Court Opinion

ID: 9555735
Source: CourtListenerOpinion
Date Created: 2023-08-14 21:04:28.197522+00
Date Added: 2024-06-11T15:41:32.402792
License: Public Domain

IN THE COURT OF CHANCERY OF THE STATE OF DELAWARE

HBK MASTER FUND L.P., and                  )
HBK MERGER STRATEGIES                      )
MASTER FUND L.P.,                          )
                                           )
            Petitioners,                   )
                                           )
      v.                                   )   C.A. No. 2020-0165-KSJM
                                           )
PIVOTAL SOFTWARE, INC.,                    )
                                           )
            Respondent.                    )

                   POST-TRIAL MEMORANDUM OPINION

                           Date Submitted: December 13, 2022
                             Date Decided: August 14, 2023

Samuel T. Hirzel, II, Elizabeth A. DeFelice, HEYMAN ENERIO GATTUSO & HIRZEL
LLP, Wilmington, Delaware; Lawrence M. Rolnick, Steven M. Hecht, Frank T. M.
Catalina, ROLNICK KRAMER SADIGHI LLP, New York, New York; Counsel for
Petitioners HBK Master Fund L.P. and HBK Merger Strategies Master Fund L.P.

Elena C. Norman, Daniel M. Kirshenbaum, YOUNG CONAWAY STARGATT &
TAYLOR, LLP, Wilmington, Delaware; Michael D. Celio, GIBSON, DUNN &
CRUTCHER LLP, Palo Alto, California; Laura Kathryn O’Boyle, Peter M. Wade, Mark
H. Mixon, Jr., GIBSON, DUNN & CRUTCHER LLP, New York, New York; Colin B.
Davis, GIBSON, DUNN & CRUTCHER LLP, Irvine, California; Counsel for Respondent
Pivotal Software, Inc.

McCORMICK, C.
       The petitioners are former Class A common stockholders of Pivotal Software, Inc.,

who exercised their appraisal rights in connection with a merger by which Pivotal’s

controlling stockholder, VMware, Inc., acquired Pivotal for $15 per share.

       Relying on a comparable companies analysis and a comparable transactions

analysis, the petitioners argue that the fair value of Pivotal stock at the time of the merger

was $20 per share. Relying primarily on a discounted cash flow analysis (“DCF”), the

respondent pegs Pivotal’s fair value at $12.17 per share. To bolster this position, the

respondent argues that the deal price of $15 per share provides a cap on fair value because

the transaction was conditioned on MFW protections. The respondent further points to the

unaffected stock price of $8.30 per share to support the argument that the deal price

exceeded fair value.

       In this post-trial decision, the court finds that the fair value of Pivotal’s Class A

common stock was $14.83 per share, and that the petitioners are entitled to this amount

plus pre-judgment interest. The court reaches this conclusion by ascribing equal weight to

adjusted versions of the comparable companies analysis advanced by the petitioners and

the DCF analysis advanced by the respondent. The court rejects the parties’ other valuation

methodologies.

       When conducting the comparable companies analysis, the court makes two

adjustments to the petitioners’ model. First, the court weighs the petitioners’ multiplier to

account more properly for Pivotal’s services segment by including companies in the

comparables sample that competed with that segment. Second, the court declines to adjust

the result for an implicit minority discount. This yields a value of $14.75 per share.
       When conducting its DCF analysis, the court makes two adjustments to the

respondent’s model. The respondent derives its fair value figure by averaging the results

of two separate DCF models, which are identical except that one applies a size premium to

the discount rate. The court rejects the respondent’s use of a size premium, relying instead

on a single DCF calculation without one.          The court also rejects the respondent’s

‘convergence’ approach to the terminal value calculation, which implemented an effective

0% perpetuity growth rate in the terminal period. Splitting the difference between the

respondent’s approach and the petitioners’ proposed 5% perpetuity growth rate, the court

applies a 2.5% perpetuity growth rate, which also falls in the range of what the respondent’s

financial adviser applied when rendering its fairness opinion. This yields a value of $14.91

per share.

       The court then reaches the $14.83 fair value figure by averaging the $14.75 per share

and $14.91 per share calculations.

       The respondent’s argument concerning the deal price raises an interesting question

about deal primacy under Delaware law—namely, whether the appraisal statute requires

deference to the deal price in controller squeeze-outs conditioned on MFW protections.

The short answer is no. The slightly longer answer is that even as the court independently

measures going concern value, companies remain incentivized to deploy strong procedural

protections for minority stockholders, as high-value deals will be vindicated in appraisal

actions. Despite the challenges the petitioners raise to aspects of the deal process, here, the

deal price is vindicated by the court’s independent valuation.

                                              2
I.        FACTUAL BACKGROUND

          The record comprises 1,532 joint trial exhibits, trial testimony from eight fact and

two expert witnesses, deposition testimony from 20 fact and two expert witnesses, and 145

stipulations of fact in the pre-trial order.1 These are the facts as the court finds them after

trial.

          A.    Pivotal

          Pivotal was a software and services company that provided Platform-as-a-Service

(“PaaS”) and cloud-based application development to enterprise customers.2 CEO Robert

Mee co-founded the company in April 2013 as a spin-off of assets held by two companies,

VMware and EMC Corporation.3 Before the merger at issue in this litigation, Pivotal had

a dual-class stock structure. Class A stock carried one vote per share while Class B stock

carried ten votes per share.4 Dell Technologies, Inc. beneficially owned approximately

94.4% of the combined voting power of both classes of Pivotal’s outstanding common

1
  See C.A. No. 2020-0165-KSJM, Docket (“Dkt.”) 155 (Joint Sched. of Evid.). This
decision cites to: trial exhibits (by “JX” number); the trial transcript, Dkts. 182–186 (by
“Trial Tr. at” page, line, and witness); the deposition transcripts of Karen Dykstra, Cynthia
Gaylor, Patrick Gelsinger, Marcy Klevorn, Madelyn Lankton, Paul Maritz, Robert Mee,
Stephanie Reiter, and Zane Rowe (by the deponent’s last name and “Dep. Tr. at”); and
stipulations of fact in the Pre-Trial Stipulation and Order, Dkt. 155 (“PTO”).
2
    PTO ¶ 58.
3
    Id. ¶ 28.
4
    Id. ¶ 29.

                                               3
stock.5 Michael Dell controlled Dell Technologies as the Chairman, CEO, and beneficial

owner of a majority of the total voting power of the outstanding shares.6

          The Pivotal Board comprised eight directors—six “Group I” directors elected by

Pivotal’s Class B stockholders and two “Group II” directors elected by both classes of

stock.7 The Group I directors were Dell, Mee, Paul Maritz, Egon Durban, Zane Rowe, and

William Green.8 The Group II directors were Madelyn Lankton and Marcy Klevorn.9

          Pivotal had two revenue streams: subscription revenue from its application

development platform called Cloud Foundry and services revenue from its software-

development services business called Pivotal Labs.10 Cloud Foundry offered a “cloud-

native platform suite” that helped customers in “building, deploying, and operating new

cloud-native software applications” on a subscription basis.11 Cloud Foundry allows

enterprises to run a set of common applications across a wide range of computers. Pivotal

Labs provided software development experts to help customers “co-develop new

applications and transform existing ones[,]” thus helping “streamlin[e] IT operations[.]”12

Although Cloud Foundry was Pivotal’s “core” offering and accounted for the “vast

5
    Id. ¶ 41.
6
    Id. ¶¶ 43–44.
7
    Id. ¶ 30.
8
    Id.
9
    Id.
10
     Id. ¶¶ 60–61.
11
     Id. ¶ 58.
12
     Id. ¶ 60.

                                             4
majority of [Pivotal’s] revenue,”13 the Pivotal Labs services revenue remained “critical” to

growth because it “was used to support the subscription revenue and make customers

successful on the platform.”14

         By early 2019, Pivotal faced challenges to its business model. For one, Pivotal’s

“high-touch” sales strategy made it difficult to serve a large set of customers.15 Also, Cloud

Foundry was highly “opinionated,” meaning that it would guide users into its pattern for

doing things and made it difficult to deviate from those patterns.16 This approach was

popular at first but, over time, “fewer and fewer customers . . . were very interested in a

very opinionated product.”17

         Perhaps most significantly, a new “industry standard” called Kubernetes threatened

to replace aspects of Pivotal’s key “value proposition.”18 Kubernetes is an open-source

platform originally designed by Google that allows for containerization of software.19

13
  Trial Tr. at 1082:15–1084:13, 1091:1–1092:5 (Mee) (describing Cloud Foundry “as the
core of Pivotal”); JX-991 at 3, 9–10 (slides from Gaylor’s presentation to the Board on July
19, 2019, describing Pivotal’s lines of businesses and displaying the proportions of
subscription revenues to total).
14
     Trial Tr. at 904:20–24, 953:5–17 (Gaylor).
15
     Id. at 494:21–495:2 (Gelsinger).
16
  Id. at 543:1–21 (Urquhart) (testifying that Cloud Foundry “ma[de] a lot of decisions on
behalf of the user that aren’t easily changed” about how to run a network, or how to
“package[]” the software “to be delivered to servers”).
17
     Id. at 545:7–13 (Urquhart).
18
  Id. at 449:10–20, 454:3–17 (Gelsinger); see also id. at 371:11–13 (stating that
Kubernetes gained “a lot of momentum” in the industry between 2018 and 2019); id. at
375:23–376:6 (Raghuram).
19
     Id. at 398:14–18 (Raghuram).

                                              5
           In layperson’s terms, containers are “discrete management clusters of software

that . . . very complex information systems would be able to access [] very efficiently.” 20

Containerization is the process whereby a developer bundles the relevant application code

together with its configuration files and libraries—supplemental code and data that the

application needs to run on a given operating system or cloud. Stated another way, a

containerized application allows a user to extract that application from its host operating

system or cloud-based platform and “plug” it into any other one.21 Containerization thus

makes an application more universally available. In this way, Kubernetes is like a

“universal power adapter.”22 Because Kubernetes is open source, “anybody is free to use

it without paying”23—thus, Pivotal’s enterprise customers could take code from

Kubernetes and develop their own system for deploying software. Cloud Foundry was not

built on or compatible with Kubernetes.24

           B.    VMware

           VMware is an enterprise software company that specializes in virtualization and

cloud computing technology.25        VMware had a dual-class stock structure, and Dell

Technologies beneficially owned approximately 97.5% of the combined voting power of

20
     Id. at 32:17–33:12 (Beach).
21
     Id. at 367:22–369:20 (Raghuram).
22
     Id.
23
     Id. at 365:12–24 (Raghuram); see also id. at 455:16–19 (Gelsinger).
24
     Id. at 374:15–375:1 (Raghuram); see also id. at 454:3–17 (Gelsinger).
25
     PTO ¶ 37.

                                              6
both classes of VMware’s outstanding common stock.26 Dell was the Chairman of the

VMware Board of Directors.27 At relevant times, VMware’s two key executives were CEO

Patrick Gelsinger and COO Raghu Raghuram.28

          VMware sells software to medium- to large-scale enterprises to manage

infrastructure underlying their applications and devices.29            VMware’s software

“abstracted” underlying hardware, effectively turning physical servers into more “virtual”

servers.30 Virtualization helps data centers reduce operating costs and manage their

systems more efficiently.31

          As early as 2016, VMware had developed what it called an “any, any, any”

strategy—its platform would ideally permit customers to run any applications on any

devices across any cloud infrastructure.32 In line with its goals of flexibility and targeting

developers, VMware decided to develop a “cloud-agnostic” platform that would allow

“developers to build new applications as if they were on a cloud, without locking

26
     Id. ¶ 42.
27
     Id. ¶ 43.
28
 Gelsinger Dep. Tr. at 17:23–25; Trial Tr. at 435:19–21 (Gelsinger) (stating that he was
CEO of VMware for approximately eight years); id. at 343:6–11 (Raghuram).
29
 Trial Tr. at 347:8–15 (Raghuram); see also id. at 349:5–351:16 (Raghuram) (describing
VMware’s business strategy).
30
     Id. at 441:10–443:14 (Gelsinger).
31
  See id. at 441:10–24 (Gelsinger) (describing inefficiencies in “server sprawl” for data
center operators “before VMware came into the market”).
32
     Id. at 349:22–351:20 (Raghuram).

                                              7
themselves into a particular cloud.”33 VMware wanted the new platform to be Kubernetes-

compatible, because it viewed Kubernetes as “the de facto top layer of [modern]

infrastructure[.]”34 VMware also wanted the new platform to become an “integrated

product” with the company’s existing infrastructure.35

           VMware and Pivotal had discussed a possible merger in early 2017.36 Within

VMware, this was referred to as “Project Peach.”37 At the time, Pivotal was evaluating

whether to sell to VMware or another potential buyer, or to conduct an initial public

offering. This strategy was referred to within Pivotal as “Project Flavor[,]” on which

Morgan Stanley advised Pivotal respecting the M&A transaction portion.38 Morgan

Stanley’s team included Managing Director Anthony Armstrong.39               Morgan Stanley

contacted several potentially interested parties in connection with Project Flavor.40 Dell

Technologies instructed Morgan Stanley that it “should call the other strategic buyers and

tell them if they are at the right price [Dell Technologies] will support the deal.”41

33
     Id. at 355:22–356:4 (Raghuram).
34
     Id. at 404:7–10 (Raghuram).
35
  Id. at 354:9–18 (Raghuram) (“There was nobody in the industry that was providing
something that was a vendor agnostic development platform and infrastructure platform.”).
36
     Id. at 718:12–719:3 (Armstrong).
37
     PTO ¶ 68.
38
     Trial Tr. at 718:12–719:3 (Armstrong).
39
     Id.
40
     Id. at 719:8–20 (Armstrong).
41
     Id. at 857:6–15 (Armstrong).

                                              8
         VMware was interested in acquiring Pivotal because it would allow VMware to

“move up the stack.”42 VMware “was largely at the lowest levels of infrastructure right

next to the hardware,” whereas Pivotal’s products were further up the stack “where people

would be developing their applications on the Pivotal platform.”43 And Gelsinger and

Raghuram believed that acquiring Pivotal would let VMware more readily target software

developers, who were becoming increasingly influential to VMware’s customer base.44

         Ultimately, Pivotal and VMware did not proceed with a merger because they could

not agree on valuation.45 Nonetheless, management of each company retained a “general

belief [at VMware] that bringing [VMware and Pivotal] together was still the right

answer.”46

         Following Project Peach, Pivotal began working toward an IPO of its Class A stock.

Morgan Stanley and Goldman Sachs acted as lead underwriters in connection with

Pivotal’s IPO.47 In April 2018, Pivotal offered its Class A stock at a price of $15 per share

on the NYSE.48

42
     Id. at 454:24–455:7, 485:2–486:8 (Gelsinger).
43
     Id. at 445:4–12 (Gelsinger).
44
  Id. at 454:24–455:7, 485:2–487:7, 488:5–10 (Gelsinger); id. at 384:8–11, 396:7–14
(Raghuram); see also id. at 446:11–15 (Gelsinger).
45
     Id. at 1174:9–19 (Hathaway).
46
     Id. at 488:16–489:17 (Gelsinger).
47
     PTO ¶¶ 72–73; JX-1361 at 31.
48
     PTO ¶ 73.

                                              9
         Also following Project Peach, Pivotal and VMware decided to partner on

developing a Kubernetes-based supplemental offering called Pivotal Cloud Software

(“PKS”).49 Mee stated that Pivotal’s long-term goal was to “converge” Cloud Foundry and

PKS “into one offering.”50 After launching PKS, however, Pivotal management came to

view the product as a disappointment.51 Potential customers did not understand why

Pivotal, known for Cloud Foundry, would provide a Kubernetes-based offering.52

Although Mee believed that Kubernetes required some refinement before developers could

use it—thus foreclosing developers from simply taking what they wanted from the open-

source code—Pivotal’s customer base did not necessarily share that view.53 Members of

Pivotal leadership also thought its technology was behind other cloud providers integrating

Kubernetes into their offerings.54

         Meanwhile, at a September 2018 offsite attended by Mee, Gelsinger, Dell, and other

representatives of Pivotal, VMware, and Dell Technologies, Pivotal learned that VMware

had developed additional containerization offerings. Mee wrote to Dell, “the reality is that

49
   Id. ¶¶ 64, 71. Pivotal referred to its Kubernetes-based offering as “PKS” rather than
“PCS” to disambiguate the phrase “PKS” from “PCF,” because otherwise, “PCS” and
“PCF” would sound similar and lead to confusion. The use of the letter “K” also was a
play on Google’s container engine abbreviation, GKE. See Mee Dep. Tr. at 49:18–53:20.
50
     JX-337 at 1.
51
  Trial Tr. at 1082:15–1083:14 (Mee) (stating that PKS, although “strong[,]” “wasn’t the
same kind of platform that Cloud Foundry was and it wouldn’t be for quite some time.”).
52
     Id. at 1127:24–1128:21 (Mee).
53
     See id.
54
     See Klevorn Dep. Tr. at 20:11–23.

                                             10
[Gelsinger] has way more stamina for this kind of knife fight than we do. . . . I’m

desperately afraid that [Gelsinger] and his team are not going to put an authentic effort into

selling PKS. . . . I think the one thing you can do is insist that [Gelsinger] get real about

PKS and SELL IT.” Dell responded, “Worth more discussion. I do agree with your last

point about selling PKS.”55

          C.     VMware And Pivotal Discuss A Strategic Transaction.

          Pivotal and VMware resumed discussions about a possible merger in late December

2018. That month, Dell and Gelsinger had preliminary discussions with other members of

the VMware Board.56 The next month, Dell broached the topic with Maritz and Mee.57

          On January 22, 2019, Mee met with Gelsinger, who expressed interest in a potential

acquisition of Pivotal and indicated that VMware would begin conducting preliminary due

diligence.58 Contemporaneously, VMware was considering other strategic transactions,

such as a purchase of a data security company or data protection assets from Dell

Technologies. VMware termed this overarching project “Project Basket.”59

          During a February 1, 2019 meeting of the VMware Board, Raghuram discussed a

strategy for developing a successful, Kubernetes-based platform. As Raghuram saw it,

there were three options for VMware: it could build Kubernetes-based technology in-

55
     JX-312 at 1; Trial Tr. at 1095:3–1098:9 (Mee).
56
     PTO ¶ 77.
57
     Id. ¶ 78.
58
     Id. ¶ 79.
59
     See Trial Tr. at 1201:2–8 (Hathaway).

                                              11
house; buy a company that had similar capabilities; or partner with another company to

develop the technology.60       Raghuram recommended the buy option by process of

elimination—building the relevant technology would “take time” to “produce a

product[,]”61 and VMware’s disappointment with PKS scared it away from a partnership.62

Raghuram further recommended that VMware buy Pivotal, noting that it had strong

“Platform IP[,]”63 high “[c]ustomer [c]redibility[,]”64 and “services to help developers

acquire customer base.”65

           After the February 1, 2019 presentation, the VMware Board decided to pursue a

potential transaction with Pivotal. VMware called this “Project Raven.”66 That day, the

VMware Board formed a special committee comprised of Karen Dykstra (Chair), Michael

Brown, and Paul Sagan (the “VMware Special Committee”).67 The VMware Board

resolved not to act on any acquisition without the VMware Special Committee’s

approval.68 Also on February 1, the VMware Special Committee held its first meeting, in

60
     Id. at 358:13–360:3 (Raghuram); JX-474 at 12; PTO ¶ 80.
61
     Trial Tr. at 359:3–8 (Raghuram).
62
     Id. at 364:10–15 (Raghuram) (stating that the PKS partnership was “not working well”).
63
     JX-474 at 13.
64
     Id.
65
     Trial Tr. at 364:2–9 (Raghuram).
66
     See generally JX-474.
67
     PTO ¶ 80; see also JX-473 at 1, 3–7.
68
   JX-473 at 5; see also Trial Tr. at 642:15–18 (Dykstra). Rowe, who was CFO of VMware
at the time, temporarily recused himself from the board of Pivotal as a result. Rowe Dep.
Tr. at 135:20–136:10; see also PTO ¶ 82.

                                             12
which it retained Gibson, Dunn & Crutcher LLP and Lazard Frères & Co. LLC as legal

and financial advisors, respectively.69

          The Pivotal Board met on January 28, 2019.70 At that meeting, neither Dell, Maritz,

nor Mee informed the rest of the Board about discussions of the VMware merger.71 In his

deposition, Maritz stated that he did not bring up the potential transaction because he was

not yet “convinced that there really was a high likelihood of something happening.”72 Mee,

however, assumed the merger would happen. He testified that a “potential merger” with

VMware was always “essentially in the background and discussed from very early days”

at Pivotal.73

          Pivotal management proceeded to explore a potential transaction with VMware,

although the Pivotal Board had not yet discussed it. On February 7, 2019, VMware sent

Pivotal a draft non-disclosure agreement, which Pivotal signed on March 7, 2019.74 On

March 8, 2019, Lazard sent Pivotal CFO Cynthia Gaylor a proposed timeline for a

transaction along with a list of initial diligence requests.75 Among other things, VMware

asked for Pivotal’s “[m]ost recent long-range plan (FY20–22)” (the “Long-Range Plan”).76

69
     PTO ¶ 81.
70
     See generally JX-456.
71
     See id.
72
     Maritz Dep. Tr. at 139:18–140:2.
73
     Trial Tr. at 1103:8–17 (Mee).
74
     PTO ¶ 83.
75
     Id. ¶ 92.
76
     Trial Tr. 1188:17–1189:10 (Hathaway); PTO ¶ 95.

                                              13
VMware especially wanted access to Pivotal’s Long-Range Plan because Project Peach

had broken down in 2018 over the parties’ disagreement on valuation.77

         As diligence proceeded, Pivotal announced its earnings on March 14, 2019. In that

announcement, Gaylor reported certain financial metrics for the fiscal year ended February

1, 2019 (“Fiscal Year 2019”) and Q4 of the same, along with projections for Fiscal Year

2020.78 In particular:

         •      For Fiscal Year 2019, Pivotal reported approximately subscription revenue
                of $400.9 million and total revenue of $657.5 million, reflecting increases of
                55% and 29% year-over-year, respectively.79

         •      For Fiscal Year 2019, Pivotal reported non-GAAP operating losses of
                approximately $71.3 million.80

         •      Forward guidance for the following Q1 of Fiscal Year 2020, which began on
                February 1, 2019: subscription revenues of $124.5 to $125.5 million; total
                revenue of $183 to $185 million, and non-GAAP operating losses of $13.5
                to $12.5 million.81

         •      Forward guidance for Fiscal Year 2020: subscription revenue of $542 to
                $547 million; total revenue of $798 to $806 million; and non-GAAP
                operating losses of $38 to $36 million.82

         •      Gaylor also disclosed that Pivotal finished Fiscal Year 2019 with $990
                million in Remaining Performance Obligation (“RPO”), representing the
                sum of short- and long-term deferred revenue (i.e., advance payments on

77
   VMware’s then-Vice President of Investment Strategy, Philip Hathaway, attributed the
failure of Project Peach back in 2017 to the parties’ inability to “align on a long-range
plan[.]”77 Trial Tr. at 1190:7–23 (Hathaway).
78
     PTO ¶ 84; see also JX-589 at 2 (Form 8-K filed March 14, 2019).
79
     See JX-589 at 4.
80
     See id. at 4, 11; see also PTO ¶ 84.
81
     See JX-589 at 5; see also PTO ¶ 85.
82
     See JX-589 at 5; see also PTO ¶ 85.

                                              14
                 contracts) with backlog (unbilled portions of existing contracts).83 Gaylor
                 also stated that Pivotal expected RPO growth for Q1 of Fiscal Year 2020 in
                 the range of the mid-teens.84

         Pivotal management and the market viewed these results as disappointing. Many

metrics fell short of what Pivotal had projected in its “Annual Plan”—a comprehensive

annual financial and operational plan that Pivotal management regularly developed and

presented to the board.85 Pivotal missed the previous year’s Annual Plan projection of total

revenue by 4%, or $26 million.86

         The Company’s disappointing revenue tracked its lower-than-expected Annual

Contract Value (“ACV”) figures.87 ACV represents annualized software subscription

revenue bookings, which Gaylor described as “the most important [internal] metric at the

company[.]”88 The Company’s miss as of March 14, 2019, was not the first time the

Company had missed ACV targets—it also missed in six prior quarters.89               Pivotal

83
     PTO ¶ 84.
84
     See JX-588 at 6.
85
  Trial Tr. at 899:10–900:24 (Gaylor). Pivotal also prepared monthly updated forecasts
using the Annual Plan. See id. at 900:20–24 (Gaylor).
86
  JX-632 at 11 (March 22, 2019 Board meeting presentation slide comparing projection of
total revenue of $683 million in February 2018 with actual results of $657 million after
February 2019).
87
     Compare JX-932 at 41, with id. at 42.
88
   Trial Tr. at 902:24–903:14 (Gaylor); see also PTO ¶ 67 (describing ACV as “a driver
of Pivotal’s internal forecasts”). At trial, Gaylor more specifically described ACV as “one
of the most important metrics for the forecast and the business model” at Pivotal, and
“determine[d] a lot of other metrics,” including subscription revenue, calculated billings,
and RPO. Trial Tr. at 902:24–903:14 (Gaylor).
89
     See JX-797 at 4; JX-932 at 41.

                                              15
management attributed the disappointing results to a mix of Kubernetes and increased

competition from public cloud providers.90

         Notwithstanding its financial misses, the next day, on March 15, the Pivotal Board

met and formed a special committee to oversee the VMware acquisition (the “Pivotal

Special Committee”).91

         The Pivotal Board appointed the two Group II directors, Klevorn and Lankton, to

the Pivotal Special Committee, of which Lankton was Chair.92 Klevorn and Lankton were

independent but inexperienced. Klevorn, who has held various positions at Ford Motor

Company, joined the Board in 2016 when Ford invested in Pivotal.93 Lankton joined the

Board in October 2018 after retiring as CIO at Travelers Insurance. Lankton had never

previously served on a board of directors.94

         Through a March 15, 2019 resolution, the Pivotal Board gave the Pivotal Special

Committee authority to recommend whether to pursue a potential transaction with VMware

and conditioned the deal on the Pivotal Special Committee’s approval.95 The Pivotal

90
     See Trial Tr. at 1127:24–1129:4 (Mee).
91
     See JX-593.
92
     See also PTO ¶¶ 87–88.
93
  Trial Tr. at 867:16–868:1 (Klevorn); see also PTO ¶ 57 (describing Klevorn’s various
positions throughout the years, such as Executive Vice President, Chief Transformation
Officer, and President of Mobility).
94
     Lankton Dep. Tr. at 6:22–7:14, 10:22–11:2, 60:7–10.
95
     See JX-593 at 4–6.

