In re Appraisal of Stillwater Mining Company ( 2019 )


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  •       IN THE COURT OF CHANCERY OF THE STATE OF DELAWARE
    IN RE APPRAISAL OF STILLWATER                )             Consol. C.A. No.
    MINING COMPANY                               )              2017-0385-JTL
    MEMORANDUM OPINION
    Date Submitted: May 23, 2019
    Date Decided: August 21, 2019
    Samuel T. Hirzel, II, Elizabeth A. DeFelice, HEYMAN ENERIO GATTUSO & HIRZEL
    LLP, Wilmington, Delaware; Lawrence M. Rolnick, Steven M. Hecht, Jonathan M. Kass,
    Glenn McGillivray, LOWENSTEIN SANDLER LLP, New York, New York; Attorneys
    for Petitioners.
    S. Mark Hurd, Lauren Neal Bennett, MORRIS, NICHOLS, ARSHT & TUNNELL LLP,
    Wilmington, Delaware; James R. Warnot, Jr., Adam S. Lurie, Brenda D. DiLuigi, Nicole
    E. Jerry, Elizabeth M. Raulston, LINKLATERS LLP, New York, New York; Attorneys for
    Respondent.
    LASTER, V.C.
    This post-trial decision determines the fair value of the common stock of Stillwater
    Mining Company (“Stillwater” or the “Company”) as of May 4, 2017, which is when
    Sibanye Gold Limited completed its acquisition of Stillwater through a reverse-triangular
    merger (the “Merger”). Pursuant to an agreement and plan of merger dated December 9,
    2016 (the “Merger Agreement”), each share of Stillwater common stock was converted at
    closing into the right to receive $18.00, subject to the right of each holder to eschew the
    merger consideration and seek appraisal.
    The petitioners perfected their appraisal rights and litigated this appraisal
    proceeding. They contended that Stillwater’s fair value was $25.91 per share. To justify
    this outcome, they relied on an expert who valued Stillwater using a discounted cash flow
    (“DCF”) model.
    The respondent in an appraisal proceeding is technically the surviving corporation,
    but the real party in interest is the acquirer. The petitioners’ true opponent in this
    proceeding was Sibanye.
    Sibanye contended that Stillwater’s fair value was $17.63 per share. To justify this
    outcome, Sibanye relied on a combination of metrics, including the deal price, Stillwater’s
    unaffected trading price with an adjustment for a valuation increase between the unaffected
    date and closing, and an expert valuation based on a DCF model.
    Sibanye proved that the sale process was sufficiently reliable to make the deal price
    a persuasive indicator of fair value. Although Sibanye argued for a deduction from the deal
    price to account for value arising from the Merger, Sibanye failed to prove that an
    adjustment was warranted.
    The parties engaged in lengthy debate over whether Stillwater’s adjusted trading
    price could provide a persuasive indicator of fair value. The reliability of the adjusted
    trading price depended on the reliability of the unaffected trading price, and both sides
    engaged experts who conducted analyses and offered opinions about the attributes of the
    market for Stillwater’s common stock. The evidence demonstrated that Stillwater’s trading
    price could provide a persuasive indicator of value, but that it was a less persuasive
    indicator than the deal price. This decision therefore does not use a trading price metric.
    Neither side proved that its DCF valuation provided a persuasive indicator of fair
    value. The experts disagreed over too many inputs, and the resulting valuation swings were
    too great, for this decision to rely on a model when a market-tested indicator is available.
    This decision concludes that the deal price is the most persuasive indicator of fair
    value. Relying on any of the other valuation metrics would introduce error. The fair value
    of the Stillwater on the valuation date was therefore $18.00 per share.
    I.      FACTUAL BACKGROUND
    The parties generated an extensive evidentiary record. They commendably reached
    agreement on 283 stipulations of fact. During four days of trial, they introduced 909
    exhibits and lodged twenty-one depositions in evidence. Three fact witnesses and seven
    expert witnesses testified live. What follows are the court’s findings based on a
    preponderance of the evidence.1
    1
    Citations in the form “PTO ¶ ––” refer to stipulated facts in the pre-trial order. Dkt.
    209. Citations in the form “[Name] Tr.” refer to witness testimony from the trial transcript.
    Citations in the form “[Name] Dep.” refer to witness testimony from a deposition
    2
    A.    The Company
    At the time of the Merger, Stillwater was a Delaware corporation engaged in the
    business of extracting, processing, smelting, and refining minerals from an orebody known
    as the J-M Reef. Located in in the western United States, the J-M Reef contains deposits
    of palladium, platinum, and rhodium, which are known in the mining industry as “platinum
    group metals” or “PGMs.” These metals are rare, and the J-M Reef is the only PGM asset
    in the United States. The other principal sources of PGMs are located in South Africa,
    Russia, and Zimbabwe, which present significantly greater political risk.
    Stillwater was headquartered in Littleton, Colorado, and its common stock traded
    on the New York Stock Exchange under the symbol “SWC.” Stillwater’s trading price was
    heavily influenced by commodity prices for palladium and, to a lesser degree, platinum.
    At the time of the Merger, Stillwater’s operations consisted of two producing mines
    in south central Montana: the Stillwater Mine and the East Boulder Mine. Stillwater’s other
    assets were development projects or exploratory properties that were not yet generating
    revenue.
    At the time of the Merger, Stillwater’s two development projects were Blitz and
    Lower East Boulder. Blitz expanded the Stillwater Mine eastward. Lower East Boulder
    was a contemplated expansion of the East Boulder mine. Stillwater’s two exploratory
    transcript. Citations in the form “JX –– at ––” refer to a trial exhibit with the page
    designated by the last three digits of the control or JX number. If a trial exhibit used
    paragraph or section numbers, then references are by paragraph or section.
    3
    properties in the J-M Reef were Iron Creek and the Boulder Extension. Outside of the J-M
    Reef, Stillwater owned two other exploratory properties: (i) Altar, a copper-gold-porphyry
    deposit in the San Juan province of Argentina, and (ii) Marathon, a copper-PGM deposit
    in Ontario, Canada.
    At the time of the Merger, Michael “Mick” McMullen served as Stillwater’s
    President and CEO and as a member of its board of directors (the “Board”). The other six
    members of the Board were independent, outside directors:
     George Bee was a mining engineer who had held senior management positions
    or served on the boards of other mining companies.
     Patrice Merrin had served as an executive or director for numerous companies
    and was a director of Glencore plc, a multi-national mining firm. Merrin chaired
    the Board’s Corporate Governance and Nominating Committee.
     Peter O’Hagan had worked at Goldman Sachs for nearly twenty-three years,
    including as co-head of its global commodities business.
     Michael Parrett was a Chartered Professional Accountant who had served in
    senior management positions and as a director for other mining companies.
     Brian Schweitzer had served as Governor of Montana. He was Chairman of the
    Board.
     Gary Sugar had spent thirty-two years at RBC Capital Markets, where he
    specialized in the mining sector. He served on the boards of other mining
    companies.
    B.    McMullen Convinces The Board To Build A Mid-Cap Mining Company.
    McMullen was hired in December 2013 as a “turnaround CEO.” McMullen Tr. 814–
    16; see Schweitzer Tr. 170. By early 2015, McMullen had refocused Stillwater’s
    operations, cut costs, and generally turned the Company around. At this point, McMullen
    believed that market conditions favored the creation of a mid-cap mining company. He
    4
    thought Stillwater could achieve this outcome either by growing through acquisitions or by
    combining with another industry player through a merger of equals.
    During a meeting of the Board in June 2015, McMullen gave a lengthy presentation
    on Company strategy that devoted twenty-six slides to various alternatives. See JX 44 at
    ‘848 to ‘874. McMullen’s presentation discussed means of increasing earnings, increasing
    the trading multiple, and optimizing the capital structure, and then turned to the pros and
    cons of selling some or all of the business. The presentation was particularly negative about
    the prospect of a sale. See 
    id. at ‘866
    to ‘868. In another presentation, McMullen devoted
    over forty slides to discussing candidates for acquisitions or mergers of equals. See 
    id. at ‘929
    to ‘970.
    In addition to his own presentation, McMullen provided the Board with
    presentations from three investment banks. McMullen had a close relationship Dan Vujcic,
    then an investment banker with Jefferies Financial Group, Inc., and the Jefferies
    presentation was the most detailed. It analyzed an acquisition of another base metals
    company, focusing on Sandfire Resources NL, Western Areas Ltd., and Panoramic
    Resources Ltd. It also analyzed the possible acquisition of a downstream company, a
    possible spinoff of Stillwater’s processing and trading business, and the option of
    maintaining the status quo. See 
    id. at ‘014
    to ‘080. A presentation from BMO Capital
    Markets was more of a high-level pitch book, but it identified selected acquisition
    opportunities. See 
    id. at ‘081
    to ‘183. A presentation from Nomura Holdings, Inc. discussed
    alternatives for refinancing Stillwater’s convertible bonds. See JX 44 at ‘164 to ‘182.
    5
    Sibanye has argued that this meeting marked the start of the Board’s careful and
    thoughtful consideration of a sale of the Company, but the purpose of the meeting was not
    to prepare the Board for a sale. McMullen hoped to convince the Board to back him in
    creating a mid-cap mining company.2 The Board, however, resisted, recalling unsuccessful
    acquisitions that had necessitated hiring a turnaround CEO in the first place. During the
    June 2015 meeting, the Board did not provide McMullen with a mandate to pursue any
    strategic options. See JX 43.
    After the June 2015 meeting, McMullen kept looking for opportunities to build a
    mid-cap mining company. During the second half of 2015, McMullen worked with
    Jefferies, BMO, and Citigroup to identify acquisition targets and merger-of-equals
    candidates.3 McMullen was focused on an acquisition, particularly “something not in the
    PGM space to diversify risk.” JX 59.
    2
    The two slides in the management presentations that addressed a sale contained
    comments like “[f]inding a willing buyer with higher priced currency is difficult,” “[m]uch
    of the value from Blitz, Lower East Boulder and recycle ramp up yet to be recognized by
    the market and potential buyers,” and the “[r]ecent downward trend in PGM prices not the
    right environment in which to be a seller.” 
    Id. at ‘866
    to ‘867. Out of the nearly 190 slides
    in the banker presentations, only one discussed a possible sale. There, BMO opined that
    selling was “unlikely to be a value maximizing strategy until value has been extracted from
    all the other alternatives” available to the Company. 
    Id. at ‘108.
           3
    See, e.g., JX 50 at ‘586 to ‘594; JX 52; JX 53; JX 55; JX 57; JX 58; JX 67; JX 68;
    PTO ¶¶ 138–39. Although principally focused on acquisitions, McMullen asked BMO in
    an October 2015 email for its views about “who would potentially be a buyer of Stillwater
    in an M+A deal?” JX 57 at ‘920. BMO sent back a list of twenty-one candidates, but
    warned that “[g]enerally as a whole we would say that we do not believe there is a high
    level of current interest and capability for an acquisition of Stillwater.” 
    Id. at ‘919.
    6
    During a meeting of the Board in October 2015, McMullen gave another
    presentation on the Company’s strategy. See JX 61 at ‘102 to ‘127. He highlighted the risks
    Stillwater faced because of its dependence on palladium, which was used principally in
    catalytic converters. His presentation discussed the disruptive threat posed by electric cars,
    which could displace gasoline-powered cars and render catalytic converters obsolete. See
    
    id. at ‘105
    (“Know Your Enemy—Electric Cars”). He recommended making a diversifying
    acquisition from which Stillwater would “emerge as a multi mine, multi commodity and
    multi jurisdiction mid cap miner with a bullet proof balance sheet.” 
    Id. at ‘127.
    He then
    reviewed six possible candidates: Sandfire, Western Areas, Panoramic, Northern Star
    Resources Ltd., Imperial Metals, and Hecla Mining Co. See 
    id. at ‘128
    to ‘179. He also
    circulated a presentation from Jefferies that discussed an acquisition of Sandfire. See 
    id. at ‘249
    to ‘292. During the weeks after the meeting, Jefferies provided McMullen with more
    detailed analyses of a deal with Northern Star, a large gold producer in Australia. See JX
    67; JX 68.
    In December 2015, McMullen and a team from Stillwater visited the mining
    operations of Northern Star, where McMullen had a close relationship with senior
    management. During the visit, McMullen met with the CEO and CFO of Northern Star and
    discussed a potential merger of equals. See PTO ¶ 145; JX 73 at ‘867; see also JX 61 at
    ‘282 to ‘286; JX 67. At this point in time, a merger of equals with Northern Star was
    McMullen’s top choice among Stillwater’s strategic options.
    During meeting of the Board in January 2016, McMullen gave another presentation
    on the Company’s strategy. See JX 86 at ‘002 to ‘040. As with the meetings in June and
    7
    October 2015, his goal was to convince the Board to authorize him to build Stillwater into
    a mid-cap metals company. See JX 78 (McMullen discussing his desire to “come away
    from [the January] board meeting with a clear mandate”). McMullen recommended a
    merger of equals with Northern Star as the best option, telling the Board that the transaction
    “would make a very strong mid cap precious metals miner.” JX 86 at ‘038. If Northern Star
    would not engage, then he recommended acquiring Sandfire or Western Areas. See 
    id. at ‘039.
    He also identified some smaller acquisitions that “should be pursued independently”
    and “[r]egardless of whether Stillwater completes one of the larger deals.” 
    Id. at ‘040.
    Later
    in the meeting, he provided additional information about the proposed M&A strategy and
    further detail about Northern Star, Sandfire, Western Areas, Panoramic, Hecla, and
    Imperial. See 
    id. at ‘’320
    to ‘367. McMullen also distributed a presentation from Jefferies
    that analyzed mergers with Northern Star and Western Areas. See 
    id. at ‘275
    to ‘319
    At the conclusion of the January 2016 meeting, the Board gave management a
    mandate, but it was broad and vague. According to the minutes, “[t]he Board provided
    management with a sense of the Board for management to continue to pursue the options
    as discussed, but to return to the Board for any final decision.” JX 90. During this litigation,
    Sibanye has argued that this mandate authorized management to pursue a sale of the
    Company, but that is not accurate.4 McMullen put it best when he told a banker at
    4
    Only one slide in McMullen’s presentation referenced a sale of the Company, and
    it advised that there was a “[v]ery limited number of potential buyers” and that because
    “commodity prices and sentiment are low,” the Company “would not realize full value
    potentially.” JX 86 at ‘025. By contrast, he presented multiple slides discussing positively
    8
    Blackstone that he had “finally convinced the Stillwater board to go off and buy some
    things.” JX 93 at ‘628; see Schweitzer Tr. 187.
    C.     The Company’s Stock Price
    While McMullen was trying to convince the Board to let him “buy some things,”
    Stillwater’s stock price was falling. The decline began in June 2016 and continued steadily
    through December. Over the course of this six month period, Stillwater’s stock price fell
    by over 40%, dropping from $14.46 per share on June 1 to $8.57 per share on December
    31. The market drop did not reflect any problems with Stillwater’s operations. Instead, it
    reflected a decline in the spot price of palladium, which fell by 27% from $773.70 per
    ounce on June 1 to $562.98 per ounce on December 31. PTO Exs. A, B.
    During the Board meeting in January 2016, McMullen had told the Board that
    “[d]espite our stock being down 40%, we still have options open to us today.” JX 86 at
    ‘012. But during the weeks following the January 2016 meeting, the stock price fell further.
    On January 19, it closed at $5.29 per share, down 38% from its closing price of $8.57 per
    share on December 31. The drop corresponded with further declines in the spot price of
    palladium, which closed on January 19 at $494.83 per ounce, down another 12% from its
    close of $562.98 per ounce on December 31.
    The Company’s dismal stock performance caused McMullen to conclude that
    Stillwater did not have a currency that it could use for either an acquisition or a merger of
    how the Company could deploy its “capital and currency” (its stock) to make an
    acquisition. See 
    id. at ‘026
    to ‘035.
    9
    equals. JX 93 at ‘628 (“[U]nfortunately the stock price has collapsed in the last 2 weeks
    and I don’t think Stillwater has the currency to do anything anymore. Ce [sic] la vie.”); see
    McMullen Tr. 826; JX 97 at ‘308 to ‘310, ‘313. He felt Stillwater had missed its
    opportunity to expand and was now just an “an option play on the P[alladium] price.” JX
    93 at ‘628; see JX 97 at ‘313
    At this point, McMullen told a banker at Blackstone that “[s]itting around for one
    or two years waiting for the price to recover” was “not my idea of a job.” McMullen Tr.
    828; JX 93 at ‘628. McMullen did not view himself as an “operational CEO.” McMullen
    Tr. 814–16. He thought he “would become bored.” McMullen Tr. 828. With his contract
    set to expire at the end of the year, McMullen began thinking about what he would do next,
    including the possibility of building a mining portfolio company for Blackstone. See
    McMullen Tr. 828; JX 93 at ‘627 to ‘628.
    D.     Sibanye Contacts McMullen.
    On January 30, 2016, Sibanye reached out through BMO to arrange a meeting
    between McMullen and Sibanye’s CEO, Neal Froneman. Without telling the Board,
    McMullen accepted.
    The meeting took place at an industry conference on March 1, 2016. PTO ¶ 161.
    When Froneman broached the subject of buying Stillwater, McMullen was receptive. He
    asked Froneman to provide “an informal proposal” in writing that included “an idea of
    valuation” and “transaction structure.” JX 109 at ‘976; see PTO ¶ 164. Froneman had the
    impression that a deal “was doable if we got the valuation right.” JX 109 at ‘976.
    10
    After the meeting, Froneman asked McMullen for “specific guidance” about what
    would be acceptable. JX 110. McMullen indicated that Sibanye’s offer should include “a
    large cash component.” JX 113 at ‘175. He also told Froneman during these early
    discussions that an acceptable transaction should be priced at a premium of 30% over
    Stillwater’s thirty-day volume-weighted average price (“VWAP”). Stewart Dep. 39; see
    also JX 162 at ‘283. Froneman agreed in principle to this pricing metric, and he began
    organizing a team to visit Stillwater’s mines. See JX 113 at ‘174 to ‘175. Froneman asked
    to enter into a confidentiality agreement to facilitate diligence, but McMullen rejected the
    request, commenting that he wanted “to see some form of indicative, non-binding and
    highly confidential terms of a transaction before we go too far down the path.” 
    Id. at ‘174.
    McMullen took all of these actions without involving the Board. Indeed, he did not
    even inform the Board about Sibanye’s approach. See Schweitzer Tr. 189–92; Wadman Tr.
    657. Instead, on March 25, 2016, he agreed to extend his employment for an additional two
    years. JX 114 § 4.1. His original employment agreement had been scheduled to terminate
    on December 31, 2016, and the Board had expected that because McMullen was a short-
    term, turnaround CEO, he would not stay beyond that date. Wadman Tr. 670–71; see
    Wadman Dep. at 341; Schweitzer Tr. 170, 193. But with acquisition talks in the offing,
    McMullen agreed to a new deal. See JX 114.
    The new employment agreement permitted McMullen to serve concurrently as a
    director of Nevada Iron Limited and New Chris Minerals Limited, which later became GT
    Gold Corp. See JX 114 § 3.1, Ex. A. During 2016, McMullen did more than serve on the
    boards of these companies. He became Executive Chairman and CEO of Nevada Iron, and
    11
    he served as Non-Executive Chairman and President of New Chris. See McMullen Tr. 863–
    64; McMullen Dep. 45, 553; JX 93 at ‘628. Both companies were Australian resource firms
    whose equity comprised a significant portion of McMullen’s net worth. JX 157 at ‘315;
    see McMullen Tr. 709, 863–64. Over the next year, while McMullen was busy selling the
    Company, he also caused Nevada Iron and New Chris to engage in transformative
    transactions.5
    In May 2016, the Board held its next regular meeting. In connection with that
    meeting, McMullen did not inform the Board about Sibanye’s approach or his discussions
    with Sibanye.6
    E.     Sibanye Submits An Indication Of Interest.
    During the first week of June 2016, executives from both Sibanye and Northern Star
    toured the Company’s mines. PTO ¶¶ 171–72. Sibanye toured as part of their exploration
    of a potential acquisition of the Company. Northern Star toured separately, ostensibly as
    part of a mutual benchmarking exercise but really in connection with a potential merger of
    equals. McMullen and the Company’s CFO, Christopher Bateman, led Sibanye and
    Northern Star on separate tours and ensured that neither saw one another. McMullen
    5
    See JX 138; JX 139 at ‘831; JX 154 at ‘087; JX 155; JX 157 at ‘315; McMullen
    Tr. 709–10; see also JX 349.
    6
    See Schweitzer Tr. 189–90. McMullen testified that he told Schweitzer and Merrin
    about Sibanye’s approach after his initial meeting with Froneman. He also claimed that he
    kept the Board informed as discussions progressed. McMullen’s self-interested testimony
    conflicted with Schweitzer’s more credible testimony and other record evidence.
    12
    claimed that despite keeping the two teams separate, each knew that the other was on site
    because McMullen and Bateman would alternate between the tours and McMullen had
    them both sign the visitors log. McMullen said he did this as a clever way to create
    competition between the firms. See McMullen Tr. 726–27.
    After the visits, McMullen believed that a deal with Sibanye was more likely than
    with Northern Star. See JX 140 at ‘048; JX 142. Toward the end of June 2016, Northern
    Star reported that they were primarily interested in a joint venture involving Blitz. JX 145
    at ‘845. That possibility did not interest McMullen. 
    Id. Meanwhile, McMullen
    pushed
    Sibanye to provide an indication of interest in advance of the Board’s next meeting, which
    was scheduled for July 28, 2016.7
    Sibanye began working with Citigroup to develop its bid. Two of the Citigroup
    bankers had previously advised McMullen and Bateman about the Company’s alternatives.
    As part of its advice, Citigroup had recommended against a sale of the Company because
    of the limited universe of potential buyers. See JX 32 at ‘829; cf. JX 42 at ‘422.
    On July 21, 2016, Sibanye provided McMullen with a non-binding indication of
    interest to acquire Stillwater at $15.75 per share in cash, which valued the Company at $1.9
    billion. PTO ¶ 177; JX 165. The letter described that price as reflecting “a 30% premium
    7
    See JX 152 at ‘532 ‘533. At trial, McMullen testified that after Sibanye conducted
    its site visit, the Board told him that they wanted “some sort of written expression of
    interest” before starting “a data room process.” McMullen Tr. 728–29. That testimony was
    not credible. The evidence indicates that McMullen did not brief the Board about a
    potential transaction with Sibanye until the July 2015 board meeting. See Schweitzer Tr.
    189–90.
    13
    to Stillwater’s volume-weighted average share price [(VWAP)] of US$12.12 over the last
    20 trading days prior to 20 July 2016.” JX 165 at ‘880; see PTO ¶ 178.
    As suggested by Sibanye’s offer, Stillwater’s stock price had mostly recovered,
    reflecting a recovery in the price of palladium. At the beginning of July 2016, the stock
    closed at $12.25 per share, up 132% from its low of $5.29 in January. During that same
    period, the palladium spot price had increased 22% to $605.63 per ounce. PTO Exs. A, B.
    Despite the stock’s performance, McMullen did not revisit potential acquisitions or a
    merger of equals. He was now focused on selling the Company. See JX 156 (email from
    Vujcic to McMullen stating, “[W]e’ll make sure the company gets sold. Don’t worry about
    that.”).
    F.         McMullen Presents The Indication Of Interest To The Board.
    On July 27 and 28, 2016, the Board held a regularly scheduled meeting. At the end
    of the two-day meeting, the directors held a forty-five minute “executive session” with
    McMullen, who distributed and walked through a presentation titled “Business
    Development Update.” JX 151 at ‘551; see Schweitzer Tr. 193; JX 526 at ‘377; Wadman
    Tr. 657–64. The presentation compared the Company’s recent performance to various
    potential transaction partners, then described the pros and cons of transactions with
    Northern Star and Sibanye. After summarizing the terms of Sibanye’s expression of
    interest, the presentation described the premium as “within the right range for shareholder
    value” and “broadly within the range of mining transactions.” JX 151 at ‘568. McMullen
    gave his “strong recommendation . . . to engage with Sibanye and attempt to conclude [due
    diligence] as quickly as possible (likely to take 2 months) and achieve a higher price.” 
    Id. 14 McMullen
    added that he would “look to engage with other potential bidders on a low key
    and informal basis to determine if there are alternative bidders.” 
    Id. He warned:
    “The list
    of other potential bidders is short given the commodity, size of transaction and whether
    [Stillwater’s] shareholders would want their paper. The process of determining if there are
    alternatives will not be a long process.” 
    Id. He also
    told the directors that “[t]he market
    appears to be open for people to carry out M+A, and asset values have risen to a level
    where you want to be a seller rather than a buyer.” 
    Id. Brent Wadman,
    the Company’s General Counsel, became concerned about what
    took place during the July meeting. He had not been asked to stay for the executive session
    and was not given access to McMullen’s presentation. See JX 526 at ‘377; Wadman Tr.
    657–64. He suspected that McMullen was running a sale process on his own, without Board
    oversight, and potentially using it as a means of exiting from the Company. Wadman
    believed that as General Counsel, he should have been involved. After the July meeting,
    Wadman asked McMullen to include him in the planning process. McMullen rebuffed him,
    saying that Wadman would be “brought in at a later date” and “offer[ing] no other
    information.” JX 526 at ‘377; Wadman Tr. 658.
    After the July meeting, McMullen told Sibanye to submit its list of due diligence
    questions so the Company could start pulling the information together. He told Sibanye to
    direct all inquiries to himself or Bateman. See PTO ¶ 181; JX 183.
    G.     McMullen Remains Committed To Sibanye.
    On August 9, 2016, Stillwater and Sibanye entered into a confidentiality agreement,
    and Sibanye gained access to the data room. PTO ¶ 183; JX 525 at 26; see also JX 194. On
    15
    August 10, the Board met again. See JX 193. McMullen testified that at this meeting, the
    Board instructed him “to go out and . . . to sign the NDAs with the likes of Sibanye, and
    then, also, . . . to get as much interest as possible.” McMullen Tr. 835.
    Rather than working closely with an investment bank to develop a process designed
    to generate “as much interest as possible,” McMullen pressed forward with Sibanye. He
    interacted with some investment banks, but in a haphazard and unstructured way. For
    example, back in July 2016, a Macquarie banker had asked McMullen to meet for a market
    update. See JX 167. On August 10, the same day that the Board met, Macquarie proposed
    a formal engagement. Five days later, McMullen told Macquarie that it was “a bit early for
    us I think to be signing anyone up.” JX 196.
    One week after the Board meeting, on August 18, 2016, McMullen and Bateman
    met with Bank of America Merrill Lynch (“BAML”), who had arranged the meeting to
    pitch Stillwater on possible mergers of equals. See JX 199; see also JX 163; JX 190. The
    BAML presentation materials did not discuss a sale of the Company or mention Sibanye,
    and McMullen and Bateman did not use the meeting to identify other possible acquirers.
    Instead, the BAML bankers got “the sense . . . that a sale was a possibility,” and so they
    decided on their own to “pivot[] to focus more, as time went on, on that.” Hunt Dep. 35.
    Acting on their own, the BAML bankers developed a list of fifteen possible
    acquirers whom they approached independently, pitching a potential acquisition of
    Stillwater as “a banker idea.” JX 206 at ‘360. The record does not reveal exactly how many
    companies BAML contacted, what the BAML bankers said, or how seriously the
    companies took the pitch. Because BAML did not know that Stillwater was in discussions
    16
    with Sibanye, they reached out to Sibanye as part of these efforts, ironically describing that
    a deal for Stillwater would be “[a] little pricey.” JX 207 at ‘093. In the end, five companies
    expressed interest: Sibanye; Hecla; Coeur Mining, Inc.; CITIC Resources Holdings
    Limited, and Anemka Resources Ltd. See JX 211; JX 213; JX 214; JX 217 at ‘588 to ‘591.
    Having made these calls on their own, the BAML bankers held a follow-up meeting
    with McMullen and Bateman on September 7, 2016. The pitch book identified the parties
    contacted and expressing interest. It then described three types of sale processes Stillwater
    could pursue: a “proprietary process” with a single bidder, a targeted auction involving a
    limited number of likely buyers, or a broad auction involving outreach to many potentially
    interested parties. JX 217 at ‘603. BAML recommended against the proprietary process
    because the absence of competition would minimize Stillwater’s negotiating leverage.
    BAML also recommended against a broad auction, given the existence of a “narrow list of
    most likely buyers.” 
    Id. This left
    a targeted auction as the recommended route.
    The pitch book described an illustrative timeline for a sale process. BAML
    recommended allocating the rest of September 2016 to contact potential buyers. During
    October and early November, the Company would enter into confidentiality agreements,
    respond to diligence requests, and then receive and evaluate initial indications of interest.
    From mid-November through early January 2017, the Company would host site visits,
    provide additional diligence, and then solicit and receive final bids. JX 217 at ‘605.
    Nothing formal came out of the September 7 meeting. McMullen and Bateman did
    not instruct BAML to proceed, nor did they take BAML’s recommendation to the Board.
    17
    Instead, McMullen and Bateman asked BAML and Vujcic, the investment banker
    who had been with Jefferies and was now working on his own, to arrange meetings with
    potential suitors at an industry conference during the week of September 20, 2016. BAML
    arranged a meeting with Coeur, and McMullen arranged a meeting with Hecla. See JX 220
    at ‘609; JX 222; JX 224; PTO ¶ 190–91. Vujcic set up meetings with Kinross Gold
    Corporation and Gold Fields Limited, neither of whom had expressed interest. During each
    meeting, McMullen conducted what he called a “soft sound” regarding potential interest in
    buying the Company. PTO ¶ 192; see 
    id. ¶¶ 193–97.
    On the last night of the conference, McMullen had dinner with Froneman.
    McMullen told him that he “remain[ed] committed” to a deal with Sibanye and that
    “no one else is in the data room,” but cautioned that he was “being flooded by investment
    banks” pitching ideas for deals with gold-mining companies. JX 231 at ‘711.
    After the conference, BAML sent McMullen “a fairly detailed timeline” for a more
    compressed sale process. JX 225 at ‘629. The new timeline contemplated the process
    starting during the last week of September and ending during the first week of December.
    See 
    id. at ‘632.
    BAML anticipated site visits taking place during November as part of the
    due diligence phase, but McMullen told BAML that the site visits needed to take place
    earlier in the process before parties sent their initial indications of interest: “Unless people
    get to site, they can’t appreciate the scale of it and will not be putting their best foot forward
    in the indicative, non binding offers.” JX 229 at ‘603. BAML revised the timeline, noting
    that they were “putting [it] together in a vacuum of info on what’s taken place.” 
    Id. At this
    18
    point, BAML had not been retained and did not yet know about Sibanye’s bid. They only
    knew about their own, independent efforts to solicit interest.
    H.     The Board Decides Not To Form A Special Committee.
    In anticipation of a board meeting on October 3, 2016, Wadman circulated a “list of
    potential buyers” to the directors. JX 234. The list identified eighteen companies and the
    status of Stillwater’s discussions with each. According to the list, Sibanye had completed
    its first phase of diligence and was working with Citigroup to secure financing. Hecla and
    Coeur had expressed interest, entered into non-disclosure agreements (“NDAs”), and
    scheduled site visits. Northern Star was listed as “interested but very foucssed [sic] on a
    gold deal.” 
    Id. at ‘630.
    Six other companies were described as “[p]otentially interested” or
    as having “some interest,” including Anglo American Platinum Limited (“Amplats”). 
    Id. Six candidates
    were described as “[u]nlikely” and two as “not interested.” 
    Id. The list
    omitted CITIC and Anemka, even though both had expressed interest when BAML called
    with its “banker’s idea.”
    The list identified a representative who was responsible for interacting with each
    company. Evidencing the uncoordinated, unstructured nature of the Company’s process,
    the list identified a hodgepodge of names. Vujcic was the contact for eight companies.
    BAML was the contact for four companies. Jefferies was the contact for another three.
    Macquarie was the contact for one company. An executive at New Chris, the company
    where McMullen served as Non-Executive Chairman and President, was listed as the
    contact for another company. No one had been formally engaged. Two companies had no
    contact listed.
    19
    During the meeting, McMullen reported on the Company’s outreach to the various
    parties. After his presentation, the directors instructed McMullen to obtain formal
    proposals from investment banks for a sell-side engagement. The Board also instructed
    McMullen to create a cash flow model that could be used to value the Company. See JX
    246 at ‘308 to ‘309.
    Ever since the July 2016 meeting, Wadman had been concerned that McMullen was
    running a sale process to facilitate his exit from the Company. After McMullen rebuffed
    him, Wadman had shared his concerns privately with Schweitzer and Merrin. See Wadman
    Tr. 664–65; Schweitzer Tr. 157–58, 194. Neither took action.
    During the October meeting, Wadman presented his concerns to the full Board and
    recommended the formation of a special committee to oversee the sale process. Lucy Stark
    of Holland & Hart LLP, the Company’s longstanding outside counsel, disagreed and
    advised the Board that she did not believe any conflict existed that warranted the creation
    of a special committee. JX 246 at ‘309; see Schweitzer Tr. 159.
    The directors other than McMullen then met in executive session. Schweitzer
    reported to Wadman that the Board had decided to form a special committee, and Wadman
    drafted a set of minutes memorializing the decision. See JX 238 at ‘245; Wadman Dep.
    134–35; see also Schweitzer Tr. 205–06. But in the meantime, McMullen learned of the
    decision from two other directors. McMullen Tr. 745–47. The final minutes described the
    outcome of the executive session as follows:
    -      No decision was made to pursue or not pursue a potential strategic
    transaction at this time. The Board further discussed the potential for a
    committee and agreed that, should the need arise, the committee would
    20
    consist of the entire Board with the exception of the CEO. It also discussed
    timing and the potential engagement of an investment banking firm to assist
    in the assessment process.
    JX 246 at ‘310.
    I.    McMullen Continues To Focus on Sibyane.
    On October 15, 2016, almost two weeks after the Board directed McMullen to solicit
    terms from investment bankers, McMullen finally drafted and sent out an email asking
    bankers to respond “by no later than COB Wednesday Oct 19 2016.” JX 279 at ‘867. Other
    than Macquarie, the record does not reflect what bankers received the email or whom
    McMullen solicited, but Macquarie, BMO, BAML, and Jefferies submitted proposals.
    On October 17, 2016, Froneman told McMullen that Sibanye’s offer of a “30%
    premium to VWAP remained unchanged” and that Sibanye’s board of directors
    unanimously supported the transaction. JX 281 at ‘425. McMullen responded that he
    remained fully supportive of the deal. He also shared that Stillwater did not yet have a
    banker, telling Froneman that he had started reaching out to investment banks on a no-
    names basis. Demonstrating his commitment to the deal, McMullen told Froneman that he
    would be happy to have Stillwater’s legal advisors start putting together an initial sales
    agreement. 
    Id. The Board
    met again on October 26 and 27, 2016. After reviewing the proposals
    from the investment banks, the Board narrowed the list to BMO and BAML. JX 295 at
    ‘790. Vujcic, whom McMullen regarded as his “in house banker,” summarized the state of
    the Company’s outreach. JX 293 at ‘521. Compare JX 262 at ‘485, with JX 234 at ‘630.
    He reported that third parties exhibited a general “[l]ack of knowledge around the
    21
    significant improvement in operations and general performance,” and he reported that a
    number of parties were either focused on other deals, not considering M&A because of
    prior bad acquisitions, or not considering PGM companies because of negative associations
    with risky jurisdictions like South Africa and Russia. JX 293 at ‘522. For the first time, the
    Board authorized management “to engage in discussions with strategic buyers, financial
    buyers or any other party interested in consummating a potential strategic transaction with
    the [Company].” JX 296 at ‘791.
    After the meeting, McMullen scheduled a second site visit for Sibanye and
    discussed the “timelines to and post announcement” with Froneman. JX 315 at ‘291 to
    ‘292; see PTO ¶ 214. Sibanye convinced McMullen that they needed to announce the deal
    by mid-December 2016. See JX 281 at ‘425; JX 282 at ‘776; see also PTO ¶ 241.
    J.     BAML Begins An Abbreviated Pre-Signing Market Check.
    On November 7, 2016, the Board formally retained BAML. PTO ¶¶ 216–17; see JX
    323 at ‘371. The Board also decided to hire “additional legal counsel with substantial
    experience in advising Delaware publicly traded companies in respect of potential strategic
    transactions.” JX 323 at ‘372. Four days later, the Board retained Jones Day. PTO ¶ 232.
    On November 8, 2016, Bateman sent BAML a package of information that included
    Sibanye’s indication of interest from July, the non-disclosure agreements with Hecla and
    Coeur, a cash flow model, and instructions for accessing the data room. See JX 325; JX
    326; JX 327; JX 328; JX 329. The next day, BAML sent management a slide deck titled
    “M&A Process Considerations.” JX 331 at ‘277.
    22
    BAML understood from management that Sibanye wanted to sign up a deal in
    December 2016, so BAML proposed to complete its outreach to a list of parties in just two
    days. That timeframe was drastically shorter than the four weeks that BAML had
    recommended in September 2016. Anyone who expressed interest would have three weeks
    to conduct diligence and submit an indication of interest, just half of the six weeks that
    BAML had recommended in September. At that point, the Board would decide whether to
    proceed with Sibanye or engage with the other bidders. PTO ¶ 226; see JX 331 at ‘280.
    Even though McMullen had previously told BAML that it was critical for potential bidders
    to visit the Company’s mines before making an initial indication of interest, BAML’s
    compressed timeline did not contemplate that step.
    BAML’s presentation identified twenty-eight third parties divided into four
    categories:
     “Interested Parties”—Sibanye, Coeur, and Hecla.
     “Possibly Interested Parties”—Gold Fields, Independence Group NL,
    Kinross, MMG Limited, Rio Tinto, and South32 Limited.
       “Additional Parties To Contact”—Alamos Gold Inc., Anemka, CITIC,
    Fresnillo plc, Goldcorp Inc., IAMGOLD Corporation, Impala Platinum
    Holdings Limited, New Gold Inc., Northam Platinum Limited, Pan American
    Silver Corporation, X2 Resources, and Yamana Gold Inc.
     “Not Interested”—Northern Star, Amplats, Eldorado Gold Corporation,
    Evolution Mining Limited, Newcrest Mining Limited, Newmont Mining
    Corporation, and OZ Minerals.
    JX 331 at ‘279. Anemka and CITIC were listed as “Additional Parties to Contact,” even
    though they had expressed interest during BAML’s earlier independent outreach.
    23
    OceanaGold Corporation and Boliden AB, whom Vujcic had included in his review of the
    Company’s outreach, were omitted from BAML’s list.
    BAML’s presentation included scripts for its bankers to use when making their calls.
    For “Possibly Interested Parties,” the script stated:
     Announce participants and remind parties of confidentiality;
     BofA Merrill Lynch has been retained by Stillwater Mining Company
    to explore strategic alternatives;
     We understand you have had some discussions previously with our
    client;
     We would like to further clarify your potential interest in Stillwater as
    the process moves forward;
     Do you have any interest to learn more?
     If so, we would suggest you sign an NDA for access to diligence on
    the company.
    PTO ¶ 225 (formatting added); JX 331 at ‘281. For the “Additional Parties To Contact,”
    the script omitted Stillwater’s name and asked generally about interest in the PGM sector.
     Announce participants and remind parties of confidentiality;
     We are calling to gauge your potential interest in a situation in the
    PGM sector;
     Our client is a leading player and low cost producer of PGMs and
    substantial organic production growth;
     Do you have any interest to learn more?
     If yes, disclose that our client is Stillwater and suggest they sign an
    NDA for access to diligence.
    24
    PTO ¶ 224 (formatting added); JX 331 at ‘281. For Hecla and Coeur, BAML planned to
    skip the call and send instructions for submitting an indication of interest by November 23.
    PTO ¶ 231; JX 336; JX 337.
    Because of the expedited timeline, BAML decided not to contact companies in the
    “Not Interested” category, even though many of those companies had said they were not
    interested when BAML previously called them with “a banker idea.” The response could
    have been different with a formal mandate. BAML’s script for “Additional Parties to
    Contact” was not likely to generate interest because it did not say anything more than “a
    situation in the PGM sector.” Because almost every other PGM company was located in a
    politically unstable jurisdiction, additional parties were less likely to have interest without
    a signal that the company involved was Stillwater. And because Stillwater had been
    advertising its interest in acquisitions, there was no reason for the additional parties to think
    that the situation involved Stillwater. See JX 124 at ‘074.
    Using its scripts, BAML contacted five of the six possibly interested parties, missing
    Gold Fields. See JX 351. BAML contacted eight of the twelve additional parties, missing
    Alamos, Goldcorp, New Gold, and Yamana Gold. See PTO ¶ 230; JX 338; JX 339; JX
    340; JX 341; JX 342. BAML contacted Northern Star, even though they were listed as not
    interested. See JX 351 at ‘953.
    Three of the companies expressed interest: Anemka, Northern Star, and X2. BAML
    sent a confidentiality agreement and an invitation to submit a bid by November 29 to
    Anemka and Northern Star. BAML sent only a confidentiality agreement to X2, which
    quickly retracted its interest. See JX 395 at ‘412; see also JX 359 at ‘413.
    25
    Sibanye learned about BAML’s market check from Bateman. JX 332 at ‘969.
    Sibanye perceived that a compressed timeline was its “only real advantage” in the process.
    
