Rev. Rul. 59-60, 1 C.B. 237">1959-1 C.B. 237, sec. 4.02(d).  Respondent's instructions to Form 706, the Federal estate tax return, have for many years required the estate to: Apply the*352  rules in the section 2031 regulations to determine the value of inactive stock and stock in close corporations.  Submit with [Schedule B] complete financial and other data used to determine value, including balance sheets (particularly the one nearest to the valuation date) and statements of the net earnings or operating results and dividends paid for each of the 5 years immediately before the valuation date.  [Form 706 Instructions 9 (Rev. July 1990); emphasis added.]In addition, the weights assigned to the various indicated values seem to have been picked out of the air.  We heard no legitimate basis for Willamette's weighting. As respondent said in Rev. Rule. 59-60: Because valuations cannot be made on the basis of a prescribed formula, there is no means whereby the various applicable factors in a particular case can be assigned mathematical weights in deriving the fair market value. For this reason, no useful purpose is served by taking an average of several factors (for example, book value, capitalized earnings and capitalized dividends) and basing the valuation on the result.  Such a process excludes active consideration of other pertinent*353  factors, and the end result cannot be supported by a realistic application of the significant facts in the case except by mere chance.  [ Rev. Rul. 59-60, 1 C.B. 237">1959-1 C.B. 237, sec. 7.]Willamette's near-exclusive reliance on earnings and cash flow is precisely the error the revenue ruling warns against, especially considering the capital intensive nature of the Company's business. To compound the problem, Willamette took a weighted average of its two methods, weighting the effective merger price at 80 percent to reflect the supposed certainty of the deal's going through, and weighting the long-term minority investment price at 20 percent.  This weighted average resulted in an indicated value of $ 2,007 per share: ApproachValueWeightWeighted ValueDiscounted Merger$ 2,077 x0.8 =$ 1,662Minority Interest1,726 x0.2 =345$ 2,007In addition to our problems with the constituent elements, we question the validity of this equation as a valuation tool.  We cannot imagine that any prospective buyer would use such an arbitrary, artificial, and subjective approach to formulate an initial offering price or to calculate a last*354  best offer. We also believe that the "average of averages" is too error-prone.  Assume that Mueller's financial results were reported with 100-percent accuracy.  Assume also that Willamette's approach was correct and that the following elements of Willamette's calculation were believed sufficiently accurate for valuation purposes 86.7 percent of the time: the market multiples for earnings and cash flow, the weighting of current versus 3-year average results, the weighting of the various fundamental approaches in reaching the "minority value", the lack of liquidity discount, and the weighting of the minority versus merger prices.  These five levels of multiplication also provide five independent opportunities for error.  Even though the parameters each are sufficiently accurate 86.7 percent of the time, the final result will be sufficiently accurate only in 86.7 5 percent of occurrences, or 49 percent of the time. *355  We heard no testimony on the error rate in Willamette's calculations.  In our own calculations, we have found that the amount of the "minority value" can be made as low as $ 1,450 (a 16-percent absolute difference) simply by reducing the market multiples by 10 percent, increasing the lack of liquidity discount by 10 percent (from 25 percent to 27.5 percent), and weighting the smaller of the elements of the weighted averages by 10 percent more (e.g., weighting the 1985 price-earnings calculation at 80 percent and the 1983-85 average price-earnings calculation at 20 percent, rather than 70-30). Having found Willamette's analysis to be materially flawed, we turn to petitioner's objection to the Willamette report and Dr. Pratt's testimony.  Petitioner assails the report and testimony as those of a "hired gun", arguing that the contractual arrangement between Willamette and respondent, and Willamette's resulting involvement in developing respondent's case, cast Willamette in the disturbing, perhaps unethical, role of advocate rather than the neutral expert required by the rules of the American Society of Appraisers and our decision in Estate of Halas v. Commissioner, 94 T.C. 570">94 T.C. 570 (1990),*356  reconsidering T.C. Memo 1989-536">T.C. Memo. 1989-536. Petitioner seeks to exclude from evidence entirely the Willamette report and Dr. Pratt's testimony. While Dr. Pratt testified, Ms. Daly, a senior associate of Willamette and a signatory with Dr. Pratt of the Willamette valuation report, sat at respondent's counsel table to provide "litigation support".  