                                               16
Special Committee had its first meeting that day, in which it retained Latham & Watkins

LLP as legal counsel and Morgan Stanley as financial advisor.96

         On March 16, 2019, Morgan Stanley banker Sterling Wilson emailed Armstrong,

the subject line of which was “Urgent read – spoke to [Robert Mee].”97 Wilson told

Armstrong that

                Rob[ert] [Mee is] getting pressure from [P]at [Gelsinger] and
                Michael [Dell] to move fast. . . . Gotta be fast. Gotta give stuff.
                Not standard process. This is a supervised process. One where
                [P]ivotal has great risk if [Dell] decides to go with [VMware],
                then [it] [d]oesn’t [sic] happen . . . [P]ivotal will lose all
                disputes in [the] future. So [it] can’t be typical m[&]a
                playbook with third party.98

         The next day, Armstrong responded, “Yep[,] got it. Advice I am giving is with that

in mind.”99 At trial, Armstrong stated that he had previously advised the Pivotal Special

Committee to “resist giving” certain information to VMware to “to try and force” VMware

“to give us a proposal before we were more forthcoming.”100 Armstrong interpreted

Wilson’s email to mean that Dell Technologies, Pivotal leadership, and VMware leadership

each had to either “have VMware acquire Pivotal or find a way to cut Pivotal loose and go

do its own thing” and there was “a decent amount of pressure” to get to an answer—merger

96
     PTO ¶ 90; see also Lankton Dep. Tr. at 55:25–56:8; 57:10–13.
97
     See JX-609 (March 16–17, 2019 email exchange between Wilson and Armstrong).
98
 Id.; see also Trial Tr. at 795:14–796:2 (Armstrong) (clarifying short-hands used in the
March 16, 2019 email).
99
     JX-609.
100
      Trial Tr. at 732:8–733:7 (Armstrong).

                                                17
or no merger—“sooner [rather] than later.”101 Armstrong stated that, although Dell and

others wanted an expedited diligence process, their pressure did not cover substantive deal

terms.102 Armstrong did not know what Wilson meant by characterizing the deal as a

“supervised process.”103

         On March 20, 2019, and in line with Wilson’s email, the Pivotal Special Committee

met and decided to provide diligence materials to VMware.104 The next day, Pivotal

opened a data room that the parties used to exchange diligence information.105 Pivotal did

not yet provide VMware with its Long-Range Plan because Pivotal had not yet updated its

projections around the IPO.106

         Around this time, the Pivotal Special Committee decided not to canvas the market

for other potential bidders. Minutes from the committee’s March 29, 2019 meeting show

that the Pivotal Special Committee was “cognizant of the risks inherent in a wider sale

process”—such as the risk that Dell could “prevent any alternative transaction from being

consummated.”107 On April 5, 2019, the Pivotal Special Committee considered the issue

again, and decided against conducting a wider sale process. It reasoned that a potential

leak would affect “customer and partner relationships[,]” “employee retention,” and the

101
      Id. at 733:17–734:2 (Armstrong).
102
      Id. at 735:1–8 (Armstrong).
103
      Id. at 738:4–9 (Armstrong) (stating that the phrase “meant nothing to me.”).
104
      JX-620.
105
      PTO ¶ 94; Trial Tr. at 1191:4–1192:1 (Hathaway).
106
      PTO ¶ 95.
107
      JX-654; see also PTO ¶ 98.

                                              18
“ongoing negotiations” with VMware.108         The Pivotal Special Committee was also

concerned that “[t]here weren’t a lot of players that would be interested in acquiring

Pivotal,” so the likelihood of an alternative transaction was low.109 Morgan Stanley

believed there was “no interest” from prior conversations it had had with potential buyers

during the Project Peach/Flavor process.110

         One of the two Pivotal Special Committee members, Klevorn, was missing in action

through much of this process.

         •      She missed the October 8, 2018 Board meeting. She later testified that her
                absence was likely due to separate duties at Ford.111

         •      She missed the January 28, 2019 Board meeting.112 Klevorn testified that
                she was “probably traveling[.]”113

         •      She arrived late to the March 15, 2019 Board meeting. She could not recall
                why.114

         •      She missed the March 22, 2019 Board meeting. She could not recall why.115

108
      JX-690.
  Lankton Dep. Tr. at 52:10–22. Minutes from the Pivotal Special Committee’s April 12,
109

2019 meeting reflect similar concerns. See JX-723.
110
      Trial Tr. at 774:9–15 (Armstrong).
111
      Id. at 992:11–993:20 (Klevorn); see also JX-318.
112
      See JX-456 at 1.
113
      Trial Tr. at 994:10–995:2 (Klevorn).
114
      See JX-593 at 1–2; Trial Tr. at 995:3–996:12 (Klevorn).
115
   See JX-632 at 1–6; Trial Tr. at 996:13–997:20 (Klevorn) (stating that she was “probably
travel[ing]” or Ford’s own “earnings or board meetings, which . . . I could not get out of.”).

                                              19
         •      She left early from the April 9, 2019 Board meeting due to a “prior
                engagement[.]”116 At this meeting, Lankton provided an update to the rest
                of the Board on the merger.

         So, through April 2019, Klevorn had either missed, was late for, or would leave

early from each Pivotal Board and Special Committee meetings. Klevorn testified that

being on the Pivotal Special Committee was “a lot of work and I don’t know, to be honest,

how I felt about it at the time.”117

         D.     The Parties Temporarily Suspend Merger Discussions.

         By the end of April, VMware decided to pause discussions with Pivotal. Earlier in

April, members of VMware management—such as Hathaway—were concerned they had

not gathered enough information to develop a “high-conviction business case” to present

to the VMware Special Committee, which would have required reviewing Pivotal’s Long-

Range Plan.118       VMware management was skeptical of Pivotal’s stated outlook,

particularly the fact that Pivotal’s annual plan for Fiscal Year 2020 “suggest[ed] a fast

recovery” from “a year of sales enablement issues” and disappointing ACV.119 Dykstra

also echoed these concerns at trial, stating that although VMware was interested in the deal,

the VMware Special Committee was “still waiting for due diligence materials” by early

116
      Trial Tr. at 997:21–998:20 (Klevorn); JX-707 at 1–9.
117
      Trial Tr. at 998:15–20 (Klevorn).
118
      Id. at 1195:14–1196:17 (Hathaway).
119
   See JX-652 at 7 (March 29, 2019 slide deck prepared by VMware employees working
with Philip Hathaway addressing deal diligence).

                                             20
April 2019.120 On April 9, 2019, the VMware Special Committee decided that “additional

information would be required before” it could make an offer to Pivotal.121

          From its initial diligence, VMware was also concerned that Pivotal lacked a clear

plan for addressing the industry shift to Kubernetes.122 Raghuram worried that Cloud

Foundry “had to be fundamentally rewritten to [take] advantage of Kubernetes,” a failure

to do which would jeopardize the business.123            VMware’s then-COO of Customer

Operations, Sanjay Poonen, for instance, asked Raghuram and others “[w]hy not just wait

another year? Let them rebuild the bus to have car parts, [i.e.], [Cloud Foundry] on

Kubernetes” and stated he was “seriously worr[ied] that [Project] Raven will bury us[.]”124

          Gelsinger met with Mee on April 10, 2019.125 It seems that he told Mee about

VMware’s hang-ups, because on April 12, 2019, Mee informed the Pivotal Special

Committee that VMware was unlikely to make an offer.126 On April 19, 2019, Morgan

Stanley advised the Pivotal Special Committee to this effect as well.127 Shortly thereafter,

the special committees suspended formal discussions and diligence.128

120
      Trial Tr. at 649:4–10 (Dykstra).
121
      JX-711 (Minutes of an April 9, 2019 Meeting of the VMware Special Committee).
122
      JX-624.
123
      Trial Tr. at 376:20–377:3 (Raghuram).
124
      JX-696 at 1; see also Trial Tr. 460:15–464:5 (Gelsinger).
125
      PTO ¶ 103.
126
      Id. ¶ 104.
127
      See JX-750.
128
      See Trial Tr. at 651:5–653:16 (Dykstra); JX-750.

                                              21
          Even though the parties had suspended diligence, both the VMware Special

Committee and its management team remained interested in a transaction with Pivotal—

just not one that would close imminently.129 Although VMware did not yet have Pivotal’s

Long-Range Plan, VMware tried to create a model of Pivotal’s valuation using publicly

disclosed information.130 By April 25, 2019, Hathaway and other members of VMware

management had developed a “four to six week” timeline and roadmap for refining a “high-

conviction business case” to present to the VMware Special Committee.131

          Dell was also still interested in pursuing the deal. On May 8, 2019, he sent Gelsinger

an email with the subject line “Raven will be very powerful[.]”132 That email attached a

report from KeyBanc Capital Markets, an investment bank, describing DockerCon 2019, a

conference hosted by the container and PaaS company Docker.133 Dell forwarded the same

email to Mee on May 23, 2019.134

          Gelsinger and Hathaway also fostered hopes of reengaging Pivotal by August

2019.135 Gelsinger responded on May 8, 2019, to Dell’s email, saying Pivotal “had a bad

Q1” but was starting to “get it” regarding Kubernetes despite “internal turmoil” getting

129
   Trial Tr. 649:4–652:6 (Dykstra); id. at 420:10–14 (Raghuram); id. at 505:23–506:14
(Gelsinger).
130
      Id. at 1197:9–1198:5 (Hathaway); see also JX-794 at 1–2.
131
      Trial Tr. at 1199:5–18 (Hathaway); see also JX-764.
132
      See JX-807 at 2–3; see also PTO ¶ 111.
133
      See JX-807 at 2–3.
134
      See id. at 1.
135
      Trial Tr. at 499:11–16 (Gelsinger); see also id. at 1202:1–23 (Hathaway).

                                                22
there.136 Gelsinger believed that the acquisition “[si]mply need[ed] to get . . . done” despite

“[t]oo much friction” between VMware and Pivotal’s “field teams[,]” which caused both

to be “less effective than desired.”137

            E.     The Parties Resume Negotiations After Pivotal’s Disappointing
                   Earnings Report.

            Meanwhile, Pivotal found itself yet again falling short of various financial targets.

On May 22, 2019, Gaylor sent the Pivotal Board a “flash summary,” which is a short-form

summary of the Company’s key financial metrics.138 The flash summary stated that ACV

and services bookings were “below plan” and “below the lower end of the range” discussed

at a prior Board meeting in April.139 Pivotal’s ACV of $11.3 million in Q1 of Fiscal Year

2020 was 61% below its Annual Plan, representing year-over-year decline of 54%.140

            The flash summary also stated that the low Q1 ACV would “compress full year

subscription revenue[,]” and that “it may take multiple quarters to get back on track and

closer to plan” to meet ACV targets.141 Although ACV is “not publicly disclose[d,]” the

136
      JX-813.
137
      Id.
138
   JX-804 at 1–2 (flash summary email dated May 22, 2019 from Gaylor to Pivotal Board);
see also Trial Tr. at 942:22–943:1 (Gaylor) (describing a flash summary as “an up-to-the-
minute or up-to-the-day or -week report that shows kind of where we’re landing for the
quarter.”).
139
      JX-804 at 1.
140
      JX-806.
141
      JX-804 at 1.

                                                 23
flash summary said that the market would pick up on the disappointing performance by

looking at Pivotal’s balance sheet and RPO metrics.142

            Dell and Mee texted about the Company’s difficulties on June 1 and 3, 2019, and

how those difficulties related to the prospective VMware transaction.143 Dell told Mee that

“the strategic alignment seems to be getting stronger which is good” and that he was

“[p]ushing for faster progress” on the deal.144

            Pivotal released its below-expectations financial results for Q1 of Fiscal Year 2020

on June 4, 2019.145 Although Pivotal met or improved upon expectations for revenue,

operating losses, and EPS, it fell short of expectations for deferred revenue and RPO.146

Pivotal’s RPO for Q1 of Fiscal Year 2020 was $880 million, which reflected 10% growth

from Q1 of Fiscal Year 2019 rather than the “mid teens” growth the Company had

forecasted.147

            Mee attributed Pivotal’s disappointing results to difficulties with “sales

execution[,]” i.e., the Company’s inability to close software deals, and “a complex

142
      Id.
143
      See JX-842; JX-850.
144
    JX-850; see also Trial Tr. at 173:4–22 (Dell) (stating that his email communicated that
“it was a good thing for the companies to do this, assuming that the independent special
committees could come to an agreement.”). At trial, Dell did not remember what he meant
by “[p]ushing for faster progress.” See id. at 174:10–14 (Dell).
145
   PTO ¶¶ 105–106, 110. Q1 of Fiscal Year 2020 refers to February 1 through May 3,
2019. See id. ¶ 32.
146
      Id. ¶ 106; Trial Tr. at 744:1–746:4 (Armstrong); JX-804 at 1–2; see also JX-899 at 4–
6.
147
      PTO ¶ 106.

                                                 24
technology landscape,”148 or the market-wide shift toward Kubernetes.149 Pivotal also

internally reported fewer-than-expected new customers, services revenue, and bookings,

with billings “down 23% [year over year.]”150 To Pivotal management, the indicators

signaled decelerating growth.151

         Contemporaneously with the earnings announcement, Pivotal management

provided the following revised guidance to the market for Fiscal Year 2020:

         •      For Q2 of Fiscal Year 2020: subscription revenue of $131 to $133 million;
                total revenue of $185 to $189 million; non-GAAP operating losses of $11 to
                $9 million; and RPO of $790 million. The projected RPO was “flat”
                compared to Q2 of Fiscal Year 2019—in other words, it reflected no
                growth.152

         •      For Fiscal Year 2020: subscription revenue between $530 and $538 million;
                total revenue between $756 and $767 million (down from $798 to $806
                million); and non-GAAP operating losses between $49 and $44 million (up
                from $38 to $36 million).153

         This guidance (the “June Guidedown”) lowered projections relative to what Pivotal

had estimated—and publicly announced—in March 2019.154             In March, Pivotal had

148
      JX-871 at 8–9.
149
      Trial Tr. at 1126:21–1129:4 (Mee).
150
      JX-899 at 4–6; see also JX-806 at 1–2; JX-935 at 23.
151
   See Trial Tr. at 923:19–23 (Gaylor) (stating that “growth [wa]s decelerating” in this
timeframe, which affected the financials); JX-932 at 23, 27–31.
152
      PTO ¶ 107; JX-867 at 5.
153
      PTO ¶ 108; JX-867 at 5.
154
    Trial Tr. at 747:18–748:2 (Armstrong); see also id. at 918:1–8 (Gaylor); see also JX-
932 at 20 (June 25, 2019 Board meeting presentation slide saying “[o]utlook for Q2f, the
rest of the year and forward trajectory lower and decelerating . . . lowered guidance for Q2
and the year”).

                                             25
projected subscription revenue between $542 and $547 million, total revenue of $798 to

$806 million, and non-GAAP operating losses of $38 to $36 million for Fiscal Year 2020.

The June Guidedown thus decreased Pivotal’s forecasts for subscription revenue by about

$4 to $17 million and total revenue by about $31 to $50 million.

         Unsurprisingly, Pivotal’s stock price declined significantly after the June

Guidedown, closing down 41.26% the next day.155 One analyst called it a “[t]rain [w]reck

[q]uarter,” noted that “it’s clear . . . that this management team does not have a handle on

the underlying issues,” and “question[ed] the deeper impact of Kubernetes on the

business.”156 VMware saw the revised earnings as a correction—Gelsinger stated that the

revised earnings and guidance put Pivotal’s valuation into “a range that seems more

reasonable with our outlook for the business.”157 Pivotal, by contrast, viewed the stock

price drop as—in Mee’s words—an “overreaction.”158

         F.     The Parties Revisit The Merger.

         VMware viewed the drop in Pivotal’s stock price as an opportunity. At a June 13,

2019 meeting of the VMware Special Committee, Raghuram addressed Pivotal’s Q1

performance and the market’s “negative reaction[.]”159 Raghuram told the VMware

155
      PTO ¶ 109.
156
   JX-935 at 24; see also JX-894 at 1 (June 6, 2019 email from Morgan Stanley to Gaylor
stating, among other things, “investors question whether Pivotal is fundamentally losing to
competitors in an intensifying competitive environment”).
157
      Trial Tr. at 476:12–16 (Gelsinger); see also JX-890.
158
      Trial Tr. at 1133:7–13 (Mee).
159
      See JX-911 at 2.

                                              26
Special Committee that, in response to its disappointing performance, Pivotal had started

to focus more on Kubernetes in its research & development plan, which was consistent

with VMware’s own long-term goals.160

            Raghuram recommended that VMware resume discussions with Pivotal. VMware

set a goal of having Project Raven and other Project Basket transactions wrapped up by the

VMware’s August 2019 “VMworld”—its “annual user conference where [it] make[s] all

of [its] strategic updates” to thousands of customers, developers, and partners.161

            The VMware Special Committee met again on June 25, 2019. Gelsinger echoed

Raghuram’s recommendation, noting that a disruption of Kubernetes is a rare opportunity

and that acquiring Pivotal would let VMware “achieve critical mass at the developer

level.”162 The VMware Special Committee authorized management to continue due

diligence with Pivotal and set a deadline for management to complete diligence and report

back by July 25.163

            On June 27, 2019, Dykstra called Lankton to express interest on behalf of VMware

in restarting negotiations.164 The parties reengaged.

160
      Id.
161
      Trial Tr. at 658:6–11 (Dykstra).
162
      JX-937 at 1.
163
   Id. at 2. The VMware Special Committee also instructed VMware management to
confirm whether VMware was “still on target to . . . announc[e] [the merger] by VMworld.”
See Trial Tr. 659:7–14 (Dykstra).
164
      PTO ¶ 111.

                                               27
          G.     Pivotal Updates Its Long-Range Plan Between June and July 2019.

          Between June and July 2019, Pivotal revised its internal financial protections, both

to account for its disappointing misses and to generate data for merger negotiations (the

“Revised Outlook”).

          Gaylor and other members of the Financial Planning and Analysis (“FP&A”) team

presented the Revised Outlook during a Pivotal Board meeting on June 25, 2019. Gaylor

remained cautiously optimistic about Pivotal’s “solid topline momentum” in her

presentation, but acknowledged the company’s overall underperformance.165 In particular,

she projected total revenue of $773 million and subscription revenue of $541 million by

end of Fiscal Year 2020, reflecting compound annual growth rates between 2017 and 2020

of 23% and 53%, respectively.166 On the other hand, she projected total and subscription

revenue growth of only 18% and 35% between Fiscal Years 2019 and 2020, respectively,

reflecting decreasing annual marginal growth.167 Her presentation also stated that Pivotal’s

“growth relative to scale is lagging a bit[.]”168

          Gaylor also lowered the Company’s annual forecasts to account for lower ACV.169

Management had slashed Pivotal’s projected Fiscal Year 2020 ACV by 33%—from $240

165
      JX-932 at 38–39.
166
      See id.
167
      See id.
168
      See id. at 39.
169
    Trial Tr. at 917:1–5 (Gaylor) (stating that the new forecast “brought down the outlook
because without ACV, [Pivotal’s] revenue [wa]s going to grow more slowly, if it doesn’t
start to decline.”).

                                               28
million to $160 million—and would need $30 million in ACV during Q2 of Fiscal Year

2020 to meet the targets set out in June 2019.170

            H.    Pivotal And VMware Revisit Diligence And Finalize The Deal.

            In July 2019, the deal acquired new urgency for VMware because IBM acquired

Red Hat, Inc., a technology infrastructure company that developed a container-based cloud

application platform called OpenShift.171      IBM and Red Hat closed the $34 billion

acquisition on July 9, 2019.172 Concerned with how the Red Hat deal might affect

VMware’s competitive standing, on July 11, 2019, Gelsinger emailed Dell, “[w]e are not

winning vs. RedHat. Much too much success for OpenShift. We need to get Raven done,

we are clumsy in competing with them.”173 Dell responded, “[we] know [IBM is] going to

push Red Hat and Openshift hard, so as you said, we need to get Raven done and then do

a full assault on the developer space.”174

            Diligence continued.   On July 2, 2019, Lazard sent Morgan Stanley updated

diligence requests, focused particularly on Pivotal’s financials and forecasts.175 Pivotal

began responding to those requests on July 12. Pivotal provided VMware with a valuation

prepared by Morgan Stanley, along with materials concerning Pivotal’s updated financial

170
      JX-991 at 18, 29.
171
      PTO ¶ 75.
172
      Id.
173
      JX-980 at 1.
174
      Id.
175
      PTO ¶ 112; JX-959; Trial Tr. at 761:17–762:6 (Armstrong).

                                              29
performance and guidance revised in June, through access to a data room.176 VMware and

Pivotal held a series of diligence sessions on July 19, 2019.177

          In a meeting on July 15, 2019, the Pivotal Special Committee considered, again,

whether to canvas the market check and, again, decided against it for several reasons.178

The Pivotal Special Committee believed that there would be limited interest from third

parties.179 Lankton did not believe that Dell would support an alternative transaction.180

And the committee worried that a market canvas would increase the likelihood of the

merger discussions becoming public and “unsettl[ing]” customers or employees.181

Morgan Stanley and Gaylor shared this concern.182

          The VMware Special Committee reconvened on July 25, 2019, and received updates

from management on Project Raven.183 Gelsinger told the VMware Special Committee

that management was nearly done with its “strategic” and “value” assessments, and he

expected to finish the Pivotal deal on time—prior to VMworld.184 John Gnuse from Lazard

176
      PTO ¶ 113.
177
      Id. ¶ 116.
178
      See JX-978.
179
      Trial Tr. at 1040:18–22 (Lankton).
180
      Id. at 1042:14–23 (Lankton).
181
      Id. at 1040:18–1041:5 (Lankton).
182
   See JX-979 at 1 (July 15, 2019 email exchange between Gaylor and Armstrong agreeing
that a market check would “take[] longer to do properly,” and citing “leak and distraction
risk”).
183
      See JX-1005.
184
      See id. at 2.

                                             30
also presented. Lazard had updated the financial models it used for valuing Pivotal in

response to Pivotal’s revised public guidance, refining areas that VMware management

believed were “overexuberant.”185 Gnuse did not believe any of the public disclosures

from Q1 of Fiscal Year 2020 resulted in material changes, given VMware’s relatively more

conservative estimates than Pivotal or investors on Wall Street.186 That day, the VMware

Special Committee decided to make an offer to acquire Pivotal.187

                 1.       The Parties Negotiate Price.

         The VMware Special Committee met on August 4, 2019.188 After confirming that

Pivotal’s flash for Q2 of Fiscal Year 2020 reflected Pivotal performing “in the range” of

its Long-Range Plan,189 the committee decided to make an initial offer of $13.75 per Class

A share of Pivotal common stock.190            The committee also decided to offer Dell

Technologies an exchange of VMware stock at market price, which Dykstra believed

would allow “a good premium for their shares.”191

185
      See Dykstra Dep. Tr. at 284:20–25.
186
      JX-1005 at 4.
187
      See JX-1012 at 2.
188
      JX-1068.
189
      Trial Tr. at 666:8–14 (Dykstra).
190
      Id.; JX-1068.
191
      Trial Tr. at 664:13–16 (Dykstra); see also JX-1033 at 3.

                                               31
          The Pivotal Special Committee met on July 31, 2019.192 Klevorn joined the meeting

late because she was busy with a meeting at Ford.193 Morgan Stanley presented at this

meeting, using a comparable companies analysis to value Pivotal, along with a trio of DCF

analyses based on low, base, and high case scenarios.194 For its comparable companies

analysis, Morgan Stanley selected companies that worked across software infrastructure

and services sectors to account for both parts of Pivotal’s business.195 The Pivotal Special

Committee approved the use of the projections in the potential merger and in Morgan

Stanley’s fairness opinion.196

          On August 4, 2019, Dykstra made the $13.75 per share offer to Lankton on behalf

of the VMware Special Committee. Dykstra attached two conditions to the offer—first, it

was subject to a majority-of-the-minority stockholder vote, and second, that the parties

must finish the deal in two weeks so that it would be ready to announce by VMworld.197

          The next day, the Pivotal Special Committee held a meeting to decide whether to

counteroffer, accompanied by Morgan Stanley, Mee, and other members of Pivotal

leadership.198 Klevorn attended, reluctantly. A few days prior, Klevorn’s assistant asked

192
      See JX-1040.
193
      See Trial Tr. at 1007:1–21 (Klevorn); see also JX-1042 at 1.
194
      JX-1041 at 15–25.
195
      See id. at 17.
196
      See JX-1040 at 1.
197
   Trial Tr. at 667:5–668:9 (Dykstra); see also JX-1065; PTO ¶ 120; JX-1068; see also
JX-937 at 1 (VMware special committee meeting minutes dated June 25, 2019, discussing
“the goal of announcing the transactions at VMworld”).
198
      See JX-1071.

                                              32
her if she could attend that meeting from 5:30 p.m. to 7:00 p.m. Klevorn responded, “[u]gh.

Was planning to do a bunch of returns at [S]omerset. I thought it was at 2???”199 After her

assistant responded about the timing, Klevorn replied, “[l]ife ruiner. Ok.”200

            At that meeting, Morgan Stanley advised the Pivotal Special Committee that it had

a choice: if Pivotal ultimately wanted above $16.50 per share, Pivotal should not respond

with a counteroffer; but if it was willing to accept a lower price, it should counter.201

Morgan Stanley also presented a set of “Potential Advocacy Points” that the Pivotal Special

Committee could use for a counteroffer.202 Those points divided into two categories—

“Helpful” and “Not Helpful[.]”203 Morgan Stanley considered Pivotal’s historical revenue

multiples to be a “[h]elpful” factor, noting that Pivotal’s stock has traded “above 6x more

than 79% of the time[,]” which Pivotal could “approach” if “we execute.”204 On the other

hand, Morgan Stanley considered the premium VMware offered to be unhelpful for further

negotiation because it was “already . . . good[,]” and it viewed the relevant “[e]quity

comparables” as “[t]oo nuanced and convoluted” to be helpful.205

199
      JX-1051 at 1.
200
      Id.
201
      Trial Tr. at 767:15–768:5, 827:5–17 (Armstrong).
202
      See JX-1074.
203
      See id. at 2.
204
   Id. Armstrong at trial testified that it is “quite common” for market participants to
“discuss and think of valuation of software companies with regard to revenue multiples.”
See Trial Tr. at 821:1–6 (Armstrong).
205
   JX-1074 at 2. Morgan Stanley also noted that the equity comparables furthermore failed
to account for a control premium. See id.