    Id. K. The
    Abbreviated Pre-Signing Market Check Continues.
    On November 17, 2016, the Board met again, with Jones Day attending for the first
    time. BAML and McMullen updated the Board on the outreach and “the Board directed
    management to continue the strategic assessment process.”8 Sibanye had already sent a
    draft merger agreement to Jones Day.
    On November 18, 2016, BAML suggested contacting Norilsk Nickel, a Russian
    mining company that had owned a majority stake in the Company between 2003 and 2010.
    JX 367. McMullen decided against it. See McMullen Dep. 476.
    On November 20, 2016, the CFO of Northern Star informed McMullen that they
    were not interested in buying Stillwater but remained interested in a merger of equals.
    Northern Star asked McMullen to send a proposal. PTO ¶ 242.
    On November 22, 2016, the CEO of Independence informed McMullen that they
    were not interested in buying Stillwater but were interested in a merger of equals. PTO ¶
    246. Independence asked to sign a confidentiality agreement and perform diligence,
    8
    JX 364 at ‘374. At trial, Schweitzer testified that this was the meeting at which the
    Board finally decided it did not need a special committee. See Schweitzer Tr. 157–58, 194.
    The minutes omit any discussion of the matter.
    26
    explaining that they had trouble reaching BAML. Independence did not receive a
    confidentiality agreement until November 25. See JX 403; JX 405.
    The Board met again on the afternoon of November 23, 2016. McMullen reported
    that he had told Sibanye that its July proposal of $15.75 per share was not sufficient. He
    also reported that Sibanye needed the transaction to be “announced by the second week in
    December”; otherwise, Sibanye would need to delay the deal until the following year so
    that it could obtain stockholder approval to raise the capital needed to fund the Merger. JX
    395 at ‘411. McMullen viewed a December signing as “ambitious given that . . . the
    Company’s assessment process with other potential parties was ongoing and would need
    to be concluded prior to proceeding with a transaction with Sibanye.” 
    Id. By the
    time of the board meeting, twenty-four parties had received some type of
    formal or informal contact from BAML or Stillwater management. Four parties—Sibanye,
    Hela, Coeur, and Anemka—had signed NDAs and accessed the data room. Four parties—
    Sibanye, Hela, Coeur, and Northern Star—had conducted site visits. Two parties—Coeur
    and Anemka—had notified BAML that they would not proceed further. PTO ¶ 235; JX
    393 at ‘868. Two other parties—Northern Star and Independence—had informed Stillwater
    that they were only interested in a merger of equals. Hecla had reported that it needed to
    find a partner and had asked Stillwater to extend its bid deadline from November 23 to
    November 30. PTO ¶ 247; JX 383. The Board extended Hecla’s deadline to November 28.
    JX 395 at ‘413. By comparison, the Board had given Sibanye until November 30 to update
    its expression of interest from July. See JX 359 at ‘414.
    27
    After receiving these updates, the Board met in executive session, and the minutes
    reflected for the first time that McMullen did not participate. See JX 395 at ‘413. The Board
    instructed BAML to evaluate a merger of equals as a potential alternative. 
    Id. When McMullen
    learned of the decision, he was skeptical, believing that a merger of equals could
    not compete with “a circa $18/share []all cash offer from S[ibanye].” JX 406 at ‘376. He
    shared his negative opinion with one of the directors, who replied that a merger of equals
    was actionable and needed to be explored as an alternative to Sibanye. See JX 401.
    McMullen and BAML worked together to update the presentation that McMullen
    had given the Board in January 2016 on a potential merger of equals. See JX 384; JX 396.
    McMullen ranked the Company’s options as follows: 1) Sibanye’s acquisition; 2) a merger
    of equals with Northern Star; and 3) do nothing or a merger of equals with Independence.
    JX 396 at ‘707.
    After the board meeting on November 23, 2016, BAML followed up with Hecla to
    solicit a specific indication of interest. See JX 394 at ‘214. Hecla did not respond, and the
    Company treated Hecla as having dropped out of the process.
    On November 29, 2016, Northam asked to be included in the process. JX 414.
    BAML sent Northam a confidentiality agreement and invited them to submit a bid by
    December 7. PTO ¶ 258; see JX 423; JX 424. That same day, Independence asked for an
    extension to the bid deadline since they were still negotiating the confidentiality agreement.
    JX 411. McMullen decided that meant that Independence was not interested.
    28
    L.     Sibanye Revises Its Price.
    As of November 20, 2016, Sibanye anticipated borrowing $2.5 billion to complete
    the Merger. Of this amount, $1.98 billion would be used to pay for the Company’s stock,
    with the consideration priced at a 30% premium over the Company’s thirty-day VWAP,
    just as McMullen and Froneman had agreed in March. See JX 378 at ‘979, ‘009, ‘016, ‘017.
    The additional $500 million would be used to pay off the Company’s debt, fund change-
    of-control payments for management, and pay transaction fees.
    But on November 30, 2016, Sibanye ran into problems. First, Sibanye realized that
    the Company’s stock price had increased to a point where the pricing metric would cause
    the total purchase price to exceed Sibanye’s financing. Using the 30% premium over the
    thirty-day VWAP, Sibanye would have to pay approximately $18.25 per share, an amount
    that would require Sibanye to supplement the transaction financing with cash on hand or
    from its revolving credit line. See JX 420 at ‘876.
    Second, Sibanye realized that it had calculated the purchase price in its indication
    of interest using a twenty-day VWAP rather than a thirty-day VWAP. 
    Id. at ‘874.
    The
    Sibanye team recognized that they had agreed in principle to a thirty-day VWAP, but when
    they sent their initial indication of interest, they used a twenty-day VWAP because the
    Company’s stock had been in a declining trend, so the shorter period resulted in a lower
    price. 
    Id. at ‘873.
    Citigroup recommended pretending that Sibanye had never agreed to a pricing
    mechanism and had instead offered a fixed price. 
    Id. The Sibanye
    team went along and
    disavowed all of the communications in which they had agreed in principle to a 30%
    29
    premium over the thirty-day VWAP. See Stewart Dep. 147–48; PTO ¶¶ 243, 245; JX 397
    at ‘448; JX 378 at ‘009, ‘016. Going forward, Sibanye would discuss price based on an
    indication of interest of $15.75 per share.
    M.     Stillwater Negotiates With Sibanye.
    On December 1, 2016, the deal teams from the Company and Sibanye met in New
    York City. Sibanye proposed to acquire the Company for between $17.50 and $17.75 per
    share in cash. PTO ¶ 261.
    On December 2, 2016, the Board met in New York City. See JX 432; JX 430.
    McMullen shared Sibanye’s revised offer. The minutes do not reflect any discussion of
    Sibanye’s departure from the prior agreement in principle on a 30% premium over the
    thirty-day VWAP or the fact that the agreed-upon pricing metric would have supported a
    price around $18.25 per share. Even though BAML had worried about Sibanye using
    precisely this tactic, and even though McMullen had assured BAML that Sibanye would
    stick to the agreed-upon pricing metric, see JX 343 at ‘740 to ‘741, no one appears to have
    mentioned the change to the Board. See JX 432 at ‘414.
    During the meeting, BAML presented its preliminary financial analysis of the
    Company. Using a discounted cash flow analysis, BAML valued the Company at between
    $10.78 and $14.14 per share. 
    Id. at ‘416.
    That same day, the Company’s stock closed at
    $15.17 per share. PTO Ex. A.
    BAML also reviewed potential merger of equals transactions with Northern Star
    and Independence. JX 432 at ‘417. According to the minutes, the Board decided not to
    pursue either transaction because: (i) the lack of synergies; (ii) “the significant disparity in
    30
    trading multiples”; (iii) “no merger-of-equals or similar transaction appeared to be
    available to the Company at this time”; (iv) “neither Northern Star nor Independence
    Mining had signed a confidentiality agreement”; and (v) “a substantial delay in the process
    to pursue such a possible transaction could result in the loss of a potential transaction with
    Sibanye.” JX 432 at ‘417; see McMullen Tr. 769. At the time, Northern Star and
    Independence had both proposed a merger-of-equals transaction and both had signed
    confidentiality agreements. There was also a meaningful probability that the Sibanye
    transaction would slip into the following year.
    During the meeting, the Board instructed management to seek a higher price from
    Sibanye. That evening, McMullen and Bateman had dinner with Richard Stewart,
    Sibanye’s Executive Vice President of Business Development. PTO ¶ 265. After the
    dinner, Stewart emailed Froneman that “Mick’s number is 18$+ and that he thinks he can
    get his board across the line on that.” JX 434 at ‘426. Froneman, Stewart, and Citigroup
    discussed the limits of Sibanye’s financing, which would support a bid up to $18.20 per
    share. A 30% premium on the twenty-day VWAP for the Company’s common stock was
    $19.20 per share. 
    Id. The group
    decided to bid $18.00 per share, observing that “if this is
    truly not good enough – they will come back but we need to be firm.” JX 434 at ‘425.
    On December 3, 2016, Stewart called McMullen and offered $18 per share. PTO ¶
    267. BAML had been expecting $19 per share. See JX 438.
    On the evening of December 3, 2016, Bateman had “a very open discussion” with
    one of Sibanye’s bankers from Citigroup, sharing information about the Board’s internal
    31
    dynamics, the Company’s lack of other prospects, and his preferences for employment. See
    JX 444. The Citigroup banker reported on the conversation as follows:
    -      1. Value. Didn’t push back, as knows we’re at our limits. Said Mick
    will recommend our proposal to the Board, [that two directors] are “very
    commercial”. [Schweitzer] is the one most focused on 30% premium to 20D
    VWAP. I reiterated that we’ve truly been talking about 30D VWAP
    internally and with [Stillwater], which he seems to understand.
    -      ...
    -      3. MOE. He seemed quite dismissive of the MOE candidate, but said
    certain Board members are keen to not shut it down completely (I suspect
    more from a litigation perspective).
    -      4. Chris’ Plans. Said he honestly hasn’t given a lot of thought to
    what’s next, and he’s generally open minded about it. . . . He could be open
    to staying with [Sibanye], but depends on the vision and the role. He would
    have no desire to be a divisional CFO, but potentially interested in an
    Americas Head position. . . .
    
    Id. Bateman participated
    in this discussion one day after Jones Day had advised the Board
    and senior management about the risk of conflicts during the negotiations. In response,
    Bateman and other members of management had represented to the Board that they had
    not had any discussions with Sibanye about their roles. See JX 432 at ‘418.
    On December 4, 2016, Stewart called McMullen and told him that $18.00 was
    Sibanye’s best and final offer. PTO ¶ 270. After Bateman’s dinner with the Citigroup
    banker, Sibanye knew it did not have to bid higher.
    Later that afternoon, McMullen shared the offer with the Board. Fearing that the
    timeline might slip into 2017, the directors instructed management “to progress discussions
    with Sibanye” and to find out whether Northam remained interested. JX 440 at ‘742.
    32
    On December 5, 2016, BAML reported that it had not heard anything from
    Northam. JX 445. That same day, Froneman called McMullen to reiterate that $18.00 per
    share was the best Sibanye could do given their financing constraints. PTO ¶ 272.
    N.    McMullen Demands His Stock Awards.
    On December 7, 2016, McMullen asked Sibanye to “put something into the merger
    agreement” about his 2017 stock awards. JX 451. According to McMullen, Sibanye had
    previously agreed to the following terms:
    -      On Closing of the deal, the value of the awards would be converted to
    cash based on the metrics of the deal (share price etc) and the amount paid
    out as per the normal vesting schedule in cash, namely 1/3 of the RSU value
    at each of the end of 2017, 2018 and 2019, and all the PSU value is paid out
    at the end of 2019. If any employee leaves for Good Cause (fired or
    diminution of job role) then the RSU’s accelerate in accordance with our plan
    docs, but the PSU amount is still paid out at the end of 2019.
    
    Id. McMullen told
    Sibanye that the Compensation Committee had “decided that the 2015
    and 2016 PSU’s would vest at 150% for each series in the event of an $18 bid.” 
    Id. O. The
    Board Approves The Merger.
    On December 8, 2016, the Board met to consider the Merger Agreement and decide
    whether to proceed with the Merger. McMullen reported that Northam had withdrawn from
    the process. JX 454 at ‘744; see JX 459. By this point, BAML had interacted with fourteen
    parties since being formally retained. Five had signed NDAs and conducted diligence. Only
    Sibanye had made a bid.
    BAML rendered its opinion that Sibanye’s offer of $18 per share was fair. The
    consideration of $18 per share represented a 21% premium to the Company’s then-current
    stock price, a 21% premium to the 20-day VWAP, and a 25% premium to the 30-day
    33
    VWAP. JX 453 at ‘260. In its presentation, BAML valued the Company between $10.58
    per share and $13.98 per share using a discounted cash flow analysis. 
    Id. at ‘279
    to ‘281.
    The Merger Agreement contained a no-shop clause with a fiduciary out that
    permitted the Company to provide information to and negotiate with a third-party bidder if
    the bidder made an “Acquisition Proposal” that constituted or was reasonably likely to lead
    to a “Superior Proposal” and the Board concluded that its fiduciary duties required it. See
    JX 525 Annex A § 6.2.4. The Board had the right to change its recommendation in favor
    of the Merger if a competing bidder made a superior proposal and the Board concluded
    that its fiduciary duties required it. The Board did not have the right to terminate the Merger
    Agreement to pursue the superior proposal. The Company had to proceed through the
    stockholder meeting and only gained the right to terminate if the stockholders voted down
    the deal.
    If the Company exercised its right to terminate after a negative stockholder vote,
    then the Company was obligated to pay Sibanye a termination fee of $16.5 million plus
    reimbursement of Sibanye’s expenses up to $10 million, for a total payment of $26.5
    million. The total payment represented approximately 1.2% of equity value, with the
    termination-fee portion reflecting 0.76% of equity value. The Company had approximately
    $110 million more cash than debt, resulting in a slightly smaller enterprise value than
    equity value. The total payment represented approximately 1.3% of enterprise value.
    The Board adopted the Merger Agreement and resolved to recommend that the
    Company’s stockholders approve it. JX 454 at ‘746. On December 9, 2016, Sibanye and
    34
    the Company announced the Merger. Sibanye’s stock price dropped 18% from $8.20 per
    share to $6.96 per share.
    The last day of unaffected trading in Stillwater’s common stock was December 8,
    2016. On that date, the Company’s shares closed at $14.68, equating to a market
    capitalization of approximately $1.8 billion. The deal price represented a 22.6% premium
    over the unaffected trading price and a 24.4% premium over the 30-day VWAP. During
    the previous two years, Stillwater’s stock price had never traded above $15.58, a level it
    reached on August 1, 2016.
    P.     Vujcic Gets Paid.
    After the Merger was signed, McMullen sent Vujcic a retroactive consulting
    agreement to compensate him for assisting with the Merger. Vujcic had two comments.
    First, he wanted confirmation that he would “not be named in the proxy.” JX 474 at ‘101.
    Second, he was disappointed with his compensation, stating:
    -      I’m a little perplexed as to why you are being so aggressive on the
    comp, especially when you are exposed to a potentially large claim from
    Jefferies and when I feel I have been pretty fair all along in (a) not locking
    you in earlier (trusted your guidance on compensation in July) and (b) in
    making every effort leading up to the board meetings in late October to give
    you the comfort to reiterate that Sibanye were the only show in town.
    
    Id. at ‘100.
    The petitioners argue that Vujcic’s statement that he made “every effort . . . to give
    you comfort to reiterate that Sibanye were the only show in town” shows that McMullen
    and Vujcic had been trying to eliminate the competition for Sibanye. That is a
    conspiratorial reading, rather than a credible reading. Vujcic was attempting to justify
    35
    receiving greater compensation by pointing to his efforts to solicit other potential bidders.
    He showed that Sibanye was “the only show in town” by engaging in outreach and
    demonstrating that no one else wanted to bid. The record does not support an inference that
    McMullen and Vujcic deceived the Board. See also McMullen Dep. 442–46.
    McMullen and Vujcic agreed on a fixed fee of $20,000 per month beginning on
    October 24, 2016, plus a discretionary bonus of $100,000. JX 477. Vujcic’s name and
    compensation arrangement did not appear in the proxy statement. See JX 525.
    Q.     Wadman’s Noisy Withdrawal
    In February 2017, McMullen and Bateman negotiated the terms of their post-closing
    employment with Sibanye. As part of those discussions, Sibanye agreed to treat the Merger
    as triggering McMullen and Bateman’s change-of-control payments, without the need for
    a second trigger such as termination or a resignation for “Good Reason.” None of the
    Company’s other employees received this special treatment. For the other employees, the
    Merger was only the first trigger, and no change-in-control benefits would be paid absent
    a second trigger.
    When McMullen reported on this agreement to the Board during a meeting on
    February 23, 2017, Wadman objected. He had been concerned since July 2016 that
    McMullen and Bateman had pursued a sale of the Company in their own interest and had
    used the deal to advantage themselves. He regarded their special deal on change-in-control
    benefits as “clearly self-dealing.” JX 526 at ‘376. The Board did not address Wadman’s
    concerns during the meeting.
    36
    One month later, Wadman resigned. In his resignation letter, Wadman restated his
    concerns about how the deal process unfolded. He noted that after the board meeting on
    February 23, 2017, McMullen and Bateman “removed [me] from all legal conversations
    and decision-making” and “prohibited me from doing my job.” 
    Id. at ‘377
    to ‘378. Quoting
    his employment agreement, Wadman resigned for “Good Reason” based on a “material
    diminution” to his “nature of responsibilities, or authority.” 
    Id. Over the
    next several days, the Company’s counsel negotiated a settlement with
    Wadman. On March 30, 2017, the Company released a Form 8-K, which stated:
    On March 29, 2017, Brent R. Wadman, our Vice President, Legal Affairs &
    Corporate Secretary, terminated employment. In connection therewith, we
    entered into an agreement with Mr. Wadman with respect to his separation
    pursuant to which we will pay him up to approximately $1.49 million. This
    amount includes the settlement of Mr. Wadman’s outstanding equity awards,
    which will continue to vest in accordance with their terms, including in
    connection with the previously announced merger with Sibanye Gold
    Limited.
    JX 527. The Form 8-K did not mention Wadman’s letter or the reasons for his resignation.
    R.     Stockholder Approval And Closing
    During Stillwater’s annual meeting on April 26, 2017, the stockholders approved
    the Merger Agreement. Under Delaware law, a merger requires the approval of holders of
    a majority of the outstanding shares, making a non-vote the equivalent of a “no” vote.
    Because stockholders can vote no by not voting, the percentage of the outstanding shares
    is the appropriate metric for evaluating the level of stockholder support for a merger. The
    Company had 121,389,213 shares outstanding. Holders of 91,012,990 shares voted in favor
    of the Merger, representing 75% of the issued and outstanding equity. Holders of
    37
    103,088,167 shares were present at the meeting in person or by proxy, so the same number
    of affirmative votes results in a misleadingly higher approval percentage of 88%. See JX
    549 at 1.
    The Merger closed on May 4, 2017. Between signing and closing, the spot price of
    palladium increased by 9.2%. The spot price of a weighted basket of Stillwater’s products
    increased by 5.9%.
    S.     Post-Closing Developments
    On July 1, 2017, Sibanye entered into employment agreements with Bateman and
    McMullen. Bateman agreed to serve as Executive Vice President—US Region, reporting
    directly to Froneman. Bateman waived his change-of-control benefits in return for a higher
    base salary and additional incentive compensation. See JX 585.
    McMullen agreed to serve as a Technical Advisor to Sibanye. His employment
    agreement permitted him “to perform the functions of that role while residing in the Turks
    and Caicos.” JX 586 at ‘041. Like Bateman, McMullen waived his change-of-control
    benefits in return for an annual salary of $712,000 plus incentive compensation. See 
    id. In November
    2017, Sibanye issued a Competent Person’s Report that valued the
    Company’s operating mines at $2.7 billion as of July 31, 2017. This valuation was 23%
    greater than the total consideration that Sibanye paid for the Company at closing, just three
    months before the valuation date for the report. PTO ¶ 102; JX 615 at 205.
    38
    T.     This Appraisal Proceeding
    Holders of 5,804,523 shares of the Company eschewed the consideration offered in
    the Merger and pursued appraisal. In August 2018, the holders of 384,000 shares settled
    their claims. The remaining petitioners litigated their claims through trial.
    II.      LEGAL ANALYSIS
    “An appraisal proceeding is a limited legislative remedy intended to provide
    shareholders dissenting from a merger on grounds of inadequacy of the offering price with
    a judicial determination of the intrinsic worth (fair value) of their shareholdings.” Cede &
    Co. v. Technicolor, Inc. (Technicolor I), 
    542 A.2d 1182
    , 1186 (Del. 1988). Section 262(h)
    of the Delaware General Corporation Law states that
    the Court shall determine the fair value of the shares exclusive of any element
    of value arising from the accomplishment or expectation of the merger or
    consolidation, together with interest, if any, to be paid upon the amount
    determined to be the fair value. In determining such fair value, the Court shall
    take into account all relevant factors.
    
