
    DFC GLOBAL CORPORATION, Respondent Below, Appellant/Cross-Appellee, v. MUIRFIELD VALUE PARTNERS, L.P., Oasis Investments II Master Fund Ltd., Candlewood Special Situations Master Fund, Ltd., CWD OC 522 Master Fund Ltd., and Randolph Watkins Slifka, Petitioners Below, Appellees/Cross-Appellants.
    No. 518, 2016
    Supreme Court of Delaware.
    Submitted: June 7, 2017
    Decided: August 1, 2017
    
      . Raymond J. DiCamillo, Esquire, Matthew D. Perri, Esquire, RICHARDS, LAYTON & FINGER, P.A., Wilmington, Delaware; Meryl L. Young, Esquire, Colin B. Davis, Esquire, GIBSON, DUNN & CRUTCHER LLP, Irvine, California; Joshua S. Lipshutz, Esquire, (argued), GIBSON, DUNN & CRUTCHER LLP, Washington, D.C., Attorneys for Respondent Below, Appellant/Cross-Appellee, DFC Global Corporation.
    Stuart M. Grant, Esquire, (argued), Kimberly A. Evans, Esquire, Vivek Upadhya, Esquire, GRANT & EISEN-HOFER P.A., Wilmington, Delaware, Attorneys for Petitioners Below, Appel-lees/Cross-Appellants, Muirfiéld Value Partners, L.P., Oasis Investments II Master Fund Ltd., Candlewood Special Situations Master Fund, Ltd., CWD OC 522 Master Fund LTD., and Randolph Watkins Slifka.
    Theodore A. Kittila, Esquire, GREEN-HILL LAW GROUP; LLC, Wilmington, Delaware; Daniel M. Sullivan, Esquire, Sarah M. Sternlieb, Esquire, HOLWELL SHUSTER & GOLDBERG, LLP, New York, New York, Attorneys for Amici Curiae Law and Corporate Finance Professors arguing in favor of the presumption the Respondent favors.
    Samuel T. Hirzel, II, Esquire, HEY-MAN ENERIO GATTUSO & HIRZEL LLP, Wilmington, Delaware; Lawrence M. Rolnick, Esquire, Steven M. Hecht, Esquire, LOWENSTEIN SANDLER LLP, New York, New York; Mark Lebo-vitch, Esquire, Jeroen Van Kwawegen, Esquire, BERNSTEIN LITOWITZ BERGER & GROSSMANN LLP, New York, New York, Attorneys for Amici Curiae Law, Economics and Corporate Finance Professors arguing against the presumption the Respondent favors.
    Before STRINE, Chief Justice; VALIHURA, VAUGHN, and SEITZ, Justices; LEGROW, Judge, constituting the Court en Banc.
    
      
       Sitting by designation under Del. Const. art. IV, § 12.
    
   STRINE, Chief Justice:

In this appraisal proceeding involving a publicly traded payday lending firm purchased by a private equity firm, the respondent argues that we should establish, by judicial gloss, a presumption that in certain cases involving arm’s-length mergers, the price of the transaction giving rise to appraisal rights is the best estimate of fair value. We decline to engage in that act of creation, which in our view has no basis in the statutory text, which gives the Court of Chancery in the first instance the discretion to “determine the fair value of the shares” by taking into account “all relevant factors.” As this Court previously held in Golden Telecom, Inc. v. Global GT LP, that language is broad, and until the General Assembly wishes to narrow the prism through which the Court of Chancery looks at appraisal value in specific classes of mergers, this Court must give deference to the Court of Chancery if its determination of fair value has a reasonable basis in the record and in .accepted financial principles relevant to determining the value of corporations and their stock.

On the record before us, however, the respondent has made two convincing case-specific arguments why the Court of Chancery’s determination of fair value cannot be sustained on appeal. For starters, the respondent notes that the Court of Chancery found that: i) the transaction resulted from a robust market search that lasted approximately two years in which financial and strategic buyers had an open opportunity to buy without inhibition of deal protections; ii) the company was purchased by a third party in an arm’s length sale; and iii) there was no hint of self-interest that comprómised the market check. 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. But, despite its own findings about the adequacy of the market check, the Court of Chancery determined it would not give more than one-third weight to the deal price for two reasons.

The first reason was that there were regulatory developments relevant to the company being appraised and, therefore, the market’s assessment of the company’s value was not as reliable as under ordinary conditions. The respondent argues that this finding was not rationally supported by the record. We agree. The record below shows that the company’s stock price often moved over the years, and that those movements were affected by the potential that the company’s industry — payday lending and other forms of alternative consumer financial services — would be subject to tighter regulation. The Court of Chancery did not cite, and we are unaware of, any academic or empirical basis to conclude that market players like the many who were focused on this company’s value would not have examined the potential for regulatory action and factored it in their assessments of the company’s value. Like any factor relevant to a company’s future performance, the market’s collective judgment of the effect of regulatory risk may turn out to be wrong, but established corporate finance theories suggest that the collective judgment of -the many is more likely to be accurate -than any individual’s guess. When the collective judgment involved, as it did here, not just the views of company stockholders, but also those of potential buyers of the entire company and those of the company’s debtholders with a self-interest in evaluating the regulatory risks facing the company, there is more, not less, reason to give weight to the market’s view of an important factor.

The Court of Chancery also found that it would not give dispositive weight to the deal price because the prevailing buyer was a financial buyer that “focused its attention on achieving a certain internal rate of return and ■ on reaching a deal within its financing constraints, rather than on [the company’s] fair value.” To be candid, we do not understand the logic of this finding. Any rational purchaser of a business- should have a targeted rate of return that justifies the substantial risks and costs of buying a business. That is true for both strategic and financial buyers. It is, of course, natural for all buyers to consider how likely a company’s cash flows are to deliver sufficient value to payback the company’s creditors and provide a return on equity that justifies the high costs and risks of an acquisition. But, the fact that a financial buyer may demand a certain rate of return on its invéstmenfc in exchange for undertaking the risk of an acquisition does not mean that the price it is willing to pay is not a meaningful indication of fair value. That is especially true here, where the financial buyer was subjected to a competitive process of bidding, thé company- tried but was unable to refinance its public debt in the period leading up to the transaction, and the company had its existing debt placed on negative credit watch within one week of the transaction being announced. The “private equity carve out” that the Court of Chancery seemed to recognize, in which the deal price resulting in a transaction won by a private equity buyer is not á reliable indication of fair value, is not one grounded in economic literature or this record. For these reasons, we remand to the Court of Chancery to reconsider the weight it gave to the deal price in its valuation, analysis.

The next issue in the respondent’s appeal involves .the Court of Chancery's-- discounted cash flow analysis. When the respondent pointed out in a reargument .motion that the Chancellor’s discounted cash flow model included working capital figures that differed from those the Chancellor expressly adopted in his post-trial opinion, the Chancellor corrected his clerical error. This would have resulted in the discounted cash flow model yielding a fair value figure lower than the deal price. But, instead of stopping there, at the prompting of the petitioners, the Court of Chancery then substantially increased its perpetuity growth rate -from 3.1% to 4.0%, which resulted in the Court of Chancery reaching a fair value akin to its original estimate of the company’s value. But, no adequate basis in the record supports -this- major change in growth rate. During the two decades before the merger leading to this appraisal, the company experienced rapid growth. The growth of the payday lending industry and its effect on poor borrowers during this period was a large driver of the regulatory reforms that the company faced, reforms that would require the company to write more loans to make the same profits as in the past. As it was, the recprd suggested that the management projections used in the Court of Chancery’s original discounted cash flow model were optimistic, and designed to encourage bidders'to .pay a high price. Those projections hockey stick up at the last two years, and therefore more working capital was required to sustain those increases, and that doesn’t even account for the likelihood that regulatory changes required more loans (i.e., working capital) to make the same profits as in the past. During the sales process, the company had to revise its aggressive projections downward, as it was not keeping pace with them. Even after revising them downward, the company fell, short of meeting them weeks after the transaction closed. Given the nature of the projection’s outyears, the fact that the industry had already gone through a period of above-market growth, and the lack of any basis to conclude that the company would sustain high growth beyond the-projection period, the record does not sustain the Court of Chancery’s decision to substantially increase the company’s perpetuity growth rate in its discounted cash' flow model after reargument.

On cross-appeal, the petitioners argue that the Court of Chancery- abused its discretion by giving weight to its comparable companies analysis, and that the only correct weighting of relevant factors would have given primary, if not sole, weight to the discounted cash flow model. We disagree. The comparable companies analysis used by the Chancellor was supported by the record; this was a rare instance where both experts agreed on the comparable companies the Court of Chancery used and so did several market analysts and others following the company. Thus, giving weight to a comparable companies analysis was within the Chancellor’s discretion.

Finally, the Court of Chancery’s decision to give one-third weight each to the deal price, thé' discounted cash flow valuation, and the comparable companies valuation was not explained. Given the Court of Chancery’s findings about the robustness of the market check and the substantial public information available about the company, we cannot discern the basis for this allocation. On remand, if the Court of Chancery chooses to use a weighting of different valuation methodologies to reach its fair value determination, the court must explain its weighting in a manner supported by the record before it.

For these reasons, we reverse and remand the Court of Chancery’s ruling. On remand, the Chancellor should reassess the weight he chooses to afford various factors potentially -relevant to fair value, and he may conclude that his findings regarding the competitive process leáding to the transaction, when considered in light of other relevant factors, such as the views of the debt markets regarding the company’s expected performance and the failure of the company to meet its revised projections, suggest that the deal price was the most reliable indication of fair value.