                                               33
          Lankton was worried about saying no to VMware. She took several notes at the

August 5 meeting illustrating her concerns. She worried about the adverse effects on

Pivotal’s relationship with VMware from backing out. For instance, one note read “Pat

[Gelsinger] . . . won’t do Pivotal any favors if the deal doesn’t happen.”206 By this, Lankton

meant that, with or without Pivotal, Gelsinger and VMware would “develop the capability”

to fill “the white space that he had in his product line” resulting in competition.207 Another

note in this vein said “Pat could say – see I told you they are unreasonable[;]” in other

words, that Gelsinger would find excessive pushback “unreasonable.”208

          Lankton was also concerned about alienating Dell. Another note read “Paul Maritz

– Michael Dell/Egon best outcome – they have to buy us. Michael [Dell] wants this deal

done!”209 Egon referred to Egon Durban, who, recall, was also on the Board.210 Dell could

not recall communicating this urgency to Lankton, but at trial stated that he was supportive

of the deal and recognized the weight his name carried at Pivotal.211

206
      See id.
207
    See Lankton Dep. Tr. at 222:24–11; see also Trial Tr. at 825:23–826:14 (Armstrong)
(stating that the Pivotal Special Committee discussed this concern). Another of Lankton’s
notes in this vein read “Michael – if Pivotal is on its own – can’t get Pat to play.” See JX-
1072 at 2.
208
      JX-1072 at 2; Trial Tr. at 1071:8–1072:3 (Lankton).
209
      JX-1072 at 2 (emphasis in original).
210
      Trial Tr. at 134:2–8 (Dell).
211
      Id. at 133:2–9, 172:1–16 (Dell).

                                             34
         Mee argued at the meeting in favor of counteroffering.212 He believed that Dykstra

and Lankton were productively negotiating, and that their “back-and-forth with a rhythm

would be disrupted by not countering[,]” a position with which Lankton agreed.213 In the

end, the Pivotal Special Committee decided to counteroffer at $16.50 per share with the

understanding that $16.50 would be a “ceiling” on the price.”214 Lankton presented the

counteroffer to the VMware Special Committee the next day at $16.50 per share, and

demanded a “go-shop” as “leverage” in price negotiations.215

         The parties haggled further. The VMware Special Committee increased its offer to

$14.25 per share but rejected the go-shop demand.216 The Pivotal Special Committee

countered with $15.75 and again insisted on the go-shop.217

         During this period, Pivotal updated its Q2 flash, which Armstrong characterized as

Pivotal “meet[ing] or slight[ly] beat[ing]” guidance from June.218 Although Gaylor and

Mee were glad, Gaylor did not believe the results affected Pivotal’s long-term outlook.219

212
      Id. at 825:12–20 (Armstrong).
213
      Id. at 1147:12–1148:16 (Mee).
214
   Lankton Dep. Tr. at 210:20–25; JX-1071 at 1; see also Trial Tr. at 827:1–828:10
(Armstrong).
215
      Klevorn Dep. Tr. at 126:13–25; PTO ¶ 122; see also JX-1076.
216
      PTO ¶ 123.
217
      Id. ¶ 124; JX-1093.
218
      Trial Tr. at 763:13–17 (Armstrong); JX-1110 (Q2 flash dated August 9, 2019).
219
   See Trial Tr. at 943:2–944:17 (Gaylor); see also JX-1055 at 2 (August 3, 2019 email
from Gaylor to Mee stating “it is unlikely that we can raise guidance for q3 and the year”);
JX-1091 (August 7, 2019 email from Gaylor to Latham and Watkins, Lankton, Klevorn,

                                             35
So, even though spirits rose off the heels of a disappointing quarter, Pivotal management

did not adjust its negotiation strategy or price offer to VMware.

         On August 14, 2019, the VMware Special Committee made what it termed a “best

and final offer” of $15.00 per share.220 The Pivotal Special Committee held a meeting to

consider it; Klevorn was absent.221 Morgan Stanley advised Lankton that Pivotal’s Q2

results would not have a material impact on its stock price.222 Acting on behalf of the

Pivotal Special Committee, Lankton agreed on August 14, 2019, to a tentative merger price

of $15 per share of Class A Pivotal stock.223

                 2.    VMware And Pivotal Finalize The Merger.

         On August 14, 2019, Dell Technologies publicly disclosed on its VMware Schedule

13D that VMware and Pivotal were “proceeding to negotiate definitive agreements with

respect to a transaction to acquire all of the outstanding shares of Class A common stock

of Pivotal for cash at a per share price equal to $15.00.”224 During the following week,

VMware and Pivotal engaged in confirmatory diligence and negotiated the deal

Morgan Stanley, and Cohen, stating that the updated forecast “likely doesn’t change the
outlook dramatically for FY20”).
220
      PTO ¶ 129.
221
      Id. ¶ 131; see also JX-1142.
222
      Trial Tr. at 763:11–766:4 (Armstrong).
223
      JX-1138.
224
      JX-1158 at 6; PTO ¶ 133.

                                               36
documents.225 On August 20, 2019, the Pivotal Special Committee decided to forego its

demand for a go-shop.226

          While the VMware Special Committee negotiated with Pivotal concerning the Class

A stock, it was also negotiating with Dell Technologies concerning the Class B stock. On

August 13, VMware offered Dell Technologies 0.055 VMware shares for each of its

Pivotal Class B shares.227 Based on then-current market prices, that ratio implied a cash

value of $8.71 per Class B share. Dell Technologies agreed on August 21.228

          Both companies’ special committees met shortly thereafter. On August 21, the

VMware Special Committee held a meeting in which Lazard presented its fairness opinion

approving $15 per share.229 Upon the VMware Special Committee’s recommendation, the

VMware Board approved the Merger.230

          The Pivotal Special Committee met on August 22. Morgan Stanley presented its

analysis of the transaction and opined that $15 per share was fair to Pivotal’s unaffiliated

Class A stockholders.231 Upon the Pivotal Special Committee’s recommendation, the

225
      PTO ¶¶ 134–135.
226
      Id. ¶ 135; JX-1208.
227
      PTO ¶ 128.
228
      Id. ¶ 136.
229
      JX-1215; JX-1216; see also JX-1223; JX-1225.
230
      PTO ¶ 137.
231
      JX-1239 at 1; see also JX-1238.

                                             37
Board approved the merger the same day.232 Shortly thereafter, Pivotal and VMware

executed the Merger Agreement and announced the merger to the public.233

         On September 4, 2019, Pivotal released its Q2 earnings report for Fiscal Year

2020.234 Although it reported disappointing non-GAAP operating losses, its revenue

results were otherwise in keeping with prior guidance from June. On September 4, 2019,

Pivotal reported subscription revenue of $135 million, total revenue of $192.9 million, and

non-GAAP operating losses of $4.5 million.235 In its Form 10-Q filed the next day, Pivotal

reported RPO of $860 million.236 Pivotal’s prior guidance from June 2019 had predicted

subscription revenue between $131 and $133 million; total revenue of $185 to $189

million; and non-GAAP operating losses of $11 to $9 million.237 So, although non-GAAP

operating losses were greater by about $4.5 to 6.5 million than expected, the Company’s

revenue results aligned with the June Guidedown.

         Although Pivotal’s September earnings figures showed it meeting many targets, by

mid-October, the Company yet again readjusted its forecasts relative to the Annual Plan.

On October 16, 2019, Pivotal management estimated in a Board presentation that total

232
      PTO ¶ 138.
233
      Id. ¶ 139; JX-1252.
234
      PTO ¶ 140; see also JX-1300 (Form 8-K Filed September 4, 2019).
235
      See PTO ¶ 140; see also JX-1300 at 4.
236
   PTO ¶ 140. Pivotal did not hold an earnings call or provide updated guidance for Q3
of FY2020. See id.
237
      PTO ¶ 107.

                                              38
revenues for Fiscal Year 2020 would likely land between $766 and $782 million,

approximately $60 million below the Annual Plan.238

          On October 10, Pivotal publicly filed the fairness opinion presentations of the

advisors to the Pivotal Special Committee, the VMware Special Committee, and the Dell

Technologies Board prior to their approval of the Transaction, along with supplemental

materials from the companies’ financial advisers.239 Those materials included Pivotal’s,

Dell Technologies’, and VMware management’s standalone projections for Pivotal,

Pivotal management’s pre-Q1 earnings projections, and VMware’s projections for Pivotal

as part of VMware.240 The definitive proxy statement for the merger, filed on November

27, also disclosed Pivotal and Dell Technologies’ management’s standalone projections

for Pivotal, as well as VMware’s projections for Pivotal as part of VMware.241

          Pivotal continued to show mixed results during Q3 of Fiscal Year 2020. On the one

hand, Gaylor on November 18, 2019 sent the Pivotal Board a Q3 Flash indicating ACV of

$31.8 million, which landed at 66% of the Annual Plan’s forecast and reflected a year-

over-year decrease of 6%.242 On the other hand, Gaylor’s Q3 Flash characterized the

overall results as “relatively strong[,]” alluding to subscription revenue “on the high end of

the forecast” while services revenue and net income “exceeded the forecast we shared at

238
      JX-1336 at 24.
239
      See generally JX-1331.
240
      See JX-1331 at 28–29, 45–47, 239, 250–51, 280, 317–18.
241
      JX-1361 at 91–96; PTO ¶ 143.
242
      JX-1357 at 1.

                                             39
the October board meeting.”243           Still, by December 6, Pivotal reported subscription

revenues and total revenues that were $5.8 million and $18.4 million below Annual Plan,

respectively, with operating losses $3 million above the Annual Plan.244

            On December 27, 2019, 92.6% of Pivotal’s unaffiliated stockholders voted to

approve the merger.245 It closed on December 30, 2019.246 The merger price was $15 per

share for the Class A stockholders and an exchange of Pivotal Class B common stock held

by Dell Technologies at a ratio of 0.0550 shares of VMware Class B stock per share of

Pivotal Class B stock, a blended price of $11.71.247

            I.     This Litigation

            The petitioners (“Petitioners”) brought this appraisal action pursuant to 8 Del. C. §

262 on March 5, 2020.248 The court held a five-day trial between July 6, 2022, and July

12, 2022.249 The parties completed post-trial briefing on November 18, 2022, and the court

heard post-trial oral argument on December 13, 2022.250

243
      Id.
244
   See JX-1365 at 4, 31. Pivotal reported Q3 subscription revenues of $139.8 million, total
revenue of $198.3 million, operating losses of $556,000, and RPO of $820 million. See
JX-965 at 7.
245
      PTO ¶ 144; JX-1386; JX-1387.
246
      PTO ¶ 145.
247
      PTO ¶ 139.
248
      See Dkt. 1 (Pet.).
249
      See Trial Tr.
250
      See Dkts. 203–204; Dkt. 210.

                                                 40
         Parallel to this case, a class of former stockholders of Pivotal brought a breach of

fiduciary duty class action against Dell, Dell Technologies, VMware, Mee, and Gaylor on

June 4, 2020.251 The parties to the class action agreed to terms of a settlement, which the

court approved on October 4, 2022.252

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.”253

         The appraisal statute requires that the court “determine the fair value of [the

petitioners’] shares exclusive of any element of value arising from the accomplishment or

expectation of the merger [or] consolidation[.]”254 “To determine the fair value of a

stockholder’s proportionate interest in the corporation, the court must ‘envisage the entire

pre-merger company as a ‘going concern,’ as a standalone entity, and assess its value as

such.’”255 “The time for determining the value of a dissenter’s shares is the date on which

the merger closes.”256 When running the fair value analysis, therefore, the court must

251
      See C.A. No. 2020-0440-KSJM, Dkt. 1 (Compl.).
252
      See C.A. No. 2020-0440-KSJM, Dkts. 246, 249.
253
   In re Appraisal of Regal Ent. Gp., 2021 WL 1916364, at *16 (Del. Ch. May 13, 2021)
(quoting Cede & Co. v. Technicolor, Inc., 542 A.2d 1182, 1186 (Del. 1988)).
254
      8 Del. C. § 262(h).
255
  Regal, 2021 WL 1916364, at *17 (quoting Dell, Inc. v. Magnetar Glob. Event Driven
Master Fund Ltd, 177 A.3d 1, 20 (Del. 2017) [hereinafter, “Dell Appeal”]).
256
  Brigade Leveraged Cap. Structures Fund Ltd. v. Stillwater Mining Co., 240 A.3d 3, 17
(Del. 2020).

                                              41
consider “the corporation’s operative reality as of the date of the merger.”257 “The concept

of the corporation’s ‘operative reality’ is important because ‘[t]he underlying assumption

in an appraisal valuation is that the dissenting shareholder would be willing to maintain

their investment position had the merger not occurred.’”258

       The petitioner bears the initial burden of demonstrating statutory compliance.

“Delaware cases uniformly place the burden of proof on the petitioner to demonstrate

compliance with the requirements of the appraisal statute.”259

       After the petitioner proves statutory compliance, the statute places the “obligation

to determine the fair value of the shares on the court.”260 “A party may seek to prove fair

value using ‘any techniques or methods which are generally considered acceptable in the

257
    In re AOL Inc., 2018 WL 1037450, at *8 (Del. Ch. Feb. 23, 2018) (citing 8 Del. C. §
262) (internal quotation marks omitted); see also Tri-Cont’l Corp. v. Battye, 74 A.2d 71,
72 (1950) (“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.”); Dell Appeal, at 20 (“The valuation should reflect the ‘‘operative
reality’’ of the company as of the time of the merger”) (quoting M.G. Bancorporation, Inc.
v. Le Beau, 737 A.2d 513, 525 (Del. 1999) (quoting Cede & Co. v. Technicolor, Inc., 684
A.2d 289, 298 (Del. 1996))).
258
   In re Stillwater Mining Co., 2019 WL 3943851, at *19 (Del. Ch. Aug. 21, 2019)
(quoting Cede, 684 A.2d at 298) (alteration in original).
259
   In re Appraisal of Dell Inc., 143 A.3d 20, 36 (Del. Ch. 2016) [hereinafter “Dell Trial”];
see also 8 Del. C. §262(g) (“At the hearing on such petition, the Court shall determine the
persons who have complied with this section and who have become entitled to appraisal
rights.”).
260
  BCIM Strategic Value Master Fund, L.P. v. HFF, Inc., 2022 WL 304840, at *15 (Del.
Ch. Feb. 2, 2022) (citing Gonsalves v. Straight Arrow Publ’rs, Inc., 701 A.2d 357, 360–61
(Del. 1997)).

                                              42
financial community and otherwise admissible in court.’”261 “Because of this statutory

mandate, the allocation of the burden of proof in an appraisal proceeding differs from

traditional adversary litigation.”262 “In an appraisal proceeding, ‘both sides have the

burden of proving their respective valuation positions[.]’”263 “[N]o presumption, favorable

or unfavorable, attaches to either side’s valuation[.]”264 “Each party also bears the burden

of proving the constituent elements of its valuation position . . . , including the propriety of

a particular method, modification, discount, or premium.”265

            “[T]he standard of proof in an appraisal proceeding is a preponderance of the

evidence.”266 “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

oppose to it, has the more convincing force and makes you believe that something is more

likely true that not.”267

261
  Regal, 2021 WL 1916364, at *17 (quoting Weinberger v. UOP, Inc., 457 A.2d 701, 713
(Del. 1983)).
262
      HFF, 2022 WL 304840, at *15.
263
  Id. (quoting Fir Tree Value Master Fund, LP v. Jarden Corp., 236 A.3d 313, 322 (Del.
2020) (alterations and internal quotation marks omitted)).
264
    In re Panera Bread Co., 2020 WL 506684, at *18 (Del. Ch. Jan. 31, 2020) (alterations,
citations, and internal quotation marks omitted).
265
      Stillwater, 2019 WL 3943851, at *18 (internal quotation marks omitted).
266
      Id.
267
   Agilent Techs., Inc. v. Kirkland, 2010 WL 610725, at *13 (Del. Ch. Feb. 18, 2010); see
also Stillwater, 2019 WL 3943851, at *18 (quoting same).

                                              43
            This court has a significant amount of discretion in discharging its statutory

mandate.268 “In some cases, it may be that a single valuation metric is the most reliable

evidence of fair value” such that “giving weight to another factor will do nothing but distort

that best estimate.”269 “In other cases, it may be necessary to consider two or more

factors.”270      “[I]n still others, the court might apportion weight among a variety of

methodologies.”271        “The Court of Chancery may ‘adopt any one expert’s model,

methodology, and mathematical calculation, in toto, if that valuation is supported by

credible evidence and withstands a critical judicial analysis on the record.’”272

            The broad discretion afforded the court in these proceedings can seem perilous for

a trial judge. As the high court has succinctly commented, “[a]ppraisals are odd.”273

Appraisal is a statutory construct, and yet, “[t]he statue does not define ‘fair value,’” which

is a “jurisprudential, rather than purely economic, construct.”274 The statute demands that

the trial court take into account “all relevant factors,”275 which the court must reduce to a

single determination of fair value. “The statutory obligation to make a single determination

268
      Regal, 2021 WL 1916364, at *17 (citing Le Beau, 737 A.2d at 525–26).
269
      Dell Appeal, at 22 (alterations and internal quotation marks omitted).
270
      Id. (internal quotation marks omitted).
271
      Id.
272
      Regal, 2021 WL 1916364, at *17 (quoting Le Beau, 737 A.2d at 526).
273
      Dell Appeal, at 19.
274
    In re Appraisal of Jarden Corp., 2019 WL 3244085, at *1 (Del. Ch. July 19, 2019)
(internal quotation marks omitted).
275
      8 Del. C. § 262(h).

                                                44
of a corporation’s value introduces an impression of false precision into appraisal

jurisprudence.”276 In the end, “[t]here may be no perfect methodology for arriving at fair

value for a given set of facts[.]”277

         Fortunately, Delaware law does not demand a quixotic quest for perfection in the

appraisal context. As the high court has assuaged, “[c]apitalism 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 procured had every domino fallen out of the

company’s way[.]”278 “Fair value does not equal best value.”279 This court’s goal is far

more modest: “explain its fair value in a manner that is grounded in the record before it”280

and “accepted financial principles.”281

         With this modest goal in mind, the analysis turns to the parties’ positions. The

parties dispute both the procedural prerequisites for appraisal and the substantive value of

Petitioners’ shares.

         First, Respondent argues that Petitioners failed to prove statutory compliance by

failing to show, for one, ownership of Pivotal stock at the relevant times and, for another,

276
      Stillwater, 2019 WL 3943851, at *20.
277
      Dell Appeal, at 22–23.
278
      DFC Glob. Corp. v. Muirfield Value P’rs, 172 A.3d 346, 370 (Del. 2017).
279
      Dell Appeal, at 23 (cleaned up).
280
      Jarden, 236 A.3d at 325 (internal quotation marks omitted).
281
      Dell Appeal, at 22.

                                              45
that their shares were not voted in favor of the merger. Petitioners argue that they have

proven all relevant standing requirements.

       Substantively, Respondent argues that each share of Pivotal was worth $12.17 on

December 30, 2019, a value it arrives at principally based on the expert report of Kenneth

M. Lehn. Lehn uses a pair of DCFs to triangulate a per-share value on August 14, 2019,

of $12.85. He then adjusts this figure using an events study to capture changes in the

market between then and the valuation date of December 30, 2019, resulting in a final price

of $12.17. Respondent also points to the ostensible reliability of the deal process and other

market factors as a cross-check on this analysis. By contrast, Petitioners rely upon the

analysis of their expert, Murray Beach, who derives a price of $20 per share based on a

cross check of comparable companies, comparable transaction, and DCF analyses.

       This decision first addresses the question of statutory compliance before turning to

the valuation analysis.

       A.     Statutory Compliance

       Section 262(a) requires, among other things, that a petitioner hold the shares for

which it seeks appraisal on the date it makes a demand for appraisal, continuously hold

such shares through the effective date of the merger, and not vote such shares in favor of

the merger nor consent to the merger in writing.282

282
   Merion Cap. LP v. BMC Software, Inc., 2015 WL 67586, at *6 (Del. Ch. Jan. 5, 2015)
(discussing 8 Del. C. § 262(a)).

                                             46
          Respondent disputes that Petitioners satisfied their evidentiary burden as to these

requirements. It observes that Petitioners called no witnesses to testify to these facts.

Respondent argues that Petitioners failed to submit any documentary evidence of their

Pivotal stock ownership. Respondent further contends that Petitioners failed to present any

evidence that Cede & Co.—the record holder—did not vote Pivotal’s shares in favor of the

merger.

          Petitioners advance a mix of factual and legal arguments in response.

          Factually, Petitioners argue that Respondent stipulated to the relevant facts in

Paragraphs 21 through 25 of the Pre-Trial Order. But the paragraphs of the Pre-Trial Order

upon which Petitioners rely do not prove the issue. Paragraphs 21 and 22 speak to

Petitioners’ beneficial ownership status, but these paragraphs are limited to Petitioners’

assertions that they beneficially owned Pivotal stock. Respondent did not confirm or deny

the truth or falsity of these assertions by agreeing to this language. Paragraph 23 states that

Pivotal received letters in which Petitioners identify themselves as beneficial owners of

Pivotal stock.283 Although Respondent has conceded that it received those letters, it has

not stipulated that the contents of those letters are true. Paragraphs 24 and 25 describe

Petitioners’ prosecution of their appraisal claims. Paragraph 24 states: “Petitioners filed a

Petition for Appraisal of Stock on March 5, 2020.”284 Paragraph 25 states: “Petitioners

283
      PTO ¶ 23.
284
      Id. ¶ 24.

                                              47
have not withdrawn their appraisal demand.”285 These paragraphs characterize Petitioners’

prosecution of their claims, but they do not address Petitioners’ ownership status at relevant

times.     Whether individually or taken together, these stipulations do not prove that

Petitioners met the ownership or voting status requirements. Petitioners cannot rely on the

Pre-Trial Order to satisfy their burden.

          Petitioners next argue that the appraisal demands themselves, coupled with

verifications to their appraisal petition, establish the requisite ownership. But the demand

letters do not satisfy Petitioners’ evidentiary burden. At most, they evince stock ownership

at the time of the demand. The December 19 letters state that Cede & Co. is the nominee

of The Depository Trust Company, and that The Depository Trust Company “is informed

by its Participant, J.P[.] Morgan Securities LLC” that HBK Master Fund L.P. and HBK

Merger Strategies Master Fund L.P. beneficially own 6,875,101 shares and 3,124,999

shares, respectively, on the date of the appraisal demand.286 The Merger closed on

December 30, 2019.

          Petitioners also argue that Respondent’s Verified List dated May 31, 2020, establish

their voting record. The Verified List similarly falls short. It characterizes Petitioners as

dissenting stockholders who “have demanded payment in connection with the Merger and

with whom agreements as to the value of their shares have not been reached with

285
      Id. ¶ 25.
286
      See Dkt. 1, Ex. A at 2–3.

                                               48
Pivotal[.]”287 The Verified List, however, also purported to reserve Respondent’s right to

challenge Petitioners’ entitlement to appraisal rights.288 As a result, it does not show

whether Petitioners dissented or whether Respondent was aware of any such dissent. The

result is that Petitioners may not rely on the Verified List.

          Although Petitioners’ factual arguments fail, one of their legal arguments saves the

day: Respondent waived its challenge to Petitioners’ standing by failing to assert the

argument in its pre-trial submissions. The Pre-Trial Order, for instance, does not include

the word ‘standing.’ Also in the Pre-Trial Order, Respondent states that it “refers the Court

to its pre-trial brief for a more complete statement of the relief sought” and to “a more

complete statement of the issues of fact that Respondent intends to establish at trial and the

statements of legal issues to be tried.”289 The Pre-Trial Order clarifies that Respondent

seeks the following relief: (i) a judicial determination that Pivotal’s Class A common stock

was worth $12.17 on December 30, 2019; (ii) that there is “good cause” to award no interest

on any appraisal award or at a rate less than the default rate of Section 262(h); (iii) an award

of costs under Court of Chancery Rule 54(d); and (iv) “such other and further relief” in the

court’s discretion.290 This list does not include standing.

          Nor did Respondent preserve its standing argument its pre-trial brief. That brief

argues that (i) Lehn’s DCF analysis is reliable evidence of Pivotal’s fair value; (ii) that

287
      Dkt. 4 (Verified List) ¶ 3.
288
      Id. ¶ 4.
289
      PTO ¶¶ 151, 153.
290
      Id. ¶ 153.

                                               49
market indicators—such as deal price and market reaction to the deal—support this result;

and (iii) that Beach’s valuation is unreliable.291 Like the Pre-Trial Order, Respondent’s

pre-trial brief does not once use the term ‘standing,’ nor does it raise the issue indirectly.

Respondent’s silence on this point effects a waiver.292

         Petitioners also raise a separate argument—that by prepaying some value of

Petitioners’ stock under Section 262(h) of the Delaware General Corporation Law,

Respondent has conceded that Petitioners have standing.293 Given the text and purpose of

that Section, however, this argument is not compelling. Section 262(h) does not, on its

face, say anything about waiver.294 It was adopted to allow “a surviving corporation

seeking to lessen the significant amount of interest that can otherwise accrue in an appraisal

action” by “prepay[ing]” the petitioner cash ahead of time.295 “As the General Assembly

explained, ‘there is no requirement or inference that the amount so paid by the surviving

291
      See Dkt. 160 (Resp’t’s Pre-Trial Br.) at 30–63.
292
   See Emerald P’rs v. Berlin, 726 A.2d 1215, 1224 (Del. 1999) (“Issues not briefed are
deemed waived.”).
293
      See Dkt. 203 (“Pet’rs’ Post-Trial Reply Br.”) at 70.
294
   8 Del. C. § 262(h) (“At any time before the entry of judgment in the proceedings, the
surviving, resulting or converted entity may pay to each person entitled to appraisal an
amount in cash, in which case interest shall accrue thereafter as provided herein only upon
the sum of (1) the difference, if any, between the amount so paid and the fair value of the
shares as determined by the Court, and (2) interest theretofore accrued, unless paid at that
time.”).
295
      Panera, 2020 WL 506684, at *43.