    8 Del. C
    . § 262(h). The statute thus places the obligation to determine the fair value of the
    shares squarely on the court. Gonsalves v. Straight Arrow Publ’rs, Inc., 
    701 A.2d 357
    , 361
    (Del. 1997).
    Because of the statutory mandate, the allocation of the burden of proof in an
    appraisal proceeding differs from a traditional liability proceeding. “In a statutory appraisal
    proceeding, both sides have the burden of proving their respective valuation positions . . .
    .” M.G. Bancorp., Inc. v. Le Beau, 
    737 A.2d 513
    , 520 (Del. 1999). “No presumption,
    favorable or unfavorable, attaches to either side’s valuation . . . .” Pinson v. Campbell-
    Taggart, Inc., 
    1989 WL 17438
    , at *6 (Del. Ch. Feb. 28, 1989). “Each party also bears the
    39
    burden of proving the constituent elements of its valuation position . . . , including the
    propriety of a particular method, modification, discount, or premium.” Jesse A. Finkelstein
    & John D. Hendershot, Appraisal Rights in Mergers and Consolidations, Corp. Prac. Series
    (BNA) No. 38-5th, at A-90 (2010 & 2017 Supp.) [hereinafter Appraisal Rights].
    As in other civil cases, the standard of proof in an appraisal proceeding is a
    preponderance of the evidence. M.G. 
    Bancorp., 737 A.2d at 520
    . A party is not required to
    prove its valuation conclusion, the related valuation inputs, or its underlying factual
    contentions by clear and convincing evidence or to exacting certainty. See Triton Constr.
    Co. v. E. Shore Elec. Servs., Inc., 
    2009 WL 1387115
    , at *6 (Del. Ch. May 18, 2009), aff’d,
    
    2010 WL 376924
    (Del. Jan. 14, 2010) (ORDER). “Proof by a preponderance of the
    evidence means proof that something is more likely than not. It means that certain
    evidence, when compared to the evidence opposed to it, has the more convincing force and
    makes you believe that something is more likely true than not.” Agilent Techs., Inc. v.
    Kirkland, 
    2010 WL 610725
    , at *13 (Del. Ch. Feb. 18, 2010) (internal quotation marks
    omitted).
    “In discharging its statutory mandate, the Court of Chancery has discretion to select
    one of the parties’ valuation models as its general framework or to fashion its own.” M.G.
    
    Bancorp., 737 A.2d at 525
    –26. “[I]t is entirely proper for the Court of Chancery to adopt
    any one expert’s model, methodology, and mathematical calculations, in toto, if that
    valuation is supported by credible evidence and withstands a critical judicial analysis on
    the record.” 
    Id. at 526.
    Or the court “may evaluate the valuation opinions submitted by the
    parties, select the most representative analysis, and then make appropriate adjustments to
    40
    the resulting valuation.” Appraisal 
    Rights, supra
    , at A-31 (collecting cases). The court may
    also “make its own independent valuation calculation by . . . adapting or blending the
    factual assumptions of the parties’ experts.” M.G. 
    Bancorp., 737 A.2d at 524
    . “If neither
    party satisfies its burden, however, the court must then use its own independent judgment
    to determine fair value.” Gholl v. eMachines, Inc., 
    2004 WL 2847865
    , at *5 (Del. Ch. Nov.
    24, 2004). But the court must also be cautious when adopting an approach that deviates
    from the parties’ positions. Doing so “late in the proceedings” may “inject[] due process
    and fairness problems” that are “antithetical to the traditional hallmarks of a Court of
    Chancery appraisal proceeding,” because the court’s approach will not have been
    “subjected to the crucible of pretrial discovery, expert depositions, cross-expert rebuttal,
    expert testimony at trial, and cross examination at trial.” Verition P’rs Master Fund Ltd. v.
    Aruba Networks, Inc., 
    210 A.3d 128
    , 140-41 (Del. 2019).
    In Tri-Continental Corporation v. Battye, 
    74 A.2d 71
    (Del. 1950), the Delaware
    Supreme Court explained in detail the concept of value that the appraisal statute employs:
    The basic concept of value under the appraisal statute is that the stockholder
    is entitled to be paid for that which has been taken from him, viz., his
    proportionate interest in a going concern. By value of the stockholder’s
    proportionate interest in the corporate enterprise is meant the true or intrinsic
    value of his stock which has been taken by the merger. In determining what
    figure represents the true or intrinsic value, . . . the courts must take into
    consideration all factors and elements which reasonably might enter into the
    fixing of value. Thus, market value, asset value, dividends, earning
    prospects, the nature of the enterprise and any other facts which were known
    or which could be ascertained as of the date of the merger and which throw
    any light on future prospects of the merged corporation are not only pertinent
    41
    to an inquiry as to the value of the dissenting stockholder’s interest, but must
    be considered . . . .9
    Subsequent Delaware Supreme Court decisions have adhered consistently to this definition
    of value.10 Most recently, the Delaware Supreme Court reiterated that “[f]air value is . . .
    the value of the company to the stockholder as a going concern,” i.e., the stockholder’s
    “proportionate interest in a going concern.” 
    Aruba, 210 A.3d at 132
    –33.
    The trial court’s “ultimate goal in an appraisal proceeding is to determine the ‘fair
    or intrinsic value’ of each share on the closing date of the merger.” Dell, Inc. v. Magnetar
    Global Event Driven Master Fund Ltd., 
    177 A.3d 1
    , 20 (Del. 2017) (quoting Cavalier 
    Oil, 564 A.2d at 1142
    –43). To accomplish this task, “the court should first envisage the entire
    pre-merger company as a ‘going concern,’ as a standalone entity, and assess its value as
    such.” 
    Id. (quoting Cavalier
    Oil, 564 A.2d at 1144
    ). When doing so, the corporation “must
    9
    
    Id. at 72.
    Although Battye is the seminal Delaware Supreme Court case on point,
    Chancellor Josiah Wolcott initially established the meaning of “value” under the appraisal
    statute in Chicago Corporation v. Munds, 
    172 A. 452
    (Del. Ch. 1934). Citing the “material
    variance” between the Delaware appraisal statute, which used “value,” and the comparable
    New Jersey statute that served as a model for the Delaware statute, which used “full market
    value,” Chancellor Wolcott held that the plain language of the statute required “value” to
    be determined on a “going concern” basis. 
    Id. at 453–55.
    But see Union Ill. 1995 Inv. Ltd.
    P’ship v. Union Fin. Gp., Ltd., 
    847 A.2d 340
    , 355–56 (Del. Ch. 2004) (“This requirement
    that the valuation inquiry focus on valuing the entity as a going concern has sometimes
    been confused as a requirement of § 262’s literal terms. It is not.”).
    10
    See, e.g., Montgomery Cellular Hldg. Co. v. Dobler, 
    880 A.2d 206
    , 222 (Del.
    2005); Paskill Corp. v. Alcoma Corp., 
    747 A.2d 549
    , 553 (Del. 2000); Rapid-Am. Corp. v.
    Harris, 
    603 A.2d 796
    , 802 (Del. 1992); Cavalier Oil Corp. v. Harnett, 
    564 A.2d 1137
    ,
    1144 (Del. 1989); Bell v. Kirby Lumber Corp., 
    413 A.2d 137
    , 141 (Del. 1980); Universal
    City Studios, Inc. v. Francis I. duPont & Co., 
    334 A.2d 216
    , 218 (Del. 1975).
    42
    be valued as a going concern based upon the ‘operative reality’ of the company as of the
    time of the merger,” taking into account its particular market position in light of future
    prospects. M.G. 
    Bancorp., 737 A.2d at 525
    (quoting Cede & Co. v. Technicolor, Inc.
    (Technicolor IV), 
    684 A.2d 289
    , 298 (Del. 1996)); accord 
    Dell, 177 A.3d at 20
    . The
    concept of the corporation’s “operative reality” is important because “[t]he underlying
    assumption in an appraisal valuation is that the dissenting shareholders would be willing
    to maintain their investment position had the merger not occurred.” Technicolor 
    IV, 684 A.2d at 298
    . Consequently, the trial court must assess “the value of the company . . . as a
    going concern, rather than its value to a third party as an acquisition.” M.P.M. Enters., Inc.
    v. Gilbert, 
    731 A.2d 790
    , 795 (Del. 1999).
    “The time for determining the value of a dissenter’s shares is the point just before
    the merger transaction ‘on the date of the merger.’” Appraisal 
    Rights, supra
    , at A-33
    (quoting Technicolor 
    I, 542 A.2d at 1187
    ). Put differently, the valuation date is the date on
    which the merger closes. Technicolor 
    IV, 684 A.2d at 298
    ; accord M.G. 
    Bancorp., 737 A.2d at 525
    . If the value of the corporation changes between the signing of the merger
    agreement and the closing, then the fair value determination must be measured by the
    “operative reality” of the corporation at the effective time of the merger. See Technicolor
    
    IV, 684 A.2d at 298
    .
    The statutory obligation to make a single determination of a corporation’s value
    introduces an impression of false precision into appraisal jurisprudence.
    [I]t is one of the conceits of our law that we purport to declare something as
    elusive as the fair value of an entity on a given date . . . . [V]aluation decisions
    are impossible to make with anything approaching complete confidence.
    43
    Valuing an entity is a difficult intellectual exercise, especially when business
    and financial experts are able to organize data in support of wildly divergent
    valuations for the same entity. For a judge who is not an expert in corporate
    finance, one can do little more than try to detect gross distortions in the
    experts’ opinions. This effort should, therefore, not be understood, as a
    matter of intellectual honesty, as resulting in the fair value of a corporation
    on a given date. The value of a corporation is not a point on a line, but a range
    of reasonable values, and the judge’s task is to assign one particular value
    within this range as the most reasonable value in light of all the relevant
    evidence and based on considerations of fairness.11
    As the Delaware Supreme Court recently explained, “fair value is just that, ‘fair.’ It does
    not mean the highest possible price that a company might have sold for had Warren Buffet
    negotiated for it on his best day and the Lenape who sold Manhattan on their worst.” DFC
    Glob. Corp. v. Muirfield Value P’rs, 
    172 A.3d 346
    , 370 (Del. 2017).
    Because the determination of fair value follows a litigated proceeding, the issues
    that the court considers and the outcome it reaches depend in large part on the arguments
    advanced and the evidence presented.
    An argument may carry the day in a particular case if counsel advance it
    skillfully and present persuasive evidence to support it. The same argument
    may not prevail in another case if the proponents fail to generate a similarly
    persuasive level of probative evidence or if the opponents respond
    effectively.
    11
    Cede & Co. v. Technicolor, Inc., 
    2003 WL 23700218
    , at *2 (Del. Ch. Dec. 31,
    2003, revised July 9, 2004), aff’d in part, rev’d in part on other grounds, 
    884 A.2d 26
    (Del.
    2005); accord Finkelstein v. Liberty Dig., Inc., 
    2005 WL 1074364
    , at *12 (Del. Ch. Apr.
    25, 2005) (“The judges of this court are unremittingly mindful of the fact that a judicially
    selected determination of fair value is just that, a law-trained judge’s estimate that bears
    little resemblance to a scientific measurement of a physical reality. Cloaking such estimates
    in grand terms like ‘intrinsic value’ does not obscure this hard truth from any informed
    commentator.”).
    44
    Merion Capital L.P. v. Lender Processing Servs., L.P., 
    2016 WL 7324170
    , at *16 (Del.
    Ch. Dec. 16, 2016). Likewise, the approach that an expert espouses may have met “the
    approval of this court on prior occasions,” but may be rejected in a later case if not
    presented persuasively or if “the relevant professional community has mined additional
    data and pondered the reliability of past practice and come, by a healthy weight of reasoned
    opinion, to believe that a different practice should become the norm . . . .” Glob. GT LP v.
    Golden Telecom, Inc. (Golden Telecom Trial), 
    993 A.2d 497
    , 517 (Del. Ch.), aff’d, 
    11 A.3d 214
    (Del. 2010).
    A.     The Deal Price
    Sibanye contends that the deal price of $18.00 per share is a persuasive indicator of
    fair value if adjusted downward to eliminate elements of value arising from the Merger.
    The petitioners argue that the deal price should receive no weight. As the proponent of
    using the deal price, Sibanye bore the burden of establishing its persuasiveness. Sibanye
    also bore the burden of proving its downward adjustment.
    1.     The Standard For Evaluating A Sale Process
    There is no presumption that the deal price reflects fair value. 
    Dell, 177 A.3d at 21
    ;
    
    DFC, 172 A.3d at 366
    –67. Relying on the statutory requirement that the Court of Chancery
    must consider “all relevant factors” when determining fair value, the Delaware Supreme
    Court has rejected “requests for the adoption of a presumption that the deal price reflects
    fair value if certain preconditions are met, such as when the merger is the product of arm’s-
    length negotiation and a robust, non-conflicted market check, and where bidders had full
    45
    information and few, if any, barriers to bid for the deal.” 
    Dell, 177 A.3d at 21
    . Yet the
    Delaware Supreme Court has also cautioned that its
    refusal to craft a statutory presumption in favor of the deal price when certain
    conditions pertain does not in any way signal our ignorance to the economic
    reality that the sale value resulting from a robust market check will often be
    the most reliable evidence of fair value, and that second-guessing the value
    arrived upon by the collective views of many sophisticated parties with a real
    stake in the matter is hazardous.
    
    DFC, 172 A.3d at 366
    . The Delaware Supreme Court has likewise cautioned that “we have
    little quibble with the economic argument that the price of a merger that results from a
    robust market check, against the back drop of a rich information base and a welcoming
    environment for potential buyers, is probative of the company’s fair value.” 
    Id. Based on
    the facts presented in DFC and Dell, the Delaware Supreme Court endorsed using the deal
    price as a persuasive indicator of fair value in those cases. Based on the facts presented in
    Aruba, the Delaware Supreme Court used a deal-price-less-synergies metric to make its
    own fair value determination.
    As a general matter, the persuasiveness of the deal price depends on the reliability
    of the sale process that generated it. When assessing whether a sale process results in fair
    value, the issue “is not whether a negotiator has extracted the highest possible bid.” 
    Dell, 177 A.3d at 33
    . “[T]the purpose of an appraisal is . . . to make sure that [the petitioners]
    receive fair compensation for their shares in the sense that it reflects what they deserve to
    receive based on what would fairly be given to them in an arm’s-length transaction.” 
    DFC, 172 A.3d at 370
    –71. “[T]he key inquiry is whether the dissenters got fair value and were
    not exploited.” 
    Dell, 177 A.3d at 33
    .
    46
    Relying on the Delaware Supreme Court’s decision in DFC, the petitioners assert
    that the deal price “deserves weight only if the merger is the product of a ‘robust market
    search’ and an arm’s-length third party transaction with ‘no hint of self-interest that
    compromised the market check.’” Dkt. 210 at 36 [hereinafter PTOB] (quoting 
    DFC, 172 A.3d at 349
    ). That is not what DFC held.
    The petitioners have accurately quoted phrases from the decision in DFC, but when
    the Delaware Supreme Court made those observations, it was describing the trial court’s
    findings regarding the sale process that took place in that case. The Delaware Supreme
    Court then determined that given those attributes, “the best evidence of fair value was the
    deal price.” 
    DFC, 172 A.3d at 349
    . The high court’s comments in DFC explained why the
    particular sale process in that case was so good as to make the deal price “the best evidence
    of fair value.” The decision did not identify minimum characteristics that a sale process
    must have before a trial court can give it weight. The decision also did not address what
    makes a sale process sufficiently bad that a trial court cannot give it weight. Technically,
    the decision did not even delineate when a sale process would be sufficiently good that a
    trial court should regard it as “the best evidence of fair value.” The Delaware Supreme
    Court could have believed the sale process in DFC warranted that level of consideration
    without excluding the possibility that a not-as-good sale process could warrant the same
    treatment.
    The same is true for the Delaware Supreme Court’s comments about the sale process
    in Dell. There, the Delaware Supreme Court described the sale process as having featured
    “fair play, low barriers to entry, outreach to all logical buyers, and the chance for any
    47
    topping bidder to have the support of Mr. Dell’s own votes . . . .” 
    Dell, 177 A.3d at 35
    .
    Based on its view of the sale process, the Delaware Supreme Court suggested that “the deal
    price deserved heavy, if not dispositive weight.” 
    Dell, 177 A.3d at 23
    . After describing the
    sale process in greater detail, the Delaware Supreme Court observed, “Overall, the weight
    of evidence shows that Dell’s deal price has heavy, if not overriding, probative value.” 
    Id. at 30.
    As in DFC, the Delaware Supreme Court was explaining why it regarded a particular
    sale process as so good that it deserved “heavy, if not dispositive weight.” The Delaware
    Supreme Court was not identifying the minimum requirements for a sale process to
    generate reliable information about fair value, nor was it enumerating qualities which, if
    absent, would render the outcome of a sale process so unreliable as to provide no insight
    into fair value.
    The Delaware Supreme Court’s decision in Aruba likewise did not address the
    minimum requirements for a sale process to generate reliable information about fair value.
    There, the trial court found the sale process to be sufficiently reliable to use the deal price
    as a valuation indicator, but declined to give it weight. The Delaware Supreme Court
    accepted that the sale process was sufficiently reliable and used the deal price as the
    exclusive basis for its own fair value determination. As with Dell and DFC, the Aruba
    decision did not have to address when a sale process was sufficiently bad that a trial court
    should decline to rely on the deal price.
    The decisions in DFC, Dell, and Aruba are highly informative because they analyze
    fact patterns in which the Delaware Supreme Court viewed the sale processes as
    sufficiently reliable to use the deal price as either (i) the exclusive basis for its own fair
    48
    value determination (Aruba), (ii) as a valuation indicator that “deserved heavy, if not
    dispositive weight” (Dell), or (iii) as a valuation indicator that provided “the best evidence
    of fair value” (DFC). But Aruba, Dell, and DFC do not establish legal requirements for a
    sale process. Whether a sale process is sufficiently good that the deal price should be
    regarded as persuasive evidence of fair value, or whether a sale process is sufficiently bad
    that the deal price should not be regarded as persuasive evidence of fair value are invariably
    fact-specific questions, and the answers depend on the arguments made and the evidence
    presented in a given case.
    2.      Objective Indicia Of Reliability
    In the recent appraisal decisions that have examined the reliability of a sale process,
    the Delaware Supreme Court has cited certain “objective indicia” that “suggest[] that the
    deal price was a fair price.” 
    Dell, 177 A.3d at 28
    ; accord 
    DFC, 172 A.3d at 376
    . The
    presence of objective indicia do not establish a presumption in favor of the deal price. The
    indicia are a starting point for analysis, not the end point, and in each of its recent appraisal
    decisions, the Delaware Supreme Court has determined that a combination of the objective
    indicia and other evidence outweighed the shortcomings in the sale processes that the
    petitioners had identified (Aruba) or which the trial court had regarded as undermining the
    persuasiveness of the deal price (Dell and DFC).
    First, the Merger was an arm’s-length transaction with a third party. See 
    DFC, 172 A.3d at 349
    (citing fact that “the company was purchased by a third party in an arm’s length
    sale” as factor supporting fairness of deal price). It was not a transaction involving a
    controlling stockholder. See 
    Dell, 177 A.3d at 30
    (citing fact that “this was not a buyout
    49
    led by a controlling stockholder” as a factor supporting fairness of deal price). Sibanye was
    an unaffiliated acquirer with no prior ownership interest in Stillwater.
    Second, the Board did not labor under any conflicts of interest. Six of the Board’s
    seven members were disinterested, outside directors, and they had the statutory authority
    under the Delaware General Corporation Law to say “no” to any merger. See 
    8 Del. C
    . §
    251(b) (requiring board adoption and recommendation of a merger agreement); 
    Dell, 177 A.3d at 28
    (citing fact that special committee was “composed of independent, experienced
    directors and armed with the power to say ‘no’” as factor supporting fairness of deal price).
    Stillwater’s stockholders were widely dispersed, and the petitioners have not identified
    divergent interests among them. Cf. 
    id. at 11
    (citing the fact that “any outside bidder who
    persuaded stockholders that its bid was better would have access to Mr. Dell’s votes” as a
    factor supporting fairness of deal price).
    Third, Sibanye conducted due diligence and received confidential information about
    Stillwater’s value. See 
    Aruba, 210 A.3d at 137
    (emphasizing that buyer armed with
    “material nonpublic information about the seller is in a strong position (and is uniquely
    incentivized) to properly value the seller”). Like the acquirer in Aruba, Sibanye “had signed
    a confidentiality agreement, done exclusive due diligence, gotten access to material
    nonpublic information,” and had a “sharp[] incentive to engage in price discovery . . .
    because it was seeking to acquire all shares.” 
    Id. at 140.
    Fourth, Stillwater negotiated with Sibanye and extracted multiple price increases.
    See 
    id. at 139
    (citing “back and forth over price”); 
    Dell, 177 A.3d at 28
    (citing fact that
    special committee “persuaded Silver Lake to raise its bid six times”). In July 2016, when
    50
    Sibanye indicated interest in a transaction at $15.75 per share, Stillwater did not rush into
    a deal. In December 2016, when Sibanye raised its indication of interest to a range of
    $17.50 to $17.75 per share, Stillwater again did not proceed. With the Board’s backing,
    McMullen demanded a higher price. When Sibanye offered $18.00 per share, the Board
    did not immediately accept. Only after Sibanye twice stated that $18.00 per share was its
    best and final offer did the Board accept that price.
    Most importantly, no bidders emerged during the post-signing phase, which is a
    factor that the Delaware Supreme Court has stressed when evaluating a sale process.12 The
    Merger Agreement did not contain any exceptional deal protection features, and the total
    amounts due via the termination fee and expense reimbursement provision were
    comparatively low, representing approximately 1.2% of equity value. Excluding the
    expense reimbursement, the termination fee reflected only 0.76% of equity value. The
    absence of a topping bid was thus highly significant.
    As noted, these are fewer objective indicia of fairness than the Delaware Supreme
    Court identified when reviewing the sale processes in DFC, Dell, or Aruba, and the
    presence of these factors does not establish a presumption in favor of the deal price.
    12
    See 
    Aruba, 210 A.3d at 136
    (“It cannot be that an open chance for buyers to bid
    signals a market failure simply because buyers do not believe the asset on sale is
    sufficiently valuable for them to engage in a bidding contest against each other.”); 
    Dell, 177 A.3d at 29
    (“Fair value entails at a minimum a price some buyer is willing to pay—
    not a price at which no class of buyers in the market would pay.”); 
    id. at 33
    (finding that
    absence of higher bid meant “that the deal market was already robust and that a topping
    bid involved a serious risk of overpayment,” which “suggests the price is already at a level
    that is fair”).
    51
    Nevertheless, the objective indicia that were present provide a cogent foundation for
    relying on the deal price as a persuasive indicator of fair value, subject to further review of
    the evidence.
    3.   The Challenges To The Pre-Signing Phase
    The petitioners have advanced a multitude of reasons why they believe the deal price
    for Stillwater does not provide a persuasive indicator of fair value. The bulk of their
    objections concern the pre-signing phase.
    As a threshold matter, the petitioners argue generally that a reliable sale process
    requires some degree of pre-signing outreach, citing a comment from the Union Illinois
    decision in which this court used a deal-price-less-synergies metric to value a privately
    held company after concluding that the company was “marketed in an effective manner.”
    Union 
    Ill., 847 A.2d at 350
    . The petitioners also cite a statement from the AOL decision to
    the effect that a sale process will provide persuasive evidence of statutory fair value when
    “(i) information was sufficiently disseminated to potential bidders, so that (ii) an informed
    sale could take place, (iii) without undue impediments imposed by the deal structure itself.”
    In re Appraisal of AOL Inc., 
    2018 WL 1037450
    , *8 (Del. Ch. Feb. 23, 2018). Neither
    decision established a rule that pre-signing outreach is invariably required before the deal
    price can serve as persuasive evidence of fair value. At least for a widely held, publicly
    traded company, a sale process could justify both sets of observations through the public
    announcement of a transaction and a sufficiently open post-signing market check.
    The petitioners’ myriad arguments about the pre-signing process in this case raise a
    fundamental question: Would the deal price provide persuasive evidence of fair value if
    52
    Stillwater had pursued a single-bidder strategy in which it only interacted with Sibanye
    before signing the Merger Agreement, recognizing that the Merger Agreement was
    sufficiently open to permit a meaningful post-signing market check? If the deal price would
    have provided persuasive evidence of fair value under those circumstances, then the
    additional efforts that Stillwater made before signing, even if disorganized and flawed,
    should not change the outcome. It is conceivable that a pre-signing process could involve
    features that undermined the effectiveness of a post-signing market check, such as never-
    waived standstill agreements containing don’t-ask-don’t-waive provisions, but that was not
    the case here. At least on the facts presented, Stillwater’s efforts were additive, not
    subtractive. They might not have added much, but they did not detract from what Stillwater
    could have achieved through a single-bidder process focused on Sibanye followed by a
    post-signing market check.
    a.      The Possibility Of A Single-Bidder Strategy
    Although the Delaware Supreme Court has not had the opportunity to consider a
    single-bidder strategy for purposes of determining the persuasiveness of a deal-price metric
    in an appraisal proceeding, extant precedent suggests that if Stillwater had pursued a single-
    bidder strategy in which it only interacted with Sibanye before signing the Merger
    Agreement, then the deal price would provide persuasive evidence of fair value because
    the Merger Agreement was sufficiently open to permit a meaningful post-signing market
    check. The reasoning that leads to this endpoint starts not with the recent triumvirate of
    appraisal cases, but rather with an important Delaware Supreme Court decision that
    restated the high court’s enhanced scrutiny jurisprudence for purposes of applying that
    53
    standard of review in a breach of fiduciary duty case. C & J Energy Servs., Inc. v. City of
    Miami Gen. Empls.’ & Sanitation Empls.’ Ret. Tr., 
    107 A.3d 1049
    (Del. 2014). The
    Delaware Supreme Court’s enhanced scrutiny jurisprudence becomes pertinent to appraisal
    proceedings because, as commentators have perceived, the deal price will provide
    persuasive evidence of fair value in an appraisal proceeding involving a publicly traded
    firm if the sale process would satisfy enhanced scrutiny in a breach of fiduciary duty case.13
    In C & J Energy, the Delaware Supreme Court held that plaintiffs who challenged
    a transaction involving only a passive, post-signing market check had not shown a
    reasonable likelihood that the director defendants had breached their fiduciary duties under
    the enhanced scrutiny standard of review. The transaction in C & J Energy was a stock-
    for-stock merger between C & J Energy Services, Inc. and a subsidiary of Nabors Industries
    Ltd. Although C & J Energy was nominally the acquirer, it would emerge from the
    transaction with a controlling stockholder, and the Delaware Supreme Court therefore
    13
    See Lawrence A. Hamermesh & Michael L. Wachter, Finding the Right Balance
    in Appraisal Litigation: Deal Price, Deal Process, and Synergies, 73 Bus. Law. 961, 962
    (2018) (commending outcomes in Dell and DFC and arguing that “the Delaware courts’
    treatment of the use of the deal price to determine fair value does and should mirror the
    treatment of shareholder class action fiduciary duty litigation”); 
    id. at 982–83
    (citing Dell
    and DFC in observing, “What we discern from the case law, however, is a tendency to rely
    on deal price to measure fair value where the transaction would survive enhanced judicial
    scrutiny . . . . Thus, in order to determine whether to use the deal price to establish fair
    value, the Delaware courts are engaging in the same sort of scrutiny they would have
    applied under Revlon if the case were one challenging the merger as in breach of the
    directors’ fiduciary duties.” (footnote omitted)); Charles Korsmo & Minor Myers, The
    Flawed Corporate Finance of Dell and DFC Global, 68 Emory L.J. 221, 269 (2018)
    (explaining that Dell and DFC “conflate questions of fiduciary duty liability with the
    valuation questions central to appraisal disputes”).
    54
    examined whether the directors had fulfilled their situationally specific duty to seek the
    best transaction reasonably available. See C & J 
    Energy, 107 A.3d at 1067
    .
    The merger in C & J Energy resulted from a CEO-driven process. Joshua Comstock,
    the founder, chairman, and CEO of C & J Energy, spearheaded the discussions. Talks
    between Comstock and the CEO of Nabors started in January 2014, and although
    Comstock discussed the deal with some of C & J Energy’s directors, he did not receive
    formal board approval to negotiate until April. Later in the process, he made a revised offer
    to Nabors without board approval. The plaintiffs argued that Comstock acted without
    authority and misled the board about key issues. The Delaware Supreme Court found “at
    least some support for the plaintiffs’ contention that Comstock at times proceeded on an
    ‘ask for forgiveness rather than permission’ basis.” 
    Id. at 1059.
    There was evidence in C & J Energy that Comstock had personal reasons to favor a
    deal with Nabors. The Nabors CEO “assured Comstock throughout the process that he
    would be aggressive in protecting Comstock’s financial interests if a deal was
    consummated.” 
    Id. at 1064.
    After the key terms of the transaction had been negotiated, but
    before it was formally approved, Comstock asked for a side letter “affirming that C & J’s
    management would run the surviving entity and endorsing a generous compensation
    package.” 
    Id. When the
    Nabors CEO balked, Comstock threatened to not sign or announce
    the deal. The Nabors CEO gave in, and the deal was announced as planned. 
    Id. at 1064–
    65. In addition, there was evidence that C & J Energy’s primary financial advisor was less
    than optimally effective and seemed to be advocating for the deal rather than advocating
    for C & J Energy. See 
    id. at 1056.
    The banker also had divergent interests because of its
    55
    role as a financing source for the deal. 
    Id. at 1057.
    There were thus reasons to think that
    the two principal negotiators for C & J—its CEO and its banker—had personal reasons to
    favor a transaction with Nabors and to push for that outcome.
    The merger agreement in C & J Energy included a no-shop clause subject to a
    fiduciary out and a termination fee equal to 2.27% of the deal value. 
    Id. at 1063.
    The period
    between the announcement of the deal on June 25, 2014, and the trial court’s issuance of
    the injunction on November 25, 2014, lasted 153 days. No competing bidder emerged
    during that period.
    On these facts, the Delaware Supreme Court found no grounds for a potential breach
    of duty, explaining that “[w]hen a board exercises its judgment in good faith, tests the
    transaction through a viable passive market check, and gives its stockholders a fully
    informed, uncoerced opportunity to vote to accept the deal, we cannot conclude that the
    board likely violated its Revlon duties.” 
    Id. at 1053.
    Elaborating, the senior tribunal
    explained that a board may pursue a single transaction partner, “so long as the transaction
    is subject to an effective market check under circumstances in which any bidder interested
    in paying more has a reasonable opportunity to do so.” 
    Id. at 1067.
    The high court
    emphasized that “[s]uch a market check does not have to involve an active solicitation, so
    long as interested bidders have a fair opportunity to present a higher-value alternative, and
    the board has the flexibility to eschew the original transaction and accept the higher-value
    deal.” 
    Id. at 1067–68.
    The transaction in C & J Energy satisfied this test. Describing the
    suite of deal protections, the Delaware Supreme Court observed that “a potential competing
    bidder faced only modest deal protection barriers.” 
    Id. at 1052.
    Later, the court reiterated
    56
    that “there were no material barriers that would have prevented a rival bidder from making
    a superior offer.” 
    Id. at 1070;
    accord 
    id. (“But in
    this case, there was no barrier to the
    emergence of another bidder and more than adequate time for such a bidder to emerge.”).
    The Delaware Supreme Court also cited with approval precedents in which a sell-side
    board had engaged exclusively with a single buyer, had not conducted a pre-signing market
    check, then agreed to a merger agreement containing a no-shop clause, a matching right,
    and a termination fee, and the resulting combination was found sufficient to permit an
    effective post-signing market check that satisfied the directors’ duties under enhanced
    scrutiny.14
    Procedurally, the Delaware Supreme Court’s decision in C & J Energy vacated an
    injunction that the trial court had entered in advance of the stockholder vote. In holding
    that the trial court had issued the injunction improvidently, the high court noted that “[t]he
    ability of the stockholders themselves to freely accept or reject the board’s preferred course
    of action is also of great importance in this context.” 
    Id. at 1068.
    The role of the vote,
    however, should not detract from the high court’s observations about the adequacy of the
    14
    See 
    id. at 1068
    n.87 (citing cases including In re Dollar Thrifty S’holders Litig.,
    