I.

A. DFC

i, DFC’s Growth

DFC Global Corporation (“DFC”) provides alternative consumer financial services, predominately payday loans. The 2014 transaction giving rise to this appraisal action resulted in DFC being taken private by Lone Star, a private equity firm.

DFC was formed in 1990. Its operations then were entirely in the United States. Since then, it has made more than 100 acquisitions to grow the business worldwide. By the time of the'sale giving rise to this appraisal (i.e., the “merger” or “transaction”), DFC operated in ten countries with more than 1,500 locations, in addition to having a substantial internet lending business. But, the bulk of DFC’s revenues came from three main markets: the United Kingdom (47%), Canada (31%), and the U.S. (12%). In the U.S., at the time of the merger, DFC operated 292 stores in 14 states, especially California, Louisiana, and Arizona, and provided loans to enlisted military personnel.

DFC entered Canada in 1996 and had 489 stores there as of the merger. DFC had grown rapidly in Canada, reaching 214 stores by 2004, and, by the time of the merger, DFC could say that it was the “largest alternative financial services retail store network in Canada based upon revenues and profitability.”

Particularly relevant for this appraisal,' DFC entered the U.K. market in 1999 and embarked on an ambitious expansion. Six years after DFC entered that market, in 2005, it had 152 stores. By 2009, only four years later, it almost doubled its footprint in the U.K. to 330 stores. And, as of the merger, DFC had nearly doubled its stores in the U.K. again, reaching 601-locations.

The rapid growth of DFC’s business can be seen in its overall revenues. In 2004, its last fiscal year before becoming a public company, DFC had total revenues of $270.6 million. As of 2013, the last fiscal year before the merger, its total revenues had increased to $1.12 billion, or 314% higher. And, this masked even stronger growth in certain segments, such as the U.K. market, which experienced some years with over 60% year-over-year growth. DFC’s rapid growth' can be seen in its strong year-over-year revenue growth post-initial public offering:.

DFC Total Revenue ($. in millions')

DFC’s strong growth exemplifies the payday loan industry’s material growth in the past two decades. Not only did the industry’s traditional storefront payday lending grow, but the industry’s online market also experienced “rapid” growth.

ii DFC’s Equity

DFC’s shares were traded on the NASDAQ exchange from 2005 until the merger. Throughout its history as a public company, the record suggests DFC never had á controlling stockholder, it had a deep public float of 39.6 million shares, and, it had an average daily trading volume just short of one million shares. DFC’s share price moved sharply in reaction to information about the company’s performance, the industry, and the overall economy, as the following chart, prepared by the petitioners’ . expert, illustrates. The chart shows that regulatory action at different times and by different regulators elicited differing responses by the market.

iii DFC’s Debt

DFC was a highly leveraged company. Its capital' structure was comprised of about $1.1 billion of debt as compared to a $367.4 million equity market capitalization, resulting in a debt-to-equity ratio of 300% and a debt-to-total-capitalization ratio of 75%. DFC’s high leverage “was viewed negatively by both equity and debt analysts,” and, as of all relevant periods, it maintained a non-investment grade credit rating. Indeed, at the beginning of 2014, one equity analyst noted that revenue declines in DFC’s U.K operation could have negative effects on DFC’s ability to both secure new loans and meet the covenants on existing loans. And, later in 2014, Standard & Poor’s (“S & P”), a credit rating agency, placed DFC on its Creditwatch Negative list based in large part on “weaker-than-expeeted financial performance, underpinned by new lending guidelines in the U.K.” Later, S & P warned that “[g]iven • the extent of the regulatory risk [DFC] is exposed to, we don’t foresee an upgrade within the next 12 months.”

iv. Regulatory Headwinds

In the years leading up to the merger, DFC faced heightened regulatory scrutiny. In Canada, DFC confronted a new regulatory environment beginning in 2007 when the provinces in which it operated started regulating it, rather than the central government.

In the U.S., the Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 created the Consumer Financial Protection Bureau, which was given regulatory, supervisory, and enforcement powers over DFC. At least one industry observer described these changes in the U.S. as “[s]weeping.” The Consumer Financial Protection Bureau completed an on-site review of DFC in 2013 and found that DFC was in violation of the Consumer Financial Protection Act. As a result, DFC had to amend its U.S. practices.

In DFC’s most important market — the U.K. — the Office of Fair Trading, DFC’s primary regulator there, issued new rules in 2012 for payday lenders restricting their use of continuous payment authority, a method for lenders to automatically collect loan balances from borrowers’ checking accounts to withdraw money very quickly after the money is deposited. In spring 2013, the Office of Fair Trading identified a number of deficiencies in DFC’s businesses, requiring changes. Then, in the fall of 2013, the Financial Conduct Authority, which replaced the Office of Fair Trading as DFC’s primary U.K. regulator, identified new Regulations that it would issue in 2014. One of those new regulations tightened-affordability assessments and another restricted rollovers where borrowers defer loan repayments by paying additional interest and fees. Before this regulation, DFC had not limited the number of rollovers its businesses would extend to borrowers, -but, after this regulation, DFC would be limited to two rollovers per loan. This was likely to hurt DFC’s U.K. business because rollovers allowed payday lenders to charge additional, higher rates of interest and fees and to keep borrowers paying those rates for extended periods of time. Indeed, as a member of DFC’s management team before the merger put it, “at one point in time you [could] roll a customer over forever and never have them pay back the loan but just monthly fees.” Thus, a rollover is essentially an extension of loan terms such that the borrower pays extra fees and interest and in exchange doesn’t have to pay back the loan as quickly as initially required. Rollovers are lucrative. When the U.S. Consumer Financial Protection Bureau examined them, it found that “most payday loans are made to borrowers who renew enough times that they end up paying more in fees than the original loan amount.”

Finally, there would be a new cap put in place limiting borrowers’ total cost of credit. In February 2014, the Office of Fair Trading warned DFC that it might not be able to meet the Financial Conduct Authority regulations and so, in March and April of that year, DFC had to take additional steps to make sure it could comply. The new U.K, regulations were likely to have a negative effect on DFC’s profitability: “As we '[DFC’s management and board] began to better understand the impact of some of the changes we’d have to make in the U.K., including limiting rollovers, limiting [continuous payment authority], and ■ all the rest, we recognized that that was going to have a negative impact on [DFC’s] earnings ....”

B. The Sale Process

Facing headwinds at least as prevalent as the tailwinds that had propelled its rapid expansion, DFC engaged Houlihan Lo-key Capital Inc., in the spring of 2012, to look into selling the company. Houlihan contacted six private equity sponsors and eventually had discussions with J.C. Flowers & Co. LLC and another sponsor, as well as an interested third party that Houlihan had not contacted. These three potential buyers conducted due diligence, but in August one of the three lost interest, and, in October, J.C. Flowers and the other potential buyer also lost interest. Over the next year, Houlihan reached out to thirty-five more financial sponsors and three strategic buyers.

In autumn 2013, DFC attempted to refinance roughly $600 million in Senior Notes. But, the offering was terminated because of insufficient investor interest. If DFC had wanted to go ahead with the refinancing, it would have needed to increase the bonds’ coupon rate. Analysts pointed to the S & P credit rating agency’s downgrade of DFC from.B + to B after the refinancing was announced and “market uncertainty around payday lending” as two factors that contributed to the termination. To be clearer about what this means, despite the lucrative fees that investment bankers make from refinancing a large tranche of public company debt and syndicating a new issue, Wall Street could not do that for DFC unless DFC was going to compensate new debtholders with a higher' interest rate reflecting DFC’s uncertain financial condition.

In September 2013, DFC renewed discussions with J.C. Flowers and began discussions with.Crestview Partners about a joint transaction. In .October, Lone.Star expressed interest in DFC. In November, DFC gave the three interested parties financial projections prepared by DFC’s management that estimated fiscal year 2014 adjusted EBITDA to be $219.3 million. On December 12, DFC learned that Crestview was no longer interested in pursuing a transaction. On the same day, Lone Star made a non-binding indication of interest in acquiring DFC for $12.16 per share. On December 17, J.C. Flowers made a non-binding indication of interest at $13,50 per share. .

On February 14, 2014, DFC’s board approved revised management projections, which were shared with J.C. Flowers and Lone .Star. These projections lowered DFC’s projected fiscal year 2014 adjusted EBITDA to $182.5 million, a 16.8% decrease from the November, projections. On February 28, Lone Star offered to buy DFC for $11.00 per share and requested a 45-day exclusivity period. Lone Star’s offer was lower than its previous indication of interest because of U.K. regulatory changes,, the threat of increased U.S. regulatory scrutiny, downward revisions in the company projections, reduced availability of acquisition financing, stock price volatility, and weak value in the Canadian dollar. On March 3, J.C. Flowers informed DFC that it was rio longer interested in pursuing a transaction because “it could not get comfortable with the Company’s regulatory exposure in the U.K.” On March 11, DFC entered into an exclusivity agreement with Lone Star.

On March 26, DFC provided Lone Star with management’s revised preliminary fiscal year 2014 adjusted EBITDA forecast, which had dropped by roughly $24 million since February. The next day, Lone Star offered to buy DFC for $9.50 per share. Lone Star explained this price reduction as a result of “further downward revisions in company projections, another reduction in available acquisition financing, continued regulatory changes in the U.K., and a class action suit against the company that was disclosed in an 8-K filed on March 26, 2014.” Lone Star gave DFC twenty-four hours to accept the offer, but later extended that deadline to April 1.