The contract between respondent and Willamette in its expert role also governed Willamette's litigation support role. 6 In the latter role, Ms. Daly was not only required to help respondent's counsel understand the vocabulary of corporate finance, but she and Dr. Pratt (who was also in the courtroom throughout the trial) were additionally responsible for analyzing the reports and testimony of petitioner's experts to aid respondent in preparing for cross-examination. We believe that Willamette's report*357  was result-oriented and that this was reflected Dr. Pratt's testimony.  As a result, Dr. Pratt's report and testimony lacked the objectivity we endorsed in Estate of Halas v. Commissioner, supra, where we held that the attorney's privilege of confidentiality does not apply to appraisers and decided that Willamette could qualify as respondent's expert over the taxpayers' objection.  In Estate of Halas we observed that appraisers, by their own Code of Conduct, have third-party responsibilities -- just as certified public accountants do -- to those who rely on their opinions, and that their determinations must be independent and objective.  We find here, as the Court of Appeals did in Midstate Fertilizer Co. v. Exchange Natl. Bank of Chicago, 877 F.2d 1333">877 F.2d 1333, 1340 (7th Cir. 1989), that Dr. Pratt offered the Court his CV rather than his economic skills.  * * * "The importance of safeguarding the integrity of the [judicial] process requires the trial * * * judge, when he believes an expert's testimony has fallen below professional standards, to say so, as many judges have done." [Citations omitted.]See also Estate of Hall v. Commissioner, 92 T.C. 312">92 T.C. 312, 338 (1989);*358 Estate of O'Keefe v. Commissioner, T.C. Memo. 1992-210; Estate of Hatchett v. Commissioner, T.C. Memo 1989-637">T.C. Memo. 1989-637; Hudspeth v. Commissioner, T.C. Memo 1985-628">T.C. Memo. 1985-628, revd. on another issue 914 F.2d 1207">914 F.2d 1207 (9th Cir. 1990). We overrule, however, petitioner's objection to the bifurcated role of Willamette in providing an opinion as to the value of the Mueller stock and providing, simultaneously, litigation support for respondent.  Like any expert, Willamette could review, question, and comment on the expert's report and testimony for the opposing party.  The conflict arose when Dr. Pratt strayed from the standard of objectivity and "cast aside his scholar's mantle and became a shill" for respondent. Midstate Fertilizer Co. v. Exchange Natl. Bank of Chicago, supra at 1340. A court may rely on one part of an expert's opinion while ignoring another.  See Parker v. Commissioner, 86 T.C. 547">86 T.C. 547, 562-563 (1986); Chiu v. Commissioner, 84 T.C. 722">84 T.C. 722, 734 (1985). A court may rely on an expert's criticism of other experts, while disregarding his testimony in support of*359  his report.  Pittsburgh Terminal Corp. v. Commissioner, 60 T.C. 80">60 T.C. 80, 89 (1973) ("Although his testimony was clearly biased in respondent's favor, respondent's expert witness demonstrated the folly of [petitioner's expert's theory]").  That is what we do here. As a result of the foregoing analysis of Willamette's methodology and credibility, we reject most of the contents of the Willamette report and Dr. Pratt's testimony, but take account of Dr. Pratt's criticisms in our analysis of petitioner's experts' reports and testimony. Petitioner's experts Frederick J. Schroeder, Jr.Frederick J. Schroeder, Jr., has been employed by First of Michigan Corp., a member of the New York Stock Exchange, since 1968.  He is an executive vice president, a member of the executive committee, and cochairman of the management committee.  His primary responsibility is the corporate finance department, helping corporations raise equity and debt financing in both public and private markets.  He also is the person who recommends which "risk arbitrage" transactions First of Michigan participates in.  He has a master's degree in business administration from Harvard University*360  and a bachelor of arts degree from Georgetown University. 7Schroeder's analysis begins with the observation that, inasmuch as an acquisition proposal was under consideration on the valuation date, traditional methods of appraising a closely held corporation are not appropriate.  Schroeder instead analyzed the transaction from the perspective of a risk arbitrageur. Schroeder testified that risk arbitrage is the practice of buying the shares of a company that is the target of a takeover proposal, subject to the risk that the takeover will not be completed.  