    14 A.3d 573
    , 612–13, 615 (Del. Ch. 2010) (finding that the target board’s use of no-shop,
    matching rights, and termination fee provisions were reasonable even though the company
    had agreed to deal exclusively with the buyer without conducting a pre-signing market
    check); and In re MONY Gp. Inc. S’holders Litig., 
    852 A.2d 9
    (Del. Ch. 2004) (finding that
    the board acted reasonably even though it did not actively shop the company because the
    board was financially sophisticated, had knowledge of the relevant industry, and there was
    a “substantial opportunity for an effective market check” after the agreement was
    announced)); 
    id. at 1069
    (citing Lyondell Chem. Co. v. Ryan, 
    970 A.2d 235
    , 243 (Del.
    2009)).
    57
    single-bidder process. Underscoring that point, the Delaware Supreme Court cited the trial
    court’s apparent belief “that Revlon required C & J’s board to conduct a pre-signing active
    solicitation process in order to satisfy its contextual fiduciary duties,” then explicitly
    rejected that understanding of the enhanced scrutiny standard. 
    Id. at 1068.
    As a result, the
    Delaware Supreme Court’s decision in C & J Energy has implications that go beyond the
    injunction context.
    One area where its implications subsequently became manifest was in a post-closing
    liability action where plaintiffs sought to recover from an alleged aider-and-abettor under
    a quasi-appraisal theory of damages. See In re PLX Tech. Inc. S’holders Litig., --- A.3d --
    -, 
    2019 WL 2144476
    (Del. May 16, 2019) (TABLE). The PLX litigation challenged a
    merger agreement in which the acquirer (Avago) purchased the target (PLX) for cash. As
    in C & J Energy, the sale process was not pristine. The trial court found that a key director
    and the company’s investment banker had divergent interests that caused them to favor a
    sale over having PLX remain independent, that Avago tipped the director and the banker
    about the timing and pricing of a deal, that the director and the banker failed to disclose the
    tip to the board while using the information to help them position PLX to be sold, and that
    the proxy statement failed to disclose these issues. See In re PLX Tech. Inc. S’holders Litig.
    (PLX Trial), 
    2018 WL 5018535
    , at *32–35, *44–47 (Del. Ch. Oct. 16, 2018) (subsequent
    history omitted). Based on these findings, the trial court found a predicate breach of
    fiduciary duty under the enhanced scrutiny standard. The trial court also found that the sole
    remaining defendant—an activist stockholder affiliated with the key director—had
    participated knowingly in the breach. See 
    id. at *48–50.
    58
    The plaintiffs’ claim foundered, however, at the damages stage. The plaintiffs
    sought to recover compensatory damages on behalf of a class of stockholders based on the
    theory that PLX should have remained independent rather than being sold. Under this
    theory, the plaintiffs sought “out-of-pocket (i.e., compensatory) money damages equal to
    the ‘fair’ or ‘intrinsic’ value of their stock at the time of the merger, less the price per share
    that they actually received,” with “[t]he ‘fair’ or ‘intrinsic’ value of the shares . . .
    determined using the same methodologies employed in an appraisal.” 
    Id. at *50
    (internal
    quotation marks omitted) (collecting cases). The plaintiffs’ expert used a DCF
    methodology to value PLX at $9.86 per share, well above the deal price of $6.50 per share.
    See 
    id. at *51.
    Although PLX’s pre-signing process was marred by breaches of fiduciary duty
    resulting from Avago’s tip to the key director and the company’s banker, the trial court
    found that the sale process as a whole was sufficiently reliable to warrant rejecting the
    plaintiffs’ valuation. The trial court explained that “[m]ore important than the pre-signing
    process was the post-signing market check.” 
    Id. at *55.
    After discussing the outcome in C
    & J Energy, the trial court reasoned that “the structure of the Merger Agreement satisfied
    the Delaware Supreme Court’s standard for a passive, post-signing market check.” 
    Id. The merger
    agreement (i) contained a no-shop with a fiduciary subject an unlimited match right
    that gave Avago four days to match the first superior proposal and two days to match any
    subsequent increase, and (ii) required PLX to pay Avago a termination fee of $10.85
    million, representing 3.5% of equity value ($309 million) and 3.7% of enterprise value
    ($293 million). See 
    id. at *26,
    *44. Avago launched its first step-tender offer on July 8,
    59
    2014. No competing bidder intervened, and the merger closed thirty-five days later on
    August 12. 
    Id. at *27.
    This time period compared favorably with other passive, post-signing
    market checks that Delaware decisions had approved.15
    On appeal, the Delaware Supreme Court affirmed the judgment based solely on the
    trial court’s damages ruling and without reaching or expressing a view on any of the other
    issues raised by the case. See PLX, 
    2019 WL 2144476
    , at *1. For present purposes, the
    damages issue is the important one, because the trial court had determined that the suite of
    defensive measures in the merger agreement, together with the absence of a topping bid,
    provided a more reliable indication of value than the plaintiffs’ discounted cash flow
    model. See PLX Trial, 
    2018 WL 5018535
    , at *44, *54–56. Notably for present purposes,
    although the burden of proof rested solely with the plaintiffs, the trial court in PLX made
    its determination using the same valuation standard that would apply in an appraisal
    proceeding. 
    Id. at *50
    .
    To reiterate, in its appraisal jurisprudence, the Delaware Supreme Court has not yet
    been asked to rule on the reliability of a sale process involving a single-bidder strategy, no
    pre-signing outreach, and a passive post-signing market check. The closest precedent is
    15
    See 
    id. at *44.
    The PLX Trial decision included an appendix that collected
    decisions approving a passive market check. The table somehow swapped the details of the
    passive market check in Braunschweiger v. American Home Shield Corporation, 
    1989 WL 128571
    (Del. Ch. Oct. 26, 1989), with the details from In re Formica Corporation
    Shareholders Litigation, 
    1989 WL 25812
    (Del. Ch. Mar. 22, 1989). A corrected version is
    attached to this decision as an appendix.
    60
    Aruba, where the dynamics of the sale during the pre-closing phase resembled a single-
    bidder strategy, although the company’s banker did engage in some minimal outreach.
    The pre-signing phase of the sale process in Aruba had two stages. See Verition P’rs
    Master Fund Ltd. v. Aruba Networks, Inc. (Aruba Trial), 
    2018 WL 922139
    , at *7–8 (Del.
    Ch. Feb. 15, 2018) (subsequent history omitted). The first stage began in late August 2014,
    when HP approached Aruba about a deal. Aruba hired an investment banker (Qatalyst),
    who identified thirteen potential partners and approached five of them. For reasons having
    “nothing to do with price,” no one was interested. 
    Id. at *10.
    Aruba and HP entered into an
    NDA that restricted HP from speaking with Aruba management about post-transaction
    employment, and HP began conducting due diligence. 
    Id. at *11.
    Despite the restriction in
    the NDA, HP asked Aruba’s CEO, Dominic Orr, if he would take on a key role with the
    combined entity. Orr replied that he had no objection. 
    Id. The parties
    seemed to be making progress towards a deal, but the HP board of
    directors balked at making a bid without further analysis, recalling the fallout from a
    disastrous acquisition in 2011. In November 2014, Aruba terminated discussions, bringing
    the first stage of the pre-signing process to a close. 
    Id. at *12.
    For its part, HP continued to evaluate an acquisition of Aruba. In December 2014,
    HP tapped Barclays Capital Inc. as its financial advisor. That firm had worked for Aruba
    and had been trying to secure the sell-side mandate. 
    Id. at *13.
    On January 21, 2015, HP’s
    CEO met with Orr for dinner. During the meeting, when HP’s CEO proposed resuming
    merger talks, Orr responded with enthusiasm and suggested trying to announce a deal by
    early March. But HP’s CEO also told Orr that because Qatalyst had represented the seller
    61
    in HP’s disastrous acquisition from 2011, HP would not proceed if Aruba used Qatalyst.
    
    Id. at *14.
    The Aruba board decided to move forward with the deal and informed Qatalyst
    about HP’s ukase. Aruba was obligated to pay Qatalyst a fee in the event of a successful
    transaction, so it kept Qatalyst on as a behind-the-scenes advisor. From then on, Qatalyst’s
    primary goal was to repair its relationship with HP, and Qatalyst regarded a successful sale
    of Aruba to HP as a key step in the right direction. Aruba also needed a new HP-facing
    banker. It hired Evercore, a firm that was trying to establish a presence in Silicon Valley.
    During the sale process, Evercore likewise sought to please HP, viewing HP as a major
    source of future business. See 
    id. at *9,
    *15–16, *19, *21.
    The ensuing negotiations proceeded quickly. HP had anticipated making an opening
    bid of $24 per share, but after Orr’s enthusiastic response, HP opened at $23.25 per share.
    
    Id. at *16–17.
    Qatalyst reached out to a sixth potential strategic partner, but it was not
    interested. 
    Id. at *17.
    The Aruba board decided to counter at $29 per share. Evercore
    conveyed the number to Barclays, but when Barclays dismissed it, Evercore emphasized
    Aruba’s desire to announce a deal quickly. 
    Id. at *17–18.
    On February 10, 2015, twenty
    days after HP resumed discussions with Orr, the Aruba board agreed to a price of $24.67
    per share. 
    Id. at *19.
    The parties negotiated a merger agreement, and on March 1, 2015,
    the Aruba board approved it.
    The post-signing phase was uneventful. On March 2, 2015, Aruba and HP
    announced the merger. The merger agreement (i) contained a no-shop clause subject to a
    fiduciary out, (ii) conditioned the out for an unsolicited superior proposal on compliance
    62
    with an unlimited match right that gave HP five days to match the first superior proposal
    and two days to match any subsequent increase, and (iii) required Aruba to pay HP a
    termination fee of $90 million, representing 3% of Aruba’s equity value. No competing
    bidder emerged, and on May 1, 2015, Aruba’s stockholders approved the merger. 
    Id. at *21–22.
    Although the sale process in Aruba had flaws, the trial court found that it was
    sufficiently reliable to make the deal price a persuasive indicator of fair value. Overall, the
    trial court viewed the HP-Aruba merger as “a run-of-the-mill, third party-deal,” where
    “[n]othing about it appear[ed] exploitive.” 
    Id. at *38.
    The petitioners argued that the deal
    price resulted from a closed-off sale process in which HP had not faced a meaningful threat
    of competition. 
    Id. at *39.
    The trial court rejected that contention, noting that the petitioners
    failed “to point to a likely bidder and make a persuasive showing that increased competition
    would have led to a better result.” Id. (citing 
    Dell, 177 A.3d at 28
    –29, 32, 34).
    The petitioners also argued that the negotiators’ incentives undermined the pre-
    signing phase, citing the desire of Aruba’s bankers to cater to HP and the more subtly
    divergent interests of Aruba’s CEO. The trial court found that although the petitioners
    proved that Aruba could have negotiated more aggressively, they did not prove that “the
    bankers, [the CEO], the Aruba Board, and the stockholders who approved the transaction
    all accepted a deal price that left a portion of Aruba’s fundamental value on the table.” 
    Id. at *44.
    In other portions of the decision, the trial court found that Aruba’s unaffected
    trading price was a reliable indicator of fair value and rejected the parties’ DCF valuations
    63
    as unreliable. These holdings left the trial court with two reliable valuation indicators: the
    unaffected trading price and the deal price. The trial court determined that the unaffected
    trading price was the better measure of the fair value of Aruba’s shares. See 
    id. at *53–55.
    On appeal, the Delaware Supreme Court reversed. The high court found that the
    trial court had incorrectly relied on the unaffected trading price, but it accepted the trial
    court’s finding that the deal price was a reliable indicator of fair value. 
    Aruba, 210 A.3d at 141
    –42.
    Addressing the petitioners’ claim that the pre-signing phase of the sale process was
    insufficient to establish a competitive bidding dynamic, the Delaware Supreme Court
    emphasized that
    when there is an open opportunity for many buyers to buy and only a few bid
    (or even just one bids), that does not necessarily mean that there is a failure
    of competition; it may just mean that the target’s value is not sufficiently
    enticing to buyers to engender a bidding war above the winning price.
    
    Id. at 136.
    Applying this principle to the facts in Aruba, the high court explained:
    Aruba approached other logical strategic buyers prior to signing the deal with
    HP, and none of those potential buyers were interested. Then, after signing
    and the announcement of the deal, still no other buyer emerged even though
    the merger agreement allowed for superior bids. It cannot be that an open
    chance for buyers to bid signals a market failure simply because buyers do
    not believe the asset on sale is sufficiently valuable for them to engage in a
    bidding contest against each other. If that were the jurisprudential
    conclusion, then the judiciary would itself infuse assets with extra value by
    virtue of the fact that no actual market participants saw enough value to pay
    a higher price. That sort of alchemy has no rational basis in economics.
    
    Id. On the
    facts presented, the level of competition in Aruba was sufficient to support the
    reliability of the deal price.
    64
    The Delaware Supreme Court also explained that the negotiations between Aruba
    and HP over price had important implications for the reliability of the deal price:
    [A] buyer in possession of material nonpublic information about the seller is
    in a strong position (and is uniquely incentivized) to properly value the seller
    when agreeing to buy the company at a particular deal price, and that view
    of value should be given considerable weight by the Court of Chancery
    absent deficiencies in the deal process.
    
    Id. at 137.
    The high court noted that HP and Aruba went “back and forth over price” and
    that HP had “access to nonpublic information to supplement its consideration of the public
    information available to stock market buyers . . . .” 
    Id. at 139.
    The Delaware Supreme Court
    elsewhere emphasized that “HP had signed a confidentiality agreement, done exclusive due
    diligence, gotten access to material nonpublic information,” and “had a much sharper
    incentive to engage in price discovery than an ordinary trader because it was seeking to
    acquire all shares.” 
    Id. at 140.
    On the facts presented, the extent of the negotiations in
    Aruba was sufficient to support the reliability of the deal price.
    The high court ultimately concluded that Aruba’s sale process was sufficiently
    reliable to render the deal price the best measure of fair value. The Delaware Supreme
    Court declined to use the trial court’s estimate of the deal price minus synergies, instead
    adopting HP’s contemporaneous synergies estimate and remanding with instructions that
    “final judgment be entered for the petitioners in the amount of $19.10 per share plus any
    interest to which the petitioners are entitled.” 
    Id. at 142.
    The Aruba decision technically did not involve a single-bidder process, but the
    dynamics closely resembled one. Although Qatalyst reached out to five bidders at the
    beginning of the first phase of the pre-signing process, none of those parties had any interest
    65
    in Aruba. After this development, both Qatalyst and Aruba’s CEO concluded that Aruba’s
    “only (but strong) weapon is to say we go alone.” Aruba Trial, 
    2018 WL 922139
    , at *10.
    Later, Aruba’s CEO had a “pretty open dialogue” with HP during which he informed HP
    that Aruba was “not running a sales process” and did not attempt to posture about pitting
    HP against anyone else. 
    Id. at *40
    (internal quotation marks omitted). During the second
    phase of the pre-signing process, after HP re-engaged, HP understood that Aruba was not
    pursuing other options. 
    Id. at *41.
    The negotiations unfolded in a manner consistent with a
    single-bidder dynamic. See 
    id. In concluding
    that the deal price was a reliable indicator of fair value, the trial court
    considered a number of factors, including that “HP and Aruba agreed to terms for the
    merger agreement that the petitioners have not meaningfully challenged.” 
    Id. at *38.
    After
    describing the suite of defensive measures in the merger agreement, the trial court noted
    that “[t]his combination of defensive provisions would not have supported a claim for
    breach of fiduciary duty.” 
    Id. The petitioners
    had argued about a lack of competition during
    the pre-signing phase, and the trial court had discussed that factor at length, ultimately
    rejecting the objection. See 
    id. at *39–41.
    On appeal, the Delaware Supreme Court
    emphasized that a failure of competition does not result simply because a limited number
    of parties bid, “or even just one bids.” 
    Aruba, 210 A.3d at 136
    . The Delaware Supreme
    Court also emphasized the reliability of the price that resulted from the “back and forth”
    between Aruba and HP. 
    Id. at 139.
    Given these precedents, I cannot agree that a reliable sale process must invariably
    involve some level of active outreach during the pre-signing phase. By making this
    66
    observation, I am not suggesting that the Delaware Supreme Court has ever endorsed a
    single-bidder process for purposes of appraisal, nor that any of the precedents that this
    decision has discussed are squarely on point. Nor am I claiming to have any privileged
    insight into how the Delaware Supreme Court would or should evaluate the persuasiveness
    of a single-bidder strategy on the facts of any particular case. It nevertheless seems to me
    that if the proponent of a single-bidder process could show that the merger agreement
    allowed for a passive post-signing market check in line with what decisions have held is
    sufficient to satisfy enhanced scrutiny, and if there were no other factors that undermined
    the sale process, then the deal price would provide persuasive evidence of fair value.
    This decision has already found that the sale process exhibited objective indicia of
    reliability. As noted and as discussed in greater detail below, the petitioners have not raised
    a meaningful challenge to the post-signing market check. The operative question for
    purposes of examining the pre-signing phase is not whether Stillwater’s process fell short
    of what would have been optimal, but rather whether the pre-signing process sufficiently
    impaired the sale process as a whole, including the post-signing phase, so as to prevent the
    deal price from serving as a persuasive indicator of fair value.
    b.      The Relative Involvement Of McMullen And The Board
    In The Pre-Signing Phase
    In their initial challenge to the pre-signing phase, the petitioners attack McMullen’s
    role in the pre-signing process. They contend that McMullen acted improperly by pursuing
    Sibanye’s indication of interest without authorization from the Board and contrary to its
    direction to pursue acquisitions or a merger of equals. See PTOB at 37. They also criticize
    67
    McMullen for starting to engage with Sibanye in January 2016, but failing to inform the
    Board until after receiving an expression of interest from Sibanye in July. During this
    period, McMullen met with Sibanye’s senior executives at least twice to discuss a sale of
    Stillwater, reached an understanding with Sibanye’s CEO on pricing the deal at a 30%
    premium over Stillwater’s thirty-day VWAP, and arranged a multi-day site visit for
    Sibanye personnel.
    The petitioners also contend that after the Board learned of Sibanye’s expression of
    interest in July 2016, the Board did not exercise meaningful oversight over the sale process.
    They accurately observe that the record lacks any evidence of meaningful engagement by
    the Board until October 3, 2016, two months before signing, when the Board received a
    report on the Company’s outreach to various parties, instructed McMullen to obtain formal
    proposals for retaining an investment bank, instructed McMullen to create a cash flow
    model that could be used to value the Company, and decided not to form a special
    committee. See JX 246.
    The petitioners correctly contend that these facts could have contributed to findings
    that McMullen and the directors breached their duty of care under the enhanced scrutiny
    standard of review.16 But the enhanced scrutiny analysis would not have ended there. The
    16
    See Citron v. Fairchild Camera & Instr. Corp., 
    569 A.2d 53
    , 66 (Del. 1989) (“[I]n
    change of control situations, sole reliance on hired experts and management can taint[] the
    design and execution of the transaction. Thus, we look particularly for evidence of a
    board’s active and direct role in the sale process.” (internal quotation marks omitted));
    Mills Acq. Co. v. Macmillan, Inc., 
    559 A.2d 1261
    , 1281 (Del. 1989) (“[A] board of directors
    . . . may not avoid its active and direct duty of oversight in a matter as significant as the
    sale of corporate control.”); Cede & Co. v. Technicolor, Inc. (Technicolor II), 
    634 A.2d 68
    C & J Energy decision likewise involved a CEO that began deal discussions without formal
    board authorization, engaged for months without formally reporting to the board, made a
    revised offer without board approval, and generally proceeded by asking for forgiveness
    rather than by getting permission. See C & J 
    Energy, 107 A.3d at 1059
    . After considering
    the totality of the sale process, the Delaware Supreme Court concluded that the facts would
    not support a fiduciary breach, placing heavy reliance on the directors’ decision to “test[]
    the transaction through a viable passive market check . . . .” 
    Id. at 1053.
    The outcome in PLX likewise shows that the existence of problems during the pre-
    signing process does not necessarily undermine the reliability of the deal price. The trial
    court in PLX found that the directors had breached their fiduciary duties under the enhanced
    scrutiny standard because of an undisclosed tip from the eventual buyer to a key director
    and the company’s banker. PLX Trial, 
    2018 WL 5018535
    , at *15–16, *32–35, *44–47.
    Despite this defect, the sale process provided reliable evidence of the company’s value
    based primarily on the adequacy of the company’s post-signing market check. See 
    id. at *55
    (“More important than the pre-signing process was the post-signing market check.”).
    345, 368 (Del. 1993) (explaining that directors must maintain “an active and direct role in
    the context of a sale of a company from beginning to end”); In re Rural Metro Corp.
    S’holders Litig., 
    88 A.3d 54
    , 91 (Del. Ch. 2014) (“As a threshold matter, the decision to
    initiate a sale process falls short under enhanced scrutiny because it was not made by an
    authorized corporate decisionmaker. The Board did not make the decision to launch a sale
    process, nor did it authorize the Special Committee to start one.”), aff’d sub nom. RBC
    Capital Mkts., LLC v. Jervis, 
    129 A.3d 816
    (Del. 2015); 
    id. (“One of
    the Delaware Supreme
    Court’s clearest teachings is that ‘directors cannot be passive instrumentalities during
    merger proceedings.’” (quoting Technicolor 
    II, 634 A.2d at 368
    )).
    69
    Applying the same damages standard that would govern in an appraisal proceeding, the
    trial court found that the sale process was sufficiently reliable to render the plaintiffs’
    damages calculation unpersuasive, resulting in a failure of proof. 
    Id. at *50
    –55. The
    Delaware Supreme Court affirmed the judgment based solely on the trial court’s damages
    ruling. See PLX, 
    2019 WL 2144476
    , at *1.
    McMullen’s unsupervised activities and the Board’s failure to engage in meaningful
    oversight until October 2016 represent flaws in the pre-signing process. They are factors
    that must be taken into account, but they do not inherently disqualify the sale process from
    generating reliable evidence of fair value.
    In this case, McMullen’s unsupervised activities did not comprise the entirety of the
    Company’s sale process. Ultimately, after the Board engaged, Stillwater formally retained
    BAML, conducted an expedited pre-signing canvass, and entered into the Merger
    Agreement. The terms of the Merger Agreement facilitated a meaningful post-signing
    market check, and no other buyer emerged even though the merger agreement allowed for
    superior bids. As in Dell, the petitioners did not point to any evidence that another party
    was interested in proceeding and would have bid if McMullen and the Board had acted
    differently. See 
    Dell, 177 A.3d at 29
    .
    c.     McMullen’s Personal Interest In A Transaction
    In their next challenge to the pre-signing process, the petitioners contend that
    McMullen undermined the sale process because he planned to leave Stillwater, and “he
    wanted the benefit of a strategic transaction (i) to boost the Company’s stock price prior to
    his departure and (ii) to maximize his payout upon stepping down as CEO.” PTOB at 39.
    70
    The petitioners correctly observe that by leaving after a transaction, McMullen would be
    entitled to unvested equity awards and accelerated retention payments that he could not
    obtain if he left without a transaction.
    The petitioners also point out that McMullen devoted considerable time to
    developing and selling his personal investments outside of Stillwater. They cite
    McMullen’s contemporaneous service in 2016 as CEO of Nevada Iron and as President of
    New Chris, even though McMullen’s employment agreement with Stillwater limited
    McMullen’s outside activities to board service and otherwise required him to devote his
    full efforts to Stillwater. See JX 114. During 2016, McMullen raised money for the
    successor company to New Chris and sold Nevada Iron. See McMullen Tr. 709, 863–64.
    The petitioners cite McMullen’s activities (i) to show that McMullen was trying to
    maximize his personal wealth before retiring to Turks & Caicos, (ii) to suggest that
    McMullen might have done a better job with the sale process if he had not been pursuing
    his other investments, and (iii) as further evidence that the Board failed to provide active
    oversight.
    Sibanye takes the extreme position that “there is no evidence to suggest that Mr.
    McMullen was motivated by anything other than maximizing stockholder value.” Dkt. 211
    at 59. Sibanye points to McMullen’s decision in March 2016 to extend his employment by
    two years, claiming simplistically that if “McMullen’s intention was truly to do a quick
    sale and leave the company, there would have been no need for him to renew his
    employment agreement since his prior contract did not expire until December 31, 2016 and
    contained essentially the same termination benefits as the new contract.” 
    Id. at 60.
    To the
    71
    contrary, McMullen understood that completing a sale to Sibanye or another buyer might
    extend past December 31. Extending his employment agreement was the smart play for
    McMullen personally. Although Sibanye has not argued this point, it was also likely good
    for Stillwater, because it avoided the prospect of a near-term issue with CEO succession.
    Sibanye has no meaningful response to McMullen’s pursuit of his other activities.
    Sibanye says they were permitted, but the petitioners have correctly described McMullen’s
    employment agreement as only authorizing board service, not his more active roles.
    Sibanye also contends that his outside interests were disclosed in public filings, but that is
    not the point. The issue is whether the interests undermined the sale process, not whether
    they were disclosed. On this final point, Sibanye asserts that the petitioners “have pointed
    to no evidence that these outside interests presented an actual conflict, that these interests
    competed with or were adverse to Stillwater’s interests, or that they otherwise interfered
    with Mr. McMullen’s ability to carry out his duties as CEO of Stillwater.” 
    Id. Sibanye has
    focused on the critical question: whether McMullen’s personal interests
    undermined the sale process. Senior executives almost invariably have divergent incentives
    during a sale process, often because of change-in-control agreements, and equally often
    because the transaction will have implications for their personal employment situations.
    Two Delaware appraisal precedents provide insight into factual scenarios involving
    divergent incentives of this type. The Aruba decision involved a sale process where the top
    executive and the company’s investment bankers had conflicting incentives. The CEO
    wanted to retire, but he cared deeply about the company and its employees. When HP
    proposed to acquire Aruba and keep the CEO on to integrate the companies, it offered the
    72
    perfect path “to an honorable personal and professional exit.” Aruba Trial, 
    2018 WL 922139
    , at *5; see 
    id. at *43
    (analyzing CEO’s conflict). Aruba’s investment bankers both
    wanted to curry favor with HP. Qatalyst was desperate to save its Silicon Valley franchise,
    and Evercore was auditioning for future business. 
    Id. at *43.
    The trial court acknowledged
    the petitioners’ concerns, but found that the conflicting incentives did not undermine the
    deal price as an indicator of fair value:
    The evidence does not convince me that the bankers, Orr, the Aruba Board,
    and the stockholders who approved the transaction all accepted a deal price
    that left a portion of Aruba’s fundamental value on the table. Perhaps
    different negotiators could have extracted a greater share of the synergies
    from HP in the form of a higher deal price. Maybe if Orr had been less eager,
    or if Qatalyst had not been relegated to the back room, then HP would have
    opened at $24 per share. Perhaps with a brash Qatalyst banker leading the
    negotiations, unhampered by the Autonomy incident, Aruba might have
    negotiated more effectively and gotten HP above $25 per share. An outcome
    along these lines would have resulted in HP sharing a greater portion of the
    anticipated synergies with Aruba’s stockholders. It would not have changed
    Aruba’s standalone value. Hence, it would not have affected Aruba’s fair
    value for purposes of an appraisal.
    