DFC approved another set of projections at the end of March 2014 (the “March Projections”) that were shared with Lone Star. These Projections included a fiscal year 2014 adjusted EBITDA forecast of $153.1 million, a 16.1% decrease from the February projections. But, they remained optimistic, especially in the later years, implying 17.6% compound annual growth in operating profit over the projection period, meaningfully above DFC’s historical 11.0% compound annual growth from 2008 to 2013 as a comparison of these two charts illustrates.

Key Metrics From DFC’s Historical Performance IS. in millions')

Key Metrics From the March Projections IS. in millions!

On April 1, DFC’s board approved the merger at $9.50 per share. The next day, DFC announced the merger and also cut its earnings outlook, reducing 2014 fiscal year adjusted EBITDA projections from $170-200 million to $151-156 million. Within one week of the merger being announced, S & P placed DFC’s long-term “B” rated debt on “CreditWatch with negative implications.” The merger closed June 13, 2014. As it turned out, DFC missed its fiscal year 2014 targets, i.e., for the fiscal year ending June 30, 2014, established in the March Projections made less than three months before, achieving only $138.7 million in EBITDA compared to the Projections’ predicted $153 million. Given the sizeable gap between DFC’s projected performance and the poor reality it achieved at the end of June, it seems likely as of the merger that it was known that DFC had already missed the March Projections. ■ ■

C. The Appraisal Trial

To understand the issues on appeal, it is useful to summarize the conflicting'positions of the parties that the Court of Chancery had to address in its post-trial decision.

i. The Petitioners’ Contentions

The petitioners pressed their' case with only a professional valuation expert; they did not enlist an industry expert and indeed do not seem to have provided other evidence making the case that either DFC or its industry were poised for impressive growth. The petitioners’ valuation expert determined DFC’s value only relying on a discounted cash flow model and used that to come to a fair value of DFC at .$17.90 per share, 88% above the $9.50 per share deal price. In other words, the petitioners argue that all of the financial and strategic buyers missed the chance to top Lone Star at, say $10 per share, and still reap a huge upside of $7.90 per share in value.

He also calculated DFC’s fair value based on a colhparable companies analysis using seven of the peer companies that he used to calculate DFC’s beta. He then calculated EBITDA multiples using the 75th percentile of the peer group, even though DFC ranked below the 50th percentile in a majority of the key metrics. That approach yielded equity values for DFC ranging from $11.38 per ■ share to $26.95 per share. Had he used the 50th percentile, i.e., the median, from his own comparables sample, his calculations would have yielded equity values ranging from around $3.00 per share -to around $13.00, putting the majority of his observations below the deal price.

ii. DFC’s Contentions

In contrast, DFC’s expert used both a discounted cash flow model, which valued DFC at $7.81, and a comparable companies analysis, which-valued DFC at $8.07 per share. He weighted each method equally and .so came to a fair value of $7.94, although ■ he also argued that the $9.50 per share deal price was a reliable indication of fair value. For the comparable companies analysis, DFC’s expert used six companies that-'constituted a subset of the seven used by the petitioners’ expert’s comparable.companies., analysis and in-calculating the beta for the petitioners’ discounted cash flow model. These six companies were also regularly used by analysts, others analyzing DFC, and DFC itself as comparable for DFC. Like the petitioners’ expert, DFC’s .expert used EBITDA multiples, but, unlike the petitioners’ expert, DFC’s expert accepted the median values- from the multiples when calculating DFC’s fair value.

DFC’s expert also performed a transaction ' multiples-based valuation ■' using merged and acquired companies, which yielded a fair value of $7.69 per share. But, he did not give this method any weight in his overall fair, value calculation because “it is difficult to obtain accurate information regarding expected synergies in the price paid for a particular business or the inclusion of a non-compete agreement, employment contract, promises, terms, or other aspects to the transaction that would affect the actual price paid for the business.”

Hi. The Court of Chancery’s Fair Value Analysis

The Court of Chancery noted the “sharp divide” between the experts’ estimates of fair value driven in large part by disagreements about the “proper inputs and methods” .-for the discounted cash flow model. So, the Court of Chancery spent much of its post-trial decision . resolving the disputes over the discounted cash, flow model. The relatively undisputed inputs were the debt-to-capital ratio, cost of debt, risk-free rate, and equity risk premium. The Court of Chancery then examined the disputed components of the weighted average cost of capital (“WACC”), especially the calculation of DFC’s beta, selected the inputs that it deemed most reasonable, and concluded that DFC’s WACC was 10.72%, falling near the midpoint of the experts’ competing 9,5% and 12.4% calculations. ■

Then, the Court of Chancery adopted management’s March Projections of working capital, despite DFC’s expert’s approach of independently calculating working capital as a percentage of total revenue. The Court of Chancery did so because there was “no compelling reason” to reject these Projections’ estimates of working capital while also relying on the projections for other elements of the discounted cash flow model. Similarly, the Court of Chancery adopted the March Projections’ estimates of DFC’s cash balances.

The experts also disagreed about how to value DFC’s cash flows beyond the five-year management projection period. DFC’s expert used a two-stage model where the first stage was the March Projections and the second stage was a terminal value calculated using the convergence formula. The petitioners’ expert used a three-stage, model .where 'the first stage was the March Projections; the second stage was . a - four-year period following those Projections where the growth rate decreased linearly from the 11.7% growth rate for 2018, to a perpetuity growth rate of 2.7%; and the third stage was a terminal -value calculated using .the Gordon Growth Model with a 2.7% perpetuity growth rate. The petitioners’ expert also created an alternate two-stage model using a-3.1% perpetuity growth rate. The Court of Chancery -recognized the uncertainty surrounding the Projections and expressed skepticism of- the linear decrease approach because of that uncertainty, and, therefore, adopted a two-stage model.

Then, the Court of Chancery considered the appropriate perpetuity growth rate. First, the Court of Chancery noted that it “often selects a perpetuity growth rate based on a reasonable premium to inflation” and “some’financial economists view the risk-free rate as the ceiling for a stable, long-term growth rate.” So, that created a band between the 2.31% median inflation rate compiled by the petitioners’ expert and the 3.14% risk-free rate both experts agreed on. The court selected 3.1% because it was at a reasonable premium to inflation but still a tick below the ceiling, risk-free rate. Finally, the Court of Chancery made some adjustments to DFC’s free cash flow to take into account stock-based compensation, which are not at issue on appeal. Using those determinations, the Court of Chancery constructed its own discounted cash flow model indicating DFC’s fair value was $13.07 per share.

The Court of Chancery next assessed the comparable companies analysis DFC’s expert used in his estimate of fair-value. The Court of Chancery determined that an approach using the six peer companies both experts agreed on and the median value of each fiscal year’s multiple was appropriate-for a comparable companies analysis and otherwise adopted DFC’s expert’s analysis and $8.07 per share fair value estimate as a component of the fair value calculation overall.

Next, the Court of Chancery considered the relevance of the deal price, $9.50 per share. The Court of Chancery recognized that “[t]he merger price in an arm’s-length transaction that was subjected to a robust market check is a strong indication of fair value” and, here:

DFC was purchased by a third-party buyer in an arm’s-length sale. The. sale process leading to the Transaction lasted approximately two years and involved DFC’s advisor reaching out to dozens of financial sponsors .as well as several strategic buyers. The deal did not involve the potential conflicts of interest inherent in a management buyout or negotiations to retain existing management — indeed, Lone Star took the opposite approach, replacing most key executives.

But, the Court of Chancery also observed that “the market price is informative of fair value only when it is the product of not only a fair sale .process, but, also of a well-functioning market.” So, the merger provided “a reasonable level of confidence that the deal price can fairly be used as one measure of DFC’s value.”

Finally, the Court of Chancery considered how much weight to give the three fair value inputs it selected. It reiterated that the three inputs meriting consideration were the discounted cash flow analysis as modified by its findings, DFC’s comparable companies analysis, and the deal price. The Court of Chancery observed:

Each of these valuation methods suffers from different limitations that arisé out of the same source: the tumultuous environment in the time period leading up to DFC’s sale. As described above, at the time of its sale, DFC was navigating turbulent regulatory waters that imposed considerable uncertainty on the company’s future profitability, and even its viability. Some of its competitors faced similar challenges. The potential outcome could have been dire, leaving DFC unable to operate its fundamental businesses, or could have been very positive, leaving DFC’s competitors crippled and allowing DFC to gain market dominance. Importantly, DFC was unable to chart its own course; its fate rested largely in the hands of the multiple regulatory bodies that governed it. Even by the time the transaction closed in June 2014, DFC’s regulatory circumstances were still fluid.

And, that “uncertainty impacted DFC’s financial projections.” “Consequently, although a discounted cash flow analysis may deserve significant emphasis or sole reliance in cases where the Court has more confidence in the reliability of the underlying projections than in the deal price, I do not believe it merits a disproportionate weighting in this case.” But:

This same uncertainty inherent in the projections underlying the discounted cash flow analysis was present in the sale process. Although the sale process extended over a significant period of time and appeared to be robust, DFC’s performance also appeared to be in a trough, with future performance depending on the outcome of regulatory decision-making that was largely out of the company’s control. Lone Star was aware of DFC’s trough performance and uncertain outlook — these attributes were at the core of Lone Star’s investment thesis to obtain assets with potential upside at á favorable price.

Furthermore, “Lone Star’s status as a financial sponsor, moreover, focused its attention on achieving a certain internal rate of return and on reaching a deal within its financing constraints, rather than on DFC’s fair value.” Finally:

The uncertainty surrounding DFC’s financial projections also affects the reliability of the multiples-based valuation, because this valuation relies on two years of. management’s projected EBIT-DA. Nonetheless, the multiples-based valuation may be less prone to long-term uncertainty compared to the discounted cash flow model, because it relies only on projections through 2015 rather than 2018, and because one third of the valuation relies on historical EBITDA data.