To justify taking the risk, an arbitrageur typically will purchase shares only at a substantial discount*361  from the takeover price.  During 1985, many arbitrage firms earned annual returns in excess of 50 percent.  This implies that, at that time, an arbitrageur who thought a transaction would be consummated 90 days in the future would try to purchase the stock at a 10.67-percent or greater discount from the offering price.  With that percentage discount, the arbitrageur could redeploy his capital three times more that year, earning an aggregate return (including compounding) of 50 percent.  See generally Wyser-Pratte, Merger Arbitrage, in The Mergers and Acquisitions Handbook 235 (Rock ed. 1987). To determine the typical arbitrage discount on the valuation date, Schroeder chose four takeover transactions announced during the first quarter of 1986.  In contrast to Willamette's hindsight method, Schroeder looked at the price of the targets 1 week after the announcement of the takeover. Schroeder determined that the targets' shares were trading at an average 11.75-percent discount to the takeover price. Schroeder then examined the circumstances of the proposed takeover as of March 24, 1986.  There was a possibility that Investcorp would back out because of the failure to comply with the*362  family veto provision at the March 21 board meeting.  There also was a possibility that the board would reject the proposal definitively at the April 4 meeting, since John Mueller's vote was not certain and the family veto provision required three affirmative votes, only two of which were assured.  Another negative factor was that a higher offer was not probable, so all the risk appeared to be on the downside.  An arbitrageur also would have had a number of other deals to invest in at that time.  On the other hand, financing for the deal appeared more solid than is typical shortly after the announcement of a deal, antitrust did not seem a major concern, and Investcorp already had done a fair amount of due diligence.  Schroeder decided that a risk arbitrageur would have required a 9-percent "pure" arbitrage discount, expecting the deal to complete in 90 days or so. In addition, in Schroeder's opinion, an arbitrageur would have demanded an additional discount to account for the possibility of shareholder rejection.  On March 24, 1986, John Schluter was on record as opposing the deal, and he had been influential in scuttling the 1982 recapitalization plan.  Schluter might have tried*363  to acquire additional shares to block the deal, and also might have filed a lawsuit to block the sale.  In addition, the estates of decedent and her son, Robert, either were undergoing or were subject to estate tax audits, and the administrators of the estates might have voted the estates' shares against the deal in an attempt to reduce the tax liability of the estates. 8 Schroeder estimated that an arbitrageur would have required an additional 5-percent discount to account for the risk of shareholder rejection. Finally, an arbitrageur would have required a discount to reflect the lack of liquidity of Mueller Co.'s shares.  An essential element of the arbitrageur's strategy is the ability to minimize losses and redeploy capital quickly to take advantage of new deals as they are announced.  Anyone purchasing 7.5 percent of the Mueller Co.'s stock on the valuation date would not have had an assured exit route; the Company was privately *364  held and there was no public market for its shares.  If the Investcorp deal fell through, the investor would have had to wait for another buyout offer, place the shares privately, or hold the shares.  Even if the Investcorp deal did close eventually, the investor would have lost access to the funds invested until the merger was consummated.  Thus, the investor would not be able to bail out of the Mueller Co. investment to take advantage of more rewarding opportunities.  To compensate for lack of liquidity, Schroeder estimated that an arbitrageur would require an additional 15-percent discount from the announced merger price. In sum, Schroeder testified that an arbitrageur would be willing to pay $ 1,527 per share, a 29-percent discount from the merger price of $ 2,150 per share. We believe Schroeder's methodology more closely represents the steps a potential investor might reason through to reach an acceptable price.  However, as Dr. Pratt pointed out, there are several weaknesses in Schroeder's numerical assumptions.  Schroeder used only four transactions in figuring the base arbitrage discount of 11.75 percent.  We do not think one can draw valid statistical assumptions from such*365  a small sample.  