    Id. at *44.
    On appeal, the Delaware Supreme Court accepted the reliability of the deal price
    as a valuation indicator and used it when making its own fair value determination. 
    Aruba, 210 A.3d at 141
    –42.
    The Dell decision also involved a conflict: Mr. Dell, the company’s founder and top
    executive, was a buy-side participant in the management buyout and would emerge from
    the transaction with a controlling stake. A special committee negotiated the terms of the
    transaction with the financial sponsor backing the deal, but the trial court regarded Mr.
    Dell’s involvement on the buy side as a factor cutting against the reliability of the deal
    price. For example, the trial court found that Mr. Dell gave the buyout group a leg-up given
    73
    his relationships within the company and his knowledge of its business, and the trial court
    accepted the testimony of a sale-process expert that if bidders competed to pay more than
    what Mr. Dell’s group would pay, then they risked overpaying and suffering the winner’s
    curse. In re Appraisal of Dell Inc. (Dell Trial), 
    2016 WL 3186538
    , at *42–43 (Del. Ch.
    May 31, 2016) (subsequent history omitted). Equally important, Mr. Dell was a net
    purchaser of shares in the buyout, so any increase in the deal price cost him money.
    If Mr. Dell kept the size of his investment constant as the deal value
    increased, then Silver Lake would have to pay more and would demand a
    greater ownership stake in the post-transaction entity. [The petitioners’ sale-
    process expert] showed that if Mr. Dell wanted to maintain 75% ownership
    of the post-transaction entity, then he would have to contribute an additional
    $250 million for each $1 increase in the deal price. If Mr. Dell did not
    contribute any additional equity and relied on Silver Lake to fund the
    increase, then he would lose control of the post-transaction entity at a deal
    price above $15.73 per share. Because Mr. Dell was a net buyer, any party
    considering an overbid would understand that a higher price would not be
    well received by the most important person at the Company.
    
    Id. at *43
    (footnote omitted). The trial court found that for purposes of price discovery in
    an appraisal case, Mr. Dell’s involvement and incentives undermined the reliability of the
    sale process and the persuasiveness of the deal price. 
    Id. at *44.
    On appeal, the Delaware Supreme Court held that Mr. Dell’s involvement in the
    buyout group had not undermined the sale process. See 
    Dell, 177 A.3d at 32
    –33. The high
    court noted that “the [trial court] did not identify any possible bidders that were actually
    deterred because of Mr. Dell’s status.” 
    Id. at 34.
    The Delaware Supreme Court also
    emphasized Mr. Dell’s willingness to work with rival bidders during due diligence and the
    absence of evidence that Mr. Dell would have left the company if a rival bidder prevailed.
    
    Id. at 32–34.
    The high court concluded that the lack of a higher bid did not call into question
    74
    the sale process, because “[i]f a deal price is at a level where the next upward move by a
    topping bidder has a material risk of being a self-destructive curse, that suggests the price
    is already at a level that is fair.” 
    Id. at 33.
    The facts of C & J Energy are also relevant. The merger in C & J Energy resulted
    from a CEO-driven process, and there was evidence that the sell-side CEO had personal
    reasons to favor the deal because he would be in charge of the combined company and
    receive significantly greater compensation. See C & J 
    Energy, 107 A.3d at 1064
    . After the
    key terms of the transaction had been negotiated, but before it was formally approved, the
    CEO went so far as to demand a side letter “affirming that C & J’s management would run
    the surviving entity and endorsing a generous compensation package.” 
    Id. When the
    acquirer balked, the CEO threatened to terminate the discussions. He got his way, and the
    deal was announced as planned. 
    Id. at 1065.
    There was also evidence that C & J Energy’s
    primary financial advisor acted as a banker for the deal rather than for C & J Energy, and
    the banker had divergent interests as a source of financing for the deal. See 
    id. at 1056–57.
    The Delaware Supreme Court held that the facts could not support a reasonable probability
    that the defendants had failed to obtain the best transaction reasonably available, relying
    heavily on the post-signing market check. See 
    id. at 1053,
    1067–68.
    In this case, McMullen’s personal interests are not as serious as the buy-side conflict
    that failed to undermine the sale process in Dell. They more closely resembled the
    divergent sell-side interests that affected the negotiators in Aruba and C & J Energy. Like
    the CEOs and bankers in those cases, McMullen’s change-of-control benefits gave him a
    personal reason to secure a deal under circumstances where a disinterested participant
    75
    might prefer a standalone option. McMullen appears to have been motivated by his desire
    to maximize his personal wealth and retire to a greater degree than the negotiators in Aruba.
    Stillwater’s general counsel (Wadman) recognized McMullen’s conflict, voiced his
    concerns to the Board, and ultimately resigned when McMullen secured more favorable
    treatment in the Merger for his own change-in-control benefits and for his CFO. See JX
    526. As a result, McMullen’s motivations most closely resembled the incentives of the
    CEO in C & J Energy, who held up the entire transaction until the acquirer agreed to a side
    letter “affirming that C & J’s management would run the surviving entity and endorsing a
    generous compensation package.” C & J 
    Energy, 107 A.3d at 1064
    . The Delaware Supreme
    Court held that the facts in C & J Energy did not provide reasonable grounds for a breach
    of fiduciary duty under the enhanced scrutiny standard of review.
    At the same time, McMullen had ample reason to pursue the best deal possible for
    Stillwater. From his testimony and demeanor, McMullen seems like someone who took
    considerable satisfaction in his ability to achieve outcomes. As a matter of professional
    pride, he wanted to sell Stillwater for the best price he could. He also had economic reasons
    to extract a higher price. As disclosed in the proxy statement for the Merger, McMullen
    held 131,248 common shares, 155,891 restricted stock unit awards, and 222,556
    performance based restricted stock unit awards, for a total of 509,695 common shares or
    share equivalents. See JX 525 at 78. At the deal price, these common shares and share
    equivalents had a value of $9,174,510. To state the obvious, every $1 increment in the deal
    price generated another half-a-million dollars for McMullen.
    76
    When directors or their affiliates own “material” amounts of common stock,
    it aligns their interests with other stockholders by giving them a “motivation
    to seek the highest price” and the “personal incentive as stockholders to think
    about the trade off between selling now and the risks of not doing so.”
    Chen v. Howard-Anderson, 
    87 A.3d 648
    , 670–71 (Del. Ch. 2014) (quoting Dollar 
    Thrifty, 14 A.3d at 600
    ); see also Lender Processing, 
    2016 WL 7324170
    , at *22 (discussing
    incentive to maximize deal price where target managers were net sellers and would not
    retain jobs post-merger).
    Consistent with his personal desire to obtain a good price for Stillwater, McMullen
    negotiated with Sibanye to increase the consideration. When Sibanye indicated interest at
    $15.75 per share in July 2016, McMullen did not rush to sign up a deal. When Sibanye
    raised indication of interest to $17.50 to $17.75 per share in December 2016, McMullen
    and the Board demanded a higher price. Even after Sibanye offered $18.00 per share,
    McMullen wanted more. Only after Sibanye twice said that $18.00 per share was its best
    and final offer did McMullen and the Board finally agree to transact.
    As with McMullen’s initiation of the sale process and the Board’s failure to engage
    in meaningful oversight of his activities until October 2016, McMullen’s personal
    motivation to exit from Stillwater and maximize his personal wealth represents a flaw in
    the sale process. Although Wadman’s noisy withdrawal highlighted these issues,
    McMullen’s personal interests as a whole do not appear materially different from interests
    that have not been sufficient in other cases to undermine the reliability of sale processes.
    On balance, the evidence does not convince me that McMullen’s divergent interests led
    either McMullen or the Board to accept a deal price that left a portion of Stillwater’s
    77
    fundamental value on the table, particularly in light of the effective post-signing market
    check that Stillwater conducted.
    d.    The “Soft-Sell”
    Turning to the details of the pre-signing phase, the petitioners contend that
    Stillwater’s pre-signing market check fell short because until BAML was formally
    retained, McMullen relied on a “soft sell” approach that provided potential buyers with
    insufficient information to conclude that Stillwater was for sale and used unauthorized
    agents who could not formally engage on Stillwater’s behalf. See PTOB at 44–45.
    The evidence demonstrates that on the facts of this case, the “soft sell” strategy was
    not an effective means of generating interest in the Company. At the same time, the “soft
    sell” effort did not do anything to harm either BAML’s abbreviated pre-signing process or
    the post-signing market check. The soft sell strategy was not a positive feature of the sale
    process, and it does not help support the persuasiveness of the deal price, but it does not
    detract from it either.
    e.    BAML’s Compressed Pre-Signing Market Check
    In a further criticism of the pre-signing phase, the petitioners contend that after
    BAML was formally retained, BAML did not have time to run an organized and
    meaningful process. The petitioners complain that BAML hastily called a list of potentially
    interested parties, who then were given only days after signing an NDA to prepare an
    expression of interest. Contrary to McMullen’s strong recommendation in September 2016
    that any bidder visit the Company’s mines before providing an expression of interest, the
    November timeline did not accommodate site visits until after a party made an expression
    78
    of interest. See JX 229 at ‘603. At trial, the petitioners introduced testimony from a sale
    process expert who questioned the effectiveness of BAML’s abbreviated pre-signing
    process. See Gray Tr. 567–68. Even Sibanye’s sale process expert questioned the
    effectiveness of the type of condensed outreach that BAML attempted to conduct. See
    Stowell Tr. 947–48.
    The petitioners have made a persuasive case that the BAML’s pre-signing process
    was suboptimal, but they have not shown that it was worthless, nor that it was harmful. To
    the contrary, when evaluated against Delaware precedents, the pre-signing efforts, while
    rushed, were a positive factor for the sale process.
    BAML received its formal mandate on November 7, 2016. The next day, BAML
    received a package of information from the Company, including Sibanye’s indication of
    interest from July, the non-disclosure agreements with Hecla and Coeur, a cash flow model,
    and instructions for accessing the data room. BAML understood that Sibanye was pushing
    to close a deal by December and swung into action to do what it could. By November 9,
    BAML had generated a plan for an expedited market check that contemplated reaching out
    to twenty parties over the next two days, working with parties who expressed interest for
    the rest of the month, and then receiving expressions of interest at the end of the month. At
    that point, the Board would decide how to proceed.
    In accordance with its expedited plan, BAML engaged directly with Sibanye, Coeur,
    and Hecla. BAML contacted five of the six parties that BAML regarded as “Possibly
    Interested,” missing one. BAML contacted eight of the twelve additional parties that
    79
    BAML had identified, missing four. BAML also contacted Northern Star, even though they
    originally had been listed as not interested.
    Ten of the fourteen parties had no interest, but four engaged. One quickly withdrew,
    two ultimately expressed interest in a merger of equals, and the fourth dropped out by late
    November. Coeur also dropped out, and Hecla indicated that it needed to find a partner to
    pursue a transaction. Although the Board extended Hecla’s deadline for submitting an
    indication of interest, and BAML followed up with Hecla, Hecla did not respond. At the
    end of November, an additional party—Northam—asked to be included in the Company’s
    process.
    During a meeting on December 2, 2016, the Board considered the status of the
    Company’s process. At that point, the Board’s only definitive expression of interest was a
    proposal that Sibanye had submitted on December 1 to acquire the Company for between
    $17.50 and $17.75 per share in cash. The Board decided to focus on Sibanye, which later
    raised its offer to $18 per share. Northam decided to withdraw, and on December 8, the
    Board approved the Merger Agreement.
    Although compressed and expedited, BAML’s outreach resulted in fourteen other
    parties hearing about Stillwater. In addition to Sibanye, a total of seven parties engaged to
    some degree. Ultimately, no one other than Sibanye submitted an indication of interest.
    The plaintiffs have criticized the timing, pacing, and scope of the pre-signing process, but
    it resulted in BAML contacting the “logical strategic buyers” before Stillwater signed up
    its deal with Sibanye. Cf. 
    Aruba, 210 A.3d at 136
    (observing that “Aruba approached other
    logical strategic buyers prior to signing the deal with HP, and none of those potential buyers
    80
    were interested.”). The number of meaningful contacts compares favorably with or is
    similar to the facts in the Delaware Supreme Court precedents.17 When considering
    whether a deal price provides persuasive evidence of fair value, it is pertinent that the
    parties contacted failed to pursue a merger when they had a free chance to do so. See 
    DFC, 172 A.3d at 376
    (citing “failure of other buyers to pursue the company when they had a
    free chance to do so” as factor supporting fairness of deal price).
    On balance, BAML’s pre-signing efforts were helpful. At a minimum, the
    abbreviated process generated incremental interest in Stillwater and gave those parties who
    engaged a leg up for the post-signing market check. Even the parties who were contacted
    but did not engage had the benefit of knowing that a transaction potentially was afoot. As
    with the “soft sell” strategy, there is no evidence that BAML’s abbreviated process did
    anything to harm the sale process. The bidders who participated in the abbreviated pre-
    signing phase were free to bid during the post-signing phase. There is no evidence that any
    were alienated or put off by the Company’s pre-signing efforts.
    17
    See 
    Aruba, 210 A.3d at 136
    –39, 142 (adopting deal price less synergies as fair
    value where company’s banker contacted five potential buyers after HP’s initial outreach,
    none were interested, sale process terminated, and sale process later resumed as single-
    bidder engagement with HP, with only one quick contact to a sixth party); 
    Dell, 177 A.3d at 28
    (finding competitive pre-signing process where Silver Lake competed one-at-a-time
    with interested parties); 
    DFC, 172 A.3d at 350
    , 355, 376 (finding “competitive process of
    bidding” where company’s banker contacted “every logical buyer,” three expressed
    interest, and two named a preliminary price with one dropping out before serious
    negotiations commenced).
    81
    BAML’s abbreviated pre-signing process was not ideal. Nevertheless, contrary to
    the petitioners’ contentions, it was a positive factor for the reliability of the sale process.
    f.     The Negotiations With Sibanye
    In their penultimate objection to Stillwater’s pre-signing process, the petitioners
    contend that Sibanye pressured Stillwater to sign a merger agreement before the
    Company’s rising stock price made what Sibanye was willing to pay look inadequate. The
    evidence demonstrates that early in his discussions with Sibanye, McMullen and Froneman
    recognized that any transaction would require a premium over Stillwater’s trading price
    and agreed in principle on a 30% premium over the thirty-day VWAP. On October 17,
    2016, Froneman told McMullen that Sibanye’s offer of a “30% premium to VWAP
    remained unchanged” and that Sibanye’s board of directors unanimously supported the
    transaction. JX 281 at ‘425. Another Sibanye executive repeated this message on
    November 22. PTO ¶ 243.
    Sibanye, however, needed to borrow the funds to acquire Stillwater, and by
    November 30, 2016, Stillwater’s share price had recovered to a point where a 30%
    premium over the thirty-day VWAP equaled $18.25 per share. Sibanye could not pay more
    than $18 per share without supplementing the consideration with cash on hand or a draw
    from its revolving credit line, which Sibanye did not want to do. Rather than sticking with
    the concept of a 30% premium over a thirty-day VWAP, Sibanye disavowed that concept,
    instead treating its prior indication of interest from July 2016 as a fixed price of $15.75 per
    share. On December 1, 2016, Sibanye proposed a transaction in a range of $17.50 to $17.75
    82
    per share, below what the 30% premium to the thirty-day VWAP would have
    contemplated.
    The petitioners object that rather than breaking off discussions or continuing the
    sale process, the Board negotiated a price of $18.00 per share, representing the maximum
    that Sibanye could pay under its financing arrangements. They argue that the highest price
    a bidder is willing to pay is not the same as fair value. See, e.g., M.P.M. 
    Enters., 731 A.2d at 797
    (cautioning that the merger price must be supported “by evidence tending to show
    that it represents the going concern value of the company rather than just the value of the
    company to one specific buyer”); In re Appraisal of Orchard Enters., Inc., 
    2012 WL 2923305
    , at *5 (Del. Ch. July 18, 2012) (“[A]lthough I have little reason to doubt Orchard’s
    assertion that no buyer was willing to pay Dimensional $25 million for the preferred stock
    and an attractive price for Orchard’s common stock in 2009, an appraisal must be focused
    on Orchard’s going concern value.”).
    The petitioners’ objection resembles similar arguments that the Delaware Supreme
    Court rejected in Dell and DFC. In Dell, the trial court found that the price negotiations
    during the pre-signing phase were limited by what the financial sponsors could pay based
    on their leverage-buyout pricing models. The respondent had conceded that the LBO model
    was not “oriented toward solving for enterprise value,” and the special committee’s
    financial advisors had briefed the committee about the LBO model and how financial
    sponsors would use it. Dell Trial, 
    2016 WL 3186538
    , at *29 (internal quotation marks
    omitted). The committee’s financial advisors used a similar model to calculate the
    maximum prices that a financial sponsor could pay. See 
    id. at *30.
    The evidence indicated
    83
    that the financial sponsors bid consistently with the results of an LBO model, and their
    negotiations with the committee proceeded within that framework. See 
    id. at *30–32.
    In
    addition to the record evidence, the trial court relied on treatises which explained how the
    price generated by an LBO model can diverge from fair value.18 Based on this evidence,
    the trial court found that the original merger consideration “was dictated by what a financial
    sponsor could pay and still generate outsized returns,” rather than Dell’s value as a going
    concern. 
    Id. at *32.
    Three months later, the trial court in DFC reached a similar conclusion when
    evaluating the deal price paid by a financial sponsor (Lone Star) to acquire the company
    (DFC) that was the subject of the appraisal proceeding. Although the trial court regarded
    the deal price as sufficiently reliable to use as a valuation input, the court expressed concern
    that “Lone Star’s status as a financial sponsor . . . focused its attention on achieving a
    18
    See Dell Trial, 
    2016 WL 3186538
    , at *29 & n.24 (citing Joshua Rosenbaum &
    Joshua Pearl, Investment Banking: Valuation, Leveraged Buyouts, and Mergers &
    Acquisitions 195–96 (2009) (“[An LBO model] is used . . . to determine an implied
    valuation range for a given target in a potential LBO sale based on achieving acceptable
    returns. . . .”); and Donald M. DePamphilis, Mergers, Acquisitions, and Other
    Restructuring Activities 506 (7th ed. 2014) (“[T]he DCF analysis solves for the present
    value of the firm, while the LBO model solves for the internal rate of return.”)); 
    id. at *29
    nn. 25, 26 (citing Rosenbaum & 
    Pearl, supra, at 195
    –96 (“In an M&A sell-side advisory
    context, the banker conducts LBO analysis to assess valuation from the perspective of a
    financial sponsor. This provides the ability to set sale price expectations for the seller and
    guide negotiations with buyers accordingly . . . .” (emphasis added)); 
    id. at 235–36
    (“Traditionally, the valuation implied by LBO analysis is toward the lower end of a
    comprehensive analysis when compared to other methodologies, particularly precedent
    transactions and DCF analysis. This is largely due to the constraints imposed by an LBO,
    including leverage capacity, credit market conditions, and the sponsor’s own IRR
    hurdles.”)).
    84
    certain internal rate of return and on reaching a deal within its financing constraints, rather
    than on DFC’s fair value.” In re Appraisal of DFC Glob. Corp. (DFC Trial), 
    2016 WL 3753123
    , at *22 (Del. Ch. July 8, 2016) (subsequent history omitted).
    The appeal from the trial-level ruling in DFC reached the Delaware Supreme Court
    before the appeal in Dell. The Delaware Supreme Court rejected the trial court’s finding
    that the buyer’s financial constraints limited the price it could pay and caused the deal price
    to diverge from fair value, stating:
    To be candid, we do not understand the logic of this finding. Any rational
    purchaser of a business should have a targeted rate of return that justifies the
    substantial risks and costs of buying a business. That is true for both strategic
    and financial buyers. It is, of course, natural for all buyers to consider how
    likely a company’s cash flows are to deliver sufficient value to pay back the
    company’s creditors and provide a return on equity that justifies the high
    costs and risks of an acquisition. But, the fact that a financial buyer may
    demand a certain rate of return on its investment in exchange for undertaking
    the risk of an acquisition does not mean that the price it is willing to pay is
    not a meaningful indication of fair value. That is especially true here, where
    the financial buyer was subjected to a competitive process of bidding, the
    company tried but was unable to refinance its public debt in the period
    leading up to the transaction, and the company had its existing debt placed
    on negative credit watch within one week of the transaction being
    announced. The “private equity carve out” that the Court of Chancery
    seemed to recognize, in which the deal price resulting in a transaction won
    by a private equity buyer is not a reliable indication of fair value, is not one
    grounded in economic literature or this record.
    
    DFC, 172 A.3d at 349
    –50. When the Delaware Supreme Court subsequently ruled on the
    discussion of the LBO model in the appeal from the trial-level ruling in Dell, the high court
    relied on its decision in DFC, explaining:
    [W]e rejected this view [in DFC] and do so again here given we see “no
    rational connection” between a buyer’s status as a financial sponsor and the
    question of whether the deal price is a fair price. After all, “all disciplined
    buyers, both strategic and financial, have internal rates of return that they
    85
    expect in exchange for taking on the large risk of a merger, or for that matter,
    any sizeable investment of its capital.”
    
    Dell, 177 A.3d at 28
    (quoting 
    DFC, 172 A.3d at 374
    –76).
    The reasoning that led the Delaware Supreme Court to reject the implications of the
    LBO model for deal pricing indicates that comparable constraints on a prevailing bidder’s
    ability or willingness to pay—whether resulting from IRR hurdles, a comparatively higher
    cost of capital, or limits on the availability of financing—should not undermine the deal
    price as an indicator of fair value if the sale process was otherwise sufficiently open. Both
    Dell and DFC suggest that a post-signing market test can be the predominant source of
    price competition. In Dell, the only participants during the pre-signing phase were the two
    financial sponsors, whom the committee permitted to participate at any one time and each
    of whom priced their deals using an LBO model. See Dell Trial, 
    2016 WL 3186538
    , at *9–
    10, *30–31, *37. In DFC, although the company initially engaged in a broad solicitation,
    the only bidders who engaged and submitted indications of interest during the pre-signing
    phase were two financial sponsors, one of whom soon dropped out. See DFC Trial, 
    2016 WL 3753123
    , at *4.
    On the facts of this case, Sibanye had the ability to pay more. Although it had not
    secured transactional financing that would have supported a price greater than $18.00 per
    share, Sibanye could have deployed cash on hand or drawn on its revolving line of credit.
    As a rational bidder for Stillwater, Sibanye understandably had a targeted rate of return
    that it needed to satisfy to justify the substantial risks and high costs of the acquisition.
    That Sibanye did not bid higher does not mean that the price it agreed to pay did not reflect
    86
    fair value when its bid prevailed. See 
    Aruba, 210 A.3d at 136
    ; 
    Dell, 177 A.3d at 28
    ; 
    DFC, 172 A.3d at 349
    –50, 374–76.
    The negotiations between Stillwater and Sibanye over price, together with Sibanye’s
    refusal to pay more, provides strong evidence of fair value. In Aruba, the Delaware
    Supreme Court explained that
    a buyer in possession of material nonpublic information about the seller is in
    a strong position (and is uniquely incentivized) to properly value the seller
    when agreeing to buy the company at a particular deal price, and that view
    of value should be given considerable weight by the Court of Chancery
    absent deficiencies in the deal process.
    
    Id. at 137.
    The high court observed that HP and Aruba went “back and forth over price”
    and that HP had “access to nonpublic information to supplement its consideration of the
    public information available to stock market buyers . . . .” 
    Id. at 139.
    The Delaware
    Supreme Court elsewhere emphasized that “HP had signed a confidentiality agreement,
    done exclusive due diligence, gotten access to material nonpublic information” and “had a
    much sharper incentive to engage in price discovery than an ordinary trader because it was
    seeking to acquire all shares.” 
    Id. at 140.
    Given these facts, the extent of the negotiations
    in Aruba supported the reliability of the deal price. The same observations apply to Sibanye
    on the facts of this case. Sibanye entered into an NDA with Stillwater, conducted extensive
    due diligence, obtained access to material nonpublic information, and was “in a strong
    position (and is uniquely incentivized) to properly value the seller when agreeing to buy
    the company at a particular deal price.”
    The fact that Stillwater and Sibanye reached agreement at $18.00 per share is
    entitled to considerable weight. Although the petitioners perceive it to be a weakness of
    87
    the pre-sale process, the Delaware Supreme Court’s precedents indicate that it was a
    strength.
    4.     The Challenges To The Post-Signing Phase
    In contrast to their many objections to the pre-signing phase, the petitioners have
    relatively few disagreements with the post-signing phase. They advance perfunctory
    challenges to the terms of the Merger Agreement, claiming that it prevented the
    stockholders from capturing the value of an increasing palladium price and foreclosed other
    bids. They also contend that the proxy statement contained disclosure violations.
    a.      The Merger Agreement And The Price Of Palladium
    The petitioners observe that the price of palladium increased between signing and
    closing. They then object that the Merger Agreement “provided no practical way for
    Stillwater’s stockholders to receive that additional value.” PTOB at 51. In cursory fashion,
    they criticize the Board for not asserting the existence of a Company Material Adverse
    Effect or invoking the fiduciary-out clause. 
    Id. at 52.
    This objection is not really a criticism
    of the sale process, but so be it.
    The petitioners never engage with the terms of the Merger Agreement and how it
    uses the concept of a Company Material Adverse Effect. The definition of a Company
    Material Adverse Effect turns on any “facts, circumstance, condition, event, change,
    development, occurrence, result, or effect” that is materially adverse to the Company. JX
    575, Annex A, at A-3. The arising of a Company Material Adverse Effect does not mean
    that something good has happened to Stillwater, like an increase in value due to rising
    commodity prices. It means something very bad has happened to Stillwater. In the Merger
    88
    Agreement, Stillwater represented that it had not suffered a Company Material Adverse
    Effect, and the Merger Agreement made the accuracy of this representation a condition to
    Sibanye’s obligation to close. See 
    id. §§ 4.10.2,
    7.2.1. The Merger Agreement also made
    the absence of a Company Material Adverse Effect a separate condition to Sibanye’s
    obligation to close. See 
    id. § 7.2.3.
    Stillwater did not obtain the right to declare something
    akin to a Company Material Beneficial Effect and terminate the Merger Agreement on that
    basis. The petitioners’ criticism that the Board did not declare a Company Material Adverse
    Effect is a turn down a blind alley.
    The petitioners likewise never engage with the terms of the Merger Agreement and
    the scope of the fiduciary out. The Board had the right to change its recommendation in
    favor of the Merger based on (i) its receipt of a “Superior Proposal” or (ii) the occurrence
    of an “Intervening Event.” See JX 525, Annex A, § 6.2.4. As permitted by Delaware law,
    see 
    8 Del. C
    . § 146, the Merger Agreement contained a force-the-vote provision that
    obligated Stillwater to take the Merger to a stockholder vote even if the Board changed its
    recommendation, but the stockholders would have the benefit of the Board’s negative
    recommendation when voting. See 
    id. § 6.17.2
    (“Without limiting the generality of the
    foregoing, the Company shall submit this Agreement for the adoption by its stockholders .
    . . whether or not a Company Adverse Recommendation Change shall have occurred or an
    Acquisition Proposal shall have been publicly announced or otherwise made . . . .”). If the
    Company’s stockholders voted down the Merger, or under other defined circumstances,
    then the Company had the ability to terminate the Merger Agreement. See 
    id. § 8.1.2(ii).
    The Board’s ability to change its recommendation for an Intervening Event, however, did
    89
    not include changes in commodity prices. The Merger Agreement defined the concept of
    an “Intervening Event” as
    any material change, event, effect, occurrence, consequence or development
    with respect to the Company or Parent, as applicable, that (i) is unknown and
    not reasonably foreseeable as of the date hereof, (ii) does not relate to any
    Acquisition Proposals, and (iii) does not arise out of or result from changes
    after the date of this Agreement in respect of prices or demand for products.
    