Having expressed doubts about each fair value input, the Court of Chancery concluded that “each of them still provides meaningful insight into DFC’s value, and all three of them fall within a reasonable range. In light of the uncertainties and other considerations described above, I conclude that the proper valuation of DFC is to weight each of these three metrics equally.” Thus, the Court of Chancery determined that the fair value of DFC was: $9.50 (deal price) + $8.07 (comparable companies analysis) + $13.07 discounts ed cash flow analysis + 3 = $10.21 per share.

D. Reargument

After reading the post-trial decision, DFC moved for reargument because the Court of Chancery had neglected to use the working capital numbers the court had adopted in its opinion in the discounted cash flow model it used to calculate DFC’s fair value. With that error corrected, and addressing certain foreign exchange adjustments, the Court of Chancery’s discounted cash flow model would yield $7.70 per share — a value similar to its comparable companies analysis — and, using the previous weighting the Court of Chancery adopted, a fair value of $8.42 per share.

The petitioners did not accept this simple math correction with equanimity. Instead, they raised an arguably new.contention in their own response and motion for reargument, which was that the level of working capital in the March Projections implied that DFC would enjoy another period of above-market growth in the perpetuity period and therefore that the Chancellor’s selected permanent growth rate of 3.1% was too low.

The Court of Chancery considered the motions and issued an order granting the motions in part and modifying the discounted cash flow model. In that order, the Court of Chancery acknowledged that it had mistakenly included working capital estimates based on modified working capital estimates made by DFC’s expert when the Court of Chancery had intended to just use the unmodified March .Projections.

■The Court of Chancery then considered the petitioners’ motion for reargument. In essence,- the petitioners said that there needed to be a particular relationship between the level of projected working capital in the discounted cash flow model and the perpetuity growth rate. In that affidavit, the petitioners’ expert argued that the permanent growth rate is a function of two elements, DFC’s return on capital and DFC’s reinvestment rate. When someone preparing a discounted cash flow analysis selects a permanent growth rate, so the petitioners’ expert’s argument went, the underlying projections for those two elements have to be sufficient to sustain that growth rate. As the Court of Chancery put it, “DFC’s projected revenue and working capital needs have a codependent relationship, ia, a high-level requirement for working capital, as reflected in [the management projections] necessarily corresponds with a higher projected growth rate.” The Court of Chancery then observed that it had selected a 3.1% perpetuity growth rate so as not to exceed the risk-free rate, but, it now realized that the risk-free rate was only the upper bound for perpetuity growth rates When companies have reached a stable stage. And, the March , Projections “assume DFC will achieve fast-paced growth throughout the projection period and therefore imply a need for a perpetuity growth rate higher than the risk-free rate.” So, the Court of Chancery determined that it needed to adopt a perpetuity 'growth rate consistent with the “relatively high level of working capital built into those projections.” Based on the contentions in a supplemental affidavit from the petitioners’ expert, the Court of Chancery concluded that the March Projections would sustain an average growth rate of 3.9% and a median growth rate of 4,2%.

The Court of Chancery adopted the petitioners’ expert’s suggestion that the correct sustainable growth rate is the midpoint between the average and median sustainable growth rates, i.e., the functions of reinvestment and return on invested capital, underlying the March Projections, 4.0%. This growth rate assumed that, despite the acknowledged risk of insolvency and shrinkage, DFC would, not only keep pace with the most dynamic mature industries in perpetuity, but exceed their growth by a healthy margin, given that 4.0% was fully 27% higher than the risk-free rate of 3.14%. Taking both revisions into account, the Court of Chancery adjusted its discounted cash flow model to $13,33 per share, 2% higher than its original DCF and 40% higher than the deal price, which, when given its one-third weight, resulted in a fair value of DFC at $10.30. per share, $0.09 higher than the post-trial opinion’s original award.

II.

On appeal, the case has reflected an emphasis on one issue that was not presented fairly to the Court of Chancery. Before us, .DFC’s central argument is that a judicial presumption in favor of the deal price should be established in appraisal cases where the transaction was the product of certain market conditions. DFC argues that those conditions pertain to this case and the Court of Chancery erred by not giving presumptive and exclusive weight to the deal price.

DFC also raises more case-specific issues on appeal. The first is a more constrained take on its deal price presumption argument, which involves the idea that based on the fact findings the Court • of Chancery made regarding the naturé of the market search, lack of conflict of interest, and other relevant economic factors bearing on the deal price, the Court of Chancery abused its discretion by only giving one-third weight to the deal price. More particularly, DFC argues that the two reasons that the :Court of Chancery gave for not giving full weight-to the deal price — the fact that DFC faced increasing regulatory constraints -that could not be priced by equity market .participants and the fact that the prevailing buyer was a private equity rather than strategic buyer — were -not rationally supported by the record...

DFC’s next case-specific argument is that the Court of Chancery erred by markedly increasing the perpetuity growth rate it used in .its discounted cash flow model after recognizing on reargument that it had used the wrong working capital figures in its original model. DFC contends that there was no record evidence justifying this sizable increase in the perpetuity growth-rate.

For their, part, on cross-appeal, the petitioners argue that the Court of Chancery abused its discretion by according weight to a comparable companies analysis, which the petitioners contend is not a reliable indicator of fair value, and that the court should have given primary, if not exclusive, weight to its discounted cash flow model.

Finally, DFC’s overall argument raises another implied argument,' which is that the Court of Chancery’s decision to afford equal weight to the deal price, its discounted cash flow model, and its comparable companies analysis was arbitrary and not based on any reasoned explanation of why that weighting was appropriate.

We deal with these issues in the order just outlined. When reviewing a decision in a statutory appraisal, we use an abuse of discretion standard and grant significant deference to the factual findings of the trial court. This Court “will accept [the Court of Chancery’s] findings if supported by the record ....”

A.

The first issue we confront is one that did riot feature iri the same way before the Charicellor. On appeal, but not below, DFC argued for the creation of a judicial presumption that the deal price is the best evidence of fair value when the transaction giving rise to appraisal results from an open iriarket check and when certain other conditions pertain. This focus has generated interest from distinguished law professors on both sides of the question, who have weighed.in'with dueling amicus briefs.

But, before the Court of Chancery, DFC merely argued that the “arms-length, corn-petitive, arid fair sales process” entitled the deal price to receive “significant weight.” DFC made a similar argmrient in its post-trial brief for the Court of Chancery. So, it is difficult to see how the argument that the deal price under these circumstances is entitled to a presumption of fair value was properly presented to the Court of Chancery and therefore can be argued to us now. We place great value on the assessment of issues by our trial courts, and it is not only unwise, but unfair and inefficient, to litigants and the development of the law itself, to allow parties to pop up new arguments on appeal they did not fully present below. For that reason alone,' we are reluctant to even consider this argument. Nonetheless, because of its relationship to more case-specific issues, we explain why, even if this were fairly presented,.DFC-has not persuaded us to adopt its position.

B.

i.

Another key problem for DFC in presenting this argument now is that a similar argument was presented and rejected recently by this Court in Golden Telecom. In Golden Telecom, the respondent company argued that this Court “should adopt a standard requiring conclusive or, in the alternative, presumptive deference to the merger price in an appraisal proceeding.” In rejecting that argument, this Court focused on the key language in 8 Del. C. § 262, stating that dissenting shareholders “shall be entitled to an appraisal by the Court of Chancery of the fair value of the stockholder’s shares of stock under the circumstances described” elsewhere in the section. The statute elaborates:

Through such proceeding the Court shall determine the fair value of the shares exclusive of any element of value arising from the accomplishment or expectation of the merger or consolidation, together with interest, if any, to be paid upon the amount determined to be the fair value. In determining such fair value, the Court shall take into account all relevant factors.

In particular, this Court focused on § 262’s requirement that the Court of Chancery consider “all relevant factors” and that “fair value” entails “the value to the stockholder of the firm as a going concern.” Thus, this Court concluded:

Section 262(h) unambiguously calls upon the Court of Chancery to perform an independent evaluation of “fair value” at the time of a transaction. It vests the Chancellor and Vice Chancellors with significant discretion to consider “all relevant factors” and determine the going concern value of the underlying company. 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. It would inappropriately shift the responsibility to determine “fair value” from the court to the private parties. Also, while it is difficult for the Chancellor and Vice Chancellors to assess wildly divergent expert opinions regarding value, inflexible rules governing appraisal provide little additional benefit in determining “fair value” because of the already high costs of appraisal actions.

DFC would have us depart from the reasoning of Golden Telecom. But, we are not convinced we should do so. As Golden Telecom found, § 262(h) gives broad discretion to the Court of Chancery to determine the fair value of the company’s shares, considering “all relevant factors.” That statutory language was a key feature in Weinberger v. UOP, Inc. Before Wein-berger, the Court of Chancery had historically employed the so-called Delaware Block Method to determine the value of shares at issue in an appraisal. Although “[t]he exact origin of the Delaware Block Method is a source of confusion,” there is no confusion that it was a judicial gloss on the appraisal statute, rather than something inevitably stemming from the text. This Court has described the .Delaware Block Method this way:

The Delaware Block Method actually is a combination of three generally accepted methods for valuation: the asset approach, the market approach, and the earnings approach. Under the Delaware Block Method, the asset, market and earnings approach are each used separately to calculate a value for the entire corporation. A percentage weight is then assigned those three valuations on the basis of each approach’s significance to the nature of the subject corporation’s business. The appraised value of the corporation is then determined by the weighted average of the three valuations.