Circumstantial evidence, such as the returns arbitrageurs were making at the time of the Investcorp-Mueller Co. deal, convinces us that Schroeder was in the ballpark, but we do not feel bound by his exact number.  Schroeder's other numbers were not as well substantiated by objective evidence, but we believe that they were not out of line with reality.  Schroeder also admitted that risk arbitrageurs in the markets for publicly held securities would not have been likely to purchase the shares, but that does not change our belief that any purchaser of the shares would have used an analysis similar to Schroeder's to arrive at an offering price that the seller of a minority interest in the company would have been willing to accept. Albert A. KochPetitioner also presented the testimony of Albert A. Koch, cofounder and managing director of Equity Partners of America, Ltd., since 1987.  Koch directs and assists in the valuation of businesses and negotiates mergers and acquisitions. Koch was managing partner of the Detroit office of the accounting firmErnst & Young from 1981 to 1987.  Koch is not involved in risk arbitrage in any way.  He graduated with honors from*366  Elizabethtown College. Koch's analysis was similar to Schroeder's.  Koch assessed the impact that several risks would have had on the price an investor would have been willing to pay for a 7.5-percent stake in the Company.  Koch opined that the transaction price was fair, that the financing seemed solid, and that the Company had an "acceptable" ability to find another merger partner if Investcorp bowed out.  Koch also believed that there was a low to moderate risk that business factors, such as general economic conditions or the loss of a Mueller Co. plant, would threaten the deal prior to closing. On the other hand, Koch characterized the following three risks as "extremely high": that shareholders would fail to approve the deal by a two-thirds majority, that a lawsuit would block the deal, and that a buyer would be stuck with an illiquid asset if the deal failed to close.  Koch stated that it was unlikely that a risk arbitrageur would be interested in such a transaction, but that a private fund operated by a large Wall Street entity might have been willing to assume the risks for a sufficiently large return. 9*367 Koch said that a buyer would have required a discount sufficient to result in a 75-percent to 150-percent annualized return.  Koch assumed the transaction would take 120 days to close.  Allowing for the effect of compounding three times a year (1 year/120 days), a 75-percent to 150-percent annualized return implies a discount of 21 percent to 35 percent.  These discounts in turn imply a price between $ 1,400 and $ 1,700. Turning to the "willing seller" portion of the willing buyer-willing seller formulation, Koch estimated that a seller would have demanded a price toward the higher end of his estimated spectrum, while the buyer would try to bargain for a lower price.  Koch concluded that the most likely result would have been a price that was the average of the two extremes, or $ 1,550 per share. Koch's analysis, rather than making the error of hindsight, makes the error of converting the deadline for the deal into the expected closing date.  Koch assumed the deal would close 120 days after its announcement.  Koch did not take into account the more probable outcome that the deal would close less than 120 days from its announcement.  If we instead use a 90-day period so that the*368  investment can be compounded four times a year, the range of discounts is 15.0 percent to 25.7 percent, or a per share price range of $ 1,597.45 to $ 1,827.50.  The midpoint of these numbers is $ 1,712.48, more than $ 150 per share greater than Koch's estimate. Koch did not adequately explain why an investor would require a 75-percent to 150-percent annualized return to buy Mueller Co. stock. Koch said that " the Mueller Co. opportunity might appeal to a limited number of investors whose threshold rate of return for ordinary investments is 40 percent to 60 percent." Koch argued that his estimate that certain significant risks were "extremely high" justified the jump in rate of return from 40-60 percent to 75-150 percent, but he did not make the connection sufficiently clear to us. We also were disturbed by the argumentative tone of the Koch report.  The report is replete with exclamation points and italicized emphasis of the major points of petitioner's argument.  Having reminded respondent of the importance of objectivity in expert testimony, we see no need to repeat the lesson here for petitioner's benefit.  We simply view the Koch report with some skepticism. Discussion*369  We find that none of the experts was entirely convincing.  