                                               50
corporation is equal to, greater than, or less than the fair value of the shares to be

appraised.’”296

         Here, Pivotal prepaid Petitioners $9.08 per share for exactly this purpose—it made

the strategic decision to limit the potentially significant interest payments it might have to

make after an adverse judgment.          Petitioners do not explain how the Company’s

prepayment of money effects a waiver of various statutory standing objections. Petitioners

cite no cases for support on this point, nor is this court aware of any. And allowing Section

262(h) to let appraisal petitioners work around their standing burden does not seem

consistent with the overarching purpose of the amendment, which was to discourage

appraisal arbitrage through economic incentives.

         Respondent also argues that Petitioners purchased Pivotal shares “for purposes of

bringing an appraisal action.”297 In other words, Respondent argues that Petitioners are

engaged in appraisal arbitrage, which (as stated previously), aspects of Section 262 seek to

discourage. Still, Respondent waived this argument by not raising it sooner.

         Even were the court to entertain Respondent’s appraisal arbitrage argument on the

merits, Petitioners ably invoke Transkaryotic’s no-tracing rule.298            As the court

summarized in Merion Capital LP v. BMC Software, Inc., a holder need only “show that it

296
   Id. (quoting Del. H.B. 371, 148th Gen. Assem., 80 Del. Laws, ch. 265, §§ 8–11 (2016)
(cleaned up)).
297
      See Dkt. 198 (“Resp’t’s Post-Trial Opening Br.”) at 41.
  Pet’rs’ Post-Trial Reply Br. at 70 (citing In re Transkaryotic Therapies, Inc., 2007 WL
298

1378345 (Del. Ch. May 2, 2007) (Chander, C.)).

                                              51
held a quantity of shares it had not voted in favor of the merger equal to or greater than the

quantity of shares for which it sought appraisal.”299 That is, the stockholder need only (i)

find the total amount of shares voted against the merger (which information is available on

public exchanges); (ii) identify how many shares he has; and (iii) determine that (ii) is

lower than (i). If so, he has met his burden.300

         Here, as of December 19, 2019, Petitioners beneficially owned a combined

10,000,100 shares of Pivotal Class A stock and asserted appraisal rights for all shares.301

The inquiry turns to whether the record holder, Cede & Co., “held a quantity of shares it

had not voted in favor of the merger equal to or greater than the quantity of shares for which

it sought appraisal[.]”302 From the record before the court, there were 35,591,973 Class A

shares not voted in favor of the merger.303 Because Petitioners’ approximately ten million

299
      2015 WL 67586, at *6 (discussing Transkaryotic, 2007 WL 1378345).
300
   In Tranksaryotic, the respondents argued that this rule makes bad policy for facilitating
appraisal arbitrage. The court reasoned that, if appraisal arbitrage is “an evil[,]” the
legislature “possesses the power to modify § 262” to alleviate the respondents’ concern.
Transkaryotic, 2007 WL 1378345, at *5. Other decisions of this court have challenged the
reasoning behind the Transkaryotic rule. In In re Appraisal of Dell Inc., the court stated
that “the rise of appraisal arbitrage suggests the need for a more realistic assessment of the
depository system that looks through Cede to the [broker-dealer or other representative of
the beneficial holder].” 2015 WL 4313206, at *23 (Del. Ch. July 13, 2015). There, the
Vice Chancellor urged a “more nuanced jurisprudence” that would use “records at the
broker level” to “more flexibl[y]” assess “questions of ownership and the ability to exercise
associated rights” as the “subject of proof.” Id. at *24. The Vice Chancellor, however,
recognized that this position is not the law. See id. at *9.
301
      See Dkt. 1, Ex. A at 2–3.
302
      BMC Software, 2015 WL 67586, at *6.
303
   JX-1386 at 2. Out of 105,538,574 shares, 69,946,601 were voted in favor of the merger.
See id. The court therefore arrives at 35,591,973 through subtraction.

                                             52
shares are fewer than the approximately 36 million shares outstanding, the record holder

held an amount “greater than the quantity of shares for which it sought appraisal[.]”304

Therefore, under Transkaryotic, Petitioners have met their burden of proof regarding the

voting record.

         To summarize, most of Petitioners’ factual arguments fall short, as does its legal

argument concerning prepayment.         Luckily for Petitioners, Respondent waived the

standing argument by failing to preserve it in its pre-trial briefing. Furthermore, Petitioners

have satisfied their burden of proof on voting under Transkaryotic. Petitioners have

therefore met their burden on standing.

         B.    Fair Value

         The parties presented a total of five valuation methods. Respondent argues that the

merger was the result of an objectively reliable process, such that the fair value is less than

the deal price of $15 per share. Respondent points to a separate market-based indicator,

the unaffected stock price of $8.30 per share, as a cross-check on its argument that the fair

value of the Company per share is lower than the deal price. Relying on its expert’s DCF

analysis, Respondent contends that the fair value is $12.17 per share, or $2.83 below the

deal price.

         Petitioners dispute that the market-based metrics on which Respondent relies are

acceptable valuation methodologies in a controller squeeze-out. They likewise dispute

Respondent’s DCF, stating that it is unduly speculative, rooted in unreliable projections,

304
      BMC Software, 2015 WL 67586, at *6.

                                              53
unreasonable based on contemporaneous analyst opinions, and wholesale inapposite for a

company like Pivotal.305 Petitioners urge the court to base fair value on revenue multiples

derived from comparable companies and precedent transactions. This approach generated

a fair value of $20 per share, or $5 above the deal price.

         Although the Delaware Supreme Court has expressly declined to adopt a

presumption in favor of any one valuation methodology over another,306 recent decisions

of Delaware courts suggested a pecking order of methodologies for determining fair value.

“In the aftermath of Dell and DFC, . . . the fair value analysis should ‘begin with the market

evidence.’”307 Among the market-based indicators, the deal price (minus synergies)

approach is the “first among equals.”308 “[A] more subjective valuation technique, like

DCF methodology or comparable company analysis, ‘is necessarily a second-best method’

when ‘market-based indicators are available.’”309

         The structure of this decision follows this hierarchy ascribed to valuation

methodologies by the Delaware Supreme Court. The court first evaluates whether the deal

price is necessarily a cap on fair value. After concluding that it is not, the court addresses

Respondent’s argument based on the unaffected stock price of $8.30. Respondent relies

305
   See Dkt. 199 (“Pet’rs’ Post-Trial Opening Br.”) at 69–70 (arguing that “[a] DCF is [n]ot
[a]ppropriate”); Pet’rs’ Post-Trial Reply Br. at 45–56.
306
  See, e.g., DFC, 172 A.3d at 388; Dell Appeal, at 21–22; Jarden, 236 A.3d at 324; AOL,
2018 WL 1037450, at *1 (“[N]o presumption in favor of transaction price obtains.”);
Panera, 2020 WL 506684, at *18–19.
307
      Regal, 2021 WL 1916364, at *19 (quoting Jarden, 2019 WL 3244085, at *2).
308
      Regal, 2021 WL 1916364, at *44.
309
      Id. at *19 (quoting Panera, 2020 WL 506684, at *40).

                                             54
on the $8.30 figure in a limited way—as context for its DCF analysis. The court gives it

equally short shift, concluding that informational inefficiencies and the controller dynamic

render the unaffected trading price no more than a point of reference. The court next turns

to Respondent’s DCF analysis. With adjustments, that analysis results in a fair value of

$14.91 per share.      The court last addresses Petitioners’ comparable companies and

comparable transactions analyses, concluding that the latter is unreliable but that the former

is reliable with some adjustment. With adjustments, that analysis results in a fair value of

$14.75 per share. Ascribing equal weight to the DCF and comparable companies analysis,

the court calculates a fair value of $14.83 per share.

                1.     Deal Price

         Respondent advances deal price as a valuation metric. Respondent does not use

deal price to set a precise fair value but argues that it supplies a cap on fair value because

the transaction was conditioned on MFW protections.310 Petitioners argue that deal price

cannot be given presumptive weight in an appraisal of a controller squeeze-out, even where

the transaction is subject to MFW.

         There is no presumption in favor of deal price.311         Nonetheless, when the

“transaction price represents an unhindered, informed, and competitive market valuation,

310
      Resp’t’s Post-Trial Opening Br. at 41–65.
311
    See, e.g., DFC, 172 A.3d at 388; Dell Appeal, at 22 (“This Court has relied on the
statutory requirement that the Court of Chancery consider ‘all relevant factors’ to reject
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 information and few,
if any, barriers to bid for the deal.” (quoting 8 Del. C. § 262(h))); Golden Telecom, Inc. v.

                                             55
the trial judge must give particular and serious consideration to transaction price as

evidence of fair value.”312 Thus, although not dispositive, deal price gets “considerable

weight” “absent deficiencies in the deal process.”313

         “The first step in using the deal price as a valuation indicator is to determine whether

the sale process that led to the deal provided a sufficiently effective means of price

discovery such that the court can regard the deal price as placing a ceiling on fair value.”314

“A deal price that results from a sufficiently effective sale process likely establishes an

upper bound for fair value because ‘it 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.’”315 Because “[t]he

appraisal statute requires that the court exclude any changes in value arising from the

accomplishment or expectation of the merger from the fair value determination,” fair value

must exclude any synergies extracted by the buyer in the sale process.316

Glob. GT LP, 11 A.3d 214, 218 (Del. 2010) (“Requiring the Court of Chancery to defer—
conclusively or presumptively—to the merger price, even in the face of a pristine,
unchallenged transactional process, would contravene the unambiguous language of the
statute and the reasoned holdings of our precedent.”); Stillwater, 2019 WL 3943851, at *21
(“There is no presumption that the deal price reflects fair value”).
312
      AOL, 2018 WL 1037450, at *1.
313
   Verition P’rs Master Fund Ltd. v. Aruba Networks, Inc., 210 A.3d 128, 137 (Del. 2019)
[hereinafter, “Aruba Appeal”].
314
      HFF, Inc., 2022 WL 304840, at *16.
315
      Id. (quoting DFC, 172 A.3d at 371).
316
      HFF, at *16.

                                                56
         “There is no checklist or set of minimum characteristics for giving weight to the

deal price.”317 Indeed, the high court has doubted its “ability to craft, on a general basis,

the precise pre-conditions that would be necessary to invoke a presumption” in favor of

deal price,318 suggesting that the high court views the analysis as an “invariably fact

specific” inquiry.319 Still, the fact patterns of recent cases are helpful because they reflect

certain “objective indicia” of reliability weighing in favor of deferring to a merger price.320

“If sufficient indicia are present, then the court ‘must determine whether they outweigh

weaknesses in the sale process, or whether those weaknesses undermine the persuasiveness

of the deal price.’”321

         The non-exhaustive list of objective criteria include: first, whether the buyer “was

an unaffiliated third party”; second, whether the “seller’s board labored under any conflicts

of interest”; third, “the existence of robust public information” about a company’s value;

fourth, “whether the bidder conducted diligence to obtain nonpublic information about the

company’s value”; fifth, “whether the parties engaged in negotiations over the price”; and

sixth, “whether the merger agreement was sufficiently open to permit bidders to emerge

during the post-signing phase.”322

317
      Panera, 2020 WL 506684, at *19.
318
      DFC, 172 A.3d at 366.
319
      Stillwater, 2019 WL 3943851, at *22.
320
      See Dell Appeal, at 28.
321
      Regal, 2021 WL 1916364, at *27 (quoting Panera, 2020 WL 506684, at *19).
322
      Regal, 2021 WL 1916364, at *28–29 (internal quotation marks omitted).

                                              57
       As Petitioners rightly observe, this non-exhaustive list of objective criteria does not

map neatly onto a controller squeeze-out. That is because the central justification for

basing fair value on deal price under Delaware law is that the process is subject to

competitive market forces.323 The Delaware Supreme Court decisions adopting deal price

as a valuation metric involved a third-party deal subject to some “unhindered, informed,

and competitive market” valuation.324 Unsurprisingly, no appraisal decision of a Delaware

court has given weight to deal price when determining fair value in the context of a

323
    See DFC, 172 A.3d at 350 (noting that the fact that a financial bidder may desire a
certain rate of return does not mean that the price it is willing to pay is not a “meaningful
indication of fair value” especially where “the financial buyer was subjected to a
competitive bidding process”); id. at 350 (remanding the court’s decision and holding that
the trial judge “may conclude that his findings regarding the competitive process leading
to the transaction, when considered in light of other relevant factors . . . suggest that the
deal price was the most reliable indication of fair value.”).
324
    AOL, 2018 WL 1037450, at *2; see also DFC, 172 A.3d at 349 (“Although there is no
presumption in favor of the deal price, under the conditions found by the Court of
Chancery, economic principles suggest that the best evidence of fair value was the deal
price, as it resulted from an open process, informed by robust public information, and easy
access to deeper, non-public information, in which many parties with an incentive to make
a profit had a chance to bid.”); Dell Appeal, at 28–30 (rejecting the trial court’s finding of
an unreliable deal process because its architects “choreographed the sale process to involve
competition[,]” the independent negotiating committee persuaded the buyer to “raise its
bid six times[,]” the company’s bankers “canvassed the interest of sixty-seven parties,” and
“this was not a buyout led by a controlling stockholder.”); Aruba Appeal at 136–40 (finding
a deal price reliable where the company had “approached other logical strategic buyers[,]”
the buyer “had signed a confidentiality agreement, done exclusive due diligence, [and]
gotten access to material nonpublic information,” and stating that “the unaffected market
price and that price as adjusted upward by a competitive bidding process leading to a sale
of the entire company was likely to be strong evidence of fair value.”).

                                             58
controller squeeze-out, which lack the competitive dynamics that render deal price

reliable.325

         Respondent seeks to break new ground, arguing that deal price should be given

deference as a valuation metric in appraisals of controller squeeze-outs that were subject

to MFW protections. There, the Delaware Supreme Court held that where a controller

squeeze-out is “conditioned ab initio” on procedural features designed to “replicate an

arm’s-length merger,”326 the transaction is reviewed under the business judgment standard

and not the entire fairness standard.327 More broadly, MFW protects controllers that “self-

disable before the start of substantive economic negotiations” and requires both sides of

the deal to “bargain under the pressures exerted on both of them by these protections.” 328

         There are sound policy reasons for allowing the procedural protections of MFW to

restore the business judgment rule in controller squeeze-outs. Then-Chancellor Strine

325
    See Kahn v. Lynch Commc’ns Sys., Inc., 638 A.2d 1110, 1116–17 (Del. 1994)
(describing the “policy rationale for the exclusive application of the entire fairness standard
to interested merger transactions” in fiduciary duty suits to be that “‘no court could be
certain whether the transaction terms fully approximate what truly independent parties
would have achieved in an arm’s length negotiation.’” (quoting Citron v. E.I. Du Pont de
Nemours & Co., 583 A.2d 490, 502 (Del. Ch. 1990)); see also In re Ezcorp Inc. Consulting
Agreement Deriv. Litig., 2016 WL 301245, at *11 (Del. Ch. Jan. 25, 2016) (“A controlling
stockholder occupies a uniquely advantageous position for extracting differential benefits
from the corporation at the expense of minority stockholders.”).
326
    Kahn v. M & F Worldwide Corp., 88 A.3d 635, 644 (Del. 2014) (“[W]here the controller
irrevocably and publicly disables itself from using its control to dictate the outcome of the
negotiations and the shareholder vote, the controlled merger then acquires the shareholder-
protective characteristics of third-party, arm’s-length mergers, which are reviewed under
the business judgment standard.”).
327
      Id. at 639–40.
328
      Flood v. Synutra Int’l, Inc., 195 A.3d 754, 763 (Del. 2018).

                                               59
articulated the policy bases for adopting the rule of MFW when announcing that rule;329

this decision could hardly improve on that discussion. It suffices to say that, when

articulating the policy reasons for adopting the rule of MFW, the court identified appraisal

as a safety valve to protect minority stockholders from any mischief that might result from

applying the business judgment rule to controller squeeze-outs.330 Were this court to rely

on MFW to determine whether to grant deal price presumptive weight in the appraisal

context, then there would be little daylight between MFW and appraisal. In that scenario,

for a deal subject to MFW protections, appraisal would not prove much of a safety valve.331

329
      In re MFW S’holder Litig., 67 A.3d 496, 528–36 (Del. Ch. 2013).
330
   See, e.g., id. at 503 (observing that it is “especially the case” that applying entire fairness
review to a transaction subject to the MFW protections “promises more cost than benefit
to investors . . . because stockholder who vote no, and do not wish to accept the merger
consideration in a going private transaction despite the other stockholders’ decision to
support the merger, will typically have the right to seek appraisal”); id. at 535 (noting that
“any minority stockholder who voted no on a going private merger where appraisal is
available, which is frequently the case, may also exercise her appraisal rights”).
331
    See also Charles R. Korsmo, Minor Myers, Appraisal Arbitrage And The Future Of
Public Company M&A, 92 Wash. U. L. Rev. 1551, 1608 (2015) (formulating a safe harbor
allowing deal price to dictate appraisal value but arguing that because the MFW standard
“would result in something far too permissive; we are not inclined to expand the safe harbor
far beyond a genuine auction for control of the company”); see also id. at 1608–09 (“In our
view, for example, the power vested in an independent board committee or a majority of
the minority shareholders to ‘say no’ to a transaction would not be sufficient. These
mechanisms set up, at best, a Hobson’s choice for existing shareholders, and it is precisely
in these scenarios where appraisal is useful.”); cf. Lawrence A. Hamermesh, Jack B.
Jacobs, Leo E. Strine, Jr., Optimizing The World’s Leading Corporate Law: A 20-Year
Retrospective And Look Ahead 26 (Fac. Scholarship at Penn Carey L., Working Paper No.
2724, 2021), https://scholarship.law.upenn.edu/faculty_scholarship/2724 (encouraging the
court to limit MFW to fiduciary duty actions challenging squeeze-out mergers because it
was “tailored specifically to the problem created by the Lynch line of cases, namely that
those cases created poor incentives in the going[-]private merger context for transactional
planners and encouraged wasteful litigation yielding no benefit for investors or society.”).

                                               60
         This conclusion is consistent with the Delaware Supreme Court’s statements in In

re Tesla Motors, Inc. Stockholder Litigation.332       There, the high court held for the

defendants in a merger that the court presumed was a controller transaction and subject to

entire fairness review. Although the high court affirmed the trial court’s finding that the

deal was entirely fair, it emphasized the “unitary” nature of the entire fairness analysis—

that findings of fair process “may seep into” findings of fair price and vice versa. 333

Relevant here, the high court quoted pre-Dell precedent stating that a “fair price

analysis . . . ‘may fall within the range of fairness for purposes of the entire fairness test

even though the point calculation demanded by the appraisal statute yields an award in

excess of the merger price.’”334 The court emphasized that the fair price aspect is “not in

itself a remedial calculation[,]” but that it “typically applies recognized valuation

standards” and is an “equivalent economic inquir[y]” to “fair value[.]”335 These statements

would not make sense were the calculation demanded by the appraisal statute the same

calculation demanded by the fair price analysis in a controller squeeze-out. For this

statement to work, the high court must not have intended to give deference to deal price in

the controller squeeze-out context.

332
      --- A.3d ----, 2023 WL 3854008 (Del. June 6, 2023).
333
   Id. at *21; see also id. at *14, 20, 34, 47–48 (emphasizing the unitary nature of the
analysis).
334
   Id. at *33 (quoting In re Orchard Enters., Inc. S’holder Litig., 88 A.3d 1, 30 (Del. Ch.
2014) (emphasis added)).
335
      Tesla, --- A.3d ----, 2023 WL 3854008, at *33 (internal quotation marks omitted).

                                              61
       Accordingly, this decision foregoes the MFW analysis urged by Respondent.

Surely, deal price is relevant. And ultimately, MFW protections might in fact operate as

intended to secure a deal price that is consistent with fair value. But the former should not

presumptively supply the latter in the context of a controller squeeze-out. The court looks

to other methods of determining fair value.

              2.        The Unaffected Stock Price

       Respondent argues that the unaffected stock price was $8.30, $6.70 below deal price

and roughly $4 below the value derived from Respondent’s primary valuation

methodology—the DCF analysis. Petitioners argue that the unaffected stock price is an

unreliable metric because several factors undermine the efficiency of the market in which

Pivotal stock traded.

       Perhaps given the disparity between the unaffected stock price and Respondent’s

DCF analysis, Respondent does not proffer the unaffected stock price as a standalone

valuation metric.336 Rather, Respondent offers it for context only. This decision follows

suit, looking to the unaffected stock price as a context clue but not an independent

determinant of fair value.

       As a context clue, the unaffected stock price is not terribly informative because

Respondent has not proven that the market for Pivotal stock was efficient at relevant times.

336
   See Resp’t’s Post-Trial Opening Br. at 62–63. Lehn calculated an adjusted unaffected
price of $7.86 on December 30, 2019, based on this figure. See JX-1446 (“Lehn Opening
Rep.”), Ex. M.

                                              62
The absence of certain material information from the market and the presence of a

controller is sufficient to foreclose reliance on the unaffected stock price.

         Delaware courts recognize that a stock’s unaffected trading price “can be a proxy

for fair value”337 where the market is efficient. Where stock trades efficiently, the price

“reflects the judgments of many stockholders about the company’s future prospects, based

on public filings, industry information, and research conducted by equity analysts.”338

         “[T]he question of efficiency is a matter of degree[,]”339 and several factors

contribute to the analysis. A market is said to be “efficient” if information concerning the

security is reflected in the security’s price.340 A market is “semi-strong efficient” if all

public information is fully reflected in the securities price and that the release of new public

information is quickly reflected in the security price.341 In a semi-strong efficient market,

“the unaffected market price is not assumed to factor in nonpublic information.”342 So,

337
    Jarden, 2019 WL 3244085, at *27; DFC, 172 A.3d at 373 (“When . . . the company had
no conflicts related to the transaction, a deep base of public shareholders, and highly active
trading, the price at which its shares trade is informative of fair value, and that value reflects
the judgment of many stockholder about the company’s future prospects, based on public
filings, industry information, and research conducted by equity analysts.”); see Dell
Appeal, at 25 (same); Regal, 2021 WL 1916364, at *24.
338
   DFC, 172 A.2d at 373; see also Regal, 2021 WL 1916364, at *24 (“Whether the trading
price should be used as a valuation indicator turns on whether the market exhibits sufficient
evidence of informational efficiency.”).
339
      Regal, 2021 WL 1916364, at *27.
340
      Lehn Opening Rep., App’x C ¶ 1.
341
      Trial Tr. at 1266:22–1267:4 (Lehn); see also Lehn Opening Rep., App’x C ¶¶ 1–3.
342
   Aruba Appeal, at 140; id. at 138 n.53 (noting different between strong and semi-strong
versions of the efficient capital markets hypothesis).

                                               63
the Delaware Supreme Court has “cautioned against reliance on a stock price that did not

account for material, nonpublic information,” which is especially salient where a trial court

finds that “certain information had not been factored into that stock price.”343

         “The question in an appraisal proceeding is whether the trading market for the

security to be valued is ‘informationally efficient enough, and fundamental-value efficient

enough, to warrant considering the trading price as a valuation indicator whether

determining fair value.’ As an initial cut at this question, the Delaware Supreme Court has

looked to an array of factors, many of which are associated with public company status.”344

         The high court has observed that “[a] market is more likely efficient, or semi-strong

efficient, if it has many stockholders; no controlling stockholder; highly active trading; and

if information about the company is widely available and easily disseminated to the

market.”345 This court has identified the following indicators of market efficiency: public

information; stock exchange listing; active trading; analyst coverage; bid-ask spread; and

market capitalization.346 The court may also consider whether a deal takes place at

“trough” pricing—where an external factor artificially “depress[es] the Company’s stock

343
      Tesla, --- A.3d ----, 2023 WL 3854008, at *46.
344
      Regal, 2021 WL 1916364, at *25.
345
      Dell Appeal, at 25 (internal quotation marks omitted).
346
      Regal, 2021 WL 1916364, at *25 (citations omitted).

                                              64
price[,]” unrecognized by the trading public, of which the acquiror takes advantage by

buying the company on the cheap.347

         Lehn testified that the market for Pivotal Class A stock was semi-strong efficient

based on a series of standard tests of market efficiency for Pivotal stock.348 Lehn observes

several factors that are compelling. For instance, Pivotal stock traded on a public market

with substantial trading volume, it had extensive analyst coverage and market makers

trading in its stock, and—based on Lehn’s event studies—its stock price has sometimes

reacted in a statistically significant manner to the announcement of earnings and other

public information.349

         Nonetheless, two significant factors undermine the reliability of the stock price on

August 14, 2019. The first is that the market price did not factor in all material information,

such as Pivotal’s Q2 Flash results as of August 14, 2019. As a result, public disclosures as

of that date did not reflect Pivotal’s operative reality.

         The June 2019 Guidedown reported low expectations on key metrics such as

deferred revenue and RPO. Thereafter, Pivotal prepared Q2 Flash results showing the

Company beating subscription guidance by 1%, RPO by 9%, and non-GAAP earnings per

share of $0.00 rather than negative $0.03 per share.350 By comparison, the Company had

347
   Dell Appeal, at 30 (internal quotation marks omitted); see also Regal, 2021 WL
1916364, at *26; DFC, 172 A.2d at 372–73 (rejecting the trial court’s analysis that a
company’s stock traded in a trough).
348
      Trial Tr. at 1266:16–1267:10 (Lehn); Lehn Opening Rep., App’x C ¶¶ 8, 10, 20–22.
349
      Lehn Opening Rep., App’x C ¶¶ 8–11, 13; id., App’x C-1.
350
      See JX-1199 at 1–2.