One of the three-approaches comprising the Delaware Block Method, the market value approach, focused on the market prices of securities when there was an active market and where no special circumstances existed to render the price unreliable. This approach is encapsulated by the observation that “[w]here there is a free and active market, averaging of market prices on the last trading day before the announcement of a merger will reflect the fair market price.”

By the time of Weinberger in 1983, important developments in corporate finance and economies had occurred, such as the articulation of the capital asset pricing model and the efficient market hypothesis, and concepts related to those, such as the discounted cash flow method of valuation. Weinberger eliminated the Delaware Block Method as the exclusive valuation methodology for appraisal. Weinberger ascribed this result to two amendments to the appraisal statute: i) the 1976 amendment that added the concept of “fair value” to the statute for-the first time; and ii) the 1981 amendment that mandated the Court of Chancery “take into account all relevant factors.” Weinberger found that these statutory amendments demonstrated “a legislative intent to fully compensate shareholders for whatever their loss may be, subject only-to the narrow limitation that one, cannot take speculative effects of the merger into account." Weinberger therefore held that the Delaware Block Method would no longer be the exclusive valuation method for appraisal, and instead adopted “a more liberal, less rigid and stylized, approach to the valuation process,” which included “proof of valué by any techniques or methods which are generally considered acceptable in the financial community and otherwise admissible in court.”

ii

Since Weinberger, and Golden Telecom itself, the key language in § 262 that those cases focused upon has remained unaltered. But,. DFC would have us put a judicial gloss on the broad “all relevant factors” language, by determining that a particular factor is more relevant than others when certain conditions pertain. We do not, however, view the statutory language as inviting us to do so. Nor are we persuaded it is advisable to do so.

As we shall discuss, wé have little quibble with the economic argument that the price of a merger’ that results from a, robust market check, against the back drop of a rich information base and a welcoming environment for. potential buyers, is probative of the company’s .fair value. But, not only do we see no license in the statute for creating a presumption that the resulting price in such a situation is the “exclusive,” “best,” or “primary” evidence of fair value, we do not share DFC’s confidence in our ability to' craft, on a general basis, the precise pre-conditions that would be necessary to invoke a presumption of that kind. We also see little need to do so, given the proven record of our Court of Chancery in exercising its discretion to give the deal price predominant,- and indeed exclusive weight, when it determines, based on the precise facts before it.that led to the transaction, that the deal price is the most reliable evidence of fair value. For these reasons, we adhere to our prior ruling-in Golden Telecom. If the General Assembly determines that a presumption of the kind sought' is in order, it has proven its attentiveness to our appraisal statute and is free to create one itself.

As our preceding discussion presages, our refusal' to craft a statutory presumption in favor of the deal price when certain conditions pertain does’ not in any way signal our ignorance to the economic reality that the sale value' resulting from a robust market check will often be the most reliable evidence of fair valué, - and that second-guessing the value arrived upon by the collective views of many sophisticated parties with a real stake in the matter is hazardous. In fact, the Chancellor himself, and his colleagues on the Court of Chancery, understand this, as both the decision in this case and other decisions of the Court make clear.

C.

Having rejected DFC’s argument that the Court of Chancery was required to give presumptive weight to the deal price, we thus now turn to the more record-specific argument about the role of the deal price in this case. DFC argues that in any assessment of the. economic value of something — be it a company, a product, or a service — economics teaches that the most reliable evidence of value is that produced by a competitive market, so long as interested buyers are given a fair opportunity to price and bid on the something in question. This argument is sensible and in accordance with economic literature. It also accords with the generally accepted view that it is unlikely that a particular party having the same information as other market participants will have a judgment about an asset’s value that is likely to be more reliable than the collective judgment of value embodied in a market price. This, of course, is not to say that the market price is always right, but that one should have little confidence she can be the special one able to outwit the larger universe of equally avid capitalists with an incentive to reap rewards by buying the asset if it is too cheaply priced.

i.

Of course, the definition of fair value used in appraisal cases is a jurisprudential concept that has certain nuances that neither an economist nor market participant would usually consider when either valuing a minority block of shares or a public company as a whole. But, those features do nothing to undermine the ability of the Court of Chancery to determine, in its discretion, that the deal price is the most reliable evidence of fair value in a certain case, and that’s especially so in cases like this one where things like synergy gains or minority stockholder discounts are not contested. In fact, if one were to look at the face of-our appraisal Statute, a case like the one before us today might seem simple. Precisely because DFC’s shares were widely traded on a public market based upon a rich information base, the “fair value of the stockholder’s shares of stock” held by minority stockholders like the petitioners, would, to an economist, likely be best reflected by the prices at which their shares were trading as of the merger.

But, in Cavalier Oil Corporation v. Harnett, and other cases, this Court eschewed that reading of the statute and adopted a definition of fair value that-is a jurisprudential, rather than purely economic, construct. That definition requires according the petitioner in an appraisal her pro rata share of the appraised company’s value as a “going concern.” By requiring that petitioners be afforded pro rata value, the Court required that any minority discount be ignored in coming to a fair value determination. At the same time, by valuing the company on its value as a “going concern,” the Court seemed to require the excision of any value that might be attributable to expected synergies by a buyer, including that share of synergy gains left with the seller as a part of compensating it for yielding control of the company. As the Court of Chancery observed in Union Illinois, Cavalier Oil and its progeny seem to require the court to exclude “any value that the selling company’s shareholders would, receive because a buyer intends to operate the subject company, not as a stand-alone going concern, but as a part of a larger enterprise, from which synergistic gains can be extracted.” This mandate seemed inspired by a desire to honor the statute’s command that the court “determine the fair value of the shares exclusive of any element of value arising from the accomplishment or expectation of the merger,” although that statutory language could be interpreted to address the narrower, if still important, policy concern that the specific buyer not end up losing its upside for purchase by having to pay out the expected gains from its own business plans for the company it bought to the petitioners. But, the broader excision of synergy gains could have also been thought of as a balance to the Court’s decision to afford pro rata value to minority stockholders.

Whatever the exact policy reason, the pro rata share of going concern value formula has been used in our state’s appraisal jurisprudence for a good time now and no party to this appeal takes issue with it. But, when that formula is distilled down, the basic economic concept of fair market value remains central to our statutory concept of fair value. Basically, Cavalier Oil focuses the appraisal proceeding on the fair market value of the company being appraised, putting aside any issues relevant to the value of petitioners’ share blocks and trying to exclude any portion of value that might be attributed to a synergy premium a buyer might pay to gain control. That is, in sum, our case law has been read to value the company on its stand-alone value.

ii.

In economics, the value of something is what it will fetch in the market. That is true of corporations, just as it is true of gold. Thus, an economist would find that the fair market value of a company is what it would sell for when there is a willing buyer and willing seller without any compulsion to buy. And, outside of the appraisal context, this Court has often embraced these concepts of value: “[I]n many circumstances a property interest is best valued by the amount a buyer will pay for it.... a well-informed, liquid trading market will provide a measure of fair value superior to any estimate the court could impose.”

Because businesses like corporations are assumed to be. valuable to their equity owners because of the profits they generate, economics and corporate finance instruct rational participants in any sale process that they should base their bids on their assessments of the corporation’s ability to generate further free cash flows, and to discount that to present value in formu.lating their offers. Likewise, the same principles instruct stockholders who buy shares of public companies to consider the free cash flows of those companies in the form of dividends and their ability to increase them over time.

Market prices are typically viewed superior to other valuation techniques because, unlike, e.g,, a single person’s discounted cash flow model, the market price should distill the collective judgment -of the many based on all the publicly available information about a given company and the value of its-shares. Indeed, the relationship between market valuation and fundamental valuation has been strong historically. As one textbook puts it, “[i]n an efficient market you can trust prices, for they im-. pound all available information about the value of each security.” More pithily: “For many purposes no formal theory of value is needed: We can take the market’s word for it.” But, a single person’s own estimates of the cash flows are just that, a good faith estimate by a single, reasonably informed person to predict the future. Thus, a singular discounted cash flow model- is often most helpful when there isn’t an observable market price,

For these reasons, corporate finance theory reflects a belief that if an asset— such as the value of a company as reflected in the trading value of its stock — can be subject to close examination and bidding by many humans with.an incentive to estimate its future cash flows value, the resulting collective judgment as to value is likely to be highly informative and that, all estimators having equal access to information, the" likelihood of outguessing the market over time and building a portfolio of stocks beating it is slight.

Other realities emphasize why real world’transaction prices can be the most probative evidence of fair value even through appraisal’s particular lens.’ As the preceding discussion emphasizes, fair valué is just that, “fair.” It does not mean the highest possible price that a company might have sold for had Warren Buffett negotiated for it on his best day and the Lenape who sold Manhattan oh their worst. Rather, as the Court of Chancery has .put it in another context:

A fair price does not mean the highest price financeable or the highest price that fiduciary could afford to pay. At least in the non-self-dealing context, it means a price that is one that a reasonable seller, under all of the circumstances, would regard as within a range of fair value; one that such a seller could reasonably accept.

Capitalism is rough and ready, and the purpose of an appraisal is not to make sure that the petitioners get the highest conceivable value that might have been procured had every domino fallen out of the company’s way; rather, it .is to make sure that they receive fair compensation for their shares in the sense that it reflects what they deserve to receive based on what would fairly be given to them in an arm’s-length transaction.