    Id. at A-6;
    cf. R. Franklin Balotti & A. Gilchrist Sparks, III, Deal Protection Measures and
    the Merger Recommendation, 96 Nw. U. L. Rev. 467, 468 (2002) (explaining the
    importance of an intervening event provision for the target who “discover[s] the world’s
    largest deposit of gold under its headquarters, causing the value of the target to increase
    dramatically”). Post-signing changes “in respect of prices or demand” for palladium thus
    would not qualify as an Intervening Event and would not support a change of
    recommendation. The petitioners’ criticism that the Board did not exercise its fiduciary out
    based on changes in commodity prices is another wrong turn.
    The record reflects that Stillwater did not want the merger consideration to float
    with the price of palladium. McMullen testified that “we wanted to know with certainty
    what was the number that we were taking to shareholders as the value proposition.”
    McMullen Tr. 770. That was a legitimate goal.
    The petitioners may well take these explanations and run with them, claiming that
    the situation was even worse than they thought because the Board lacked the power to do
    things that the petitioners previously believed the Board had merely failed to consider.
    Regardless, the petitioners’ bottom-line criticism of the Merger Agreement misses the
    point of what the contract was trying to accomplish. The Merger Agreement was not
    90
    attempting to give the stockholders the benefit of a transaction that included the potential
    upside or downside that would result from changes in the price of palladium after signing.
    The Merger Agreement was trying to provide stockholders with the ability to opt for the
    comparative certainty of deal consideration equal to $18.00 per share.
    More broadly, the petitioners are mistaken when they claim that there was no
    practical way for Stillwater’s stockholders to receive the additional value that the increased
    commodity price could generate. If Stillwater’s stockholders had wanted to capture the
    increased value of palladium, then they could have voted down the Merger and kept their
    shares. The spot price of palladium was readily available public information that
    Stillwater’s stockholders could take into account when deciding how to vote.
    b.      The Merger Agreement And Competing Bids
    In conclusory fashion, the petitioners object that the Merger Agreement “contained
    a no solicitation provision and 5-day matching rights,” which the petitioners characterize
    as “more buyer friendly than the protections provided in AOL that this Court described as
    creating ‘structural disadvantages dissuading any prospective bidder.’” PTOB at 51–52
    (quoting AOL, 
    2018 WL 1037450
    , at *9, and noting that the decision “describe[ed] a no-
    shop provision with a 3.5% termination fee and unlimited 3-day matching rights”). The
    petitioners argue that Sibanye’s matching rights deterred interested buyers from making a
    topping bid because Sibanye could simply match any competing proposal.
    The AOL decision was a fact-specific ruling that turned on the court’s view of the
    sale process in that case, after hearing the witnesses at trial and considering the evidentiary
    record. The Dell and DFC decisions issued while the matter was pending, and the trial
    91
    court requested supplemental briefing on the effect of those decisions. Both sides continued
    to argue for determining fair value based on financial metrics rather than by relying on the
    deal price. AOL, 
    2018 WL 1037450
    , at *1. The court nevertheless examined the sale
    process and regarded the persuasiveness of the deal price as “a close question.” 
    Id. On balance,
    the court decided not to rely on the deal price, except as cross check to a DCF
    valuation. In reaching this outcome, the court placed heavy weight on a comment made by
    AOL’s CEO, shortly after the signing of the deal, in which he said he was “committed to
    doing the deal with Verizon” and emphasized that he “gave the team at Verizon my word
    that . . . this deal is going to happen.” 
    Id. at *9.
    The court found that the comment “could
    reasonably cause potential bidders to pause when combined with the deal protections here.”
    
    Id. A trial
    court’s job is to make that type of decision and determine when the evidence
    warrants a case-specific departure from a general rule.
    The broader Delaware corpus supports the general principle that the package of
    defensive measures found in the Merger Agreement in this case is sufficient to permit an
    effective post-signing market check, even when matching rights are present. As noted,
    commentators have perceived that under the Delaware Supreme Court’s recent appraisal
    decisions, a sale process involving a publicly traded firm will function as a reliable
    indicator of fair value as long as it would pass muster if reviewed under enhanced scrutiny
    in a breach of fiduciary duty case. See Hamermesh & 
    Wachter, supra, at 962
    , 982–83;
    Korsmo & 
    Myers, supra, at 269
    . Based on numerous trial court precedents, the suite of
    deal protection measures in the Merger Agreement would not have supported a claim for
    92
    breach of fiduciary duty.19 The suite of deal protections in the Merger Agreement compared
    favorably with the deal protections in C & J Energy and PLX, which this decision has
    discussed at length.
    19
    See, e.g., Dent v. Ramtron Int’l Corp., 
    2014 WL 2931180
    , at *8–10 (Del. Ch. June
    30, 2014) (rejecting fiduciary challenge to “(1) a no-solicitation provision; (2) a standstill
    provision; (3) a change in recommendation provision; (4) information rights for [the
    acquirer]; and (5) a $5 million termination fee” where termination fee represented 4.5% of
    equity value and change-of-recommendation provision included unlimited matching right);
    In re BJ’s Wholesale Club, Inc. S’holders Litig., 
    2013 WL 396202
    , at *13 (Del. Ch. Jan.
    31, 2013) (rejecting fiduciary challenge to a merger agreement with a no-shop provision,
    matching and information rights, a termination fee representing 3.1% of deal value, and a
    force-the-vote provision; observing that “under Delaware law, these deal protection
    measures, individually or cumulatively, have routinely been upheld as reasonable”); In re
    Novell, Inc. S’holder Litig., 
    2013 WL 322560
    , at *10 (Del. Ch. Jan. 3, 2013) (describing
    “the no solicitation provision, the matching rights provision, and the termination fee” as
    “customary and well within the range permitted under Delaware law” and observing that
    “[t]he mere inclusion of such routine terms does not amount to a breach of fiduciary duty”);
    In re Synthes, Inc. S'holder Litig., 
    50 A.3d 1022
    , 1049 (Del. Ch. 2012) (finding that a
    termination fee of 3.05% of equity value, a no-solicitation provision with a fiduciary out
    and matching rights, a force-the-vote provision, and a voting agreement that locked up at
    least 33% of the company shares in favor of the merger were not unreasonable deal
    protection devices); In re Answers Corp. S’holders Litig., 
    2011 WL 1366780
    , at *4 & n.47
    (Del. Ch. Apr. 11, 2011) (describing “a termination fee plus expense reimbursement of
    4.4% of the Proposed Transaction’s equity value, a no solicitation clause, a ‘no-talk’
    provision limiting the Board’s ability to discuss an alternative transaction with an
    unsolicited bidder, a matching rights provision, and a force-the-vote requirement” as
    “standard merger terms” that “do not alone constitute breaches of fiduciary duty” (quoting
    In re 3Com S’holders Litig., 
    2009 WL 5173804
    , at *7 (Del. Ch. Dec. 18, 2009))); In re
    Atheros Commc’ns, Inc. S’holder Litig., 
    2011 WL 864928
    , at *7 n.61 (Del. Ch. Mar. 4,
    2011) (same analysis for no-solicitation provision, matching right, and termination fee); In
    re 3Com, 
    2009 WL 5173804
    , at *7 & n.37 (rejecting challenge to merger agreement with
    a no-solicitation provision, matching rights, and a termination fee in excess of 4% of equity
    value; describing provisions as having been “repeatedly” upheld by this court and
    collecting authorities).
    93
    The Aruba decision involved a similar suite of deal protections. The merger
    agreement in that case “prohibited Aruba from soliciting competing offers and required the
    Aruba Board to continue to support the merger, subject to a fiduciary out and an out for an
    unsolicited superior proposal” and included a termination fee equal to 3% of the merger’s
    equity value. Aruba Trial, 
    2018 WL 922139
    , at *21, *38. The matching rights were similar
    too: HP had “an unlimited match right, with five days to match the first superior proposal
    and two days to match any subsequent increase, and during the match period Aruba had to
    negotiate exclusively and in good faith with HP.” 
    Id. at *38
    (footnote omitted). Viewing
    the deal protections holistically, the Delaware Supreme Court found that potential buyers
    had an open chance to bid, which supported the high court’s use of a deal-price-less-
    synergies metric to establish fair value. See 
    Aruba, 210 A.3d at 136
    .
    The Delaware Supreme Court has explained that a post-signing market check is
    effective as long as “interested bidders have a fair opportunity to present a higher-value
    alternative, and the board has the flexibility to eschew the original transaction and accept
    the higher-value deal.” C & J 
    Energy, 107 A.3d at 1068
    . This description comports with
    guidance from a frequently cited treatise, which identifies “critical aspects” of a merger
    agreement that does not “preclude or impermissibly impede a post-signing market check.”
    1 Lou R. Kling & Eileen T. Nugent, Negotiated Acquisitions of Companies, Subsidiaries
    and Divisions § 4.04[6][b], at 4-89 to -90 (1992 & Supp. 2019).
    First, the economics of the executed agreement must be such that it does not
    unduly impede the ability of third parties to make competing bids. Types of
    arrangements that might raise questions in this regard include asset lock-ups,
    stock lock-ups, no-shops, force-the-vote provisions, and termination fees.
    94
    The operative word is “unduly;” the impact will vary depending upon the
    actual type of device involved and its specific terms.
    ***
    Second, the target should be permitted to disclose confidential information
    to any third party who has on its own (i.e., not been solicited) “shown up” in
    the sense that it has submitted a proposal or, at a minimum, an indication of
    interest which is, or which the target believes is, reasonably likely to lead to
    (and who is capable of consummating) a higher competing bid. In this regard,
    the target should also be able to negotiate with such third parties. This
    removes any informational advantage that the initial (anointed) purchaser
    may have.
    ***
    Finally, the target board of directors should have the contractual right,
    without violating the acquisition agreement, to withdraw or modify its
    recommendation to shareholders with respect to the transaction provided for
    in the executed acquisition agreement.
    
    Id. at 4-90
    to -94.1 (footnotes omitted).
    Using this framework, the deal protections did not preclude or impermissibly
    impede a post-signing market check. For starters, any party could submit a bona fide
    written Acquisition Proposal. If the Board determined that the Acquisition Proposal
    “constitutes, or could reasonably be expected to result in, a Superior Proposal” and entered
    into an “Acceptable Confidentiality Agreement” with the party making the proposal, then
    the Board could “engage in negotiations or discussions with, or furnish any information
    to,” the party making the Acquisition Proposal. JX 545, Annex A, § 6.2.2. Additional
    requirements included that the Company notify Sibanye within twenty-four hours of its
    determination, furnish Sibanye “substantially concurrently” with any information provided
    to the third party, and not share any of Sibanye’s confidential information unless required
    95
    by law. 
    Id. The Company
    also had to notify Sibanye of the terms of the Acquisition
    Proposal and the identity of the third party making it, then keep Sibanye informed of any
    developments on a reasonably prompt basis. 
    Id. § 6.2.3.
    After that point, if the Board determined that the Acquisition Proposal constituted a
    Superior Proposal and that its fiduciary duties required it, then the Board could change its
    recommendation in favor of the Merger, provided that before doing so, the Board gave
    Sibanye five days in which to match the Superior Proposal or otherwise offer changes to
    the Merger Agreement to avoid the change of recommendation. The Board could also
    withdraw or modify its recommendation for an Intervening Event, again conditioned on
    giving Sibanye five days in which to propose changes to the Merger Agreement to avoid
    the change of recommendation. If the stockholders voted down the deal, then Stillwater
    could terminate the Merger Agreement, subject only to paying a termination fee and
    expense reimbursement equal to 1.2% of the Merger’s equity value.
    The post-signing market check began on December 9, 2016, when Sibanye and the
    Company announced the Merger. It ended on April 26, 2017, when the Company’s
    stockholders approved the Merger Agreement. The resulting passive market check lasted
    138 days, close to the 153 days in C & J Energy and far longer than many of the passive,
    post-signing market checks that the Delaware courts have approved. See App.
    During the post-singing market check, no one bid. The failure of any other party to
    come forward provides significant evidence of fairness, because “[f]air value entails at
    minimum a price some buyer is willing to pay—not a price at which no class of buyers in
    the market would pay.” 
    Dell, 177 A.3d at 29
    ; see 
    id. at 32,
    34. The absence of a higher bid
    96
    indicates “that the deal market was already robust and that a topping bid involved a serious
    risk of overpayment,” which in turn “suggests the price is already at a level that is fair.” 
    Id. at 33.
    As in Aruba, “[i]t cannot be that an open chance for buyers to bid signals a market
    failure simply because buyers do not believe the asset on sale is sufficiently valuable for
    them to engage in a bidding contest against each other.” 
    Aruba, 210 A.3d at 136
    . Instead it
    suggests that “the target’s value is not sufficiently enticing to buyers to engender a bidding
    war above the winning price.” 
    Id. c. The
    Stockholder Vote
    In their last challenge to the post-signing phase, the petitioners assert that the
    stockholders approved the Merger based on incomplete and misleading information. They
    devote only two pages in their opening brief to this argument, the bulk of which describes
    the legal principles that apply in fiduciary duty cases. See PTOB at 53–54 (citing Morrison
    v. Berry, 
    191 A.3d 268
    , 282–83 (Del. 2018); and Corwin v. KKR Fin. Hldgs., LLC, 
    125 A.3d 304
    , 312 (Del. 2015)). The factual description of their disclosure theory appears in
    just three sentences:
    Stillwater’s stockholders were told McMullen led the sale process, but they
    were never informed that he was preparing to leave the Company or the scope
    of his outside business ventures. In addition, Stillwater stockholders were
    told that Wadman left the Company prior to closing, but they were never
    informed of the context of his departure or his “noisy exit.” Stillwater’s
    stockholders were also provided no information regarding the Company’s
    exploration zones.
    PTOB at 53–54. They devote the same amount of space to this theory in their reply brief,
    although the text extends over three pages. Dkt. 228 at 26–28. In their reply brief, they
    argue that stockholders should have been told that Wadman raised concerns about
    97
    McMullen’s conflicts of interest and “his manner of soliciting interest from third parties,”
    and that Wadman was “retaliated against for doing so.” 
    Id. at 27.
    They also argue that
    stockholders should have been told that McMullen “was in violation of his 2016
    employment agreement” while running the sale process because of his roles with Nevada
    Iron and New Chris. 
    Id. The petitioners
    ’ argument about Stillwater’s exploration zones does not appear to
    hold up under their own understanding of the law. The petitioners elsewhere argued
    persuasively that under Industry Guide 7, promulgated by the Securities and Exchange
    Commission, Stillwater was not permitted to disclose information about the value of the
    Company’s exploration zones. See, infra, Pt. II.B.3.a.
    The disclosure theories about McMullen and Wadman would likely have some merit
    if the petitioners had done more to articulate them, support them with case law, and explain
    their relationship to a determination of fair value. Presumably the petitioners’ believe that
    if stockholders had been told that McMullen was pursuing a sale in part because of his
    personal interest in exiting the Company and that Wadman resigned because of disputes
    over how McMullen handled the sale process, then some stockholders might have
    questioned whether the deal price reflected fair value.
    These contentions would have to overcome the doctrine against self-flagellation.
    See, e.g., Loudon v. Archer-Daniels-Midland Co., 
    700 A.2d 135
    , 143 (Del. 1997). That
    said, the proxy statement should have disclosed McMullen’s interest in retiring, his roles
    with GT Gold and New Chris, and their implications for his employment agreement.
    98
    Stockholders also should have been told that Wadman resigned because of disputes with
    senior management about the conduct of the sale process.
    Although I have tried to give the petitioners the benefit of the doubt by crediting
    their conclusory assertions in this fashion, I am not convinced that their arguments are
    sufficient to undermine the stockholder vote as an expression of the preference of a
    supermajority of Stillwater’s stockholders for a sale rather than having the Company
    continue as a standalone entity. The Delaware Supreme Court has explained that “[t]he
    issue in an appraisal is not whether a negotiator has extracted the highest possible bid.
    Rather, the key inquiry is whether the dissenters got fair value and were not exploited.”
    
    Dell, 177 A.3d at 33
    . The disclosures that the petitioners say the Company should have
    made could have affected stockholders’ views about whether their negotiators had
    extracted the highest possible bid. If stockholders had been provided with information
    about McMullen’s interests and Wadman’s withdrawal, then perhaps some stockholders
    would have inferred that a different negotiator might have pushed for more from Sibanye
    or worked harder during the pre-signing phase to find a bidder who could have paid a
    higher price (an inference undercut by the absence of any topping bid during the post-
    signing phase). They would not have had any reason to revise their assessment of the
    Company’s prospects as a standalone entity or to vote down the Merger in the belief that
    the Company was more valuable as a going concern in its operative reality as a widely
    held, publicly traded firm.
    Because of the disclosure issues, this decision does not give heavy weight to the
    stockholder vote. Nevertheless, the vote remains a positive factor when evaluating whether
    99
    the deal price reflected fair value. If stockholders believed that the Company was worth
    more, they could have voted down the Merger and retained their proportionate share of the
    Company as a going concern. By approving the Merger at $18.00 per share, they evidenced
    their belief that the deal price provided fair value and was not exploitive.
    5.     The Sale Process Was Reliable.
    Sibanye proved by a preponderance of the evidence that the sale process made the
    deal price a persuasive indicator of fair value. The sale process was not perfect, and the
    petitioners highlighted its flaws, but the facts of this case, when viewed as a whole,
    compare favorably or are on par with the facts in C & J Energy, PLX, DFC, Dell, and
    Aruba.
    The sale process that led to the Merger bore objective indicia of fairness that
    rendered the deal price a reliable indicator of fair value. To reiterate, it was an arm’s-length
    transaction. It was approved by an unconflicted Board and by Stillwater’s stockholders.
    And it resulted from adversarial price negotiations between Stillwater and Sibanye. Most
    significantly, no bidders emerged during the post-signing phase, despite a Merger
    Agreement that contained a suite of deal protections that would pass muster under
    enhanced scrutiny.
    The petitioners pointed to problems during the early phases of the sale process
    before the Board began exercising serious oversight and before BAML was retained. Those
    flaws are factors to consider, but they do not undermine the reliability of the sale price
    given what happened later. BAML’s pre-signing canvass was a positive factor. The
    negotiations with Sibanye were also a positive factor. And the process culminated in an
    100
    effective, albeit passive, post-signing market check. If Stillwater had pursued a single-
    bidder strategy and only engaged with Sibanye, then the terms of the Merger Agreement
    would have facilitated a sufficiently reliable post-signing market check to validate the deal
    price. Stillwater did more than what would have been sufficient under a single-bidder
    scenario.
    It is theoretically possible that a more thorough pre-signing process or more
    vigorous negotiations might have generated a higher transaction price for Stillwater’s
    stockholders, but the issue in an appraisal “is not whether a negotiator has extracted the
    highest possible bid.” 
    Dell, 177 A.3d at 33
    .
    Capitalism is rough and ready, and the purpose of an appraisal is not to make
    sure that the petitioners get the highest conceivable value that might have
    been procedure had every domino fallen out of the company’s way; rather, it
    is to make sure that they receive fair compensation for their shares in the
    sense that it reflects what they deserve to receive based on what would fairly
    be given to them in an arm’s-length transaction.
    
    DFC, 172 A.3d at 370
    –71. “[T]he key inquiry is whether the dissenters got fair value and
    were not exploited.” 
    Dell, 177 A.3d at 33
    .
    The Merger in this case was rough and ready. McMullen and the Board did not
    adhere to the best practices and transactional niceties that an advisor steeped in Delaware
    decisions would recommend. Nevertheless, given the arm’s-length nature of the Merger,
    the premium over market, and the substance of what took place during the sale process, it
    is not possible to say that an award at the deal price would result in the petitioners being
    exploited.
    101
    6.      The Adjustment For Value Arising From The Merger
    Section 262 provides that “the Court shall determine the fair value of the shares
    exclusive of any element of value arising from the accomplishment or expectation of the
    merger or consolidation . . . .” 
    8 Del. C
    . § 262(h). “[I]t is widely assumed that the sale price
    in many M&A deals includes a portion of the buyer’s expected synergy gains, which is
    part of the premium the winning buyer must pay to prevail and obtain control.” 
    DFC, 172 A.3d at 371
    . “In an arm’s-length, synergistic transaction, the deal price generally will
    exceed fair value because target fiduciaries bargain for a premium that includes . . . a share
    of the anticipated synergies . . . .” Olson v. ev3, Inc., 
    2011 WL 704409
    , at *10 (Del. Ch.
    Feb. 21, 2011). “[S]ection 262(h) requires that the Court of Chancery discern the going
    concern value of the company irrespective of the synergies involved in a merger.” M.P.M.
    
    Enters., 731 A.2d at 797
    . To derive an estimate of fair value, the court must exclude “any
    synergies or other value expected from the merger giving rise to the appraisal proceeding
    itself . . . .” Golden Telecom 
    Trial, 993 A.2d at 507
    . This means the trial court “must
    exclude . . . the amount of any value that the selling company’s shareholders would receive
    because a buyer intends to operate the subject company, not as a stand-alone going concern,
    but as part of a larger enterprise, from which synergistic gains can be extracted.” 
    Aruba, 210 A.3d at 133
    (internal quotation marks omitted).
    Sibanye’s valuation expert was Mark Zmijewski, an emeritus professor of finance
    at the University of Chicago and a consultant at Charles River Associates. Zmijewski
    opined that the evidence he reviewed did “not indicate that the Transaction resulted in
    quantifiable synergies.” JX 652 ¶ 66 [hereinafter Zmijewski Rep.]; see Zmijewski Tr. 1146.
    102
    Sibanye told its stockholders that the price did not reflect any synergies. JX 421 at ‘224.
    McMullen testified at trial that he did not believe there were any synergies arising from the
    Merger. McMullen Tr. 801. There is accordingly no reason to exclude any value from the
    deal price based on synergies.
    In this proceeding, Sibanye argued that despite the absence of quantifiable cost
    synergies or revenue synergies, it willingly paid more than fair value for Stillwater,
    resulting in a portion of the consideration reflecting value “arising from the
    accomplishment or expectation of the merger or consolidation . . . .” 
    8 Del. C
    . § 262(h). In
    its opening brief, Sibanye argued that it paid a premium for two strategic reasons: (i) to
    facilitate entry into the United States and (ii) to expand its share of the PGM market.
    Sibanye also argued that it could pay a premium in the Merger because after the Merger, it
    could obtain a better rating on its debt. See also Zmijewski Tr. 1120–22; JX 397 at ‘452;
    JX 498 at 20; JX 486 at 1; Rosen Tr. 407–08. Each of these reasons identifies a valuable
    aspect of Stillwater based on its operative reality as a going concern. Stillwater was the
    only PGM producer located in the United States, and it generated significant cash flow.
    None of these features represented a source of value “arising from the accomplishment or
    expectation of the merger or consolidation.”
    Sibanye failed to meet its burden of proof to establish a quantifiable amount that the
    court should deduct from the deal price. This decision does not make any downward
    adjustment to the deal price to compensate for combinatorial value.
    103
    7.     The Adjustment For Changes In Value Between Signing And
    Closing
    Under Section 262, the time for determining the value of a dissenter’s shares is the
    point just before the merger closes. See Appraisal 
    Rights, supra
    , at A-33. The deal price
    provides a data point for the value of the company as of the date of signing, but the
    valuation date for an appraisal is the date of closing. Consequently, if the value of the
    corporation changes between the signing of the merger and the closing, the fair value
    determination must be measured by the “operative reality” of the corporation at the
    effective time of the merger. Technicolor 
    II, 684 A.2d at 298
    .
    In a merger involving a widely held, publicly traded company, some gap between
    signing and closing will usually exist. The customary need to prepare and disseminate
    disclosure documents, then complete a first-step tender offer or obtain a stockholder vote
    will typically result in several months elapsing between signing and closing. See Robert T.
    Miller, The Economics of Deal Risk: Allocating Risk Through MAC Clauses in Business
    Combination Agreements, 50 Wm. & Mary L. Rev. 2007, 2018–19 (2009) (discussing
    timelines for various transaction structures). If regulatory approvals are required, the
    temporal gap can expand. 
    Id. at 2020–23.
    During this period, the value of the company
    could rise or fall.
    Despite the customary existence of a temporal gap between signing and closing,
    Delaware appraisal decisions have typically not made adjustments to the deal price to
    reflect a valuation change during the post-signing period. In Union Illinois, this court relied
    for the first time on a deal-price-less-synergies metric when determining the fair value of
    104
    a privately held bank (UFG). See Union 
    Ill., 847 A.2d at 343
    . Six months elapsed between
    signing and closing, and the petitioners objected to using the deal price because of the
    temporal gap. The trial court described this argument as a “quibble” and as “not a forceful
    objection,” because “[t]he negotiation of merger terms always and necessarily precedes
    consummation.” 
    Id. at 358.
    Turning to the facts of the case, the court found that the
    petitioners were not able “to cite any rational explanatory factor that indicates why an
    investor would perceive UFG’s future more optimistically on New Year’s Eve 2001 than
    they did on the preceding Fourth of July.” 
    Id. UFG had
    experienced “a modest upward
    adjustment in its [net income margin] in the second half of 2001,” but the court saw no
    evidence that the increase was sustainable or would alleviate UFG’s problems complying
    with capital adequacy standards. 
    Id. Although UFG
    had refinanced its debt, the loan came
    from the acquirer, and UFG was not in a position to either service that debt or refinance it
    completing the merger. 
    Id. The court
    concluded that “[c]onsidered fairly, the record does
    not support the idea that UFG was more valuable at the end of 2001 than it was when the
    Merger Agreement was signed.” 
    Id. In PetSmart,
    this court awarded fair value based on the deal price in a case involving
    a publicly traded firm. See In re PetSmart, Inc., 
    2017 WL 2303599
    , at *2 (Del. Ch. May
    26, 2017). The court regarded the petitioners’ argument that the merger price “was stale by
    the time of closing” as “at best speculative.” 
    Id. at *31.
    Citing Union Illinois, the court
    explained that “[m]ergers are consummated after the consideration is set. That temporal
    separation, however, does not in and of itself suggest that the merger consideration does
    105
    not accurately reflect the company’s going concern value as of the closing date.” 
    Id. The court
    then turned to the petitioners’ case-specific arguments:
    Petitioners would have me conclude that the Merger Price was stale because,
    in the gap between signing and closing, PetSmart’s fortunes took a
    miraculous turn for the better. While the record indicates that the Company
    did enjoy some favorable results in Q4 2014, such as an uptick in comparable
    store sales growth, I am not convinced that these short-term improvements
    were indicative of a long-term trend. In fact, all testimony at trial was to the
    contrary—the Board, as well as Teffner, believed that the Q4 results were
    temporary and provided no basis to alter their view of the Company’s long-
    term prospects. These perceptions were born out in Q1 2015 (when the
    Merger closed) during which PetSmart’s comparable store sales dropped to
    1.7%. At year end, PetSmart reported comparable store sales growth of 0.9%,
    a 40% miss from the Management Projections in just the first projection year.
    