                                               65
missed its RPO projections in the prior quarter by somewhere between 5% and 10%, a miss

that Gaylor had described as one of several drivers of the Company’s Q1 shortcomings in

Pivotal’s June 4, 2019 earnings call.351 Because certain material “information about the

company” was not “widely available and . . . disseminated to the market,” it is hard to

conclude that the market for Pivotal Class A stock was a reliable metric on August 14,

2019, the last trading day before the merger was announced.352

          When a company’s unaffected stock price fails to incorporate material, non-public

information, the court sometimes relies upon deal price instead.353 For instance, the court

in Aruba rejected a stock price valuation in favor of a deal-price-minus-synergies

framework, reasoning that the parties to the deal had conducted diligence under

confidentiality with “a much sharper incentive to engage in price discovery than an

ordinary trader[.]”354 So, although the Aruba court critiqued the unaffected stock price as

an inaccurate reflection of fair value, it had another market mechanism to rely on—the deal

price.355 Here, however, the record presents an unusual circumstance: the market did not

price in material information that the parties to the deal had, and the deal price is unreliable

351
      JX-861 at 5.
352
    Dell Appeal, at 25 (internal quotation marks omitted). With that starting point being
tainted, it is hard to see how to back out a non-speculative value as of the closing date of
December 31, 2019, that excludes the announcement of the merger.
353
      See, e.g., Aruba Appeal, at 133–34.
354
      Id. at 140.
355
   See Tesla, --- A.3d ----, 2023 WL 3854008, at *46 (stating that “[t]he issue in Aruba
was that [the buyer] had access to nonpublic information that the market did not factor in,
thus giving [the buyer] an advantage.”).

                                              66
because of the controller dynamic. To the extent the court might attempt to rely upon

contemporaneous, market actors for price discovery, it is caught between a rock and a hard

place.

         Additionally, the presence of a controlling stockholder provides reason to be

skeptical of arguments touting market efficiency.356 Delaware case law has held that the

presence of a controller is relevant to the efficiency analysis.357            One group of

commentators has explained the several ways in which a controlled company’s stock

market cannot price in all sources of going concern value. As they reason, the “market for

corporate control is . . . absent [from controlled companies] because the controller can veto

any transaction that it disfavors.”358 So, the usual pressure that the market for control exerts

on management is absent. Also, market participants “value the firm based on the plans of

the controller[,]” so the price will fall where the market believes that “the controller will

356
   See Jarden, 2019 WL 3244085, at *27 (stating that a stock market was efficient where
a company “had no controlling shareholder[,]” a “94% public float[,]” and other factors
weighed in favor of efficiency); Regal, 2021 WL 1916364, at *26 (“The Delaware Supreme
Court has expressed support for relying on the trading price when a company is widely
traded and has ‘no controlling stockholder.’” (quoting Dell Appeal, at 25)); DFC, 172 A.3d
at 352 (stating that a company’s stock price is efficient partially because it “never had a
controlling stockholder”).
357
    Several cases simply allude to the absence of a controlling stockholder as a factor
weighing in favor of stock market efficiency, but do not elaborate on why. See Jarden,
2019 WL 3244085, at *27; Dell Appeal, at 25; DFC, 172 A.3d at 352. In Regal, the court
has expressed concern that a controller engaging in “block sales” can create “an overhang
that capped the price of [the company’s] stock.” Regal, 2021 WL 1916364, at *26. The
court thus was concerned with a controller’s potential manipulation of the stock price, but
it did not dwell extensively on the policy rationale beyond that.
358
  Lawrence A. Hamermesh & Michael L. Wachter, Rationalizing Appraisal Standards in
Compulsory Buyouts, 50 Bos. Coll. L. Rev. 1021, 1035 (2009).

                                              67
under-manage the firm or divert resources to its own use in a way that evades judicial

oversight[.]”359 A controlling stockholder’s presence can thus send signals to the markets

to discount certain aspects of the company’s business from the trading price.

            Moreover, disregarding the controlling stockholder from an efficiency analysis

would “engender uniquely detrimental incentives.”360 If an opportunistic or malfeasant

controller announces a bad squeeze-out that markets predict will harm the minority

stockholders (rightfully), traders will bid down the stock price. In that scenario, it does not

make sense to let the controller point to the minority stock price drop as a reflection of fair

appraisal value. Of course, the court would have to conduct market tests to back out an

unaffected stock price figure, which might correct the controller’s artificial depression.

Still, allowing controllers to taint the starting point of the analysis appears to muddy waters

and leave the act of correction to the vagaries that can accompany judicial discretion.

            Lehn testified that there is no academic support among financial economists for the

view that a controller’s presence makes a stock market “inherently inefficient” and unlikely

to “react to value-relevant information.”361 As far as information access is concerned, Lehn

has a point—Pivotal’s earnings calls, regular financial reporting, and the like are not

unreliable simply because VMware controlled the company. Nonetheless, as stated above,

Delaware’s market efficiency analysis is not exclusively concerned with the stock market’s

359
      Id.
360
      Id.
361
      Lehn Opening Rep. ¶ 60 n.76.

                                                68
information access. It also addresses the dynamics and incentives of corporate control.

The result is that the presence of a controlling stockholder should weigh against a finding

of efficiency.

         In any event, “efficiency is a matter of degree.”362 The market for Pivotal stock

lacked access to material information on the relevant date Respondent advances. That is

enough to undercut the reliability of the stock price. The presence of a controlling

stockholder raises additional cause for doubt. In this context, it is hard to make much of

the $8.30 trading price.

                 3.    DCF Analysis

         Respondent urges the court to adopt Lehn’s DCF-based analysis, which generates a

fair value of $12.17 per share.363 To get to that number, Lehn conducts two DCF analyses

using different discount rates. In one model, he calculates the discount rate using a “low-

end” weighted average cost of capital (“WACC”) of 7.69%. In the other, he uses a “high-

end” WACC of 8.97%, which is equal to the low-end WACC plus a “size premium” of

1.28%.364 Aside from the discount rate, all inputs into Lehn’s two DCF analyses are the

same. Lehn calculates prices per share of $13.83 and $11.87, respectively, and posits that

the midpoint of $12.85 is a fair value.365 He then adjusts the midpoint value of $12.85 to

account for “changes in the value of the market and peer company indexes” between

362
      Regal, 2021 WL 1916364, at *27.
363
      See Resp’t’s Post-Trial Opening Br. at 65–78.
364
      See Lehn Opening Rep., Exs. S-1, S-2.
365
      Lehn Opening Rep. ¶ 84; id., Exs. S-1, S-2.

                                              69
August 14, 2019, the last day before news of the merger reached the market, and December

30, 2019, the appraisal date.366

         Petitioners do not dispute Lehn’s selected discount rates or his approach of

averaging two parallel DCF analyses that use different discount rates, although the court

independently questions inputs in the second DCF model. Petitioners instead attack the

Lehn’s free cash flow projections and terminal value on the grounds that the management

projections from which Lehn derived these inputs are unreliable.367 Although Petitioners’

own expert, Beach, also conducted a DCF analysis as a cross-check to his comparable

companies analysis discussed below, Petitioners do not argue that Beach’s DCF is a

reliable reflection of fair value.

         “The DCF method is a technique that is generally accepted in the financial

community.”368 A DCF analysis required three key inputs: (i) a projection of future cash

flows over a discrete forecast period; (ii) a discount rate used to calculate present value;

and (iii) a terminal value, or the expected value of the firm beyond the forecast period.369

366
      See Lehn Opening Rep. ¶ 85; id., Ex. T.
367
    See Pet’rs’ Post-Trial Opening Br. at 69–70; Pet’rs’ Post-Trial Reply Br. at 45–56.
Petitioners also challenge Lehn for merely seeking to corroborate his opinion that the
merger price reflected fair value, showing that he performed the analysis “with bias.” See
Pet’rs’ Post-Trial Reply Br. at 46–47. The court does not find this argument persuasive,
as it merely shows that Respondent’s expert had a motive to produce a result favoring
Respondent. That much is apparent from the adversarial nature of litigation.
368
      Stillwater, 2019 WL 3943851, at *60.
369
    In re Radiology Assocs., Inc. Litig., 611 A.2d 485, 490 (Del. Ch. 1991) (“[A]n
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

                                                70
         “[T]he reliability of a DCF analysis depends on the reliability of the inputs to the

model.”370 “Although 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.”371

         The court’s first task is to assess the reliability of the financial projections that Lehn

used to derive future cash flows and terminal value. The court concludes that the financial

projections are conservative, such that they are useful for a DCF only if the model adjusts

for their conservative skew. In adopting a modified version of Lehn’s DCF model to

determine fair value, the court drops Lehn’s second DCF based on the high-end WACC,

which applies a size premium, and rejects a portion of Lehn’s methodology for calculating

the terminal value.

                       a.      Free Cash Flows

         “Delaware law clearly prefers [discounted cash flow] valuations based on

contemporaneously prepared management projections because management ordinarily has

which to discount to a present value both the projected net cash flows and the estimated
terminal or residual value.” (internal quotation marks omitted)); Ramcell, Inc. v. Alltel
Corp., 2022 WL 16549259, at *10–11 (Del. Ch. Oct. 31, 2022); Kruse v. Synapse Wireless,
Inc., 2020 WL 3969386, at *12 (Del. Ch. July 14, 2020); see also Trial Tr. at 1331:20–
1332:6 (Lehn) (explaining that he used these three factors in his DCF analysis); Lehn
Opening Rep. ¶ 66 (same).
370
   In re U.S. Cellular Operating Co., 2005 WL 43994, at *10 (Del. Ch. Jan. 6, 2005); see
also Deane v. Maginn, 2022 WL 16557974, at *23 (Del. Ch. Nov. 1, 2022) (“An
informative DCF valuation requires reliable projections.” (internal quotation marks
omitted)).
371
      Dell Appeal, at 37–38; see also AOL, 2018 WL 1037450, at *11 (quoting id.).

                                                71
the best first-hand knowledge of a company’s operations.”372 “Under Delaware appraisal

law, when management projections are made in the ordinary course of business, they are

generally deemed reliable.”373

            Delaware courts have identified numerous factors as relevant concerning the

reliability of management projections. Management projections lack “sufficient indicia of

reliability” where, for example,

            •     They were prepared “outside of the ordinary course of business.”374

            •     They were prepared “by a management team that never before had created
                  long-term projections.”375

            •     They were prepared “by a management team with a motive to alter the
                  projections, such as to protect their jobs.”376

            •     They were prepared “when the possibility of litigation, including an appraisal
                  action, was likely and probably affected the neutrality of the projections.”377

            •     They were prepared using “speculative” or “arbitrary” assumptions or
                  assumptions that suggest a “dramatic turnaround in a company despite no
                  underlying changes that would justify such an improvement of business.”378

372
      Doft & Co. v. Travelocity.com Inc., 2004 WL 1152338, at *5 (Del. Ch. May 20, 2004).
373
    Huff Fund Inv. P’ship v. CKx, Inc., 2013 WL 5878807, at *9 (Del. Ch. Nov. 1, 2013)
(alterations and internal quotation marks omitted).
374
   LongPath Cap., LLC v. Ramtron Int’l Corp., 2015 WL 4540443, at *10 (Del. Ch. June
30, 2015).
375
      Id.
376
      Id.
377
      Id.
378
      Id. at *13–14, 16 (considering each of these factors).

                                                 72
            •     They reflect “results that are hoped for” as opposed to “the expected cash
                  flows of the company.”379

            •     There was no process by which the board “reviewed and discussed” the
                  projections with management.380

            Courts also consider the distinction between “bottom-up” and “top-down” processes

for preparing projections.381 Bottom-up forecasting “start[s] with detailed information

drawn from business units, then aggregate[s] it to create a company-wide forecast.”382 By

contrast, top-down forecasting “relies on broad assumptions about the company’s

performance and industry trends.”383 “Projections prepared using a bottom-up process

generally are more reliable than projections prepared using a top-down process.”384

            As the basis for his DCF analysis, Lehn used the base case projections Morgan

Stanley presented to the Pivotal Special Committee on August 22, 2019 (the “August 22

Base Projections”).385 As Lehn explained, his typical “practice [is] to believe that the

management of the company you’re attempting to value has more knowledge about the

379
   In re PetSmart, Inc., 2017 WL 2303599, at *32 (Del. Ch. May 26, 2017) (internal
quotation marks omitted).
380
      Regal, 2021 WL 1916364, at *22.
381
      Id. at *21 (internal quotation marks omitted).
382
      Id.
383
      Id.
384
   Id. (internal quotation marks omitted); see also PetSmart, 2017 WL 2303599, at *34
n.386 (“[M]anagement’s projections were top down rather than bottom up projections,
which is contrary to best practices.”) (internal quotation marks omitted).
385
   Lehn Opening Rep. ¶¶ 67–68; compare JX-1242 at 25, with Lehn Opening Rep., Exs.
S-1, S-2.

                                               73
firm than outside valuation experts[.]”386 Also, all three companies involved in the

merger—Pivotal, VMware, and Dell Technologies—developed financial projections for

Pivotal on a standalone basis. For each year in the projection period, the August 22 Base

Projections were higher in terms of both revenue and EBITDA than either the Dell

Technologies or VMware standalone cases. The fact that Lehn would have reached a lower

valuation had he instead used the VMware or Dell Technologies standalone cases bolstered

his confidence in relying on the August 22 Base Projections.387

         The August 22 Base Projections primarily came from an earlier DCF model Pivotal

prepared sometime in July 2019 in connection with Pivotal’s tax planning (the “Tax

Model”).388 Aspects of the Tax Model’s genesis, original purpose, and construction are

mysterious, making the reliability assessment difficult. Reconstructing these facts requires

a brief detour through Pivotal’s creation of the Revised Outlook. The court attempts to

piece together the critical details below.

                            i.      Management Develops Three-Year Projections
                                    Based on Sensitivities Analyses.

         The starting period is April 2019, when Pivotal management began preparing a set

of three-year revenue projections after the Board approved the Annual Plan.389 This was

386
   Trial Tr. at 1336:11–19 (Lehn); see also Lehn Opening Rep. ¶ 68 (“I [] used the Pivotal
Base Case in my DCF analysis because it was prepared by Pivotal management
contemporaneous to the announcement of the Merger and reflected management’s view of
Pivotal’s business at the time.” (internal quotation marks omitted)).
387
      Lehn Opening Rep. ¶ 68, id., Ex. N.
388
      See JX-1010.
389
      PTO ¶ 99; JX-720; Trial Tr. at 927:6–930:16 (Gaylor).

                                             74
consistent with Pivotal’s prior practice of keeping three-year projections of certain

performance metrics on hand and updating them on a rolling basis.390 The three-year

projections created in April or May 2019 established low, base, and high case revenue

estimates for Fiscal Years 2020 through 2022.391

          To calculate each of the low, base, and high cases, Pivotal undertook sensitivities

analyses. In other words, management modeled low, base, and high scenarios for total

revenue over a three-year timeframe by analyzing the effects that various market factors

have on revenue metrics like ACV.392 These factors included subscription renewal rates

from existing customers (low case of 75%, base case of approximately 82%, and a high

case of 90%), Pivotal’s ability to generate synergies from PKS development as opposed to

cannibalization of existing offerings, and the amount of market competition Pivotal might

face over the three-year period.393

          Based on these sensitivities, management projected the following estimates of total

revenue for low, base, and high case scenarios for Fiscal Years 2020 through 2022:394

                          FY2020                  FY2021               FY2022
 Low Case                 $833                    $1,058               $1,218
 Base Case                $840                    $1,114               $1,498
 High Case                $846                    $1,154               $1,590

390
      See Trial Tr. at 921:23–922:13 (Gaylor).
391
      See JX-720 at 15–17; PTO ¶ 99.
392
   See JX-720 at 5–6; id. at 11 (stating that the company’s “[r]evenue outlook” is “driven
by ACV and renewals”).
393
      See id. at 5.
394
      The data is taken from id. at 11. All numbers in millions USD.

                                                 75
         Along with total revenue projections, management calculated other metrics, such as

year-over-year revenue growth rates, subscription revenue totals and growth rates, gross

margins, free cash flow, R&D as a percentage of revenue, and various ACV projections.395

         It is unclear from the record how management canvassed the qualitative factors in

their sensitivities analysis to produce quantitative revenue projections. Because, however,

these projections were prepared by an experienced management team operating in the

ordinary course of business, they have some indicia of reliability.

         By June 2019, Pivotal’s Q1 earnings would prove disappointing, due to

underwhelming ACV results. Accordingly, Pivotal’s Financial Planning and Analysis

(“FP&A”) team—which reported to Gaylor as CFO—lowered the company’s annual

forecast. In Gaylor’s words, the new, more pessimistic annual forecast “brought down the

outlook because without ACV, [Pivotal’s] revenue [wa]s going to grow more slowly, if it

doesn’t start to decline.”396

         Also in June, the FP&A team created the Revised Outlook, in which it lowered

Pivotal’s three-year projections for fiscal years 2020 through 2022. Pivotal management

conducted revised sensitivities analyses that accounted for lower ACV and revenue growth

395
      JX-720 at 10–17.
396
      Trial Tr. at 917:1–5 (Gaylor).

                                             76
rates.397 Management also created operating income projections for Fiscal Years 2020

through 2022.398

         Gaylor presented the Revised Outlook at a Pivotal Board meeting on June 25,

2019.399 The sole document in the record evidencing the Revised Outlook is Gaylor’s slide

deck from that meeting. Her slides do not explicitly state the total revenue projections for

Fiscal Years 2020 through 2022, but they do provide total revenue growth rates for the

same period broken out into low, base, and high case projections (along with “plan”

estimates).400 The court can discern total revenue projections from the Revised Outlook

by applying these growth rates to Pivotal’s Fiscal Year 2019 actual revenue results of $657

million.401 That exercise reveals the following:

                             FY2020                FY2021               FY2022
 Low Case                    $756                  $847                 $940
 Base Case                   $776                  $916                 $1,071
 High Case                   $789                  $955                 $1,174

         Like the April projections, neither the record nor the parties have explained the

precise link between the qualitative sensitivities analysis and the quantitative projections

397
   JX-964 at 1, 27; Trial Tr. at 750:8–17 (Armstrong) (stating that, given the “change in
the[] business,” management “believed that their current LRP . . . was no longer viable”).
398
      JX-932 at 43.
399
   The Board meeting minutes for that day are four pages long, and merely state that Gaylor
“discussed financial models, trends, and the outlook for FY20.” See JX-931 at 2.
400
      JX-932; JX-964.
401
    See JX-932 at 38, 42. The total revenue growth rates are as follows: for fiscal year
2020—15% (low), 18% (base), 20% (high); for fiscal year 2021—12% (low), 18% (base),
and 21% (high); for fiscal year 2022—11% (low), 17% (base), and 23% (high). See id. at
42.

                                            77
in the Revised Outlook. Once again, however, these projections were prepared by an

experienced management team operating in the ordinary course of business, so they have

some indicia of reliability.

                           ii.      Morgan Stanley Develops An Initial Set Of Ten-
                                    Year Free Cash Flow Projections Based On The
                                    Three-Year Forecasts.

         On July 7, 2019, Gaylor gave the slide deck from her June 25 presentation to

Morgan Stanley to help them construct various DCF models.402 Morgan Stanley took

several weeks to “understand the assumptions that are driving the model[,]”403 and used

the Revised Outlook to prepare an initial set of extrapolated projections through Fiscal

Year 2029.

         On July 25, 2019, Morgan Stanley emailed Gaylor its forecasts for review, in

advance of a call that same day.404 Because Pivotal management had provided data for

Fiscal Years 2020–22 only, Morgan Stanley conducted extrapolations for Fiscal Years

2023–29. Altogether, Morgan Stanley projected street, low, base, and high cases for

revenue, EBITDA, taxes, stock-based compensation, net working capital, and capital

expenditures through Fiscal Year 2029.405

402
      See JX-964.
403
      Trial Tr. at 752:23–753:5 (Armstrong).
404
   JX-998 (July 25, 2019 email from Armstrong to Gaylor attaching a “draft valuation
deck” and saying “[s]peak in 15 mins.”).
405
      Id. at 24–26.

                                               78
         With its own (admittedly lawyerly) math, the court can trace Morgan Stanley’s

footsteps in calculating free cash flow projections from these figures.                        In line with

established valuation practice, it seems Morgan Stanley calculated free cash flows for each

year by determining EBITDA, subtracting taxes, stock-based compensation, and capital

expenditures, and adding back changes in net working capital.406

         Although the court cannot reconstruct every aspect of Morgan Stanley’s July 25

projections, the bottom line seems to be that the most critical variables in constructing free

cash flow derived from underlying revenue growth assumptions. The result was:407

                  FY20      FY21    FY22     FY23      FY24        FY25     FY26     FY27     FY28     FY29

 Revenue          $773      $912    $1,067   $1,229    $1,392      $1,551   $1,700   $1,831   $1,938   $2,015

 EBITDA           $(23)      $10     $70     $125          $192    $271     $358     $453     $550     $645

 Taxes                 -      -       -       $(1)         $(13)   $(29)    $(48)    $(68)    $(90)    $(112)

 Stock-Based      $(85)     $(89)   $(93)    $(107)    $(121)      $(135)   $(148)   $(159)   $(169)   $(175)
 Compensation
 Change in Net        $12    $8      $3       $3            $2      $2       $1       $1        -        -
 Working
 Capital
 Capital          $(11)     $(13)   $(15)    $(16)         $(18)   $(19)    $(20)    $(20)    $(20)    $(20)
 Expenditures
 Free      Cash   $(107)    $(84)   $(35)     $3           $42      $89     $144     $205     $271     $337
 Flow

406
   See id. at 23–26; see also Charles H. Meyer, Accounting and Finance for Lawyers 373
(2d ed. 2002) (stating that one can compute unlevered free cash flows as “(i) the projected
net income after tax, plus (ii) the noncash charges deducted in computing net income (e.g.,
deferred taxes and depreciation expense), less (iii) the projected capital expenditures
necessary to produce the projected net income, less (iv) the projected increase in the net
working capital necessitated by the business (other than cash and short-term
investments).”). Cash flow is unlevered when it does not serve as a security interest for
debt.
407
      JX-998 at 25.

                                                      79
                            iii.   Morgan Stanley Uses Pivotal’s “Tax Model” To
                                   Revise Its Ten-Year Free Cash Flow Projections.

         Enter the Tax Model. After Gaylor and Armstrong spoke on July 25 to review

Morgan Stanley’s figures, Gaylor forwarded the Tax Model to Morgan Stanley. Gaylor

had the Tax Model on hand in connection with a tax-related analysis in either June or early

July.408

         The Tax Model comprised two DCF valuations based on the ten-year period of

Fiscal Years 2020–29. One DCF was for a “minimum viable product” (or “MVP”) case,

and the other was for a “high case.”409 No one who testified at trial recalled who, exactly,

prepared the Tax Model.410

         When forwarding the Tax Model, Gaylor suggests that Morgan Stanley use the

revenue figures only. She wrote in her July 25 email to Armstrong, Wilson, and others at

Morgan Stanley not to “focus on the dcf itself all that much” because there was “an error

in the original model” and that the model was “mainly focused on topline growth[.]”411 To

408
    See Trial Tr. at 965:9–13 (Gaylor) (“Q. So the long-term projections that you sent to
Morgan Stanley appear to be from that tax analysis done in late June or early July; is that
fair? A. Looks that way.”).
409
      See JX-1010 at 2–3.
410
    Stephanie Reiter, Pivotal’s Vice President of FP&A at relevant times, stated in her
deposition that Jason Hurst, a “corporate development leader” at Pivotal, was responsible
for keeping ten-year projections for purposes of tracking goodwill and other accounting
goals. See Reiter Dep. Tr. at 102:11–106:20. Although the Company thus kept some form
of ten-year forecast, it is not clear what the Company did to generate the tax model. See
also Trial Tr. at 959:12–19 (Gaylor) (expressing uncertainty over who at Pivotal prepared
the tax model, though noting that it was likely someone from Pivotal’s tax and accounting
team).
411
      JX-1010 at 1.

                                            80
aid in their forecasting, she said they “may want to look at the level of investment in the

various acv scenarios” and “tweak a bit[,]” noting that it “likely results in more fcf” because

“you wouldn’t need to invest as much in s&m[.]”412

       As for the Tax Model’s “topline,” the MVP case aligned with the base (and not the

low) case in the Revised Outlook and the high case aligned with the high case in the

Revised Outlook. For Fiscal Years 2020–22, the MVP case projected annual revenue of

$773, $908.5, and $1,062.9 million, respectively—approximately what is implied by the

Revised Outlook’s base case revenue growth rates.413 For fiscal years 2020–22, the high

case projected annual revenue of $773.2, $955.4, and $1,170.6 million, respectively—

approximately what is implied by the Revised Outlook’s high case revenue growth rates.414

       Although the Fiscal Year 2020–22 portions of the Tax Model appear to have been

lifted clean from the Revised Outlook, the revenue projections for Fiscal Years 2023–29

seem to be extrapolations based on the Revised Outlook figures for 2022 (the “MVP

Extrapolations”). Pivotal management did not prepare outyear extrapolations in the

412
   Id. “fcf” here seems to refer to “free cash flow,” and “S&M” seems to refer to “selling
and marketing.”
413
   Compare id. at 2, with JX-932 at 42 (projecting base case revenue growth rates that the
court analyzed earlier).
414
   The Revised Outlook predicted high case growth rates of 20%, 21%, and 23% for fiscal
years 2020–22. Starting with the $657.5 million actual revenue figure from fiscal year
2019, the implied total revenue figures from the Revised Outlook should be $789, $954.69,
and $1,174.27 million. It seems whoever created the Tax Model started with a base case
projection for Fiscal Year 2020 (approximately $773 million), which lowers the rest of the
high case projections slightly. Why this choice was made is unclear.

                                              81
ordinary course of business. As Gaylor testified at trial, the extrapolations for Fiscal Years

2023–29 were “not something [Pivotal management] update[s] regularly.”415

         Morgan Stanley used the MVP Extrapolations to create a slide deck for a Pivotal

Special Committee meeting on July 31, 2019.416            This slide deck presented case

comparisons for revenue, EBITDA, and EBITDA margin between Fiscal Years 2019–29

for street, low, base, and high cases.417 Morgan Stanley also included a set of DCFs, the

base case for which drew upon the MVP Extrapolations for revenue, changes in net

working capital, and capital expenditures in calculating free cash flow.418

                           iv.       The Pivotal Special Committee Approves Morgan
                                     Stanley’s Revised Projections.

         At the July 31 meeting, the Pivotal Special Committee approved Morgan Stanley’s

projections—which were based on the MVP Extrapolations—for its financial analysis and

fairness opinion.419

         With the Pivotal Special Committee’s blessings, Morgan Stanley transplanted its

forecasts into the August 22 Base Extrapolations, which consisted in identical factors and

inputs—revenue, EBITDA, taxes, stock-based compensation, change in net working

415
      Trial Tr. at 959:12–960:7 (Gaylor).
416
  JX-1041 (revised slide deck dated July 31, 2019) at 23–25; JX-1037 at 1 (email from
Morgan Stanley to Gaylor and others attaching same); Trial Tr. at 940:4–12 (Gaylor).
417
      JX-1041 at 13–14.
418
      See JX-1037 at 25; JX-1041 at 24.
419
      JX-1040 at 1.