The real world evidence regarding public company M & A transactions underscores this. Various factors prevalent in our economy, which include Delaware’s own legal doctrines such as sell-side voting rights, Revlon, Unocal, the entire fairness doctrine, and the pro rata rule in appraisals, have caused the sell-side gains for American public stockholders in M & A transactions to be.robust. Part of why the synergy excision issue can be important is that it is widely assumed that the sales 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. For that reason, there is a rich literature noting that the buyers in public company acquisitions are more likely to come out a loser than the sellers, as competitive pressures often have resulted in buyers paying prices that are not justified by their ability to generate a positive return on the high costs of acquisition and of integration. As one authority summarizes:

According to McKinsey research on 1,415 acquisitions from 1997 through 2009,. the combined value of the acquirer and target increased by about 4 percent on average. However, the evidence is also overwhelming that, on average, acquisitions do not create much if .any value for the acquiring company’s shareholders. Empirical studies, examining the reaction of capital markets to M & A announcements ' find that the value-weighted average deal lowers the acquirer’s stock price between 1 and 3 percent. Stock returns following the acquisition are no better.. Mark Mitchell and Erik Stafford have found that acquirers underperform comparable companies on shareholder returns by-5 percent during the three years following the acquisitions.

Similarly, another study summarized its findings by simply stating: “Target firm shareholders are clearly winners in merger transactions.”

in.

DFC argues that, -with a company like itself, it was particularly unlikely that the market would somehow miss out if it had great growth prospects. After all, DFC’s stock was listed on a major U.S. exchange, traded actively, and had moved sharply over the years when the company was poised for growth or facing dimming prospects. And, DFC was also actively examined by the debt markets, which rated and analyzed its creditworthiness. And of course, here, these market participants’ judgments were supplemented by those of the numerous strategic and financial buyers who were contacted by Houlihan during the sales process and given a chance to buy DFC and to receive non-public information about it.

Because the Court of Chancery found that the sales process was robust and conflict-free, DFC argues that the Court of Chancery erroneously relied on two factors to diminish the role of the deal price in its fair value determination. To wit, that: i) DFC “appeared to be in a trough, with future performance depending on the outcome of regulatory decision-making that was largely out of the company’s control”; and ii) Lone Star’s status as a financial sponsor “focused its attention on achieving a certain internal rate of return and on reaching a deal -within its financing constraints, rather than on DFC’s fair value.” Although the Court of Chancery has broad discretion to make findings of fact, those findings of fact have to be grounded in the record and reliable principles of corporate finance and economics. Despite the vigorous efforts of the petitioners to justify the Court of Chancery’s fact findings for according the deal price one-third weight, we fail to discern an adequate record to support them.

a.

First, the Chancellor found that the deal price was unreliable because DFC was in a trough with future performance dependent upon the outcome of regulatory actions, but he cited no economic literature to suggest that markets themselves cannot price this sort of regulatory risk. The payday lending industry is hardly unusual in being subject to regulatory risks. Publicly traded companies in industries like tobacco, energy, pharmaceuticals, and certain commercial products are subject to close regulation, the development of which can affect their future cash flows. Precisely because of that reality, the market’s assessment of the future cash flows necessarily takes regulatory risk into account as it does with all the other reasonable uncertain factors that affect a company’s future. In this case, the payday lending industry was long subject to regulatory risk, albeit of a changing character. As one- equity analyst report observed, regarding the industry, “[rjegulatory risk is persistent, but [it] has always been.”

Beyond the reality that prevailing economic theories assume that markets take information about all sorts of risk, including regulatory risk, into account and price that information into the things traded on those markets, the record reveals that equity analysts, equity buyers, debt analysts, debt providers and others were in fact attuned to the regulatory risks facing DFC. For one thing, in the years leading up to the merger, DFC’s stock price fluctuated, but it had an overall downward trend. Although the Canadian regulatory reform did not appear to negatively affect DFC’s stock price, the extensive U.K. regulatory overhaul did seem to contribute to the decline in stock price. This highlights an important point.

That Weinberger got rid of the Delaware Block Method does not mean that the pre-transaction trading price of a public company’s shares is not relevant to its fair value in appraisal, particularly given the focus on going concern value. Historically, appraisal actions have., had the most utility when private companies are being acquired or for public companies subject to a conflicted buyout, situations where market prices are either unavailable altogether or far less useful. When, as here, the company had no conflicts related to the trans.action, a deep basé of public 'shareholders, and highly active trading, the price at which its shares trade is informative of fair value, as that value reflects the judgments of many stockholders about the'company’s future prospects, based on public filings, industry information, and research conducted by equity analysts.

And, during the relevant period, DFC’s regulatory -risk was being watched by two other key sets of folks who had money at stake: potential buyers in the sale process and participants in the debt markets.

The buyers who were part of the sales process — and who ultimately decided not to pursue a transaction with DFC — considered regulatory risk. In the spring of 2012, Houlihan contacted six financial sponsors about a possible transaction. Three parties were interested and conducted due diligence. But, by October of that year, all three lost, interest. Over the next year, Houlihan contacted an additional thirty-five financial sponsors and three strategic buyers. Three-interested parties emerged and were given access to management’s projections. Lone Star and J.C. Flowers submitted non-binding indications of interest in late 2013, and only one party, Lone Star, continued to express. interest after receiving additional projections from management in early 2014. That these other potential buyers dropped out of the sales process after receiving confidential information about DFC suggests that these parties were aware of the “trough” DFC was in at the time and the uncertain future regulatory risk it faced, and ultimately did not think a transaction with DFC was worth pursuing. Indeed, J.C. Flowers cited the regulatory risk facing the. company as its reason for not wanting to pursue a transaction with DFC.

Finally, the debt markets for DFC took into consideration the regulatory risk DFC was facing. In the fall of 2013, the same time that Houlihan , was actively seeking buyers for DFC, DFC attempted to refinance around $600 million in Senior Notes. But, there was not enough investor interest and the offer was terminated. In other words, participants in the public bond markets weren’t convinced they would get their money back if they gave it to DFC, and DFC was not offering enough interest to compensate investors for the risk they saw in the company. Furthermore, in a May ,2014 presentation to certain rating agencies, DFC discussed the recent U.K. regulatory, changes and the challenges it was causing DFC, including its negative effect on DFC’s revenue. DFC also discussed the U.S. regulatory environment and mentioned that the Consumer Financial Protection Bureau had conducted an on-site review of DFC in 2013, and since then the company undertook certain corrective actions to enhance compliance. At the same time, DFC claimed that there was long-term opportunity to grow and expand as competitors struggled under the stricter regulatory framework. But, the Chancellor found that one of the reasons Lone Star lowered its offer to $9.50 was because its financing available for the transaction had fallen by $100 million due to DFC’s reductions in projected - EBIT-DA, which were of course related to; the stricter regulations in the U.K. This confirms that debt investors also cared about and tracked DFC’s regulatory challenges and took them into account when deciding if and at what yield it would invest in DFC’s debt. As is the case with refinanc-ings, so too do banks like to lend and syndicate the acquisition debt for an M & A transaction if they can get it done. That is how they make big profits. That lenders would not finance a buyout of DFC at a higher valuation logically signals weakness in its future prospects, not that debt providers and equity buyers were all mistaken. So did the fact that DFC’s already non-investment grade debt suffered a downgrade in 2013 and then was put on a negative credit watch in 2014.

Thus, the record demonstrates that the markets factored regulatory risk into DFC’s pricing. Although the Court- of Chancery gave DFC credit- for being in a “unique position,” that story was the same one that DFC told to sell-itself to numerous buyers, the debt markets, and its existing stockholders. That this growth story was not accepted by the markets does not mean that the markets ignored it. Rather, the equity and credit markets were intensely focused on the extent to which DFC could address the new regulatory burdens and how they affected its potential for future growth.

Cr1'

The second reason, the Chancellor gave for finding the deal price unreliable was that Lone Star, a private equity firm, required a specific rate of return on its transaction with DFC. But, all disciplined buyers, both strategic, and financial, have internal rates of return that they expect in exchange for taking on the large risk of a merger, or for that matter, any sizeable investment of its. capital. That a buyer focuses on hitting its internal rate of return has no rational connection to whether the price it pays as a result of a competitive process is a fair one. That is espe-dally so when there, are objective factors that support the fairness of the price paid, including: i) the failure of other buyers to pursue the company when they had a free chance to do so; ii) the unwillingness of lenders to lend to the buyers because of fears of being paid back; iii) a credit rating agency putting the company’s long-term debt on negative credit watch; and iv) the company’s failure to meet its own projections. ¡Importantly, the Court of Chancery determined that there was no conflict of interest. Indeed, the- court observed that “[t]he deal did not involve the potential conflicts of interest inherent in a management buyout or negotiations to retain existing management — indeed, Lone Star took the opposite approach, replacing most key executives.”

Especially untenable is the idea that the deal price cannot be relied upon as á reliable indicia of fair value because lenders would not finance the acquisition by Lone Star at a higher price. Lenders get paid before equity. They' make profits by, lending. If lenders fear getting paid back, then that is not a reason to think that the equity is being undervalued. Furthermore, the fact that the ultimate buyer was alone at the end provides no basis for suspicion given the Chancellor’s own view of the process and the uncontradicted evidence of record finding that: i) there was no conflict of: interest; ii) Houlihan had approached every logical buyer; iii) no one was willing to bid more in the months leading up to the transaction before management significantly adjusted downward its projections; and iv) management continued to miss its targets after Lone Star was the only buyer remaining. Thus, the record does not include the sorts of flaws in the sale process that could lead one to reasonably suspect that the ultimate price paid by Lone Star was not reflective of DFC’s fair value. For these reasons, we cannot sustain the Chancellor’s decision to give only one-third weight to the deal price because the factors he cited in giving it only that weight were not supported by the record.

d.