    Id. (footnotes omitted).
    The petitioners in PetSmart thus failed to carry their burden of
    proving that the value of the company had changed.
    Most recently, in Columbia, this court awarded fair value based on the deal price in
    another case involving a publicly traded firm. See In re Appraisal of Columbia Pipeline
    Gp., Inc., 
    2019 WL 3778370
    , at *1 (Del. Ch. Aug. 12, 2019). The company developed,
    owned, and operated natural gas pipelines, storage facilities, and other midstream assets,
    and it had a business plan that called for raising large amounts of equity financing through
    a master limited partnership (“MLP”). Before agreeing to be acquired, the company had
    been unable to use the MLP structure to raise capital because of adverse trends in the MLP
    financing market. The merger agreement was signed on March 17, 2016, and the
    transaction closed on July 1, 2016. The petitioners argued that in the interim, the market
    for MLP equity had improved and prices for energy commodities had increased. See 
    id. at *45.
    The court found that the petitioners had not carried their burden of proving how to
    106
    quantify the alleged improvements in the form of a higher deal price. 
    Id. The court
    also
    found that the improvement in two MLP indices did not persuasively support the claim that
    the company would have been able to raise capital efficiently through its MLP. The court
    similarly rejected any valuation increase based on the prices of energy related commodities,
    because everyone agreed that the company’s value did not depend on commodities. As a
    midstream company, it did not own, buy, or sell the commodities that it transported or
    stored. 
    Id. The one
    arguable exception is Lender Processing, where this court awarded fair
    value based on the value of the deal price at closing, rather than at signing, where the deal
    consideration consisted of 50% cash and 50% stock. See Lender Processing, 
    2016 WL 7324170
    , at *1, *8. Because of the stock component, the value of the merger consideration
    increased from $33.25 per share at signing to $37.14 per share at closing. 
    Id. The petitioners
    pointed to the existence of the temporal gap as a reason not to rely on the deal price or other
    market-based metrics associated with the signing of the deal. The respondent pointed to
    the absence of a topping bid as validating the deal price. After reviewing the evidence, the
    court concluded that the final merger consideration “was a reliable indicator of fair value
    as of the closing” and that “because of synergies and a post-signing decline in the
    Company’s performance, the fair value of the Company as of the closing date did not
    exceed” that amount. 
    Id. at *23.
    The acquirer’s expert had not tried to quantify the
    synergies or the amount of the post-signing valuation decline, and the court concluded that
    the respondent had failed to carry its burden of proof on those issues. 
    Id. at *33.
    By using
    the deal price as measured at closing rather than at signing, the Lender Processing decision
    107
    accounted for changes in value between signing and closing, but without making an explicit
    adjustment.
    All four precedents considered whether the deal-price metric needed to be adjusted
    to reflect changes in value between signing and closing. The decisions thus indicate that an
    adjustment to the deal price can be warranted. But the decisions also show that the
    proponent of the adjustment must carry its burden by identifying a persuasive reason for
    the change and proving the amount.
    At a minimum, it would seem to make sense to adjust the deal price for inflation.
    When the parties agreed to the deal price on December 8, 2016, they reached agreement
    on a price measured in dollars valued as of that date. Between that date and the closing on
    May 4, 2017, the purchasing power of those dollars declined. If Stillwater had precisely
    the same value in the abstract on May 4, 2017, as it did on December 8, 2016, it would still
    be necessary to adjust the number of dollars used to express that value to reflect the
    intervening decline in what the value of a dollar represented. Adjusting the deal price for
    inflation would achieve this result.20
    20
    The pop-culture illustration of this principle is J. Wellington Wimpy’s offer to
    “gladly pay you Tuesday for a hamburger today.” See J. Wellington Wimpy, Wikipedia,
    https://en.wikipedia.org/wiki/J._Wellington_Wimpy (last visited Aug. 20, 2019). Setting
    aside credit risk, dollars paid next Tuesday are worth less than dollars paid today, so the
    same price paid next Tuesday is a pleasant deal for Wimpy. The same is true for Sibanye
    in an appraisal. Valuing Stillwater at $18.00 per share based on an agreement reached on
    December 8, 2016, then using that figure to determine value as of May 4, 2017, lets Sibanye
    use December’s dollars for a valuation in May. The statutory interest award is measured
    from closing, so that aspect of the appraisal remedy does not pick up the decline in the
    purchasing power of dollars used to measure the deal-price metric. In this respect, the
    petitioners are differently situated than stockholders who did not pursue their appraisal
    108
    As their valuation expert, the petitioners relied on Howard Rosen, a senior managing
    director at FTI Consulting. When adjusting the unaffected trading price, Rosen used an
    inflation rate of 2% per annum to account for the decrease in the value of dollars between
    signing and closing, then made further adjustments. See JX 728 ¶¶ 5.19, 5.25 to 5.28. A
    similar inflation-based adjustment could be made to the deal price, generating a value on
    the closing date of $18.14 per share, but no one argued for it.
    The nature of Stillwater’s business makes this case a plausible one for an upward
    adjustment that goes beyond inflation. Stillwater was a mining concern that primarily
    produced palladium and platinum. Stillwater’s cash flows depended on the prices of those
    metals, so when the prices of those metals increased or decreased materially, the value of
    the Company increased or decreased materially as well. The Company’s annual report for
    2016 explained the relationship as follows:
    The Company’s earnings and cash flows are sensitive to changes in PGM
    prices – based on 2016 revenue and costs, a 1% (or approximately $7 per
    ounce) change in the Company’s average combined realized price for
    palladium and platinum would result in approximately a $7.1 million change
    to before-tax net income and a change to cash flows from operations of
    approximately $3.9 million.
    rights. They accepted the $18.00 per share and received it, without interest, shortly after
    May 4, 2017, once the merger consideration payouts were processed through the clearing
    system. The appraisal petitioners did not accept that outcome. They opted for appraisal and
    sought a determination of Stillwater’s fair value as of May 4, 2017. Sibanye can argue
    legitimately that the deal price of $18.00 per share provides the best evidence of fair value,
    but that is a price calculated in December 2016 dollars, not May 2017 dollars.
    109
    JX 728 ¶ 5.21 (quoting Stillwater Mining Company, Annual Report (Form 10-K) (Feb. 16,
    2017)). The Merger was signed on December 9, 2016. The Merger closed on May 4, 2017.
    Between signing and closing, the prices of palladium and platinum increased materially,
    with a direct effect on Stillwater’s value. 
    Id. ¶ 5.20.
    Rosen determined that the sales-weighted price of Stillwater’s commodities
    increased by 5.9% between signing and closing. Using the formula in Stillwater’s annual
    report, Rosen calculated the valuation impact of the additional cash flow as ranging from
    $248 million (using a 11.2% WACC) to $285 million (using a 10% WACC), which equated
    to an increase of between $2.00 to $2.30 per share. 
    Id. He regarded
    his estimate as
    conservative because he kept production constant and did not account for new sources,
    such as Blitz, coming on line. 
    Id. ¶¶ 5.23
    to 5.25. Rosen used this figure to make
    adjustments to the unaffected trading price. In theory, he could have made similar
    adjustments to the merger price.
    As this discussion indicates, the petitioners never argued for an adjustment to the
    deal price based on an increase in value between signing and closing. As discussed in the
    next section, Sibanye argued that the court could make an adjustment to the unaffected
    trading price and use the adjusted trading price as an indicator of fair value. The petitioners
    countered that argument by proposing an adjustment of their own that resulted in the
    adjusted trading price exceeding the deal price. Those arguments addressed the trading
    price, not the deal price. There could be considerable conceptual overlap between the
    approaches, but there could also be significant differences.
    110
    A petitioner seeking to make valuation-based adjustments to a reliable deal price
    also would need to confront the implications of the post-signing market check. As in
    Lender Processing, a respondent in an appraisal case could easily argue that if a company’s
    value increased between signing and closing, then a competing bidder would have
    perceived that value and offered more than the deal price. The respondent would argue that
    if no one bid, then that fact would call for rejecting the petitioners’ evidence of a valuation
    increase. There are several possible responses to this argument.
    One response is a relatively small point from a valuation perspective: the
    termination fee. Using this case as an example, if a topping bidder made a Superior
    Proposal, and if the Board changed its recommendation, and if the stockholders voted down
    the Merger, then Stillwater would have to pay Sibanye a termination fee of $16.5 million
    plus reimbursement of Sibanye’s expenses up to $10 million, for a total payment of $26.5
    million or 21.6 cents per share. Those amounts would reduce Stillwater’s value to the
    acquirer, making the acquirer neutral as to any increase in Stillwater’s value that did not
    clear that level. The point of indifference is actually higher, because a competing bidder
    would incur expenses of its own to make the competing bid. Ignoring those incremental
    expenses and focusing only on the sell-side fees, Stillwater’s value could increase by up to
    $26.5 million without a rational acquirer having any reason to bid. The absence of a topping
    bid could not rule out a valuation change of this magnitude, but an award above the deal
    price that fell within the range permitted by the termination fee would likely be cold
    comfort to the typical appraisal petitioner.
    111
    A more significant counterargument would focus on the timing of the valuation
    change. A premise that underlies the effectiveness of the post-signing market check is that
    other bidders learn that the target is for sale when the deal is announced, can examine the
    target for themselves, and if they value the target more highly (taking into account
    synergies and other sources of bidder-specific value), then they can intervene. Under this
    theoretical framework, competing bidders can begin work shortly after the announcement,
    giving them the full timeline between the signing and the vote in which to intervene. When
    the potential overbid would be induced by a change in the value of the target company, the
    time for the competing bidder to act does not begin with the announcement of the deal, but
    rather when the bidder learns of the valuation change. The delayed signal shortens the
    amount of time for the bidder to intervene. As the date of the stockholder vote approaches,
    it becomes less likely (all else equal) that a bidder will intervene, if only because less time
    is available in which to do so. Because of this effect, a failure to bid during the post-signing
    phase provides a much noisier signal about changes in the target’s value than it does about
    the absence of higher-valuing bidders. In this case, the increase in value that resulted from
    changes in the spot price did not really begin until February 2017, two months after signing.
    It dropped in March, then picked up again in April, when the stockholder vote took place.
    A third counterargument would examine the possibility of changes in value after the
    stockholder vote but before closing. As this case illustrates, a competing bidder’s only
    meaningful opportunity to intervene is before the stockholders approve the transaction. In
    a case where closing is delayed significantly after the stockholder vote because of issues
    such as the need for regulatory approvals, the post-vote temporal gap would matter more.
    112
    Perhaps the most significant problem with relying on a post-signing market check
    to rule out an increase in the target’s standalone value is that the resulting valuation
    improvement would be available to any bidder. The competition for the incremental value
    would likely operate as a common value auction, defined as an auction in which “every
    bidder has the same value for the auctioned object.” Peter Cramton & Alan Schwartz,
    Using Auction Theory to Inform Takeover Regulation, 75 L. Econ. & Org. 27, 28–29
    (1991). In a competition for that incremental value, the incumbent bidder’s matching right
    would loom large. To make it worthwhile to bid, a potential deal jumper would not only
    have to perceive that the value of the target had increased above the level set by the deal
    price plus the termination fee and fee reimbursement plus the deal jumper’s likely
    transaction costs, but also perceive a pathway to success that was sufficiently realistic to
    warrant becoming involved, taking into account the potential reputational damage that
    could result from being unsuccessful. Unless the competitor had a unique reason to value
    the increased cash flows more highly than the incumbent, the competitor should expect the
    incumbent to match any incremental bid.21 In a case like this one, where the valuation
    21
    See Fernán Restrepo & Guhan Subramanian, The New Look of Deal Protection,
    69 Stan. L. Rev. 1013, 1058–63 (2017) (analyzing implications of matching rights); Brian
    JM Quinn, Bulletproof: Mandatory Rules for Deal Protection, 32 J. Corp. L. 865, 870
    (2007) (analyzing matching rights as the functional equivalent of a right of first refusal and
    explaining that “[t]he presence of rights of first refusal can be a strong deterrent against
    subsequent bids” because “[s]uccess under these circumstances may involve paying too
    much and suffering the ‘winner’s curse’”); see also Marcel Kahan & Rangarajan K.
    Sundaram, First-Purchase Rights: Rights of First Refusal and Rights of First Offer, 12 Am.
    L. & Econ. Rev. 331, 331 (2012) (finding “that a right of first refusal transfers value from
    other buyers to the right-holder, but may also force the seller to make suboptimal offers”);
    Frank Aquila & Melissa Sawyer, Diary of a Wary Market: 2010 in Review and What to
    113
    increment would result from improved commodity prices that would be available to all
    bidders, a strong argument can be made that a competitor would not think that it had the
    ability to outbid the incumbent and would not try.
    The respondent in an appraisal proceeding could make similar arguments about the
    stockholder vote. If the reasons for the valuation increase were public, and stockholders
    still voted for the deal, then their behavior would provide contrary market evidence
    undermining the claim of increased value. In this case, the increase in commodity prices
    was publicly available information, and Stillwater’s stockholders had the ability to vote
    down the deal if they thought the increased value from improving commodity prices
    changed matters. One obvious response to this argument is that to vote down the deal,
    stockholders would have had to prefer returning to Stillwater in its operative reality as a
    widely traded firm, where their only the options for liquidity were either to sell into the
    market or hold out for a higher-priced takeover down the road. Given these choices,
    stockholders might well have preferred the surer option of the deal price, even if they
    believed that the Company’s value had increased between signing and closing such that the
    deal price no longer reflected fair value.
    Expect in 2011, 12 M & A Law. Nov.-Dec. 2010, at 1 (“Match rights can result in the first
    bidder ‘nickel bidding’ to match an interloper’s offer, with repetitive rounds of incremental
    increases in the offer price. . . . [M]atch rights are just one more factor that may dissuade a
    potential competing bidder from stepping in the middle of an already-announced
    transaction.”); David I. Walker, Rethinking Rights of First Refusal, 5 Stan. J.L. Bus. & Fin.
    1, 20–21 (1999) (discussing how a right of first refusal affects bidders).
    114
    As this discussion shows, whether to adjust the deal price for an increase in value
    between signing and closing presents numerous difficult questions. In this case, the
    petitioners did not argue for an adjustment to the deal price, and so the parties did not have
    the opportunity to address these interesting issues. The court will not take them up at this
    late stage in the proceeding. The petitioners accordingly failed to prove that the deal price
    should be adjusted upward to reflect a change in value between signing and closing. See
    Columbia, 
    2019 WL 3778370
    , at *45. This decision finds that the deal price of $18.00 per
    share provides reliable evidence of fair value.
    B.     The Adjusted Trading Price
    Sibanye contended that Stillwater’s adjusted trading price is a reliable indicator of
    the fair value of the Company. Sibanye generates the adjusted trading price by making
    adjustments to the unaffected trading price, so the reliability of the adjusted trading price
    depends on the reliability of the unaffected trading price. As the proponent of using this
    valuation indicator, Sibanye bore the burden of establishing its reliability and
    persuasiveness.
    Assessing the reliability of the trading price for Stillwater’s common stock means
    getting “deep into the weeds of economics and corporate finance.” In re Appraisal of
    Jarden Corp., 
    2019 WL 3244085
    , at *1 (Del. Ch. July 19, 2019). The thicket of market
    efficiency is one such place where “law-trained judges should not go without the guidance
    of experts trained in these disciplines.” 
    Id. In this
    case, both sides retained financial experts
    who tried to lead the court through the undergrowth. Zmijewski addressed these issues for
    115
    Sibanye. Israel Shaked, a professor of economics and finance at Boston University,
    addressed these issues for petitioners.
    1.     Informational Efficiency and Fundamental-Value Efficiency
    The experts agreed on the difference between informational efficiency and
    fundamental-value efficiency. See Zmijewski Tr. 1087; JX 651 ¶¶ 13–27, 33–41
    [hereinafter Shaked Rep.]. “[I]nformational Efficiency . . . is concerned with how rapidly
    security prices reflect or impound new information that arrives to the market.” Shaked Rep.
    ¶ 33 (quoting Alex Frino et al., Introduction to Corporate Finance 305 (5th ed. 2013)).
    There are three recognized types of informational efficiency:
     Weak: a company’s stock price reflects all historical price information.
     Semi-Strong: a company’s stock price reflects all publicly available information.
     Strong: a company’s stock price reflects both publicly available information and
    inside information.
    No one claimed that the market for Stillwater’s common stock could be informationally
    efficient in the strong sense. Everyone focused on whether the market for Stillwater’s
    common stock was informationally efficient in the semi-strong sense. All of the references
    in this decision to informational efficiency as it relates to Stillwater’s common stock
    therefore contemplate informational efficiency in the semi-strong sense.
    “While informational efficiency is a function of speed and how quickly new
    material information is incorporated into a stock’s price, fundamental value efficiency is
    an incremental function of how accurately a market in which a stock trades discretely
    incorporates new material information.” Shaked Rep. ¶ 42. The price of a security in a
    116
    market that is fundamental-value efficient should reflect its intrinsic value, defined as “the
    present value of all cash payments to the investor in the stock, including dividends as well
    as the proceeds from the ultimate sale of the stock, discounted at the appropriate risk
    adjusted rate.” Shaked Rep. ¶ 40. (internal quotation marks omitted). In other words, a
    stock trading in a market that is fundamental-value efficient is one in which the trading
    price “fully reflects all estimates, guidance and other public, material information that
    portray the risks and returns of a stock accurately, including all key drivers.” 
    Id. ¶ 41.
    The experts agreed that it is impossible to observe whether a stock trades in a market
    that is fundamental-value efficient. See Zmijewski Tr. 1088, 1153–54; Shaked Report ¶ 41.
    According to the petitioners, this concession means that Sibanye cannot meet its burden of
    proof.
    While theoretically valid, the petitioners’ argument goes too far. Whether called
    fundamental value, true value, intrinsic value, or fair value, the really-real value of
    something is always an unobservable concept. No valuation methodology provides direct
    access to it. Fundamental value is like a Platonic form, and the various valuation
    methodologies only cutouts casting shadows on the wall of the cave. The real issue is not
    whether a particular method generates a shadow (they all do), but rather whether the
    shadow is more or less distinct than what other methods produce.
    Reliance on the trading price of a widely held stock is generally accepted in the
    financial community, and the trading price or metrics derived from it are regularly used to
    estimate the value of a publicly held firm based on its operative reality in that configuration.
    For purposes of determining fair value in an appraisal proceeding, therefore, the trading
    117
    price has a lot going for it.22 Like democracy, the trading price may be imperfect, but it
    often will serve better than the other metrics that have been tried. Cf. Winston Churchill,
    Churchill by Himself 574 (Richard Langworth ed., 2008). The petitioners’ admittedly valid
    objection that it is impossible to prove that a trading price reflects fundamental value is
    thus not one that automatically disqualifies the use of the trading price as a valuation
    indicator in an appraisal.
    In this regard, it is important to recognize that informational efficiency and
    fundamental-value efficiency are not all-or-nothing concepts. See Bradford Cornell & John
    Haut, How Efficient Is Sufficient: Applying the Concept of Market Efficiency in Litigation,
    22
    See, e.g., Richard A. Booth, Minority Discounts and Control Premiums in
    Appraisal Proceedings, 57 Bus. Law. 127, 151 n.130 (2001) (“[M]arket price should
    ordinarily equal going concern value if the market is efficient.”); William J. Carney &
    Mark Heimendinger, Appraising the Nonexistent: The Delaware Court’s Struggle with
    Control Premiums, 152 U. Pa. L. Rev. 845, 847–48, 857–58 (2003) (“The basic conclusion
    of the Efficient Capital Markets Hypothesis (ECMH) is that market values of companies’
    shares traded in competitive and open markets are unbiased estimates of the value of the
    equity of such firms.”); 
    id. at 879
    (noting that the appraisal statute requires consideration
    of all relevant factors and stating that “in an efficient market, absent information about
    some market failure, market price is the only relevant factor”); Lawrence A. Hamermesh
    & Michael L. Wachter, The Short and Puzzling Life of the “Implicit Minority Discount” in
    Delaware Appraisal Law, 156 U. Pa. L. Rev. 1, 52 (2007) (“Take the case of a publicly
    traded company that has no controller. Efficient market theory states that the shares of this
    company trade at the pro rata value of the corporation as a going concern.”); 
    id. at 60
    (“As
    a matter of generally accepted financial theory . . . , share prices in liquid and informed
    markets do generally represent th[e] going concern value . . . .”); see also Lawrence A.
    Hamermesh & Michael L. Wachter, Rationalizing Appraisal Standards in Compulsory
    Buyouts, 50 B.C. L. Rev. 1021, 1033–34 (2009) (positing trading prices should not be used
    to determine fair value if there is either no public market price at all, if the shares are illiquid
    or thinly traded, or if there is a controlling stockholder, implying that outside of these
    scenarios, “because financial markets are efficient, one can simply use the market value of
    the shares”).
    118
    74 Bus. Law. 417, 418 (2019). A stock trading in a national market like the New York
    Stock Exchange will have more attributes of informational efficiency than a stock trading
    over the counter, but a party might be able to show that the particular over-the-counter
    market had sufficient attributes to regard the trading price as informationally efficient. The
    attributes of the over-the-counter market are likely to be consistent with a greater degree
    of informational efficiency than thinner and chunkier markets, such as markets for houses
    or entire companies.
    Fundamental-value efficiency is likewise a matter of degree. A market could be
    precisely fundamental-value efficient in that it accurately prices the asset at exactly its true
    value. Or it might be nearly fundamental-value efficient in that it accurately prices the asset
    within some percentage, say plus or minus 3%, of its true value. Or it might be
    approximately fundamental-value efficient in that it accurately prices the asset within some
    wider range of its true value, such as a factor of two. See 
    id. at 422
    (“We might define an
    efficient market as one in which price is within a factor of 2 of value, i.e., the price is more
    than half of value and less than twice value.” (quoting Fischer Black, Noise, 41 J. Fin. 553
    (1986))).
    Although it is impossible to test for fundamental value, there are indicators of
    fundamental-value efficiency. One indicator is directional consistency, in which the market
    for a security reacts positively to new material information that is positive, and negatively
    to new material information that is negative. See Shaked Rep. ¶¶ 43–44. Another indicator
    is proportionality, which examines not only whether the direction of the reaction to new
    material information is consistent with its content, but also whether the extent of the
    119
    reaction corresponds with the informational content. See 
    id. ¶ 45.
    In simplified terms, if a
    company announces a positive earnings surprise and its stock price increases, then that
    outcome is directionally consistent. If the stock price increases by an amount generally
    proportionate to the present value of the earnings surprise, then that outcome is
    proportionally consistent. A market that evidences directionality and proportionality is
    more likely to be fundamental-value efficient. A market that lacks evidence of
    directionality and proportionality is less likely to be fundamental-value efficient. See 
    id. ¶ 46.
    The question in this case is thus not whether the market for Stillwater’s common
    stock was or was not informationally efficient. Nor is it whether the market for Stillwater’s
    common stock was or was not fundamental-value efficient. The question is whether the
    market for Stillwater’s common stock was informationally efficient enough, and
    fundamental-value efficient enough, to warrant considering the trading price as a valuation
    indicator when determining fair value. Put differently, the operative question in this case
    is whether Sibanye proved that Stillwater’s common stock traded in a market having
    attributes that made the trading price a sufficiently reliable valuation indicator to be taken
    into account when determining fair value, either in conjunction with other metrics, or even
    as the sole metric, with the answer turning on both the attributes of the market for
    Stillwater’s common stock, and also on the relative reliability of the trading price compared
    to other metrics like the deal price and the outputs of DCF models. See, e.g., Jarden, 
    2019 WL 3244085
    , at *4, *27–31 (determining fair value based on the unaffected trading price
    after concluding that it was comparatively the most reliable valuation indicator); Cornell
    120
    & 
    Haut, supra, at 425
    (“What is important in legal applications is not some abstract notion
    of market efficiency. Rather, what is important is whether the market is sufficiently
    efficient in any particular situation.”).
    2.    Evidence Of Market Efficiency
    The experts disagreed about the extent to which the market for Stillwater’s shares
    was efficient. The experts discussed factors that courts have considered as indicative of
    informational efficiency. The experts also conducted event studies and opined on their
    implications for informational efficiency, directionality, and proportionality.
    a.      The Cammer And Krogman Factors
    Zmijewski examined whether the market for Stillwater’s shares exhibited attributes
    that courts have associated with informational efficiency. He relied on an instruction from
    Sibanye’s counsel that “Delaware Courts cite as attributes of market efficiency
    characteristics such as market capitalization, public float, weekly trading volume, bid-ask
    spread, analyst following, and market reaction to breaking news and information.”
    Zmijewski Rep. ¶ 49. He also analyzed the existence of market makers, eligibility to file
    SEC Form S-3, institutional ownership, and autocorrelation of stock returns, noting that
    these additional factors were considered in Cammer v. Bloom, 
    711 F. Supp. 1264
    (D.N.J.
    1989), and in Krogman v. Sterritt, 
    202 F.R.D. 467
    (N.D. Tex. 2001). Zmijewski Rep. ¶ 51.
    For simplicity, and following the parties’ lead, this decision refers to these attributes as the
    “Cammer and Krogman factors,” even though not all of them were considered in those two
    cases.
    121
    Based on his review of the record, Zmijewski reached the following conclusions
    about these attributes:
     Market Capitalization: Zmijewski opined that “firms with a larger market
    capitalization tend to have larger institutional ownership,” “tend to be listed on the
    New York Stock Exchange,” and are therefore more likely to have shares that trade
    in markets that are informationally efficient. Zmijewski Rep. App. C ¶ 35 (citing
    Randall S. Thomas & James F. Cotter, Measuring Securities Market Efficiency in
    the Regulatory Setting, 63 L. & Contemp. Probs. 105, 115 (2000) (JX 896)). The
    Company’s market capitalization averaged approximately $1.3 billion, exceeding
    roughly 60% of the combined equities of companies listed on the New York Stock
    Exchange and NASDAQ. 
    Id.  Public
    Float: Zmijewski opined that having a large percentage of shares in the
    public float is indicative of a trading market that is informationally efficient. 
    Id. ¶¶ 42–43
    (noting that the Delaware Supreme Court in Dell cited a public float of 1.5
    billion shares representing 84.29% of the outstanding stock, and in DFC cited a
    public float of 37.5 million shares representing 95% of the outstanding stock). The
    Company’s public float consisted of 106 million shares representing 87.4% of the
    outstanding stock. 
    Id. ¶ 44.
        Weekly Trading Volume: Zmijewski opined that an average weekly trading
    volume of at least 2% warrants a “strong presumption” of informational efficiency.
    
    Id. ¶ 2
    (quoting 
    Cammer, 711 F. Supp. at 1286
    ). The average weekly turnover for
    Stillwater was 6.8%. 
    Id. ¶ 3.
        Bid-Ask Spread: Zmijewski opined that a bid-ask spread of less than 2.5% is
    indicative of a trading market that is informationally efficient. 
    Id. ¶¶ 37–38
    (citing
    
    DFC, 172 A.3d at 352
    ; 
    Dell, 177 A.3d at 1
    , 5–6, 24–27, 41; In re Sci.-Atlanta, Inc.
    Sec. Litig., 
    571 F. Supp. 2d 1315
    , 1340 (N.D. Ga. 2007); Cheney v. Cyberguard
    Corp., 
    213 F.R.D. 484
    , 501 (S.D. Fla. 2003); and 
    Krogman, 202 F.R.D. at 478
    ). The
    Company’s average daily bid-ask spread was 0.10%. 
    Id. ¶ 39.
        Analyst Coverage: Zmijewski opined that the presence of at least five analysts
    following a company is indicative of a trading market that is informationally
    efficient. 
    Id. ¶¶ 4–6
    (relying on Thomas & 
    Cotter, supra, at 115
    ). Seven analysts
    followed the Company. 
    Id. ¶ 7.
        Market Makers: Zmijewski opined that the presence of at least nineteen market
    makers is indicative of a trading market that is informationally efficient and that the
    same inference can be drawn when a company’s shares trade on a centralized
    auction market like the New York Stock Exchange. 
    Id. ¶¶ 8–9
    (citing 
    Cammer, 711 F. Supp. at 1293
    ; 
    Cheney, 213 F.R.D. at 499
    –500; In re Dynex Capital, Inc. Sec.
    Litig., 
    2011 WL 781215
    , at *5 (S.D.N.Y. Mar. 7, 2011); and Zvi Bodie et al.,
    122
    Investments 62–70 (12th ed. 2018)). The Company’s stock traded on the New York
    Stock Exchange and had eighty-two market makers. 
    Id. ¶ 10.
        SEC Form S-3 Eligibility: Zmijewski opined that a company’s eligibility to
    register shares using SEC Form S-3 eligibility is indicative of a trading market that
    is informationally efficient. 
    Id. ¶ 11
    (citing 
    Cammer, 711 F. Supp. at 1284
    ). A
    company is eligible for Form S-3 if it, among other things, has been subject to the
    Securities Exchange Act of 1934 reporting requirements for more than one year,
    filed documents in a timely manner, and shown that it has not failed to pay certain
    obligations. 
    Id. The Company
    filed Forms S-3 in 1996, 1998, 2001, 2009, and 2010.
    