                                             82
capital, and capital expenditures.420 The only additional factor in their final calculations

was stock-based compensation, which followed the Revised Outlook through 2022 and

decreased by approximately 2.5% year-over-year thereafter.421 Morgan Stanley’s final

estimates of base case free cash flows for each year were greater than the MVP free cash

flow estimates in the Tax Model.422

         Somewhat consistently with the Tax Model, the EBITDA margins that Morgan

Stanley presented on July 31 diminish marginally between Fiscal Years 2019 and 2029,

cumulating in a high case of 25.9%, a base case of 25.6%, a street case of 25.3%, and a

low case of 23.8%.423 Although not stated outright, it seems Morgan Stanley computed

these EBITDA margins in part by tinkering with the Tax Model, which predicted Pivotal

arriving at an approximate operating-profit-to-revenue margin of 25% for its terminal

period. From there, Morgan Stanley seems to have backed out the slightly higher free cash

flow projections than the MVP scenario of the Tax Model. Again, this is the court’s best

guess.

         Lehn adopted the free cash flows from Morgan Stanley’s August 22 Base

Projections, with two minor changes. For one, Morgan Stanley had deducted stock-based

compensation (“SBC”) from free cash flow after calculating Earnings Before Interest and

420
      Compare JX-1010 at 2, with JX-1242 at 25; see also JX-1361 at 5.
421
      See JX-1242 at 25.
422
      Compare JX-1010 at 2, with JX-1037 at 25, and JX-1041 at 24.
423
      See JX-1041 at 13; JX-1037 at 15 (same).

                                             83
Taxation (“EBIT”) and taxes.424 Lehn, by contrast, did not deduct SBC after calculating

EBIT, but factored SBC into his EBIT calculation “as is more common,” in his view.425

For another, Lehn multiplied Morgan Stanley’s free cash flow projection for fiscal year

2020 by 0.46, a “stub” factor accounting for the fact that Fiscal Year 2020 was about

halfway over by his August 2019 valuation date.426 This has the effect of increasing the

total valuation, as Pivotal’s free cash flow projection through the end of Fiscal Year 2020

were negative.427

            Petitioners do not challenge these modifications. Lehn’s modifications to the

August 22 Base Projections do not affect the court’s reliability assessment of Lehn’s

model.

                              v.       The August 22 Base Projections Are Conservative
                                       But Reliable.

            Petitioners levy several challenges at Lehn’s choice of free cash flows. Some

succeed; others do not.

            Petitioners first argue that the August 22 Base Projections are unreliable because

they rely on the Tax Model and MVP Extrapolations, which were not created in the

ordinary course of business.428 Petitioners are correct on this point. Pivotal did not

424
      Id. at 46 n.87.
425
      Id.
426
      See Lehn Opening Rep., Ex. S-1 n.13, Ex. S-2 n.13.
427
   See id., Ex. S-1 (projecting unlevered free cash flows of -$74 million for Fiscal Year
2020).
428
      Pet’rs’ Post-Trial Reply Br. at 49–52.

                                                84
regularly update the Tax Model or its forecasts through 2029.429 The fact that management

was not in the habit of forecasting that far our undermines, to a degree, the assumptions

that go into relying on management’s contemporaneously prepared projections for free

cash flows.430

         Petitioners next argue that Morgan Stanley’s free cash flow forecasts skew

conservative and are insufficiently rigorous.431 They base this argument primarily on

contemporaneous communications. Namely, on July 1, 2019, Gaylor emailed Pivotal Vice

President of FP&A, Stephanie Reiter, stating “the tax model is super conservative vs a

model of what we are more likely to do – thinking through that and timing for updating the

[long-term] model[.]”432 Reiter disagreed, responding “[t]he tax model is equal to the mid

case of the [long-term] model for the years in which we forecast – so LTM mid case for

429
   See Trial Tr. at 959:15–960:7 (Gaylor) (describing the tax IP model as “not something
we update regularly.”); id. at 939:2–9 (Gaylor) (“It looks like at this point in time we were
likely doing IP tax analysis. And so we put together some materials related to that.”); see
also JX-1010 at 1. Reiter in her deposition described a process in which Pivotal’s FP&A
team created ten-year forecasts for accounting purposes, but the record indicates that those
are separate from the tax model in question. See Reiter Dep. Tr. at 102:13–105:14.
430
   PetSmart, 2017 WL 2303599, at *33 (finding that management’s five-year projections
were not reliable for a DCF analysis where management’s regular practice was to create
annual budgets instead, because “[t]hese budgets were nothing like the five-year
projections management was directed to prepare when the Board decided to explore a sale
of the Company”); Regal, 2021 WL 1916364, at *22 (stating that management’s lack of
experience preparing the “five-year projections” used in a DCF model weighed against
their reliability because management “only prepared an annual operating budget” on a
regular basis).
431
      Pet’rs’ Post-Trial Reply Br. at 49–53.
432
      JX-958 at 1–2 (emphasis added).

                                               85
F[Y]20–FY22 is the same as the tax model.”433 In other words, Reiter characterized the

Tax Model’s MVP scenario as a base case, or mid case, analysis.

            Gaylor pushed back, replying that she “know[s] [the MVP] is consistent” with the

Revised Outlook, but that “the sensitivities we did for the board [were] not super

rigorous.”434 So, Gaylor “worr[ied] it is too conservative if we do better in [the second half

of the year] to be the new 3yr outlook[.]”435 Gaylor did not clarify what part of the

sensitivities analysis was non-rigorous. Reiter stated in response that the latest ACV

outlook from June 2019 would “only depress the mid case at this point” and that the “high

case is super bullish” which would “capture any incremental upside vs. mid case if we

surprised ourselves and outperformed.”436

            At trial, Gaylor testified that Reiter’s point “makes sense” due to the Revised

Outlook from June. She explained that “by the time we were at this point in the year, . . .

the model was coming down. That three-year sensitivity was coming down because the

business wasn’t doing as well.”437 She said that the MVP scenario was developed to be a

conservative estimate “in the beginning of the year, in like, the February, March time

frame.”438 On cross-examination, however, counsel refreshed her recollection that the

433
      See id. at 1.
434
      Id.
435
      Id. (internal quotation marks omitted).
436
      JX-1532 at 1.
437
      Trial Tr. at 960:8–23 (Gaylor).
438
      Id. at 959:20–960:7 (Gaylor).

                                                86
MVP scenario in the Tax Model was prepared in June or July—after Pivotal had issued the

Revised Outlook.439

         In other words, the tax professional at Pivotal who prepared the MVP model appears

to have prepared it as a conservative estimate even after Pivotal revised its sensitivities

analysis with the Revised Outlook. Although Gaylor’s confusion on this point appears to

have been genuine, it is hard to credit her testimony given that it arose in the context of

litigation and given the lack of additional detail in the record on the who/what/where/when

of the Tax Model.

         There are additional factors that raise questions concerning the reliability of the

MVP Extrapolations, and thus, the August 22 Base Projections and Lehn’s model. For

one, management developed them with a top-down methodology rather than a bottom-up

one.440 The imprecision of a top-down approach can threaten the reliability of the forecasts

used.441 The risks of a top-down approach are magnified where, as here, the court is left

to speculate about the process used to create the relevant forecasts.

         And although it is true, as Respondent argues, that Pivotal management, the Pivotal

Special Committee, and the Board reviewed, approved, or adopted the August 22 Base

439
      Id. at 965:9–13 (Gaylor).
440
    See Gaylor Dep. Tr. at 433:17–434:3 (“Q. Were the out years of the 10-year tax plan
just extrapolated from that year’s corporate plan of record? . . . A. I don’t—I don’t
remember exactly how the extrapolation was done, but there wasn’t a bottoms-up—you
know, based on the three-year LRP, that would have then informed some of the trajectories
in the, you know, out years. But the out years would have been more tops down than
bottoms up.”).
441
      See, e.g., PetSmart, 2017 WL 2303599, at *34 n.386.

                                             87
Projections, it is hard to conclude that the Pivotal Special Committee served as a reliable

check for errors in data. Lankton had no experience with DCF modeling.442 Klevorn was

effectively absent from the process.443 And, there is some evidence that the Pivotal Special

Committee, Pivotal management, and Morgan Stanley responded to perceived pressure

from Dell to solidify the deal.444 These facts undermine the likelihood that anyone

reviewed Morgan Stanley’s model for accuracy.

         In the end, although the record does not inspire a huge amount of confidence in the

August 22 Base Projections, they are not a death knell to Lehn’s DCF. Petitioners do not

criticize specific data points in the Tax Model or August 22 Base Projections. They argue

that the Revised Outlook (and thus the MVP scenario) was unduly pessimistic in light of

Pivotal’s Q2 Flash. And this has some intuitive appeal. Yet, although it is true that the Q2

442
      Trial Tr. at 1039:22–24 (Lankton).
443
   See, e.g., JX-1126 (August 13, 2019 email from Klevorn to Lankton stating, “I am really
sorry I have been so out of pocket these last few weeks.”); Trial Tr. at 998:15–999:11
(Klevorn) (stating that being on the Pivotal Special Committee “was a lot of work and I
don’t know, to be honest, how I felt about it at the time.”).
444
    See, e.g., JX-1072 at 2 (Lankton’s note to self from August 5, 2019 Pivotal Special
Committee meeting stating “Michael [Dell] wants this deal done!”, that the CEO of
VMware had said it “won’t do Pivotal any favors if the deal doesn’t happen[,]” and
referencing a “moral obligation”); Trial Tr. at 1106:7–15 (Mee) (stating that, as early as
January 2019, Mee believed that the deal was “likely” to happen because when “the largest
shareholder of both [companies] and the CEO of the acquiring company are very positive
about doing [the deal] that it’s probably going to happen.”); JX-609 (March 16–17, 2019
email exchange between Wilson and Armstrong in which Wilson told Armstrong that Dell
and Gelsinger were pressuring Mee to “move fast” on the deal, that the deal is “a supervised
process” where Pivotal would suffer risks if Dell “decides to go with” VMware but the
deal “[d]oesn’t happen[,]” and that it “can’t be [a] typical m[&]a playbook with third
party.”).

                                             88
Flash spoke of “solid momentum” going into the second half of fiscal year 2020, it is not

apparent that that momentum would continue indefinitely.445 So, it still seems reasonable

to use the Revised Outlook as the groundwork for a set of free cash flow projections over

a ten-year timeframe as Morgan Stanley and Lehn did.

         Additional factors weigh in favor of relying on the management-prepared data here.

Swapping out Morgan Stanley’s original July revenue forecasts for the MVP

Extrapolations had the effect of increasing—rather than decreasing—the free cash flow

projections Morgan Stanley independently considered to be genuine base case projections.

And, as Lehn noted, the August 22 Base Projections were higher in terms of both revenue

and EBITDA than either the Dell Technologies or VMware standalone cases, which

bolsters the court’s confidence in relying on the August 22 Base Projections.446

         Moreover, were the court to totally disregard management’s projections, it would

be left with a Stealers Wheel stuck-in-the-middle problem: The only alternative data set in

the record to support free cash flow estimates are Beach’s forecasts created for this

litigation. And those are entirely speculative.

         To calculate free cash flow, Beach first takes management estimates for Fiscal Year

2020 from Pivotal’s October 16, 2019 Board meeting.447 He then assumes that Pivotal

would proceed into a “rapid growth period” in Fiscal Years 2021–23, the magnitude of

445
      See JX-1056 at 1.
446
      Lehn Opening Rep. ¶ 69; id., Ex. N.
447
      JX-1445 (“Beach Opening Rep.”) ¶ 153 (citing JX-1336 at 34).

                                             89
which he estimates based solely on an industry analyst’s forecast for the PaaS market.448

The results are annual revenue growth rates of 21.1%, 19.6%, and 15.6% for 2021, 2022,

and 2023, respectively. Then, he assumes constant annual revenue growth of 15.6%

between Fiscal Years 2023 and 2025, which decreases gradually to 8% in Fiscal Year

2029.449 Beach considers these growth rates to be “reasonable and conservative” in light

of “anticipated long-term demand and adoption of the hybrid and multi cloud

technologies[.]”450

         Beach’s projections seem to reflect hindsight bias and to be anchored in overly

optimistic assumptions about Pivotal’s performance. The record does not support a finding

that Pivotal was poised to experience a short-term period of high growth.451

448
      Beach Opening Rep. ¶ 153.
449
      Id.; see also id., Ex. 14 (presenting discounted cash flow analysis).
450
      Beach Opening Rep. ¶ 153.
451
   Petitioners raise a related objection to both Lehn’s DCF and the use of a DCF method
generally on this point: That Pivotal’s high growth potential means any DCF would
undervalue it. This argument is unpersuasive, for a few reasons.
To portray Pivotal as high growth, Petitioners point to Pivotal’s Q2 Flash updated RPO
projections to argue that its prior June Guidedown was unnecessary. See Pet’rs’ Opening
Br. at 90–98. But a company does not become high growth simply because it missed its
projected earnings on one occasion and later learned it was on track later.
In reality, Pivotal’s growth was on the decline between Fiscal Years 2017 and 2019.
Pivotal was a relatively mature company by August 14, 2019. Although formed in 2013,
it was the result of an asset spin-off from assets created as early as 1989. PTO ¶ 28.
Further, the record shows that it faced significant challenges in the market when
Kubernetes rose to preeminence. See, e.g., Trial Tr. at 344:14–18, 375:8–377:3
(Raghuram). Petitioners point to figures from Gaylor’s July 19, 2019 Board presentation,
reflecting that Pivotal’s constant annual growth rate for subscription and total revenue
between Fiscal Years 2017 and 2020 were approximately 53% and 23%, respectively. JX-
991 at 9; see also Pet’rs’ Post-Trial Reply Br. at 43–44 (citing id.). But the same charts
that Petitioners cite show declining annual growth rates, consistent with a maturing

                                                90
Notwithstanding the difficulties Pivotal experienced, it is perhaps reasonable to assume

that Pivotal would follow general PaaS market trends within a year of the merger. But

beyond that, it is unduly speculative to attribute high growth to Pivotal simply because the

industry will probably grow. This assumption ignores the long-run challenge to Pivotal’s

business model that Kubernetes presented. And it ignores the development of even newer

technology in an industry famous for rapid changes.

       Under the circumstances, the court could disregard the DCF method wholesale

because the free cash flow inputs do appear relatively conservative. A superior alternative,

in the court’s view, is to use Lehn’s free cash flows as a starting point for a DCF, but to

adjust other aspects of the DCF model as necessary to account for the conservative skew.

The court proceeds through the rest of Lehn’s model with that understanding in mind.

                     b.     Discount Rate

       The next step is to determine a discount rate. As stated earlier, Lehn runs two

parallel DCF analyses—one based on a ‘low-end’ Weighted Average Cost of Capital

(“WACC”) of 7.69% and the other based on a ‘high-end’ WACC of 8.97%.

company. JX-991 at 9. The long-term trend was toward declining revenue both in total
terms and subscriptions, not explosive growth.
Essentially, Petitioners urge the court to view a mature, multi-billion-dollar company as a
high-growth tech startup—a view that the record does not support. Petitioners’ challenge
to the DCF model on this basis fails.

                                            91
          Typically, an analyst uses the WACC as a discount rate.452 Because Pivotal had no

debt at relevant times, the WACC is equal to its cost of equity.453 Lehn calculates Pivotal’s

cost of equity under the Capital Asset Pricing Model (“CAPM”), which “measures

company risk by measuring the correlation of its stock price to market changes, known as

beta.”454 Expressed formulaically, CAPM equals the risk-free rate (“commonly estimated

as the yield on a U.S. Treasury Security”) plus Pivotal’s beta multiplied by an equity market

risk premium.455 Lehn arrives at 7.69%, which serves as his low-end WACC. The court

need not dwell on this part of his analysis. CAPM is one of the two most common methods

for calculating the cost of equity,456 and Petitioners do not challenge Lehn’s calculation

here.

          To create his high-end WACC, however, Lehn adds a “size premium” to the

WACC. A size premium, sometimes called a “small cap premium[,]” is based on the

“rationale . . . that a small business faces greater overall risk than a larger, more diversified

one.”457 As two analysts explain:

452
      See Lehn Opening Rep. ¶ 69.
453
    See id.; JX-900 at 14 (Form 10-Q dated June 6, 2019 describing Pivotal’s revolving
credit facility and stating that “as of May 3, 2019, no amounts were outstanding”); JX-1305
at 14 (Form 10-Q dated September 5, 2019 stating same).
454
  Tim Koller, Marc Goedhart & David Wessels, Valuation: Measuring and Managing the
Value of Companies 272 (6th ed. 2015).
455
      See Lehn Opening Rep. ¶ 70.
456
      Koller et al., supra at 273.
457
   In re Cellular Telephone P’ship Litig., 2022 WL 698112, at *53 (Del. Ch. Mar. 9, 2022);
see also Lehn Opening Rep. ¶¶ 73–75 (applying a size premium because “some academic

                                               92
                  In the long run, higher returns are related with higher risk. . . .
                  To reflect the putative additional risk of smaller companies
                  adequately, the cost of equity derived from the CAPM is
                  ‘adjusted’ with a size premium and perhaps a unique risk
                  premium. In theory, the smaller a company’s market
                  capitalization, the higher the size premium.458

            Lehn calculates a size premium of 1.28% based on cross-reference to a well-

recognized data source on size premiums for companies of various market

capitalizations.459

            The “theory of size premium adjustment is not free from controversy”460 and “[t]he

academic world is . . . divided on this question.”461              Historically, many valuation

professionals have applied size premiums using published studies supplied by Ibbotson or

Duff & Phelps.462 But Delaware courts have a mixed track record on the issue. As Lehn

notes, some Delaware cases deploy size premiums in measuring CAPM.463 At least one

research has found that actual realized stock returns for small capitalization companies are
larger than predicted by the CAPM”).
458
   Edmund H. Mantell & Edward Shea, Development and Application of Business
Valuation Methods by the Delaware Courts, 17 Hastings Bus. L.J. 335, 357 (2021).
459
      See Lehn Opening Rep. ¶¶ 73, 73 n.100.
460
   Mantell & Shea, supra at 357; see also Dunmire v. Farmers & Merchants Bancorp of
W. Penn., Inc., 2016 WL 6651411, at *12 n.139 (Del. Ch. Nov. 10, 2016), j. entered sub
nom. In re Dunmire v. Farmers & Merchants Bancorp of W. Penn., Inc., 2016 WL 7104382
(Del. Ch. Dec. 5, 2016); Ramcell, 2022 WL 16549259, at *22 (quoting id.); Beach Opening
Rep. ¶¶ 168–169.
461
      Beach Opening Rep. ¶ 168.
462
      Id.
463
  See Lehn Opening Rep. ¶ 73 n.99 (citing Reis v. Hazelett Strip-Casting Corp., 28 A.3d
442, 475 (Del. Ch. 2011); Del. Open MRI Radiology Assocs., P.A. v. Kessler, 898 A.2d
290 (Del. Ch. 2006); In re Orchard Enters., Inc., 2012 WL 2923305, at *18 (Del. Ch. July

                                                  93
decision has expressed skepticism, however, noting that “[t]o judges, the company specific

risk premium often seems like the device experts employ to bring their final results into

line with their clients’ objections, when other valuation inputs fail to do the trick.”464

       In a convincing piece published in 2015, Professor Aswath Damodaran called into

question the empirical data that was used as the basis for applying a size premium. He

describes its continuing use as a matter of “inertia,” and recommends that valuation experts

adopt an “innovative better practice.”465 Namely, he recommends that, to the extent a

18, 2012); Gearreald v. Just Care, Inc., 2012 WL 1569818, at *10 (Del. Ch. Apr. 30,
2012)).
464
    Kessler, 898 A.2d at 339, 339 n.129 (adopting a size premium in calculating a discount
rate because in the court’s then-current experience, “most testimonial experts and
investment bankers using CAPM tend to accept the size factor as relevant” even though
the size premium question is a subject of “great debate”); see also In re AT&T Mobility
Operations Hldgs. Appraisal Litig., 2013 WL 3865099, at *3 (Del. Ch. June 24, 2013)
(declining to adopt a size premium because the small company being valued “operated as
part of a larger entity”); ONTI, Inc. v. Integra Bank, 751 A.2d 904, 920 n.71, 921–22 (Del.
Ch. 1999) (adopting a size premium, but observing that there is academic dispute on the
subject and adjusting the expert-proposed estimates to account for potential “data
snooping” used to measure it); Cellular Telephone, 2022 WL 698112, at *54 (applying a
size premium, but noting that question “in this case presents a close question”); but see
Orchard, 2012 WL 2923305, at *21–22 (adopting a size premium in a CAPM calculation
for a company whose market capitalization fell between $1–76 million); Just Care, Inc.,
2012 WL 1569818, at *10 (adding an equity size premium to a CAPM model to “account
for the higher rate of return demanded by investors to compensate for the greater risk
associated with small company equity.”); Merion Cap., L.P. v. 3M Cogent, Inc., 2013 WL
3793896, at *19–20 (Del. Ch. July 8, 2013) (applying a size premium based on research
that found a “statistical relationship between market capitalization and equity size
premium”); see also In re Emerging Commc’ns, Inc. S’holders Litig., 2004 WL 1305745,
at *20 (Del. Ch. May 3, 2004) (describing size premiums, or small-company premiums, as
addressing “the incremental risk, not fully captured by beta, that typically accompanies a
small sized firm.”).
465
  Aswath Damodaran, The Small Cap Premium: Where is the beef?, Musings on Markets
(Apr. 11, 2015), https://aswathdamodaran.blogspot.com/2015/04/the-small-cap-premium-

                                              94
company is exposed to greater risks due to size, a valuation expert could account for that

with lower reinvestment and expected growth outlooks.466

         Damodaran’s observations, coupled with this court’s previously expressed

concerns, counsel in favor of a cautious approach to size premia. Applying a size premium

might be appropriate in certain scenarios, but the proponent of a size premium bears the

burden of proving the factual bases for applying one.467 In this case, Respondent did not

make such a showing, and the use of conservative free cash flow estimates appears to

address any idiosyncratic growth-related risks not captured by beta.

          Accordingly, rather than following Lehn’s bifurcated approach of running parallel

DCFs, the court conducts a single DCF analysis using Lehn’s low-end WACC of 7.69%

as a discount rate.

                       c.    Terminal Value

         The final component of a DCF is terminal value—“the value beyond the discrete

forecast period.”468 Put differently, “[t]he terminal value is the present value of all the

company’s future cash flows beginning after the projection period.”469

factfiction-and.html) [hereinafter “Small Cap Premium”]; see also Beach Opening Rep. ¶
168 n.249 (citing same).
466
      See Small Cap Premium.
467
    See HFF, 2022 WL 304840, at *15 (“In an appraisal proceeding, ‘both sides have the
burden of proving their respective valuation positions[.]’” quoting Jarden, 236 A.3d at 322
(alterations and internal quotation marks omitted)); see also Stillwater, 2019 WL 3943851,
at *18 (discussing the allocation of burden of proof).
468
      Lehn Opening Rep. ¶ 77.
469
      Ramcell, 2022 WL 16549259, at *24.

                                             95
         The experts dispute whether Pivotal will grow in the terminal period. The non-

technical summary is that Beach believes Pivotal will experience high growth, whereas

Lehn believes it will experience none. Beach’s position is overly optimistic. Lehn’s

position is overly pessimistic. The court endorses a middle ground.

         Beach advocates for a non-convergence approach to the Gordon Growth Model,

which requires calculating free cash flows in the terminal period at a positive perpetuity

growth rate (“PGR”).470 “A perpetual growth model assumes cash flows to grow at a

constant rate in perpetuity.”471 This court has stated the elements of the Gordon Growth

Model as

                                     TV = FCFt+1/WACC – g

where “TV = Terminal value, FCFt+1 = Free cash flow in the first year after the explicit

forecast period, WACC = Weighted average cost of capital, and g = Expected growth rate

of free cash flow into perpetuity.”472

         One issue with using a perpetual growth model is determining an appropriate PGR

(or ‘g’ in the above-quoted formula). “Conventional valuation wisdom holds that the

perpetuity growth rate generally should fall somewhere between the rate of inflation and

470
    See Beach Opening Rep. ¶ 175; JX-1448 (Beach Rebuttal Rep.) ¶¶ 89, 89 n.122; see
also Cede & Co. v. JRC Acq. Corp., 2004 WL 286963, at *4 (Del. Ch. Feb. 10, 2004)
(describing the perpetuity growth model); Glob. GT LP v. Golden Telecom, 993 A.2d 497,
511 (Del. Ch. 2010) (“[A] terminal value is calculated to predict the company’s cash flow
into perpetuity.”).
471
      Ramcell, 2022 WL 16549259, at *24.
472
      3M Cogent, 2013 WL 3793896, at *21.

                                             96
the projected growth rate of the nominal gross domestic product (‘GDP’).”473 According

to Beach, U.S. government estimates for the U.S. economy foresee 3.9% long-run nominal

GDP growth and long-run inflation of 2%.474 Presumably relying on similar data, Morgan

Stanley ran DCFs based on PGRs of 2.5%, 3%, and 3.5% for each of the street, low, base,

and high case models it prepared (resulting in 12 total share price estimates).475

         Nonetheless, Beach recommends a PGR of 5%—above the upper bound of U.S.

growth forecasts. Beach justifies this choice by assuming that Pivotal’s software sales will

drive growth at a higher rate than the rest of the U.S. economy.476 He assumes that software

development and engineering are “some of the economy’s fastest growing areas” and that

“data management is in high demand” because other sectors of the economy will be reliant

on software for “processing huge amounts of data and the application of predictive

473
    In re Cellular Telephone P’rship Litig., 2022 WL 698112, at *40 (Del. Ch. Mar. 9,
2022); see also Golden Telecom, 993 A.2d at 511 (“A viable company should grow at least
at the rate of inflation and . . . the rate of inflation is the floor for a terminal value estimate
for a solidly profitable company that does not have an identifiable risk of insolvency.”).
474
   Beach Opening Rep. ¶¶ 176–177 (citing Federal Open Market Committee, Minutes of
the Federal Open Market Committee (Sept. 17–18, 2019), available at
https://www.federalreserve.gov/monetarypolicy/fomcminutes20190918.htm           (accessed
Feb. 9, 2022)). Beach calculates long-term nominal GDP by combining the Federal
Reserve’s long-run target inflation rate of 2% and the reported long-run real GDP growth
of 1.9%. See Beach Opening Rep. ¶ 176 n.256. The court sees no reason to challenge
Beach’s estimate.
475
      See JX-1242 at 23–26.
476
      Beach Opening Rep. ¶ 177; see also Trial Tr. at 210:21–211:11 (Beach).