DFC’s next case-specific argument is that the Court of Chancery improperly revised its discounted cash flow-valuation to increase the perpetuity growth rate it used from 3.1% to 4.0% — a 29% increase in the growth rate — after it acknowledged on reargument -that it had made a clerical error and used a lower working capital number in its model than it intended. The Court of Chancery adopted the working capital estimates from the March Projections in its opinion, but in its model, the Court of Chancery inadvertently used DFC’s expert’s working capital estimates, which were lower than those in the March Projections. Just correcting that error alone would have resulted in a discounted cash flow value of $7.70 per share. This value would have been corroborated by the Court of Chancery’s comparable companies analysis, which indicated a value, of $8.07 per share, and would have been far more in line with the $9.50 deal price than the $13.07 per share value resulting from its original discounted cash flow calculation.

i.

But, in their own motion for reargument, the petitioners argued that the Court of. Chancery’s original discounted cash flow .analysis, even with the corrected working capital figures, contained a fundamental methodological flaw, albeit one that apparently also infected elements of their own expert’s analyses prepared for trial. Specifically, the petitioners maintained that “the Court failed to take into account the required correlation between a company’s [permanent] growth rate, discount rate, and level of working capital necessary to sustain growth.” By using the working capital estimates contained in the March Projections and adopting a 3.1% permanent growth rate, the petitioners’ argument went, the Court of Chancery had supposedly used variables at odds with each other,- leading to “illogical results.” As the petitioners explained it, because DFC is a lending business, DFC’s “revenue and working capital outflows have a codependent.... and directionally consistent relationship that should- be reflected in .any free cash flow calculation.” Because the March Projections predicted a revenue growth rate of 11.7% in their final year, then, with an estimated $90 million of working capital to support that growth, that together they implied a higher ongoing investment in working capital and therefore a higher growth rate in the perpetuity period.

DFC disagreed with the petitioners’ contention, arguing that this sort of change was not appropriate for a motion seeking reargument because the petitioners did not “demonstrate that ‘the ' Court has' overlooked a controlling precedent or misapprehended the law or facts of the case,’ ” .which the methodological error was not, and because the petitioners’ argument essentially “rehashes an issue already considered” by the Court of Chancery, selecting an appropriate perpetuity growth rate.

ii

Instead of simply correcting the clerical error, however, the Court of Chancery not only fixed its working capital assumption, but then revised sharply upward its estimate for the perpetuity growth rate in response to the petitioners’ argument. The Court of Chancery stated:

5. In re-examining the working capital assumptions inflts discounted cash flow analysis, the Court realizes that it misapprehended another material fact in constructing its model, namely, the need to maintain an appropriate correlation between the level of projected working capital and the perpetuity growth rate. In the Opinion, the Court adopted the 3.1% perpetual growth rate from [petitioners’ expert’s] two-stage discounted cash flow model, which was performed as an alternative to his three-stage growth model. In doing so, the Court observed that a sharp growth rate drop-off “from the. projection period to the terminal period is not ideal but not necessarily problematic.” In reconsidering the issue, however, the Court realizes it failed to appreciate the extent to which DFC’s projected revenue and working capital needs have a codependent relationship, ie., a high-level requirement for working capital, as reflected in DFC’s March Projections, necessarily corresponds with a high projected growth rate.
6. The Court also based its selection of a 3.1% growth rate on the theory that a company’s perpetuity growth rate should not exceed the risk-free rate, which both parties agreed was 3.14% in this case. But this proposition is only applicable to companies that have reached a stable stage. The March Projections assume DFC will achieve fast-paced growth throughout the projection period and therefore imply a need for a perpetuity growth rate higher than the risk-free rate.
7.■ Because the Court ■ adopted the Working capital assumptions in the March Projections, the Court should have adopted- a perpetuity growth rate more consistent with' the rela- ■ tively high level of working capital built into those projections. In Petitioners’ motion for reargument, -[petitioners’ expert] demonstrates that, as a matter of economics,’ the March Projections support an average sustainable growth rate of 3.9% and'a median sustainable growth rate of 4.0%, representing the midpoint of the median and average growth rates underlying the March Projections, is proper in this ease. Although a perfect projection of the future is never attainable, the 4.0% perpetuity growth rate that [petitioners’ expert] derived using a recognized economics formula corrects the Court’s original model in a' reasonable manner. Therefore, the Court adopts this higher perpetuity growth rate in its revised discounted cash flow model.

On appeal, DFC argues that this change was unjustified by the record..

in.

We agree with the respondent that the record evidénce does not’ rationally support the Court of Chancery’s'decision to increase its original discounted cash flow model value on reargument from an original rate that was just shy of the ceiling, risk-free rate for a stable-state company, to a much higher 4.0% perpetuity growth rate. By embracing the idea that using the March Projections required increasing the perpetuity growth rate, the'Court of Chancery compounded its reliance upon the Projections that assumed DFC could grow rapidly again through 2018, The aggressive upward move to increase the perpetuity value on reargument by 0.9% inflated the Chancellor’s original discounted cash flow estimate to $13.33, which was 40% above the deal price. Simply given the Court of Chancery’s own findings about the extensive market check, the value gap already reflected in- the court’s original discounted cash flow estimate of $13.07 should have given the Court doubts about the reliability of its discounted cash flow analysis. And, a less-than-clear expert affidavit, not well grounded in record evidence, on a reargument motion where there was no opportunity for cross-examination of the petitioners’ expert, to better understand his contentions, is a poor basis to switch out the vehicle driving a large part of the value in a discounted cash flow analysis.

Our non-exclusive reasons for finding that the record did not support the 29% upward increase in the perpetuity growth rate made after reargument are:

a) the linkage of projected working capital in the March Projections to DFC’s perpetuity growth rate the petitioners urge is methodologically suspect and not supported by anything in the Projections themselves or testimony about them;
b) the increase in the perpetuity value failed to take into account that DFC and its industry had already experienced nearly a generation of rapid growth;
c) the petitioners’ assertion thát DFC was primed for another period of rapid growth was not grounded in any testimonial or document evidence either about DFC specifically or the payday lending industry more generally;
d) DFC-was experiencing strong regulatory pushback and, that pushback was affecting DFC’s profitability ' and working capital, i.e., loans, .that DFC would need to make to generate profits; and finally
e) the petitioners’ assertion was at tension with several of their expert’s own assumptions in his original analysis, including-his assumptions that DFC’s beta was most akin to the beta of a company performing in line.with the overall market and that DFC was therefore at a steady state of growth.

We now discuss each reason-in turn.

a.

First off, we are not convinced that the petitioners’ description of the methodological tension they identified .in. the. Court of Chancery’s initial approach to. the discounted cash flow model accurately describes best,practices in using discounted cash flow models for valuation. Specifically, the idea that in a discounted cash flow model, there is a “required correlation,” between the level of working capital growth in the specifically projected years and the terminal growth calculation does not fit well with general principles of valuation. The Gordon Growth Model, which the Court of Chancery used in its calculations and which no one disputes is an appropriate tool' here, is “used to value a firm that is in ‘steady state’ with dividends growing at a rate that can be sustained forever.” Other' texts on valuation suggest that’ the perpetuity growth rate should be based on the expected long-term industry growth rate, on the assumption that in this period the company being valued will grow with its industry or economy as a whole, rather than exhibit its own distinct growth characteristics. But, as the petitioners’ expert asserted, their entire theory was based on the belief that “the last explicit period’s [of the March Projections] revenues and operating margins have not reached a steady state.” Indeed, if the record, unambiguously supported the proposition that DFC was to continue a new spurt of growth past 2018, it would have been more appropriate to project' out to a point where steady-state growth began. By doing that, the appraiser would have to assess with discipline the next period after the projections end and also the potential that the period might be negative, as well as that another period of above-market growth might be followed by a terminal growth rate more like inflation than the risk-free rate. Especially when, as here, the underlying projections assumed away important downside risks during the projection period, a consideration of downside scenarios, not just positive ones, must factor into this process, whether a multi-stage model is used or the future is encapsulated in a single perpetuity growth value. Put simply, the theoretical link the petitioners urge between the discounted cash flow model’s optimistic forecast period and the perpetuity period is not as strong as they suggest or as the Chancellor accepted.

To this point, the petitioners don’t, situate changes in DFC’s working capital in the specific payday lending context where, like other types of lenders, DFC’s working capital is largely driven by loan growth. Industries are different. By way of exam-pie, a home builder might purchase a large quantity of lumber in year 1 in anticipation of building many houses in year 2, and thus experiencing material revenue increases in year 2. There is no record evidence suggesting that payday lenders booked working capital in this manner or that the 2018 working capital (which already supported hockey stick growth in that period) portended boom years ahead. That sort of story is not in the petitioners’ briefs themselves or any other part of the record. In other words, DFC’s loan growth had to come from somewhere and the petitioners never put their finger on where that would be.

Likewise, the Court of Chancery understood that the March Projections were designed to help sell the company at a favorable price, and thus assumed very strong growth through 2018. Had the petitioners’ expert believed that the working capital in the March Projections signaled another year of strong growth in 2019, and for. years after, it is difficult to understand why the Projections did not say that was so and why it was so. As the record before us stands, the petitioners’ assertion that those Projections silently .projected another period of above-market growth beyond 2018 is without support in the Projections themselves,( management testimony, or industry analysis.