    Id. ¶ 12.
        Institutional Ownership: Zmijewski opined that having a significant percentage
    of stock owned by institutional investors is indicative of a trading market that is
    informationally efficient. 
    Id. ¶ 46
    (citing Thomas & 
    Cotter, supra, at 106
    , 119). As
    of September 30, 2016, institutions held approximately 90% of the Company’s
    outstanding stock. 
    Id. ¶ 47.
        Autocorrelation: Zmijewski opined that a lack of autocorrelation in a company’s
    stock return is indicative of a trading market that is informationally efficient. 
    Id. ¶ 48.
    Autocorrelation measures the extent to which the next day’s stock price
    movement can be predicted based on the current day’s stock price. Zmijewski found
    no evidence of statistically significant autocorrelation during the 254 trading days
    preceding the announcement of the Merger. 
    Id.  Cause
    And Effect: Zmijewski opined that market reactions to significant events are
    indicative of informational efficiency. 
    Id. ¶ 13
    (citing 
    Cammer, 711 F. Supp. at 1287
    ). Zmijewski found that after the Merger announcement, there was a quick and
    significant increase in trading volume. 
    Id. ¶ 17.
    The first news of the Merger was
    released at 1:04 a.m on December 9, 2016. Pre-market trading opened at 4:00 a.m.
    The first trade occurred at 4:01 a.m. at $17.50. The Company’s stock closed that
    day at $17.32 per share, with 38 million shares having traded. The day before, the
    Company’s stock closed at $14.68 per share, and only 3.2 million shares were
    traded. 
    Id. ¶¶ 15–16;
    see Zmijewski Tr. 1096.
    Having considering the Cammer and Krogman factors, Zmijewski opined that “[t]he
    evidence indicates that Stillwater’s common stock traded in a semi-strong efficient
    market.” Zmijewski Rep. ¶ 49.
    In response, Shaked disputed whether the Cammer and Krogman factors established
    informational efficiency to a sufficiently reliable degree. He opined that “the Cammer and
    Krogman factors have not been academically tested and are not truly conclusive in judging
    123
    a market as semi-strong form efficient, but merely an indicator that a market is likely semi-
    strong form efficient.” Shaked Rep. ¶ 23. The petitioners did not cite any academic studies
    or provide other forms of evidence that would undermine the use of the Cammer and
    Krogman factors, at least as a starting point for assessing informational efficiency.
    Zmijewski did not engage on this issue. He analyzed the factors because he understood that
    courts considered them.
    b.     The Event Studies
    The experts also conducted event studies. Zmijewski’s event study tested for a
    cause-and-effect relationship between new information and a trading price reaction, which
    would provide evidence of informational efficiency. He examined five events—the four
    quarterly earnings releases leading up to the announcement of the Merger plus the
    announcement itself. Zmijewski characterized the events as positive or negative, and
    examined the market evidence to determine if the observations resulted in statistically
    significant abnormal returns. Three of the five did, but one of those was the reaction to the
    announcement of the Merger. Shaked persuasively observed that finding a statistically
    significant relationship between the trading price and the announcement of the Merger was
    trivial. See Shaked Tr. 468–69.
    For the remaining four observations, Zmijewski found that only two resulted in
    statistically significant abnormal returns, and he admitted that he would have expected the
    rate of statistically significant results in an informationally efficient market to be higher.
    Zmijewski Tr. 1101. The events themselves do not suggest any reason why the market
    would have reacted in one instance and not the other. For example, for both the fourth
    124
    quarter of 2015 and the third quarter of 2016, Stillwater announced higher earnings per
    share, yet only the former resulted in a statistically significant abnormal return.
    Shaked conducted three event studies, and he analyzed the results not only for
    evidence of a cause-and-effect relationship consistent with informational efficiency, but
    also for evidence of directionality and proportionality that would provide indications of
    fundamental value efficiency. In his first study, Shaked looked at eleven quarterly earnings
    releases during the three-year period leading up to the announcement of the Merger and
    characterized their informational content as positive or negative. He then examined
    whether the announcement resulted in abnormal returns consistent with the direction of the
    news. Shaked observed that only six of the eleven releases resulted in a directionally
    consistent reaction; five of the eleven did not.
    In his second study, Shaked examined articles, analyst reports and SEC filings
    during the same three-year period, yielding a total of 181 events that he believed contained
    material new information. News of the 181 events was published on a total of fifty-six
    days, resulting in fifty-six observations. Although there are reasons to question some of
    Shaked’s events, on the whole, his identification appears credible. Of these fifty-six
    observations, only twelve resulted in statistically significant abnormal returns that were
    consistent with the directional content of the information. Moreover, there were thirty-eight
    days in the study period when there was a statistically significant abnormal return but no
    material news announcement.
    In his third study, Shaked tested for proportionality by examining the reaction of the
    Company’s stock to the announcement of a significant increase in the expansion of its
    125
    mining operations in its earnings announcement for the third quarter of 2016. In the prior
    quarterly earnings releases, the Company forecast that the expansion would produce
    between 150,000 and 200,000 PGM ounces per year. JX 134 at 13; JX 187 at 17. In the
    earnings announcement for the third quarter of 2016, the Company increased the projection
    to between 270,000 and 330,000 PGM ounces per year. JX 309 at 16; see JX 306. Shaked
    estimated the pre-tax net income that would result from the increased output, taking into
    account the additional costs. He then prepared a discounted-cash-flow model that assumed
    production would ramp up by 25,000 ounces per year until 2022, continue at 125,000
    ounces per year until 2031, then stop with no terminal value. Based on this model, Shaked
    calculated a net present value of $111.6 million for the increased production, which should
    have equated to a 7.08% abnormal return. Although the stock reacted positively, the
    observed abnormal return was only 0.39%. Shaked concluded that the Company’s stock
    did not react in a proportionate manner, further undermining the claim of informational
    efficiency.
    c.     The Assessment Of Market Efficiency
    Absent any countervailing evidence, Zmijewski’s analysis of the Cammer and
    Krogman factors would support a finding that the trading market for Stillwater’s common
    stock had sufficient attributes to be regarded as informationally efficient. Shaked pointed
    out that the Cammer and Krogman factors have not been shown to provide a reliable
    126
    indication of informational efficiency, but given the weight of authority on this issue, an
    absence of evidence on this point is no longer enough.23
    The event studies, however, cut in the opposite direction. Courts applying the
    Cammer and Krogman factors have generally given greater weight to event studies
    compared to the other factors.24 Based on his studies, Shaked opined that Stillwater’s stock
    23
    The experts’ exploration of the Cammer and Krogman factors has left me with
    significantly less confidence in them than I had before this litigation. There appears to be
    substantial overlap among the factors, such that a single attribute, like a New York Stock
    Exchange listing, would correlate with and lead to the satisfaction of multiple factors. For
    an issuer to satisfy multiple Cammer and Krogman factors is thus likely less significant
    than it might seem. It is also striking how many of the Cammer and Krogman, at least based
    on Zmijewski’s report, stem from judicial opinions or law review articles, rather than from
    financial or economic papers. I am left with the concern that the Cammer and Krogman
    factors may be a convenient heuristic that law-trained judges deploy as a matter of routine,
    rather than because they have support in reliable research. That said, the absence of
    evidence is not necessarily evidence of absence, and the record in this case does not provide
    grounds to call the Cammer and Krogman factors into doubt.
    24
    See, e.g., In re DVI, Inc. Sec. Litig., 
    639 F.3d 623
    , 634 (3d Cir. 2011) (“[B]ecause
    an efficient market is one in which information important to reasonable investors . . . is
    immediately incorporated into stock prices, the cause-and-effect relationship between a
    company’s material disclosures and the security price is normally the most important factor
    in an efficiency analysis.” (internal quotation marks omitted)), abrogated on other grounds
    by Amgen Inc. v. Conn. Ret. Plans & Tr. Funds, 
    568 U.S. 455
    (2013); In re Xcelera.com
    Sec. Litig., 
    430 F.3d 503
    , 512 (1st Cir. 2005) (describing the cause and effect prong of
    Cammer as “in many ways the most important” and explaining that “[i]n the absence of
    such a relationship, there is little assurance that information is being absorbed into the
    market and reflected in its price”); 
    Cammer, 711 F. Supp. at 1287
    (“[S]howing a cause and
    effect relationship between unexpected corporate events or financial releases and an
    immediate response in the stock price” is “the essence of an efficient market and the
    foundation for the fraud on the market theory.”); see also Teamsters Local 445 Freight
    Div. Pension, Fund v. Bombardier Inc., 
    546 F.3d 196
    , 207 (2d Cir. 2008) (quoting
    Xcelera.com for the import of the cause and effect prong of Cammer). That said, the cause-
    and-effect factor is not dispositive. Beaver Cty. Empls.’ Ret. Fund v. Tile Shop Hldgs., Inc.,
    
    2016 WL 4098741
    , at *10–11 (D. Minn. July 28, 2016) (collecting cases and explaining
    127
    did not trade in a manner consistent with informational efficiency, and Zmijewski’s event
    study generated relatively unconvincing results. Given this evidence, it is difficult to
    conclude that Stillwater’s stock was informationally efficient to a degree sufficient to use
    the trading price as an indicator of fair value when a superior market-based metric, like the
    deal price, is available. That does not mean that Stillwater’s stock was not informationally
    efficient, only that the deal price is a superior market-based metric for purposes of
    determining fair value.
    Shaked’s event studies also raised questions about the degree of directionality and
    proportionality exhibited by the market for Stillwater’s common stock. This evidence does
    not mean that Stillwater’s stock price was unreliable, but it does make it difficult to
    conclude that Stillwater’s stock was fundamental-value efficient to a degree sufficient to
    use the trading price as an indicator of fair value when a superior market-based metric like
    the deal price is available.
    3.     Evidence Of Information Gaps
    The petitioners advance two other challenges to the reliability of Stillwater’s trading
    price. Because everyone agrees that the market for Stillwater’s common stock could only
    be informationally efficient in the semi-strong sense, the trading price could only account
    for publicly available information. The petitioners argue that material information about
    Stillwater’s inferred reserves was not publicly available, meaning that the trading price
    that “[t]he weight of authority on this issue favors” a finding of market efficiency without
    a favorable resolution of the cause and effect factor).
    128
    could not be a reliable indicator of fundamental value. They also cite evidence indicating
    that the parties themselves did not trust the market’s estimation of the Company’s value.
    The former point is another strike against the trading price; the latter is not.
    a.      Industry Guide 7
    The petitioners argue that Stillwater’s trading price is not a reliable indicator of
    value because the market did not have access to material information related to the
    Company’s value. On this issue, the petitioners relied on another expert: Thomas
    Matthews, a Principal Resource Geologist at Gustavson Associates. Matthews discussed
    the constraints imposed by Industry Guide 7, which specifies what the United States
    Securities and Exchange Commission permits a mining company to disclose. See JX 843
    [hereinafter Industry Guide 7]; 17 C.F.R. 229.801(g).
    To oversimplify a significantly more complex area, Industry Guide 7 only permits
    a mining company to disclose information about proven reserves or probable reserves. A
    proven reserve is a mineral deposit where (i) “quantity is computed from dimensions
    revealed in outcrops, trenches, workings or drill holes,” (ii) “grade or quality are computed
    from the results of detailed sampling,” and (iii) “the sites for inspection, sampling and
    measurement are spaced so closely and the geologic character is so well defined that size,
    shape, depth and mineral content of reserves are well-established.” Industry Guide 7 ¶
    (a)(2). A probable reserve is a mineral deposit where “the sites for inspection, sampling,
    and measurement are farther apart or are otherwise less adequately spaced,” resulting in a
    “degree of assurance” that is “lower than that for proven reserves” but still “high enough
    to assume continuity between points of observation.” 
    Id. ¶ (a)(3).
    Industry Guide 7 does
    129
    not permit a mining company to disclose information about inferred resources, which are
    mineral deposits where the quantity, grade, and quality “can be estimated” based on
    “geological evidence,” “limited sampling,” and “reasonably assumed, but not verified,
    geological and grade continuity.” JX 7 at 4; see Industry Guide 7 ¶ (b)(5), Instruction 3.
    Since at least 2012, the Society for Mining, Metallurgy and Exploration, Inc. has
    criticized this aspect of Industry Guide 7, complaining that the restrictions on reporting
    “limits the completeness and relevance of SEC reports for investors.” JX 15 at 1. The
    Society contrasted Industry Guide 7 with the standards applied in other countries, which
    permit this disclosure. 
    Id. at 2.
    In 2016, the SEC acknowledged the issue and proposed
    revisions to Industry Guide 7, but the new rules did not go into effect until 2018, long after
    the Merger closed. See Modernization of Property Disclosures for Mining Registrants,
    Exchange Act Release No. 34-84509, 
    2018 WL 5668900
    (Oct. 31, 2018).
    Under Industry Guide 7 as it existed during the period leading up to the Merger,
    Stillwater could disclose information about the Stillwater Mine and East Bolder Mine, but
    could not disclose information about the inferred resources at Blitz, Lower East Boulder,
    Iron Creek, Altar, and Marathon. See JX 727 ¶ 13 (Matthews Reb. Rep.). For Blitz, the
    Company possessed but could not disclose “a resource estimation, a conceptual mine plan,
    material movement schedules, a capital and operating cost review, and a preliminary
    economic analysis for the Blitz expansion.” 
    Id. ¶ 12.
    The Company could only disclose
    certain drill data and briefly describe production target ranges, estimated capital spend, and
    timeframes. See 
    id. ¶ 14.
    130
    The parties disagreed about whether disclosure of this information would cause
    investors to place a higher or lower valuation on the Company, but they agreed that it
    created an information gap for purposes of trading in the Company’s stock. See 
    id. ¶ 16;
    Zmijewski Tr. 1151. Zmijewski argued that because the effect of the information was
    unknowable, the court should assume that the absence of the information did not bias the
    trading price up or down. Sibanye also pointed out that some of the information was
    available in a filing that Stillwater made in March 2011 under the laws of Canada. See JX
    9 at ‘055; cf. JX 501 at ‘345.
    Stillwater’s inability to disclose information about inferred resources under Industry
    Guide 7, combined with its partial disclosure of some of this information in a Canadian
    filing from 2011, are negative factors for purposes of using the Company’s trading price
    as a valuation indicator. They are not dispositive in their own right, but they undermine the
    relative persuasiveness of the trading price.
    b.     Contemporaneous Evidence Of A Valuation Gap
    The petitioners also cite contemporaneous evidence in the record in which
    knowledgeable insiders affiliated with Stillwater, its advisors, or Sibanye regarded the
    trading price as an unreliable indicator of value. For example:
     In May 2015, Stillwater management told the Board that “[m]uch of the value from
    Blitz, Lower East Boulder and recycle ramp up yet to be recognized by the market
    and potential buyers.” JX 41 at ‘715.
     In January 2016, the Board thought that “the stock had been forced down
    significantly and . . . didn’t feel it really was reflective of what was going on in the
    business.” McMullen Dep. 145.
    131
     In June 2016, Froneman described the markets as “a bit all over the place lately.”
    JX 152 at ‘532.
     In their second and third quarter 2016 reports, BMO analysts thought the
    Company’s stock price did not reflect the value of Blitz. See JX 766 (stating in
    October 2016 that “[e]ven with arguably conservative assumptions, we maintain our
    opinion that the magnitude of the growth potential at Blitz is not factored into SWC
    shares”); Shaked Rep. ¶ 124 (quoting a June 2016 BMO report stating that “Blitz
    remains an underappreciated growth opportunity”).
     In October 2016, Vujcic told the Board that the market perceived PGMs as “exposed
    to irrational producer behaviour in both South Africa and Russia.” JX 293 at ‘522.
     During October, November, and December 2016, Stewart repeatedly stated that
    “[a]t an offer price of ~US$2bn (30% premium to 30 day VWAP) we are effectively
    paying a full price for the existing operations, 50% of Blitz and getting the
    remaining upside optionality for free.” JX 282 at ‘775; see JX 410; JX 378 at ‘009;
    JX 447 at ‘981. He did not believe the market was “really considering Blitz.” JX
    397 at ‘451; see JX 280 at ‘279 (describing the Company’s underperformance as
    “unlikely to remain as market recognises improvements are sustainable and Blitz
    comes on line”).
     In late November 2016, two weeks before signing, Stewart stated that the market
    was “currently at or near the bottom of the PGM cycle,” suggesting a depressed
    stock price. JX 410 at ‘099; see PTO ¶ 257; see also JX 280 at ‘279; JX 399 at ‘407.
     In early December 2016, days before signing, McMullen commented on how the
    price of palladium had been artificially depressed. See JX 437 at ‘471 (noting that
    palladium was “finally starting to reflect the fundamentals”)
     After announcing the Merger, Sibanye received two “deal of the year” awards and
    commented in both instances that the Merger was signed “at an opportune time in
    the commodity price cycle.” JX 511; JX 641 at 1.
     At trial, Schweitzer testified that “[t]he company’s stock price was all over the place
    from 2013 to 2016” and that he and “McMullen both believed there was a disconnect
    between the price of metals and the share price for Stillwater stock.” Schweitzer Tr.
    173.
    This evidence as a whole is less extensive and persuasive than what the record
    demonstrated about the contemporaneous views of knowledgeable insiders regarding the
    existence of a valuation gap in Dell, and the Delaware Supreme Court in that case found
    132
    that the trial court erred by giving weight to that evidence. See Dell, 
    177 A.3d 25
    –26; cf.
    Dell Trial, 
    2016 WL 3186538
    , at *33–36. This decision therefore does not give any weight
    to the petitioners’ weaker showing in this case.
    4.     The Comparative Reliability Of The Trading Price
    Through Zmijewski’s analysis of the Cammer and Krogman factors, Sibanye made
    an initial showing that would be sufficient to support the reliability of the trading price as
    a valuation indicator absent contrary evidence. The results of the experts’ event studies and
    the limitations imposed by Industry Guide 7 provided contrary evidence. Based on the
    parties’ showings, the trading price is a less persuasive and less reliable valuation indicator
    in this case than the deal price. The lack of a reliable trading price does not undermine a
    court’s ability to rely on the deal price, where the persuasiveness of the deal price has been
    established by analyzing the sufficiency of the sale process. See Columbia, 
    2019 WL 3778370
    , at *49.
    This decision does not find that the trading price was so unreliable that it could not
    be used as a valuation indicator. If a market-tested indicator like the deal price was
    unavailable, then this decision might well have given weight to the trading price. Had this
    decision been forced to take that route, it would not have relied on the unaffected trading
    price, because Sibanye did not argue for its use, but instead would have taken into account
    the adjusted trading price.
    Based on the record that the parties generated, Sibanye did not carry its burden to
    establish that the adjusted trading price was a sufficiently reliable valuation indicator for
    the court to use in determining fair value. The reliability of the adjusted trading price
    133
    depended on the reliability of the unaffected trading price, and the record provides
    sufficient reason for concern about incorporating a trading price metric. This decision
    therefore does not give any weight to the adjusted trading price.
    C.     The Discounted Cash Flow Models
    The petitioners and Sibanye each introduced a DCF valuation prepared by an expert.
    The petitioners relied on Rosen, whose DCF model generated a value of $25.91 per share.
    Sibanye relied on Zmijewski, whose DCF model generated a value of $17.03 per share.
    The difference amounts to approximately $1 billion in value.
    The DCF method is a technique that is generally accepted in the financial
    community. “While the particular assumptions underlying its application may always be
    challenged in any particular case, the validity of [the DCF] technique qua valuation
    methodology is no longer open to question.” Pinson, 
    1989 WL 17438
    , at *8 n.11. It is a
    “standard” method that “gives life to the finance principle that firms should be valued based
    on the expected value of their future cash flows, discounted to present value in a manner
    that accounts for risk.” Andaloro v. PFPC Worldwide, Inc., 
    2005 WL 2045640
    , at *9 (Del.
    Ch. Aug. 19, 2005).
    The DCF model entails three basic components: an estimation of net cash
    flows that the firm will generate and when, over some period; a terminal or
    residual value equal to the future value, as of the end of the projection period,
    of the firm’s cash flows beyond the projection period; and finally a cost of
    capital with which to discount to a present value both the projected net cash
    flows and the estimated terminal or residual value.
    In re Radiology Assocs., Inc. Litig., 
    611 A.2d 485
    , 490 (Del. Ch. 1991) (internal quotation
    marks omitted).
    134
    In Dell and DFC, the Delaware Supreme Court cautioned against using the DCF
    methodology when market-based indicators are available. In Dell, the high court explained
    that “[a]lthough widely considered the best tool for valuing companies when there is no
    credible market information and no market check, DCF valuations involve many inputs—
    all subject to disagreement by well-compensated and highly credentialed experts—and
    even slight differences in these inputs can produce large valuation gaps.” 
    Dell, 177 A.3d at 37
    –38. The high court warned that when market evidence is available, “the Court of
    Chancery should be chary about imposing the hazards that always come when a law-trained
    judge is forced to make a point estimate of fair value based on widely divergent partisan
    expert testimony.” 
    Id. at 35.
    Making the same point conversely in DFC, the Delaware
    Supreme Court advised that a DCF model should be used in appraisal proceedings “when
    the respondent company was not public or was not sold in an open market check . . . .”
    
    DFC, 172 A.3d at 369
    n.118. The high court commented that “a singular discounted cash
    flow model is often most helpful when there isn’t an observable market price.” 
    Id. at 370.
    This case illustrates the problems that the Delaware Supreme Court identified. The
    experts disagreed over many inputs, with small changes producing large swings in value.
    The briefing focused on eight inputs, with four generating the bulk of the difference.
    First, the experts debated whether to apply a small-company risk premium,
    otherwise known as a size premium. Zmijewski applied a size premium of 1.66%, relying
    on Duff & Phelps, 2017 Valuation Handbook – U.S. Guide to Cost of Capital (2017). Rosen
    did not apply one, arguing that it was not warranted. To the extent the court disagreed, he
    argued for using a premium of 1.5% drawn from Ibbotson Associates, SBBI 2013 Valuation
    135
    Yearbook (2013). The scholarly literature on whether and how to apply a size premium is
    less than enlightening. The same respected scholars have found different results depending
    on the data set,25 and others have engaged in vigorous debate about how to interpret the
    data and what inferences to draw.26 This one dispute results in a valuation swing of $2.13
    per share, accounting for approximately 24% of the difference between the two models.
    25
    Compare Eugene F. Fama & Kenneth R. French, A Five-Factor Asset Pricing
    Model, 116 J. Fin. Econ. 1 (2015) (JX 681) (finding evidence of size premium in asset
    pricing models), and Eugene F. Fama & Kenneth R. French, Common Risk Factors in the
    Returns on Stocks and Bonds, 33 J. Fin. Econ. 3 (1993) (JX 680) (finding evidence that
    stocks with smaller market capitalizations tended to have higher average returns), with
    Eugene F. Fama & Kenneth R. French, Size, Value, and Momentum in International Stock
    Returns, 105 J. Fin. Econ. 457 (2012) (JX 679) (finding no evidence of a size premium in
    any region based on analyses of international stock returns from November 1989 to March
    2011).
    26
    Compare, e.g., Cliff Asness et al., Size Matters, If You Control Your Junk, 129 J.
    Fin. Econ. 479, 479 (2018) (finding “[a] significant size premium . . . , which is stable
    through time, robust to the specification, more consistent across seasons and markets, not
    concentrated in microcaps, robust to non-price based measures of size, and not captured by
    an illiquidity premium” and arguing that challenges to the existence of the size premium
    “are dismantled when controlling for the quality, or the inverse ‘junk’, of a firm”), and
    Roger Grabowski, The Size Effect Continues To Be Relevant when Estimating the Cost of
    Capital, 37 Bus. Valuation Rev. 93 (2018) (responding to criticisms of Ang, infra), with
    Aswath Damodaran, The Small Cap Premium: Where is the Beef?, Musings on Markets
    (Apr. 11, 2015) (JX 682 at 1) (commenting that “the historical data, which has been used
    as the basis of the argument [for size premia], is yielding more ambiguous results and
    leading us to question the original judgment that there is a small cap premium” and that
    “forward-looking risk premiums, where we look at the market pricing of stocks to get a
    measure of what investors are demanding as expected returns, are yielding no premium for
    small cap stocks”), http://aswathdamodaran.blogspot.com/2015/04/the-small-cap-
    premium-fact-fiction-and.html, and Clifford Ang, The Absence of a Size Effect Relevant to
    the Cost of Equity, 37 Bus. Valuation Rev. 87 (2018) (JX 732 at 3–4) (concluding from
    survey of empirical literature that either “(1) investors . . . do not believe a size effect exists
    and, therefore, do not demand compensation for it, or (2) investors . . . believe a size effect
    exists, but believe the adjustment for the size effect is not made in the cost of equity”).
    136
    Second, the experts debated the size of the equity risk premium. Zmijewski used a
    historic supply-side risk premium of 5.97% published by Duff & Phelps. See JX 837; JX
    893. Duff & Phelps advised practitioners to deduct 1.08% from this measurement to
    account for “the WWII Interest Rate Bias.” JX 893 at 34. Zmijewski did not make the
    adjustment, explaining that it would not make sense to exclude the effect of interest rate
    controls during World War II, while failing to account for other periods of government
    control, such as the extreme phases of interest rate repression and quantitative easing that
    followed the 2008 financial crisis. Zmijewski Tr. 1042–43. Rosen used a forward-looking
    premium of 5.34%, derived from a model created by Aswath Damodaran. See JX 678.
    Zmijewski criticized the model, explaining that a user could generate approximately
    seventy different equity risk premiums by manipulating the inputs and objecting to some
    of Rosen’s selections. See JX 893 at 47; JX 894; Zmijewski Tr. 1053–54. This one dispute
    results in a valuation swing of $1.33 per share, accounting for approximately 15% of the
    difference between the two models.
    Third, the experts disputed which set of commodity price forecasts to use to generate
    cash flows. Zmijewski relied on price forecasts prepared by another expert for Sibanye. JX
    710 (Burrows Rep.). Rosen relied on price forecasts from Bloomberg. JX 654 ¶ 8.21
    (Rosen Rep.). This one dispute results in a valuation swing of $0.82 per share, accounting
    for approximately 9% of the difference between the two models.
    Zmijewski has acknowledged that “there is much weaker evidence of a size effect since
    the original [article finding the effect] was published.” JX 836 at 322.
    137
    Fourth, the experts diverged in their treatment of Stillwater’s exploration areas.
    Sibanye argued that any valuation of these properties would be speculative and instructed
    Zmijewski not to try. Zmijewski Tr. 1074–75. Rosen estimated an “in-ground metal dollar
    value” for the properties, then relied on a report that examined PGM transactions in South
    Africa to estimate that exploration properties could be worth “between .5 percent and 2.5
    percent of the estimated in situ dollar value of metal.” Rosen Tr. 277–78; see JX 765. The
    respondent’s mining expert identified many problems with Rosen’s method. See JX 768.
    The dispute over the exploration areas results in a valuation swing of more than $2.00,
    accounting for approximately 23% of the difference between the two models.
    Four other disputes account for the remaining valuation swing of $3.00 per share.
    Those disagreements concern how to account for the resources in mine-adjacent areas, the
    amount of excess cash, the value of inventory, and the value of Altar. As with the four
    major disputes, both sides have good reasons for their positions.
    The legitimate debates over these inputs and the large swings in value they create
    undercut the reliability of the DCF model as a valuation indicator. If this were a case where
    a reliable market-based metric was not available, then the court might have to parse through
    the valuation inputs and hazard semi-informed guesses about which expert’s view was
    closer to the truth. In this case, there is a persuasive market-based metric: the deal price
    that resulted from a reliable sale process. Dell and DFC teach that a trial court should have
    greater confidence in market indicators and less confidence in divergent expert
    determinations. See 
    Dell, 177 A.3d at 35
    –38; 
    DFC, 172 A.3d at 368
    –70 & n.118.
    Compared to the deal-price metric, the DCF technique “is necessarily a second-best method
    138
    to derive value.” Union 
    Illinois, 847 A.2d at 359
    . This decision therefore does not use it.
    See In re Appraisal of Solera Hldgs., Inc., 
    2018 WL 3625644
    , at *32 (Del. Ch. July 30,
    2018).
    III. CONCLUSION
    The fair value of the Company’s common stock at the effective time of the Merger
    was $18.00 per share. The legal rate of interest, compounded quarterly, shall accrue on the
    appraised value from the effective date until the date of payment. The parties shall
    cooperate to prepare a form of final order. If there are additional issues that need to be
    resolved, then the parties shall submit a joint letter within fourteen days that identifies them
    and proposes a path to bring this matter to a conclusion at the trial level.
    139
    APPENDIX
    Case                    Time Between       Time from           Total Time     Termination Fee      Other Deal
    Announcement       Commencement        for                                 Protection
    of Deal and        of Tender Offer     Purposes of                         Measures
    Commencement       to Closing          Court
    of Tender Offer                        Decision
    Yanow v. Sci.           4 business days,   19 business         23 business    Expense              Window-
    Leasing, Inc., 1988     4 calendar days    days, 28            days, 32       reimbursement        shop, 16.6%
    WL 8772 (Del. Ch.                          calendar days       calendar                            stock option
    Feb. 5, 1988)                                                  days                                lock-up
    In re Fort Howard       4 business days,   25 business         29 business    $67.8 million;       No-shop
    Corp. S’holders         4 calendar days    days, 38            days, 42       1.9% of equity       permitting
    Litig., 1988 WL                            calendar days       calendar       value                target to
    83147 (Del. Ch.                                                days                                provide
    Aug. 8, 1988)                                                                                      information
    and
    negotiate
    (i.e., a
    window-
    shop).
    In re KDI Corp.         4 business days,   24 business         28 business    $8 million; 4.3%     Window-
    S’holders Litig.,       6 calendar days    days, 35            days, 41       of equity value      shop
    
    1988 WL 116448
                                calendar days       calendar
    (Del. Ch. Nov. 1,                                              days
    1988)
    In re Formica Corp.     3 business days,   30 business         33 business    Graduated fee        Strict no-
    S’holders Litig.,       3 calendar days    days, 43            days, 46       capped at 1.9% of    shop
    
    1989 WL 25812
                                 calendar days       calendar       equity value
    (Del. Ch. Mar. 22,                                             days
    1989)
    Braunschweiger v.       Single-step merger. No tender offer. 143 business     4.5% of equity       None
    Am. Home Shield         days, 205 calendar days, between announcement of      value
    Corp., 1989 WL          merger and stockholder vote approving deal.
    128571 (Del. Ch.
    Oct. 26, 1989)
    Roberts v. Gen.         5 business days,   25 business          30 business   $33 million; 2% of   Window-
    Instr. Corp., 1990      7 calendar days    days, 35             days, 42      equity value         shop
    WL 118356 (Del.                            calendar days        calendar
    Ch. Aug. 13, 1990)                                              days
    McMillan v.             Single-step merger. No tender offer. 102 business     $3.1 million; 3.5%   Window-
    Intercargo Corp.,       days, 148 calendar days between announcement of       of equity value      shop
    
    768 A.2d 492
    (Del.      merger and stockholder vote approving deal.
    Ch. 2000)
    In re Pennaco           9 business days,   20 business         29 business    $15 million; 3% of   Window-
    Energy, Inc.            17 calendar days   days, 28            days, 45       equity value         shop
    S’holders Litig., 787                      calendar days       calendar
    A.2d 691 (Del. Ch.                                             days
    2001)
    In re Cysive, Inc.      Single-step merger. No tender offer. 45 business      Expenses up to       Window-
    S’holders Litig., 836   days, 63 calendar days between announcement of        $1.65 million; up    shop with
    A.2d 531 (Del. Ch.      merger and stockholder vote approving deal.           to 1.7% of deal      matching
    2003)                                                                         value                rights
    140
    In re MONY Gp.            Single-step merger. No tender offer. 82 business    $50 million; 3.3%     Window-
    Inc. S’holder Litig.,     days, 121 calendar days between announcement of     of equity value;      shop
    
    852 A.2d 9
    (Del. Ch.      merger and stockholder vote approving deal.         2.4% of deal value
    2004)
    In re Dollar Thrifty      Single-step merger. No tender offer. 100 business   $44.6 million with    Window-
    S’holder Litig., 14       days, 144 calendar days between announcement of     up to additional $5   shop with
    A.3d 573 (Del. Ch.        merger and stockholder vote approving deal.         million in            matching
    2010)                                                                         expenses; 4.3% of     rights
    deal value after
    accounting for
    options, RSUs and
    performance units.
    In re Smurfit–Stone       Single-step merger. No tender offer. 89 business    $120 million;         Window-
    Container Corp.           days, 123 calendar days between announcement of     3.4% of equity        shop with
    S’holder Litig., 2011     merger and stockholder vote approving deal.         value                 matching
    WL 2028076 (Del.                                                                                    rights
    Ch. May 20, 2011)
    In re El Paso Corp.       Single-step merger. No tender offer. 51 business    $650 million;         Window-
    S’holder Litig., 41       days, 75 calendar days between announcement of      3.1% of equity        shop with
    A.3d 432 (Del. Ch.        merger and stockholder vote approving deal.         value                 matching
    2012)                                                                                               rights
    In re Plains Expl. &      Single-step merger. No tender offer. 79 business    $207 million; 3%      Window-
    Prod. Co. S’holder        days, 117 calendar days between announcement of     of deal value         shop with
    Litig., 2013 WL           merger and stockholder vote approving deal.                               matching
    1909124 (Del. Ch.                                                                                   rights
    May 9, 2013)
    C & J Energy              Single-step merger. No tender offer. 130 business   $65 million;          Window-
    Servs., Inc. v. City of   days, 189 calendar days between announcement of     2.27% of deal         shop
    Miami Gen. Empls.’        merger and stockholder vote approving deal.         value
    and Sanitation
    Empls.’ Ret. Tr., 
    107 A.3d 1049
    (Del.
    2014)
    141