                                                97
analytics in forming new applications, strategies, and services.”477 So, Beach reasons that

the typical use of nominal GDP growth as a cap is inapplicable here.478

            In the other corner, Lehn expects zero growth. Lehn testified that “there comes a

point where you’re confined to returns equal to your cost of capital” in order to capture

“economic reality[,]” “even for really well-managed companies[.]”479 In Lehn’s view, “a

sound DCF has to . . . reflect that reality” as a matter of course.480 With this key

assumption, Lehn calculates terminal value in two steps.481 First, he calculates Pivotal’s

terminal year net operating profit after tax, subject to certain adjustments (“NOPAT”).482

Second, he divides NOPAT by the discount rate.483 In his low-end WACC model, the

477
      Beach Opening Rep. ¶ 177.
478
    Beach also adjusts his growth forecasts by assuming a “plowback ratio” of 2.9%, which
is the nominal growth rate of 5% minus an approximate inflation rate of 2.1%. See Beach
Opening Rep. ¶ 184. This ratio accounts for the rate at which additional net investment is
necessary to sustain growth during the terminal period. Lehn also uses a plowback concept
by adjusting his terminal value calculation for changes in R&D expenses. See Lehn
Opening Rep. ¶ 79. The court declines to adopt a plowback ratio. Trying to ascertain a
plowback ratio a decade from the valuation date appears speculative at best, at least under
these facts, given the highly changing nature of the industry in which Pivotal operates.
479
      Trial Tr. at 1346:6–1347:5 (Lehn).
480
   See id. at 1346:22–1347:5 (Lehn); see also id. at 1332:10–19 (Lehn) (stating that he
“assumed that beyond the forecast period, Pivotal would generate returns on new
investment that was equal to its cost of capital, which means that growth beyond the
forecast period would be value neutral.”).
481
      Lehn Opening Rep. ¶ 78.
482
      Id.
483
      Id.

                                               98
result is approximately $4.87 billion.484 Because this figure is reached in Fiscal Year 2029

dollars, Lehn discounts it by its WACC and arrives at a present value of approximately

$2.51 billion.

         Neither expert’s view is entirely persuasive. The difficulty with Beach’s industry-

centric approach is banal: it is simply hard to know where the software industry, or the

PaaS market specifically, will be at the end of the decade. Although in some contexts, the

court has adopted PGRs that track industry growth rates rather than GDP,485 here, Beach’s

assumptions seem to import a high dose of speculation into an already speculative inquiry.

Indeed, Beach himself admits that the speculative element is unavoidable, as it informs his

misgivings about the DCF method generally.486

         On the other hand, Lehn’s zero-growth assumption is misplaced under these facts.

Lehn provides no basis in the record to suppose that Pivotal will have reached a steady

state at the outset of the terminal period instead of doing so at some point during the

terminal period. Although Lehn believes his zero-growth approach reflects economic

reality generally, he departs from Morgan Stanley’s contemporaneous view that Pivotal’s

PGR would fall somewhere between 2.5% and 3.5%.487 Lehn might be right to suppose

484
   Id., Exs. S-1, S-2. Lehn also makes adjustments to his NOPAT estimate by accounting
for net R&D expenses and changes in net working capital. See Lehn Opening Rep., Ex. R.
485
   See, e.g., Ramcell, 2022 WL 16549259, at *25 (rejecting an expert’s use of a “generic
growth rate” for perpetuity growth rates based in part on the expert’s failure to “look at
industry growth rates.”).
486
      Beach Opening Rep. ¶¶ 75, 150.
487
   See JX-1242 at 23–26 (providing low, base, street, and high case valuations of Pivotal
based on PGRS of 2.5%, 3%, and 3.5% as of August 22, 2019).

                                             99
that there is “a limit to the number of things” management “can do that create value for

investors” after a certain period.488       Nonetheless, Pivotal’s investment bank and

management seem to have endorsed a different view. This contemporaneous assessment

weighs greater here, as Morgan Stanley and Pivotal management are more familiar with

Pivotal’s long-term prospects than Lehn is.

         Also, the revenue projection Lehn uses to kickstart his NOPAT calculations start

with $2.315 billion in revenue for Fiscal Year 2029—taken directly from the August 22

Base Projections and thus the MVP Extrapolations.489 By relying on this figure as the sole

source of value in the terminal period, Lehn already imports the conservative skew of the

MVP Extrapolations into the terminal value. By contrast, calculating terminal value with

an above-zero growth rate can potentially correct for a conservative skew in the Fiscal Year

2029 free cash flow projection. Accordingly, rather than using Lehn’s adjusted NOPAT /

WACC formulation of terminal value, the court uses the Gordon Growth Model and

perpetual growth.

         The next task is determining an appropriate PGR. The court adopts the low end of

Morgan Stanley’s PGR from their August 22 valuation—2.5%. This figure falls between

the forecasted low end of inflation (2%) and nominal GDP growth (3.9%) that Beach

supplied, avoiding the industry-specific risks of Beach’s formulation.        And using a

488
      See Trial Tr. at 1346:22–1347:5 (Lehn).
489
   Compare Lehn Opening Rep., Exs. R, S-1, S-2, with JX-1010 at 2 (Lehn’s free cash
flow projections reflecting the same Fiscal Year 2029 projected revenue as the MVP
Extrapolations).

                                              100
relatively lower end seems to reflect accurately Pivotal’s status as a maturing company that

would be unlikely to sustain high growth during the terminal period. At the same time,

however, using a figure above zero avoids the overly pessimistic view of Lehn’s model.

The middle road between Beach’s 5% and Lehn’s 0% PGR is the most reliable figure.

                       d.    Lehn’s Market Adjustment

         Finally, the court addresses Lehn’s market adjustment to the DCF analyses. Lehn

first uses his dual-DCF method to calculate Pivotal’s stock price on August 14, 2019, which

he argues is $12.85. Then, he accounts for “market and industry factors” between August

14 and December 30, 2019, generating a final price of $12.17.490

         The court declines to adopt a similar market adjustment. The market indices upon

which Lehn relied reflected market growth between August and December 2019—in other

words, the market did better in December than it had in August.491 But Lehn’s analysis has

Pivotal’s stock price declining. Although Lehn stated that his model is “well-accepted”

and “objective[,]” he did not explain how increasing market indicators lead to a decreased

price.492 Respondent has thus not met its burden of showing the market adjustment to be

reliable. The court therefore disregards this part of Lehn’s analysis.

         That said, the court still needs a mechanism to bridge the gap between the August

14 valuation date that it implicitly adopted and the closing date of December 30, because

fair value must be determined as of the date of closing. One solution is to adjust the weight

490
      See Trial Tr. at 1360:16–1361:14 (Lehn).
491
      Id. at 1448:19–1449:11 (Lehn).
492
      Id. at 1450:22–1451:11 (Lehn).

                                            101
of the “stub” factor Lehn applies to the free cash flow projections for Fiscal Year 2020. As

stated earlier, Lehn multiplies Morgan Stanley’s free cash flow forecast for Fiscal Year

2020 by 46% because there were only five and a half months remaining that Fiscal Year.

By the same logic, one can multiply the Fiscal Year 2020 free cash flow by 8.33% because

only one month remained in Fiscal Year 2020 as of December 30, 2019 (it ended on

January 31, 2020).493 By adjusting the stub factor accordingly, the court thus more readily

approximates a valuation as of December 30, 2019.

         This solution is not ideal. Indeed, were there a rival set of reliable projections

treating the valuation date as ground zero, the court would use that instead. But in the

absence of superior data, this approach does the trick.

                      e.     DCF Valuation Summarized

         Summarizing the inputs, the sum of the free cash flows for Fiscal Years 2020

through 2029 discounted at 7.69% is $868.13 million.

         Next is calculating the terminal value. The free cash flow forecast initiating the

terminal period is $339.57 million. The WACC is 7.69%. The PGR is 2.5%. By the

court’s calculations, this results in a fair value of $6,706.34 million in dollars at the end of

Fiscal Year 2029. After a steep discount,494 the result is a present value of $3,196.92. This

493
      See JX-1365 at 9 (Form 10-Q dated December 6, 2019).
494
   Following suit with Lehn, the court applies the same discount factor in the terminal
period that the court uses for free cash flow in Fiscal Year 2029. See Lehn Opening Rep.,
Ex. S-1. This approach makes sense because the terminal value is measured in Fiscal Year
2029 dollars. Rather than using the midpoint convention for the terminal value portion,
however, the court uses a year-end convention because the valuation occurs at the end of

                                             102
creates a tentative enterprise value of approximately $4,065.05 million. Following Lehn,

to compute total equity value, the court also adds back current assets—$809 million in cash

and $51.3 million in net operating losses, while subtracting out a minority interest of $0.7

million.495 The sum is $4,924.65 million. Divided by 330.4 million shares, the price per

share is $14.91.

          It is worth noting that the court’s valuation does not change significantly even when

leaving Lehn’s stub factor in place for Fiscal Year 2020 as he originally had it. Running

the same computations, the price per share shifts downward to $14.82 per share. The figure

moves down, rather than up, because Pivotal’s free cash flows in Fiscal Year 2020 were

negative. The small magnitude of difference here gives the court additional comfort that

its stub factor adjustment is not troublesome.

                        f.     Petitioners’ High Terminal Value Argument

          Petitioners bring a separate objection to bear on Lehn’s DCF. They argue that Lehn

wrongly derives 73% of the total enterprise value from the terminal value, which reflects

cash flows over ten years into the future.496 The terminal values of Lehn’s DCF models

are approximately 75% and 72% of the cash flow for each of his low- and high-end WACC

models, respectively.497 Here, the court’s terminal value constitutes 65% of its overall DCF

Fiscal Year 2029, right before the terminal period starts. This has the effect of a higher
discount, which further allays the court’s concerns about over-correction.
495
      See id.
496
      Pet’rs’ Post-Trial Reply Br. at 47.
497
   For the low-end WACC model, the court gets to this figure by dividing Lehn’s present
value of the terminal value, $2,509, by the free cash flow value of $3,351.

                                               103
valuation. That figure rises to approximately 79% when excluding current assets like cash

and net operating losses (and thus valuing Pivotal exclusively as a function of its future

cash flows).

         This court has, at times, refused to rely on DCF models that are “so heavily

dependent on the determination of [the company’s] terminal value” that the “entire

exercise” becomes speculative.498 Similarly, the court has considered a terminal value

“representing over 70% of [the company’s] estimated total present value” to be a “red

flag.”499

         Respondent counters that, on other occasions, the court has adopted DCF models

deriving the vast majority of their value from the terminal value.500 Respondent points to

the following cases:

         •      Kruse v. Synapse Wireless, Inc., where the court adopted a DCF model
                bearing a terminal value of 100% of the enterprise value in a five-year
                model;501

498
    Gray v. Cytokine Pharmascis., Inc., 2002 WL 853549, at *9 (Del. Ch. Apr. 25, 2002).
It is worth noting that Gray contains some distinguishing features. In Gray, the court
disregarded an expert’s DCF with a terminal value between 75% and 85% of the total
valuation because it “amount[ed] to little more than a special case” of an expert’s parallel
comparable companies analysis. See id. The court there also disregarded the expert report
at issue because it disregarded more accurate projections drafted by management. See id.
at *8. By contrast, here, Lehn uses his DCF analysis to urge against a comparables analysis
and in favor of management-drafted projections. Nonetheless, the point from Gray remains
that a DCF model’s reliance on terminal value can be grounds to render it a speculative
analysis.
499
      Gholl v. Emachines, Inc., 2004 WL 2847865, at *13 (Del. Ch. Nov. 24, 2004).
500
      Dkt. 204 (“Resp’t’s Post-Trial Reply Br.”) at 9–10.
501
      2020 WL 3969386, at *18–19.

                                             104
         •      In re Jarden Corporation, where the court adopted a DCF model bearing a
                terminal value of 77% of the of the enterprise value in a five-year model;502

         •      Crescent/Mach I Partnership, L.P. v. Turner, where the court adopted a DCF
                model bearing a terminal value of approximately 75% of the enterprise value
                in a five-year model;503

         •      In re PNB Holding Co. Shareholders Litig., where the court conducted a DCF
                calculation bearing a terminal value of approximately 75% of the enterprise
                value in a five-year model.504

         To Petitioners’ credit, Respondent’s cases are distinguishable insofar as they

involve DCF analyses conducted over five- rather than ten-year timeframes. Common

sense indicates that a terminal value after ten years is inherently more speculative than after

five years.505 But Respondent is correct to dispel the notion that a high terminal value is a

barrier to the use of a DCF, both here and in general. It is also not damning that Lehn’s or

the court’s model derive a substantial portion of Pivotal’s overall worth from cash flows

over five years in the future—that much seems to be an occupational hazard of the ten-year

DCF method endorsed by both experts, Morgan Stanley, and Pivotal management.

         Put simply, courts should continue to scrutinize DCFs with high terminal values,

although the inquiry is not dispositive. Here, the high percentage is not a cause for concern.

Because the free cash flow projections likely understate present value, it stands to reason

502
   2019 WL 4464636, at *4 (Del. Ch. Sept. 16, 2019) (reargument decision presenting
DCF with terminal value of $12,928 million and total enterprise value of $1,613 million).
The court adopted this DCF as a cross-check on an unaffected stock market valuation. See
Jarden, 2019 WL 3244085, at *3.
503
      2007 WL 1342263, at *10–11, 14–15 (Del. Ch. May 2, 2007).
504
      2006 WL 2403999, at *31 (Del. Ch. Aug. 18, 2006).
505
      Cf. Aswath Damodaran, The Dark Side of Valuation 331 (3d Ed. 2018).

                                             105
that an accurate valuation would compensate through adjustments in the terminal period.

And the court has addressed the aspects of Lehn’s terminal value that appear speculative.

In sum, Petitioners’ instincts are not misplaced, but they are accounted for under the

circumstances.

                4.     Comparable Companies Analysis

         Petitioners request that the court adopt Beach’s analysis of fair value based on

revenue multiples for comparable publicly traded companies. Respondent argues that

Beach’s analysis is unreliable in several ways, stating that Beach fails to compare Pivotal

to genuinely comparable companies.

         A comparable companies analysis is a “standard valuation technique whereby

financial ratios of public companies similar to the one being valued are applied to a subject

company.”506 The approach looks to relative valuation and assumes that the same or

equivalent assets have equal or equivalent value.507

         This court has “discretion to view [a] comparable companies analysis as providing

relevant insights into [a company’s] value based on inferences from how the market valued

companies in the same industry, facing most of the same risks.”508 “This methodology is

appropriate only where the guideline companies selected are truly comparable. . . . The

506
      In re BGC P’rs, Inc. Deriv. Litig., 2022 WL 3581641, at *32 (Del. Ch. Aug. 19, 2022).
507
      Beach Opening Rep. ¶ 120.
508
      DFC, 172 A.2d at 387.

                                             106
selected companies need not be a perfect match but, to be reliable, the methodology must

employ ‘a good sample of actual comparables.’”509

          A comparable companies analysis has upsides and downsides. The upsides are that

“revenue multiples are available even for the most troubled firms and for very young

firms[,]” revenue multiples are “difficult to manipulate[,]” and they are “not as volatile as

earnings multiples, and hence are less likely to be affected by year-to-year swings in a

firm’s fortunes.”510     Their primary downside is that they can “lull” an analyst into

“assigning high values to firms that are . . . losing significant amounts of money[.]”511 And

the analyst must assure herself that the comparable companies she uses to derive a revenue

multiple are meaningfully similar to the company being valued.512

          Beach’s comparable companies analysis involves five steps. These are: (a) selecting

the appropriate type of revenue multiplier and deriving that data for the target company;

(b) identifying a set of genuinely comparable companies; (c) calculating total enterprise

value; (d) adding back current assets like cash and stock option proceeds to convert the

total enterprise value figure into total equity value; and (e) addressing the propriety of

adding a control premium to adjust for a minority discount. Each component is discussed

in turn.

509
      Maginn, 2022 WL 16557974, at *24 (quoting Orchard, 2012 WL 2923305, at *10).
510
   Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the
Value of Any Asset, 543 (3d ed. 2012).
511
      Id. at 542.
512
      See Borruso v. Commc’ns Telesys. Intern., 753 A.2d 451, 455–56 (Del. Ch. 1999).

                                              107
                          a.     Revenue Multiplier

            There are two standard types of revenue multipliers: price-to-sales ratio and value-

to-sales ratio.513 A price-to-sales ratio divides the market value of a company’s equity by

revenue.514 A value-to-sales ratio divides a company’s total enterprise value by revenue,

where total enterprise value (or “TEV”) is the sum of the company’s market capitalization

and its net debt (the market value of its debt minus cash and other current assets).515 Using

a price-to-sales ratio “across firms in a sector with different degrees of leverage” can lead

to “misleading conclusion” because its focus on the market price of equity does not account

for variations in debt between companies.516 By contrast, a value-to-sales ratio is “more

robust” than the price-to-sales ratio because “it is internally consistent.”517

            Beach uses a value-to-sales ratio.518 He relies on Last Twelve Month (“LTM”) and

Next Twelve Month (“NTM”) revenues to create a pair of multipliers—one backward-

looking, and the other forward-looking.519 He uses NTM revenue because forward-looking

estimates “provide good insight into a company’s future cash flows[;]” nonetheless, he

513
      Damodaran, supra at 543.
514
      Id.
515
   Id.; see also Beach Opening Rep. ¶ 122; see also Enterprise Value, Corporate Finance
Institute, available at https://corporatefinanceinstitute.com/resources/valuation/what-is-
enterprise-value-ev/ (May 3, 2023) (defining enterprise value).
516
      Damodaran, supra at 543.
517
      Id.
518
      Beach Opening Rep. ¶ 122.
519
      Id. ¶¶ 122, 127–128.

                                                108
cautions that they “are subject to greater uncertainty than historically reported metrics.”520

So, Beach also considers LTM revenue to remove “the effects of any discrepancies in

revenue estimates between market analysts, management, and the broader market.”521

            Although Respondent objects to many aspects of Beach’s model, Respondent does

not challenge Beach’s use of a value-to-sales ratio, and rightly so.522 Pivotal lacks debt,

but that does not mean its peers do too. Focusing on the relationship between total

enterprise value and sales prevents an upward skew in the revenue multiples that could

otherwise result were the court to compare Pivotal to highly levered peers. It was also

appropriate for Beach to use of both LTM and NTM revenue estimates. Heading off the

inherent risk in using a DCF based on ten years of performance, Beach’s revenue multiplier

relies in total on two years’ worth of information. Half of that data derives from real-world

practice. The other half is based on projections over a single year.

            To calculate Pivotal’s revenue multiplier, Beach takes Pivotal’s reported LTM

revenue as of December 30, 2019, as $746.2 million.523 But he also uses an alternative

measure of LTM revenue to cross-check that figure by taking one third of the revenue

Pivotal earned in Q4 2019, adding the midpoint of management’s latest full-year forecast

for Fiscal Year 2020, and subtracting one third of the implied revenue for Q4 of Fiscal

520
      Id. ¶ 122.
521
      Id.
522
    See generally Resp’t’s Post-Trial Opening Br. at 79–84; Resp’t’s Post-Trial Reply Br.
at 19–39.
523
      Beach Opening Rep. ¶ 146.

                                             109
Year 2020 from that forecast.524 At trial, he stated that he did so to get “as close to the

trailing 12 months as of the date of the valuation as I could” to account for growth.525

Respondent does not challenge this choice and it was reasonable.

         To derive his NTM revenue estimate, Beach does not rely on Pivotal’s projections.

He instead draws data from Capital IQ, an information services company that provides

market data.526 Capital IQ calculates the mean estimate of Pivotal’s revenue growth from

a range of analysts, which in this case projects $867.6 million.527 Respondent does not

challenge Beach’s choice to rely on market data and it too was reasonable. The court was

able to rely indirectly on Pivotal’s revenue forecasts in the DCF model by adjusting the

model to account for a potentially bearish forecast, but the comparable companies

framework does not allow for similar adjustments. By using four estimates, rather than

two, Beach appropriately provides a cross-check on each.

                       b.      Comparable Companies

         As stated earlier, “[t]he selected companies need not be a perfect match but, to be

reliable, the methodology must employ ‘a good sample of actual comparables.’”528 So, for

instance, the court must be confident that its analysis does not generate a “wide range of

values” that “implicitly violates the law of one price[,] which holds that similar assets

524
      Id. ¶¶ 131, 131 n.207.
525
      Trial Tr. at 183:11–184:5 (Beach).
526
      See Beach Opening Rep. ¶ 122 n.193.
527
      See id. ¶¶ 122, 122 n.193, 129.
528
      Maginn, 2022 WL 16557974, at *24 (quoting Orchard, 2012 WL 2923305, at *10).

                                             110
should sell for a similar price.”529 “The burden of establishing that the companies used in

the analysis are sufficiently comparable rests upon the party advancing the comparables

method.”530

         To create his sample set, Beach first collects the companies that Morgan Stanley,

Lazard, and Moelis each provided for their own comparable companies analysis between

Pivotal’s IPO in 2018 through the merger date in 2019. 531 Beach then makes several

revisions to the sample set.

         Beach first excludes and adds several companies from the set based on the nature of

their business. Beach excludes IT service companies that Morgan Stanley had included as

part of its analysis,532 because in his view, Pivotal was more a software company than a

services company.533 He also excludes companies such as Dropbox, Pegasystems, and

Box, which “do not primary serve enterprise customers” and are “too narrowly focused”

on particular “end-user functions[,]” or are otherwise “not engaged in creating cloud or

529
    Gholl, 2004 WL 2847865, at *6; see also JRC Acq., 2004 WL 286963, at *3 n. 28
(finding that a “wide divergence in transaction multiples is troubling because it violates the
law of one price, which holds that in a well-informed and efficient market, similar assets
should sell for similar prices, adjusting for scale.” (citing Bradford Cornell, Corporation
Valuation: Tools For Effective Appraisal And Decision Making 56–57 (1993))).
530
      Maginn, 2022 WL 16557974, at *24.
531
      Beach Opening Rep. ¶ 124; see also id., Ex. 4.
532
      See Beach Opening Rep. ¶ 125; see also id., Ex. 5.
533
      Beach Opening Rep. ¶ 125; Trial Tr. at 105:24–107:19 (Beach).

                                             111
multi-cloud platforms or providing application development.”534 He further adds other

companies that he thought were comparable to Pivotal.535

            Beach next culls his set to firms with NTM revenue growth estimates between 10%

and 25% to exclude certain companies that either dramatically over- or under-performed

relative to Pivotal.536 The median revenue estimate of 16.7%, which is close to Pivotal’s

expected 16.3% NTM revenue growth that market analysts calculated,537 requires that he

exclude Citrix Systems, FireEye, Atlassian, MongoDB, and Twilio from the overall

sample.538

            Beach produces a final set of eight companies (Cloudera, Talend, Appian, Nutanix,

New Relix, Domo, Splunk, and VMWare). Beach computes a median NTM revenue

multiple of 4.9x and a median LTM revenue multiple of 5.8x.539

            Respondent attacks Beach’s set of comparable companies on three grounds. First,

Respondent argues that Beach wrongly excluded services companies from his list of

comparables, arguing that this decision wrongly displaces real-world evidence that market

534
      Beach Opening Rep. ¶ 126.
535
      Id.; see also Trial Tr. at 111:13–112:10 (Beach).
536
   Beach Opening Rep. ¶ 128. Beach came up with 10% as a lower bound because it is
“approximately 5% less than analysts’ NTM growth estimates for Pivotal of 16%” and
came up with 25% as “approximately 5% more than Gartner’s projected PaaS market
growth for calendar year 2020 of 21%.” See id.
537
      Id.
538
      See id., Ex. 7 (summarizing growth rates of each relative to Pivotal’s).
539
      Beach Opening Rep. ¶ 128.

                                               112
participants considered Pivotal’s services business relevant to its overall valuation.540

Second, Respondent observes that several companies in Beach’s set have much greater or

smaller market capitalization relative to Pivotal, thus suggesting they are not genuinely

peer companies.541 Last, Respondent points to the wide disparity of multiples Beach

discovered, ranging from lows of 3.6x (LTM) and 3.1x (NTM) to highs of 10.7x (LTM)

and 8.6x (NTM). Respondent argues that this undermines the law of one price.542

          Respondent’s first critique warrants adjustment to Beach’s set of comparables,

because Respondent is correct to criticize the categorical exclusion of services companies

from the comparables set. It is true that Pivotal’s software business was its primary

offering, and that Pivotal focused more on software such that services declined over time

as a percentage of overall revenue.543 Still, the services business was not nominal.

According to Pivotal’s 10-Q for Q2 of Fiscal Year 2020, as of August 2, 2019, services

accounted for approximately 30% of revenue.544 An accurate sample set would give some

deference to this significant, albeit declining, portion of Pivotal’s revenue to adjust

Pivotal’s change in focus.

540
      Id. ¶ 44.
  Resp’t’s Post-Trial Opening Br. at 80–81 (addressing Splunk Inc., VMware, and
541

Domo).
542
      Id. at 81–82.
543
      See JX-964 at 13; see also Pet’rs’ Post-Trial Opening Br. at 78 (citing same).
544
    See JX-1305 at 4 (reflecting quarterly subscription revenue of $134,990,000 and
services revenue of $58,006,000 for a total of $192,996,000). Although this is quarterly
rather than annual data, it shows a reliable, contemporaneous breakdown of Pivotal’s
business before it signed the merger agreement on August 14, 2019.

                                              113
         To balance these considerations, the court brings the services companies identified

as comparables by Morgan Stanley into the comparables set. Unlike Morgan Stanley,

however, the court uses a weighted revenue multiplier. A portion accounts for Pivotal’s

software business, and a portion accounts for services. The court weighs Pivotal’s software

and services segments 75% and 25%, respectively—three quarters of the multiplier value

derives from a survey of comparable software companies, while one quarter derives from

the comparable services companies from Morgan Stanley’s valuation.               This choice

accounts for Pivotal’s segment breakdown in August 2019—before it consummated the

merger—and for the fact that software was growing as a percentage of overall revenue.