However, we are persuaded that the Schroeder approach is the most representative of the likely thought processes of a hypothetical willing buyer or seller. We agree that a buyer and a seller, each presumed to be committed to maximum economic advantage, would use the $ 2,150 takeover price as a starting point and discount the price to reflect the risks of nonconsummation and lack of liquidity. Respondent argues that arbitrageurs are not the only category of potential purchasers of stock, and in fact are not the most likely market.  Among the alternatives respondent lists are: the public market, companies contacted by Morgan Stanley who might be interested in the Company, other potential buyers not located by Morgan Stanley because there was no public announcement of the deal, a leveraged buy-out, a professional outside investor, a recapitalization, or existing shareholders. A public offering of a minority interest in the Company does not seem to us to have been a reasonable alternative.  Such an offering would have required considerable time and expense.  Indeed, it seems likely that dividing a minority interest into even*370  smaller units of ownership might further depress the value of the shares.  A public offering of a larger block of stock would have had greater interest to investors in the public market, but a holder of 7.5 percent of the shares would not have had the power to launch such an undertaking.  A large public offering was not under consideration at the time of decedent's death, and no reasonable buyer or seller would act on speculation that it would occur. The also-rans in the bidding for the Company were not a likely market either, because those bidders made their offers for all the shares.  There is no evidence suggesting that they were looking for a passive minority investment, with the possible exception of KKR, which operated an arbitrage fund, but which had made a lower offer for the Company in its entirety. Respondent theorizes that companies not contacted by Morgan Stanley might have been interested in buying a 7.5-percent interest in the Company, but we heard no evidence to convince us either (1) that Morgan Stanley failed to identify any potential purchaser of the Company, or (2) that such a purchaser would have wished to acquire a 7.5-percent interest in the Company.  Although*371  there was no public announcement, Morgan Stanley had cast a wide net and the deal was not a secret.  Indeed, Morgan Stanley received several unsolicited offers, none of which made a difference in the final bidding. The alternative suggestion of a leveraged buy-out does not make sense.  In effect, the Investcorp deal was a leveraged buyout, and probably the best such deal available to shareholders. Management did not appear particularly interested in mounting a competing bid, and had substantial incentives to see the Investcorp deal through to completion.  Schluter's proposal was not likely to do anything but disrupt the Investcorp deal. Respondent argued that a recapitalization was an alternative.  A 7.5-percent shareholder would have had no power to effect a recapitalization of the Company, at least not without acquiring another 60 percent or so of the outstanding shares. Finally, petitioner counters respondent's "professional investor" and "other shareholder" scenarios by pointing out that respondent has identified no individual or group of professional outside investors who would have been interested in acquiring the Company.  In any event, we believe such investors would*372  analyze the deal much the same as we have. We believe that respondent, and to some extent petitioner, misapprehends the willing buyer-willing seller test.  We need not identify exactly who the buyer would be or even what class of investors the buyer would belong to.  The "willing buyer" is supposed to be a hypothetical amalgam of potential buyers in the marketplace.  Although we have, in prior opinions, identified types of hypothetical buyers, we did so only to determine which valuation approach, among several reasonable approaches, would result in the highest bid, and therefore the one most acceptable to a willing seller. See, e.g., Estate of Newhouse v. Commissioner, 94 T.C. 193">94 T.C. 193, 245 (1990) ("The choice of the appropriate valuation methodology for a particular stock is, in itself, a question of fact" (emphasis added)); Perdue v. Commissioner, T.C. Memo. 1991-478 (dividing rare coin market into numismatists and "glamour" purchasers).  The question is not so much "who", but "how". We agree with Schroeder and Koch that a buyer would consider three principal adverse factors in deciding what he would be willing to pay for 7.5 percent of *373  the Mueller Co. shares: shareholder rejection, a lawsuit, and lack of liquidity. It is also our task to find the price at which a willing seller would sell.  