Although an imperfect tool, this weighting is the fairest possible account for Pivotal’s

growth path.

         Respondent’s second critique has some appeal but does not warrant an adjustment.

Respondent argues that wide disparity in market capitalization is a barrier to comparability.

Respondent observes that the market capitalization of several companies is either far bigger

than Pivotal’s or far smaller: Splunk had a market capitalization of $22 billion, VMware

had a market capitalization of $67 billion, and Domo had a market capitalization of

approximately $600 million.545 Pivotal’s was $1.6 billion.546

         There is no bright-line rule addressing the role relative market capitalization plays

in creating a list of comparable companies. This court has considered size differences

545
      Trial Tr. at 251:7–18, 266:3–6, 267:2–9 (Beach).
546
      Id. at 251:3–6 (Beach).

                                              114
between companies to be a meaningful but not dispositive consideration when selecting

comparables.547 In Jarden, for example, the court stated that “[t]he notion that a company

with a very large market capitalization is not a true peer of a company with a relatively

smaller market capitalization has a certain lay appeal[,]” but ultimately decided it was not

a “determinant of market multiples[.]”548 In this case, it is appropriate to include Domo,

VMware, and Splunk in the sample because these companies are all established players in

the cloud infrastructure software space, much like Pivotal. Their inclusion therefore seems

wise not only because they are at comparable levels of maturity with Pivotal, but because

including these large players more holistically accounts for market-wide growth trends.549

         Respondent’s third critique, that the wide dispersion of revenue multipliers runs

afoul of the law of one price, likewise does not move the needle. This is a valid objection

to Beach’s initial set of companies, but the court’s weighted multiples approach appears to

mitigate the concern. Although there is still some dispersion in revenue multipliers among

547
    See, e.g., Reis, 28 A.3d at 477 (rejecting a comparable companies approach where the
sample companies were “much bigger” than the valuation target, “enjoy better access to
capital,” “have deeper management teams[,]” and “have achieved consistent growth”
compared to the valuation target’s “erratic” earnings over the same period); Gray, 2002
WL 853549, at *9 (rejecting a comparable companies approach where the expert referred
to companies that were “much larger than [the company at issue] both in terms of revenue
and market capitalization.”).
548
      Jarden, 2019 WL 3244085, at *34 (internal quotation marks omitted).
549
    Beach emphasized at trial, and the court agrees, that the comparables approach is
strongest when it creates a holistic scan of the market in which the company participates.
See Trial Tr. at 341:10–19 (Beach) (“Q. Why didn’t you just pick Appian as a comp and
use their multiples and be done with it? What would that have done to your valuation, by
the way? A. . . . [I]t’s the entire set that represents what I think is a good representation
of the market and the drivers around the market that Pivotal is in.”).

                                            115
the software companies after the weighted multiple are applies, the overall set falls within

a tighter range.550 Further, the court adopts Beach’s approach of using the median revenue

multiplier from the data set, rather than relying on a mean. 551 These steps account for

outliers and draw the total sample into the realm of reliability.

         The refined comparable companies set, based on Beach’s set for the software

companies and Morgan Stanley’s for the services companies,552 is therefore as follows:

                                          TEV / NTM                 TEV / LTM Revenue
 Company                 Segment          Revenue Multiple          Multiple
 Cloudera                Software                            3.6                    4.1
 Talend                  Software                            4.3                    5.1
 Appian                  Software                              8                    9.3
 Nutanix                 Software                            3.8                    4.5
 New Relic               Software                            5.6                    6.5
 Domo                    Software                            3.1                    3.6
 Splunk                  Software                            8.6                   10.7
 VMware                  Software                            6.1                    6.9
 Accenture               Services                            2.8                      3
 Cognizant
 Technology              Services                            1.9                       1.9
 Atos SE                 Services                            0.9                       0.8
 Infosys                 Services                            3.1                       3.3
 Wipro                   Services                            1.9                         2
 Genpact                 Services                            2.4                       2.7

         Based on the above chart, the court derives the following revenue multiple medians:

550
  See Maginn, 2022 WL 16557974, at *25–26 (using a comparable companies analysis
where revenue multipliers ranged from a low of 0.39x to a high of 11.28x).
551
      Trial Tr. at 112:11–23 (Beach).
552
      See Beach Opening Rep., Exs. 5–6.

                                             116
                                         Unweighted      Weighted TEV
          Unweighted TEV Weighted TEV / TEV / LTM        / LTM
 Segment / NTM Revenue     NTM Revenue   Revenue         Revenue
 Software             4.95        3.7125             5.8            4.35
 Services             2.15        0.5375            2.35         0.5875

         The combined, weighted revenue multiples are 4.25 and 4.94 (both rounded

slightly) for NTM and LTM revenue, respectively.

                      c.     Total Enterprise Value

         Putting it all together, the court applies the TEV / NTM revenue multiplier to

Beach’s NTM analyst consensus revenue estimate of $867.6 million. It derives a total

enterprise value of $3,687,300,000. Applying the same to his alternative NTM revenue

projection of $930 million results in a total enterprise value of $3,952,500,000. The court

applies the TEV / LTM revenue multiplier to Beach’s LTM analyst consensus revenue

estimate of $746,200,000. The total enterprise value is $3,684,362,500. Applying the

same to his alternative LTM revenue accounting of $765,000,000 results in a total

enterprise value of $3,777,187,500.

                      d.     Converting Total Enterprise Value To Price Per Share

         Beach’s comparable companies analysis, modifications and all, generates an

estimate of Pivotal’s total enterprise value.      As stated earlier, total enterprise value

measures a company’s equity plus debt minus current assets like cash and cash

equivalents.553 But Section 262 does not demand an estimate of total enterprise value; the

court’s mandate is to determine the fair value of Petitioners’ pro rata equity stake in Pivotal

553
      See Damodaran, supra at 543.

                                             117
as a going concern. In other words, one needs to add back current assets to the total

enterprise value to determine the company’s total equity value (of which Petitioners are

entitled to their pro rata share). Accordingly, Beach added net cash of $821.9 million and

proceeds from exercising options of $275.6 million to each of his projections.554 Because

Pivotal had no debt, these maneuvers back out total equity value. The court does the same.

          Beach’s next step is to take the midpoint of the two NTM equity value figures and

the two LTM equity value figures he generates—which following his numbers, result in

stock price values of $16.80 and $16.65, respectively.555 Instead, the court takes the

average of its four weighted total equity value figures, yielding $4,872,837,500. The court

then divides this figure by 330.4 million, the number of fully diluted shares outstanding.

The result is $14.75 per share.

                       e.    The Minority Discount

         Petitioners ask the court to adopt Beach’s approach of layering an additional

premium on top of the comparable companies valuation because “minority shares in a

corporation trade at a discount for lack of control.”556 In other words, Beach’s comparable

companies approach calculates a minority interest, not a control block, because the revenue

multiplier is based in part on stock market prices of comparable companies (which,

according to some Delaware precedent, reflect purely ‘minority’ interests). To adjust for

554
      Beach Opening Rep. ¶ 129; see also Trial Tr. at 190:8–23 (Beach).
555
      Beach Opening Rep. ¶¶ 132–133.
556
      Pet’rs’ Post-Trial Opening Br. at 87–89; see also Beach Opening Rep. ¶¶ 136–138.

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this, Beach calculates a control premium by reference to change-of-control transactions in

the software industry.557

         Respondent argues that accounting for a minority discount inflates the valuation by

awarding deal synergies.558 Lehn challenges Beach’s use of a control premium, stating that

there is no “academic consensus that there is always a minority discount.”559 At trial, he

further testified that the existence of a minority discount “depends on the facts and

circumstances of the company,” that “there are cases where minority shareholders are net

beneficiaries of a controlling shareholder,” and that Beach’s approach is “simply

inappropriate.”560

         In essence, the parties dispute the concept of an implied minority discount as a

component of going concern value for any company. Regrettably, Delaware law on the

topic is opaque. But attempting to make sense of such a mess is the plight of the trial judge.

Hence, the following college try.

         The concept of the implicit minority discount appears to trace back to Cavalier Oil.

There, a minority stockholder sought appraisal after a cash-out merger of a closely held

corporation. The respondent argued that the stockholder’s pro rata share should have been

reduced by a “minority discount”—a discount for the fact that the petitioner owned only a

“de minimis” interest, which the respondent reasoned was worth less than its proportionate

557
      Beach Opening Rep. ¶ 137; id., Ex. 9.
558
      Resp’t’s Post-Trial Opening Br. at 82–84; Resp’t’s Post-Trial Reply Br. at 30–33.
559
      Trial Tr. at 1367:16–1368:2 (Lehn).
560
      Id. at 1367:16–1368:11 (Lehn).

                                              119
equity stake in the company.561 The Supreme Court rejected this argument, stating that

“[t]he application of a discount to a minority shareholder is contrary to the requirement that

the company be viewed as a going concern.”562             The court thus reasoned that a

stockholder’s status as a minority interest holder should not weigh against it in the fair

value analysis.

         The Cavalier Oil court refused to discount the value of a minority stockholder’s

shares based on a respondent’s control-related theory. But later courts invoked Cavalier

Oil to justify adding control premia to valuations based on trading value for stock. The

adapted theory is that stock markets trade only for minority interests, so the stock price is

implicitly “discounted” relative to the value a controller would derive from owning the

company.563

         This notion of an implicit minority discount has also arisen when using a

comparable companies valuation.564 The minority discount appears because the court’s

multiplier typically uses publicly traded stock information as a benchmark—for instance,

stock-price-to-revenue, stock-price-to-EBITDA, or stock-price-to-earnings ratios. Based

loosely on Cavalier Oil, the theory goes that each company’s stock price in the

comparables dataset only refers to the price of a minority stake in that company, rather than

561
      Cavalier Oil, 564 A.2d at 1144.
562
      Id. at 1145 (internal quotation marks omitted).
563
      See Jarden, 2019 WL 3244085, at *31 (explaining the theory).
564
   See, e.g., Hodas v. Spectrum Tech., Inc., 1992 WL 364682 (Del. Ch. Dec. 8, 1992);
Kleinwort Benson Ltd. v. Silgan Corp., 1995 WL 376911, at *3 (Del. Ch. June 15, 1995);
Rapid-Am. Corp. v. Harris, 603 A.2d 796, 806 (Del. 1992); Borruso, 753 A.2d at 457–59.

                                              120
the price of a control block. So, when one uses a stock-price-to-revenue metric, one is

really considering the ratio of a minority interest to revenue.565 Therefore, after deploying

the multiplier, one must add a control premium to right the ship to find inherent value.

       Several aspects of this implicit minority discount concept appear questionable. In

the first instance, it is not apparent that implicit minority discounts, if they exist, are in fact

ever-present across companies. It seems preferable to leave the issue of whether a

particular stock market trades only in “minority” interests to a case-by-case assessment of

the record and each company’s stock market, rather than attaching what is effectively a

rebuttable presumption that a company’s stock price requires adjustment.

       Also, the idea that all stock trades at a discount seems to clash with the semi-strong

efficient market hypothesis, which otherwise posits that a fully informed, efficient market

will accurately reflect value. On these and related bases, commentators have critiqued the

concept for years, also accusing the courts of misinterpreting Cavalier Oil and of lacking

a basis in finance theory.566

565
   Doft, 2004 WL 1152338, at *10 (“Delaware law recognizes that there is an inherent
minority trading discount in a comparable company analysis because ‘the [valuation]
method depends on comparisons to market multiples derived from trading information for
minority blocks of the comparable companies.’” quoting Agranoff v. Miller, 791 A.2d 880,
892 (Del. Ch. 2001)); see also Borruso, 753 A.2d at 457–58 (stating that “the comparable
company method produces a minority valuation of the shares subject to appraisal” and
adjusting the court’s comparables analysis to “eliminate the implicit minority discount”).
566
   See, e.g., 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,
16–24 (2007) (tracing the origin and development of the concept and critiquing its
conceptual basis); William J. Carney & Mark Heimendinger, Appraising The Nonexistent:
The Delaware Courts’ Struggle With Control Premiums, 152 U. Pa. L. Rev. 845, 879

                                               121
            Two recent cases cast doubt on the wisdom of applying an implicit minority

discount. In Jarden, the trial court gave “substantial weight” to a company’s unaffected

stock market price, which traded in an efficient market.567 Although the petitioner asked

for a control premium to balance out the minority discount, the court declined to do so.

The court reasoned that the company’s management was “well known to stockholders and

well known to the market. But for the Merger, they were not going anywhere as the

Company was not for sale.”568 The court viewed any “agency costs” arising from being a

minority stockholder as “embedded in” the company’s operative reality already.569

            Although the Jarden court did not announce a categorical rule, its analysis reflects

a high degree of skepticism for the implicit minority discount theory. The court looked at

the minority discount as a price for the inherent agency costs that result by virtue of every

corporation’s separation of ownership and control. But the Jarden trial court also reasoned

that a fully informed market could value such agency costs without the need for judicial

add-ons. Jarden’s approach thus reflects a faithful adherence to the efficient markets

hypothesis, and in its wake, it is hard to imagine why the court should add a minority

discount to the stock price of a non-controlled company.

(2003) (“Modern financial theory . . . do[es] not support the current use of control
premiums in appraisal proceedings.”).
567
      See Jarden, 2019 WL 3244085, at *31.
568
      Id.
569
      Id.

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            The Delaware Supreme Court’s decision in Aruba also advances an indirect

conceptual challenge to the control premiums used to buffer out implicit minority

discounts. There, the trial court found both the deal price and a separate thirty-day trading

price metric to be reliable. The trial court opted for the trading price metric over a deal-

price-minus-synergies figure.570 Among other things, the trial court was chary of its

synergies estimate, in part because the acquired company’s representatives “bargained less

effectively than they might have” but the court had “no way to gauge the marginal impact

of their ineffectiveness[.]”571 The trial court prepared a rough estimate of synergies, but

was concerned that the estimate failed to include agency cost reductions resulting from the

merger.572 Reasoning that a separate deduction of agency costs would open a can of worms

relating to measurement issues, the trial court opted for what it deemed a more

“straightforward and reliable” metric—the unaffected trading price.573

            The high court reversed on appeal, holding instead that a deal-price-minus-synergies

framework was appropriate because the deal process was reliable. In relevant part, the high

570
   Verition P’rs Master Fund Ltd. v. Aruba Networks, Inc., 2018 WL 922139, at *53–55
(Del. Ch. Feb. 15, 2018).
571
      Id. at *45.
572
   Id. at *54 (stating that a “difficulty” with the court’s “deal-price-less-synergies figure”
was that it “continues to incorporate an element of value resulting from the merger. When
an acquirer purchases a widely traded firm, the premium that an acquirer is willing to pay
for the entire firm anticipates incremental value both from synergies and from the reduced
agency costs that result from unitary (or controlling) ownership. Like synergies, the value
created by reduced agency costs results from the transaction and is not part of the going
concern value of the firm.” (citations omitted)).
573
      Id.

                                                123
court admonished the trial court for distinguishing agency cost reductions resulting from

combined control from synergies. The high court stated that:

                Synergies do not just involve the benefits when, for example,
                two symbiotic product lines can be sold together. They also
                classically involve cost reductions that arise because, for
                example, a strategic buyer believes it can produce the same or
                greater profits with fewer employees—in English terms,
                rendering some of the existing employees redundant. Private
                equity firms often expect to improve performance and squeeze
                costs too, including by reducing agency costs. Here, the Court
                of Chancery’s belief that it had to deduct for agency costs
                ignores the reality that [the buyer’s] synergies case likely
                already priced any agency cost reductions it may have
                expected.574

         In other words, the high court synonymized agency cost reductions with the benefits

of control. And control, in turn, was a type of synergy—already baked into the trial court’s

analysis without requiring a separate discount for agency costs. In that context, the high

court said that the trial court should have simply deducted synergies from deal price and

ignored the agency cost deduction, which would “double count[]” part of the synergies.575

         This aspect of the Aruba decision did not address implicit minority discounts. Nor

did it address comparable companies analyses. Nonetheless, it treated control premia as a

type of merger synergy. Control premia do resemble synergies—an acquiror may reduce

costs, issue dividends, and replace management with people who will carry out its agenda.

Such are the benefits of buying an entire company. If control premia are a category of

574
      Aruba Appeal, at 134 (citations and internal quotation marks omitted).
575
   Id. at 139; see also id. at 134 (stating that “there was no reasonable basis to infer that
[the acquired company] was cheating itself out of extra agency cost reductions by using
only the cost reductions that were anticipated in commercial reality.”).

                                             124
synergies, however, then adding a control premium in an appraisal proceeding unwittingly

incorporates synergies into the court’s valuation.          Quantifying a control premium

necessarily contemplates third-party sale value, rather than going concern value. And the

court may not consider third-party sale value under the appraisal statute.576

       Taken together, Jarden and Aruba implicitly (i) reject the notion that markets

generally discount value for lack of control; and (ii) state that control premia are synergies,

so even if there is an inherent discount, the control differential should not get priced into

going concern value. Jarden rejects the implicit minority discount’s omnipresence as a

distortion of stock market realities. And Aruba implicitly rejects it as a backdoor inclusion

of synergies. Both cases avoided far-sweeping statements to this effect. But adopting a

control premium simply because a comparables analysis uses stock market indices appears

inconsistent with the letter and spirit of each decision.

       To be sure, a minority discount may still be a useful tool in some circumstances.

Where the court uses a controlled company’s stock price as a basis for its valuation, for

instance, controller overhang might get priced into the minority share value and require an

upward adjustment. This is not surprising, because controllers can create inefficiencies in

market prices that threaten their reliability (as discussed earlier). But that version of a

576
   8 Del. C. § 262(h) (“[T]he Court shall determine the fair value of the shares exclusive
of any element of value arising from the accomplishment or expectation of the merger.”);
see also Union Ill. 1995 Inv. Ltd. P’ship v. Union Fin. Grp., Ltd., 847 A.2d 340, 343 (Del.
Ch. 2004) (interpreting Section 262(h) to “exclude[] synergies in accordance with the
mandate of Delaware jurisprudence that the subject company in an appraisal proceeding
be valued as a going concern.”).

                                             125
minority discount—about which Lehn testified—is not the implicit minority discount that

courts have believed accompanies every company’s stock price.

         The above analysis is enough to reject Beach’s inclusion of a control premium here.

But even were the court to keep the implicit minority discount practice alive, there are

measurement-related issues with Beach’s estimate. Control premia vary widely, and there

is no hard-and-fast rule for selecting a high or low premium.577 Beach turns to a set of ten

precedent transactions of companies that he believes are comparable to Pivotal. For each

transaction, he compares the deal price per share with the stock price one day, one week,

and one month before the deal to determine a set of premia. He ascertains median premia

of 17.81% (one day before deal), 20.67% (one week before the deal), and 25.29% (one

month before the deal), and chooses 18% as a “conservative” estimate.578 Beach justifies

this addition by observing that strategic transactions for public companies force acquirors

to “pay a premium over the public stock price to entice investors to accept its offer and to

reflect the value of full control.”579

         Even accepting that the transactions Beach considered involve genuinely

comparable companies to Pivotal, Beach’s control premium ignores other synergies that

577
   See, e.g., Harris v. Rapid-Am. Corp., 1992 WL 69614, at *3–4 (Del. Ch. Apr. 6, 1992)
(adding a 44% control premium to account for a minority discount adjustment); Hodas v.
Spectrum Tech., Inc., 1992 WL 364682, at *2 (Del. Ch. Dec. 8, 1992) (adopting a 30%
minority discount adjustment); Doft & Co. v. Travelocity.com Inc., 2004 WL 5366732, at
*10 (Del. Ch. May 20, 2004) (using a “30% adjustment”); Silgan, 1995 WL 376911, at *4
(adopting a 12.5% minority discount adjustment).
578
      Trial Tr. at 188:4–21 (Beach); see also Beach Opening Rep. ¶ 136; id., Ex. 9.
579
      Beach Opening Rep. ¶ 136.

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are likely included within the deal premia he sampled.580 Beach testified that from his

review, there “wasn’t a lot of synergies” based on the analysts’ reports and proxy

statements he surveyed for these deals.581

         The difficulty with Beach’s testimony is that it is effectively a gut-check. The

median gap between stock price and deal price could be explained by a great many things,

all of which require scrutinizing the circumstances surrounding each transaction. Beach

may have a good sense for where synergies arise. But the litigation context of his testimony

undermines his credibility on this point. Absent additional evidence in the record that the

ten deals he sampled in fact ignored synergies, the court cannot rely on this part of Beach’s

analysis.

         Furthermore, Beach errs by applying the control premium at the end of his

comparable companies analysis, after accounting for non-stock assets.582 Beach’s revenue

multiple is based on comparable companies’ total enterprise value rather than stock value

alone. This metric factors in the value of each comparable company’s debt in addition to

equity. By waiting until the end to multiply his total enterprise value figure by 18%, Beach

artificially magnifies the effect of the minority discount.

         The court declines to adopt Beach’s control premium.

580
   See Andalaro v. PFPC Worldwide, Inc., 2005 WL 2045640, at *18 (Del. Ch. Aug. 19,
2005) (stating that, in using comparable precedent transactions to determine a control
premium, the court must exclude “any portion of the average premia from [the expert’s]
sample to account for the sharing of synergies by the buyer with the seller.”).
581
      Trial Tr. at 191:22–192:7 (Beach).
582
      See Beach Opening Rep. ¶¶ 134–136.

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                5.      Comparable Transactions Analysis

         Petitioners also urge the court to rely upon Beach’s analysis of comparable

transactions for fair value. Beach’s comparable transactions analysis relies on data from

ten other transactions in the software space, landing at price estimates between $23.15 and

$21.94 per share based on NTM-derived equity values and LTM-derived equity values,

respectively.583 Petitioners favor this analysis for largely the same reasons they urge the

court to adopt Beach’s comparable companies analysis.584 Respondent likewise opposes

this analysis for the same reasons it objected to his comparable companies analysis.585

         “A comparable transactions analysis is an accepted valuation tool in Delaware

appraisal cases. The analysis involves identifying similar transactions, quantifying those

transactions through financial metrics, and then applying the metrics to the company at

issue to ascertain a value.”586 “As with the comparable companies analysis, the utility of

the comparable transactions methodology is directly linked to the similarity between the

company the court is valuing and the companies used for comparison.”587

         Beach surveys 14 transactions, but only includes ten in his sample.588           The

companies in his sample are (i) Callidus Software, a cloud-based sales, marketing, learning,

583
      Id. ¶¶ 148–149.
584
      Pet’rs’ Post-Trial Opening Br. at 70–71.
585
      Resp’t’s Post-Trial Opening Br. at 84–85.
586
      Highlands Cap., Ltd. v. AXA Fin., Inc., 939 A.2d 34, 54 (Del. Ch. 2017).
587
      3M Cogent, 2013 WL 3793896, at *7 (alterations and internal quotation marks omitted).
588
      Beach Opening Rep., Ex. 12.

                                             128
and customer experience company; (ii) Ultimate Software Group, a cloud-based human

capital management solutions company; (iii) Broadsoft, a software and services company

that assists telecommunications services provides deliver cloud-based “uniform

communications” to enterprise customers; (iv) Athenahealth, a network-based medical

record, revenue cycle, patient engagement, care coordination, and population health

services company that works with hospital and ambulatory clients; (v) Barracuda

Networks, a cybersecurity and data protection company; (vi) Apptio, a cloud-based

platform with a suite of SaaS applications for a broad spectrum of industries; (vii) ICE

Mortgage Technology, a cloud-based platform provider for the mortgage finance industry;

(viii) Red Hat, an open-source software solutions company that works with a range of

customers; (ix) Imperva, a cybersecurity and data protection company; and (x) Carbon

Black, a cloud-native endpoint protection company offering technology that uses SaaS

toward cybersecurity ends.589

            Only about half of the above-listed companies are comparable to Pivotal. Critically,

many of them focus on either a particular customer niche or technology. Broadsoft targets

telecommunications, Athenahealth focuses on healthcare, Barracuda and Imperva focus on

cybersecurity, Ultimate Software Group targets human resources, and ICE Mortgage

Technology provides a platform for the mortgage finance industry.

589
      Id.

                                                129
         Pivotal, by contrast, was a generalist company; it targeted enterprises as customers,

regardless of their industry.590 For obvious reasons, the composition of a company’s

customers influences its revenue forecasts, growth potential, and susceptibility to industry-

specific shocks. Industry- or segment-specific companies do not appear sufficiently

comparable to Pivotal.

         After culling the dissimilar firms, the court is left with a sample of four companies:

Callidus, Apptio, Red Hat, and Carbon Black. This list fails for reliability for two reasons.

The first is that it is too short—a sample of four transactions is unlikely to represent

industry standards effectively, even assuming comparability. The second is generating a

revenue multiple from these four companies over-weighs Pivotal’s software business

relative to its services business, as discussed previously. Petitioners have therefore failed

to meet their burden that Beach’s comparable transactions analysis is reliable.

III.     CONCLUSION

         The court’s DCF produces a value of $14.91. The court’s comparable companies

analysis produces a value of $14.75. To derive fair value, the court weighs each valuation

evenly. The result is a per-share fair value of Pivotal Class A stock of $14.83 as of

December 30, 2019.

         A final word on interest. As discussed previously, Respondent prepaid a portion of

the appraisal value to Petitioners in accordance with Section 262(h). Because the court has

awarded an amount greater than Respondent’s prepayment, Petitioners are entitled to

590
      See, e.g., PTO ¶ 28.

                                              130
interest on the “difference . . . between the amount so paid and the fair value of the shares

as determined by the Court[.]”591

         In the Pre-Trial Order, Respondent requests a determination that “good cause exists

to award no interest on any appraisal award, or alternatively, to award interest at a rate less

than the default rate specified in 8 Del. C. § 262(h) or otherwise on different terms than the

default terms specified in 8 Del. C. § 262(h).”592 Respondent does not seem to advance

any good cause argument in its pre-trial or post-trial briefing, nor did it raise the issue at

post-trial oral argument. The argument is therefore waived. Pre-judgment interest is set at

the statutory rate as applicable.

         Respondent shall prepare a form of order implementing this decision within ten

days, providing Petitioners at least five days to review the form.

591
      8 Del. C. § 262(h).
592
      PTO ¶ 153.

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