Logically, a willing seller would sell only to the willing buyer making the highest bid. We assume that the potential buyers of the shares would bid up the price of the shares until the person who values the shares most highly -- that is, the person who is most certain that the Investcorp deal will go through, or who is most willing to take the risk that it will not -- wins the bidding.  The final result is not an average of the high and low ranges (as Koch suggests) because we assume the price is determined by an "auction" in the marketplace, not the give-and-take of one-on-one negotiation. First, there is the matter of a base arbitrage discount. This discount is the starting point -- more or less the average discount an investor would demand for a risk arbitrage investment.  We believe that there were potential investors who were more risk-tolerant than the risk arbitrageur Schroeder described who would have been interested in a minority investment in the Company's stock. We therefore place a value of 6 percent, rather *374  than 9 percent, on this base discount. Second, a potential buyer would consider the risk that shareholders would reject the deal.  It was not entirely clear at the valuation date what the outcome of a shareholder vote would be.  The Company's chief executive was pessimistic that the deal would go through, and most of the shareholder blocks had not expressed an opinion.  On the other hand, only Schluter had gone on record as opposing the deal.  Another fact to consider is how persuasive management could be expected to be in selling the deal to shareholders. Could it have been expected on the valuation date that someone would hit on an idea that would weaken the resistance of wavering shareholders, such as John Mueller's suggestion to donate the family memorabilia to a local college? Another factor to consider is that most of the shares were held in trust.  The trustees owed a fiduciary duty to the beneficiaries to protect their economic interests.  Respondent argues that if the trustees had voted against the Investcorp deal, they would have been derelict in their fiduciary duties.  Although the Investcorp deal was attractive, we believe that a trustee could have voted against the*375  deal for legitimate reasons.  Besides, we are not so much concerned with the trustees' legal obligations as with what they were likely to do, even if in violation of those obligations.  The trustees were primarily members of the Mueller family.  We believe that it would have seemed uncertain to a prospective outside purchaser of shares that the trustees would disregard the Company's family heritage. All these factors indicate to us that a reasonable investor might have assumed that family resistance to the sale could be overcome, but still be concerned that the deal might not win two-thirds shareholder approval.  Such an investor would have demanded an additional 5-percent discount, as Schroeder suggested. Third, the hypothetical buyer would have considered the risk that Schluter or another dissenter would file a lawsuit. We need not decide what the probable outcome of a potential lawsuit would have been in order to determine the value of the shares; we only must try to gauge how the possibility of the suit would affect the fair market value of the shares.  Estate of Newhouse v. Commissioner, supra at 232-233. We heard no testimony from two key participants*376  in the March 21, 1986, board meeting where the merger was first voted on.  Dudley Godfrey, the board member who telephoned John Mueller to obtain his views, might have shed additional light on whether John Mueller had indeed voted at that meeting.  He could have testified that the phone call was audible to all directors, or that it was not.  We did hear testimony from another attorney in Godfrey's law firm, Kenneth Hunt, who was at the meeting, but his recollection of events was not very clear.  We also heard testimony from John Mueller and Powers on this point.  Respondent argues that because Godfrey was not called, we should draw the inference that his testimony would have hurt petitioner, citing Wichita Terminal Elevator Co. v. Commissioner, 6 T.C. 1158">6 T.C. 1158 (1946), affd. on other grounds 162 F.2d 513">162 F.2d 513 (10th Cir. 1947). We disagree.  In Wichita Terminal Elevator, the taxpayer submitted practically no evidence.  Petitioner in the instant case submitted reams of exhibits and hours of testimony.  If respondent believed Godfrey's testimony would have damaged petitioner's case, respondent could have called him as a witness to impeach the recollections*377  of Hunt, Powers, and John Mueller. We also heard no testimony from John Schluter.  Obviously, only he could state definitively what his motivations and intentions were.  Respondent again suggests that we employ Wichita Terminal Elevator to draw inferences against petitioner.  We again suggest that respondent could have called Schluter as an impeachment witness.  In addition, we are not so sure that Schluter's testimony would have been relevant.  We are here concerned not with Schluter's actual state of mind, but with the perception of his motivations and intentions by others.  Other witnesses testified sufficiently about Schluter's apparent motives and intentions. Returning to the issue of the likelihood of a lawsuit, we observe that Investcorp could have walked away from the deal if a lawsuit materialized. 10 On March 24, 1986, a reasonable investor could have surmised that a lawsuit could have raised the issue of the validity of the board action at the March 21 meeting, 11 or other issues yet to be exposed in the proxy statement.  At the time of decedent's death, Schluter had not yet threatened suit, although a reasonable investor would have foreseen that possibility.  After*378  decedent's death, Schluter sent mixed signals.  On the one hand, he claimed that he only wanted the best price for shareholders. On the other, he rattled his saber over nit-picky points in the proxy statement, possibly indicating that he would block the merger at any price.  The Company hired special litigation counsel to prepare for the possibility that Schluter would sue. *379  A reasonable investor might have discounted the possibility of a lawsuit, or assumed that such a suit would be quickly settled or dismissed.  We note that no lawsuit ever was filed.  Although no one could have known on the valuation date that no suit would be filed, the fact that no suit was filed suggests the reasonableness of a belief that no suit would be filed.  See Estate of Gilford v. Commissioner, 88 T.C. 38">88 T.C. 38, 52 (1987). Thus, we believe that a discount of no more than 2.5 percent is in order to account for this risk. Third, there is the problem of lack of liquidity. We assume that any rational investor would prefer a liquid to an illiquid investment.  But the degree of this preference is a matter of uncertainty.  Two factors lead us to believe that a lower discount than suggested by Schroeder is appropriate.  First, we believe that the prospect of a quick takeover made these shares considerably more liquid.  Second, part of the reason for the shareholder rejection and litigation discounts is the lack of liquidity of the shares.  To the extent Schroeder's 15-percent lack of liquidity discount was not reduced to reflect the lack of liquidity components*380  of the other discounts, it was too large.  We find that a lack of liquidity discount of 7.5 percent is appropriate. Taking all these factors into account, we believe that a discount from the takeover price of 21 percent is appropriate.  This results in a per share fair market value of $ 1,700.  We have therefore found that the value of the 8,924 shares of the Company includable in decedent's gross estate was $ 15,170,800. An appropriate order will be issued.Footnotes1. The estate tax return showed 3,500 shares as held by "Ebert B. Mueller, Trustee Under Will -- Marital Trust," 274 shares as held by "Ebert B. Mueller, Trustee Under Life Insurance Agreement -- Marital," and 5,150 shares as held by "Bessie I. Mueller Trust -- property transferred August 9, 1979." Ebert B. Mueller was decedent's husband, who predeceased her.  There is no dispute that these shares were includable in the gross estate. The parties have not argued that the holding of the shares in three separate trusts should have any impact on our valuation analysis.  We therefore value these shares as if they were held by a single entity on the valuation date.↩2. The parties stipulated that "The minutes of the Mueller Co. Board meetings for the years 1981 through 1986 disclose no action of the board which did not meet the requirements of [the family veto provision]." However, those minutes reflect that the provision probably was not followed at the Mar. 21, 1986, meeting and clearly was not followed at the Nov. 19, 1985 meeting, at which the board voted to form a committee to interview investment bankers.  John Mueller was not present at the November 19 meeting, and Philip Mueller voted against the resolution, leaving only two family designated directors who could have "assented to" the board's action.  However, the vote to form the committee was not likely to (and did not) lead to a legal challenge, inasmuch as thereafter the entire board unanimously approved the committee's choice of Morgan Stanley as investment banker.↩3. Inasmuch as decedent's personal representative did not elect the alternate valuation date under sec. 2032, the valuation date is the date of decedent's death.↩4. Dr. Pratt testified: Willamette has either the most comprehensive, or one of the most comprehensive libraries in the United States, on the subject of valuation of companies and interests of companies.  It contains SEC filings, company annual reports.  It contains a great deal of both national and regional economic data.  It contains a great deal of industry data.  It contains a large number of court cases, involving valuation disputes, which are indexed with respect to both the type of case, and the issues involved in the case.  It has a key word index file by subject, for various types of things, such as, for example, arbitrage, which is one of the items in it.  And it has articles from the financial literature, organized by subject matter, and indexed and so forth, as well as a lot, of course, [of] books, periodicals kept from many years back, and statistical services from which we derive valuation data.↩5. We are puzzled that Morgan Stanley's potential breakup fee ($ 3 million) approximated its actual compensation ($ 2.675 million plus expenses), thus making it indifferent, in the short term, to whether Mueller Co. was sold.  However, Morgan Stanley certainly would have preferred the deal to go through to protect its reputation and build additional business in the future.  Also, Morgan Stanley did have an incentive to maximize the price paid by the acquiror, since each additional million dollars added to the acquisition price in excess of $ 260 million resulted in $ 50,000 in additional compensation.  The fact that Morgan Stanley was not successful in obtaining a price greater than $ 270 million does not change the fact that it had a substantial incentive to do so.↩5. We are puzzled that Morgan Stanley's potential breakup fee ($ 3 million) approximated its actual compensation ($ 2.675 million plus expenses), thus making it indifferent, in the short term, to whether Mueller Co. was sold.  However, Morgan Stanley certainly would have preferred the deal to go through to protect its reputation and build additional business in the future.  Also, Morgan Stanley did have an incentive to maximize the price paid by the acquiror, since each additional million dollars added to the acquisition price in excess of $ 260 million resulted in $ 50,000 in additional compensation.  The fact that Morgan Stanley was not successful in obtaining a price greater than $ 270 million does not change the fact that it had a substantial incentive to do so.↩6. Respondent resisted the Court's attempt to obtain a copy of the engagement letter.  We rely on Dr. Pratt's testimony as to its contents, which are not in dispute.↩7. Respondent made much of Schroeder's lack of academic credentials and his absence from the rolls of the American Society of Appraisers.  The Federal Rules of Evidence, however, make clear that experts are to be judged by what they know, not where or how they learned what they know.  Fed. R. Evid. 702↩; 28 U.S.C. app. at 767 (1988) (Notes of Advisory Committee).8. We express no opinion on whether such a tactic would have been well founded.↩9. KKR, which bid between $ 235 million and $ 240 million for Mueller Co., operated such a fund.  This does not necessarily mean KKR would have taken an arbitrage position in the Company; KKR was bidding on its own account for the entire Company.↩10. Respondent suggests that Investcorp may not have known about the family veto provision of the bylaws, and therefore Investcorp would not have even considered the option of walking away.  We believe it unlikely that an acquiring company with a professional and experienced staff could spend 300 man-hours on due diligence and not read the target company's bylaws. ↩11. Respondent argues that the board did in fact comply with the bylaw provision because John Mueller either did "assent" to the deal (even though he was not present at the meeting), or authorized Godfrey to vote in favor of the measure on his behalf.  As to the second argument, it is hornbook law that directors may not vote by proxy.  2 Fletcher Cyc. Corp., sec. 427, at 324 (1990); Henn & Alexander, Laws of Corporations and Other Business Enterprises, sec. 208, at 565 (3d ed. 1983).  In any event, we need not decide whether these arguments would have carried the day in a lawsuit. The fact that these arguments could have been made, in our view, would have increased the uncertainty over the resolution of a lawsuit, and therefore would have increased the probability of a lawsuit, rather than a settlement without litigation.  This in turn would have increased the probability that Investcorp would withdraw.↩