As important, if one number is to encompass the future, as the perpetuity growth rate did here, and even if it should account for company-specific performance, it not only has to account for the possibility that the company might have another period of above-market growth, but also the possibility that it would fail altogether, or in the long run not keep up with the real growth of the economy. And, the original perpetuity growth rate used by the Court of Chancery for DFC was already bullish as it was nearly at the risk-free rate, and this assumed that DFC would grow at that rate forever. Adding another 0.9% to that assumption, by implying that the unbroken, sunny sky assumptions of the March Projections implicitly signaled another period of robust, above-market growth is an enormous step, which had to be rooted in record evidence that, the Chancellor had found to determine viable growth prospects justifying that huge move forward. • ■

b.

We next note that the Court of Chancery’s assumption that DFC would outpace the growth of the real economy did not take into account an important reality that is found undisputed in the record. DFC was not a startup in a brand new industry but had already experienced a period of strong growth. Since 1990, it had gone on a buying spree, with over 100 acquisitions resulting in, among other things, 900 retail stores by the time of the transaction. It had also experienced strong revenue growth: for example, from 2008-13, DFC’s European operations had enjoyed a 21.7% compound annual growth rate. And in the U.S. and Canada, DFC already had grown enormously in the past. More generally, DFC had more than one year of 20-30% year-over-year revenue growth. This was true of the payday lending industry as a whole. The. record thus suggests, if anything, a matured industry whose period of above-average growth was past.

c.

Nor can we find in the record any evidence supporting a reasonable inference that DFC was .actually primed for a new, extended period of high growth beyond the projection period in the March Projections that already implied robust growth. The absence of evidence here is. not surprising given that thé petitioners did not present an industry expert, rely upon management testimony, or even point.to analyst commentary on the likely growth of the payday lending industry in the markets where DFC operated. Instead, they solely presented at trial, and on reargument, the views of a professional expert in valuation. Determining the perpetuity growth rate of any company always hazards error as it involves an important prediction distilled into one number; calculating one based on a supplemental affidavit of a valuation expert not grounded in record evidence, or subject to cross-examination in the context of a reargument motion increases the speculative risk in that endeavor.

That danger was even higher here, where the Court of Chancery’s original discounted cash flow.model already was founded on projections- that the Chancellor himself was concerned were too rosy. And, there were other reasons to believe that the March Projections were too positive. Finding that the working capital set forth in those Projections implied another period -of materially higher growth was at odds with the Court of Chancery’s own finding that “DFC was navigating turbulent regulatory waters that imposed considerable uncertainty on the company’s future profitability, and even its "viability.” Those risk's were supported in the record by the fact that DFC’s long-term debt was noñ-investment grade and was on negative credit watch.-

Notably, less than three months after those Projections were approved, DFC missed its targets for the full 2014 fiscal year by about 10%. And, of course, these Projections predicted revenue and profit growth in the 11-12% and 19-21% ranges respectively, which was better than" much of DFC’s recent performance, and as good as many of the years during its faster-growth period. Looked at another way, the Projections involved the assumption that the company would experience 17.6% compound annual growth in operating profit when in the historical 2008-13 period its operating profit had experienced only 11% compound annual growth. This was a context where the -record reflects many reasons to suspect that .the reversal in revenue growth would continue into the future. For one thing, check cashing, one of DFC’s material businesses, was in decline because fewer' people used checks. For another, DFC' had 601 stores in the U.K. as of '2014, an area twice the size of Pennsylvania and slightly smaller than Oregon. How many new stores could they expect io open there?

And, the petitioners do not explain what exactly it is about 2018 that implies rapid growth for the next period. In their Motion for Reargument, the petitioners' simply state that “[a]s explained in'detail in the [expert affidavit], the working capital projections in the March Projections at the 10.72% discount rate adopted by the Court require-the application of a PGR higher than 3,1%.” The-affidavit isn’t-more illuminating. It states, based on-the original expert report, that “the last-explicit period’s revenues and operating margins, have not reached a steady-state,” and that because those Projections “reflect a $90 million increase in working capital for fiscal year 2018,” “a much higher PGR than 3.1%” is required. But, that does not explain why, even if the March Projections were not already optimistic, that increase in working capital would be sustained in a fashion that fits with a perpetuity growth rate 27% greater than the risk-free rate.

Given the real risk of default, the actual record of declining performance by the company, and DFC’s failure to meet the Projections before the transaction closed, a strong argument can be made that the March Projections should have been discounted, or some substantial weight given to another discounted cash flow model more balanced in terms of its considerations of the company’s vulnerability. Yet, despite these risks and rather gloomy outlook, the Court of Chancery swallowed the March Projections whole, generously giving DFC credit for a period of projected growth until 2018. Thus, the original perpetuity growth rate itself seems generous to the petitioners, in light of the evidence in the record. After all, as the petitioners’ expert admits, no company is likely over time to grow at a rate much faster than the rate of inflation, and that, at best, a company might reach the rate of nominal gross domestic product growth for the economies it operates in. The Court of Chancery’s initial perpetuity growth rate— 3.1% — already gave DFC credit for growing in perpetuity above the 2,31% median inflation rate and just a shave below the 3.14% risk-free rate that is viewed to be the ceiling for a stable, long-term growth rate.

The Court of Chancery’s decision is all the more puzzling because this was not the sort of situation where a company conducts an auction to sell itself and only after a winning bidder is locked in at a particular price does good news start to flow in. Rather, the facts here suggest the opposite: after Lone Star obtained exclusivity, the news about DFC just kept getting worse. In earlier parts of the process, in fact, potential buyers took a pass when DFC was in a stronger position.

d.

Not only that, but the robust historical growth across the entire industry had also triggered a multinational pushback by regulators concerned about payday lenders’ treatment of financially vulnerable citizens. And, the result of that pushback undermines the petitioners’ contentions that DFC was primed for a new spurt of growth, and that the historical relationship between revenues ' and working capital would remain the same. Beginning in 2012, DFC started to be regulated in moré than the “limited amount” it had been historically in the U.K, its most important. market. And, of course, this was also accompanied by greater regulatory scrutiny in the U.S. and other markets.

In contrast to the Canadian regulatory changes occurring around 2012, which had focüsed in part on aspects of payday lénd-ing that did not have as much effect on DFC’s preexisting businesses, the new regulations DFC was facing in the U.K. were both more strict and more likely to affect its business The proposed regulatory changes in the U.K. bear directly on the issue of whether the March Projections’ estimates of working capital involved an implicit prediction of another period of strong growth beyond 2018. As discussed earlier, the regulatory changes in the U.K. fundamentally involved a public policy decision that the payday lending industry was extracting excessively unfair returns from its customers. Thus, the changes that DFC confronted limited its ability to reap as much profit from each of its loan customers as it had in the past, by constricting such practices as rolling over debt repeatedly, using methods to reliably and automatically deduct payments from borrower accounts, and by requiring stricter assessments of creditworthiness. And, across all of its markets, this concern about whether the payday lending industry was fairly treating its clients pervaded regulatory comment and consideration, and portended a future where a greater number of loans would be required than in the past to generate the same profits. So, if anything, the record suggests that DFC’s lending was in the process of being less profitable. Even by the second half of 2013, DFC’s results began to reflect the U.K.’s new regulatory environment, including higher default rates and lower profitability, and that was before the Financial Conduct Authority’s more stringent regulation came into effect. The petitioners do not address these realities, beyond the statement that DFC’s revenues, lending volume, and working capital are related. But, these developments, which are supported by the record, contradict the unsupported contention of the petitioners, accepted by the Court of Chancery, that the relationship between DFC’s revenue and its working capital would remain the same.

e.

The petitioners’ argument on reargument was also in tension with their initial position as presented by their expert. The petitioners’ expert used a 2.7% perpetuity growth rate in his three-stage model and, in his alternative two-stage model, proposed a 3.1% perpetuity growth rate. And, both the two-stage and three-stage models used the March Projection’s working capital figures, which the Court of Chancery adopted over DFC’s expert’s modified working capital figures. In fairness to the petitioners’ expert, his three-stage model produced a result equivalent to a two-stage model using a 3.5% terminal growth rate, $17.90 per share, but it is still telling that he selected a lower terminal growth rate when constructing his standalone two-stage model, and that even that relatively high terminal growth rate was lower than the one he urged on reargument. Indeed, the petitioners’ initial expert report stated: “[bjased on my review of economists’ long-term growth estimates, DFC Global’s management projections and long-term growth rates in the record, it is my opinion that a reasonable long-term growth rate falls between the average estimates of the inflation rate (2.3%) and the risk-free rate as of the Appraisal Date (3.1%).”

Furthermore, it is difficult to square the petitioners’ contention on reargument that DFC was not approaching a point where it could be considered at steady state in 2018 to calculate the perpetuity value' with the beta that' the petitioners’ expert used in calculating DFC’s cost of capital. Beta measures expected market risk. It represents the covariance between the rate of return on a company’s stock and the overall market return. A stock with a beta of 1.0 should have an expected return equal to that of the market, and “[e]quity betas increase with the risk of the business.” DFC had a historical two-year weekly levered beta of 1.59. The petitioners’ expert relied on a relevered peer-based beta in addition to DFC’s relevered historical beta, reaching a beta range of .88-1.18 for his cost of capital calculation, “due to concern that DFC Global’s high leverage and the potential impact of the U.K. regulatory changes on DFC Global’s recent stock returns mean that its firm-specific beta estimate might not represent the best estimate of the Company’s long-term systematic risk, as well as to minimize the impact of measurement error from estimating beta based on a single company’s beta.” But, a beta around 1.0, which indicates that a company was reaching a point of maturation, suggests that the petitioners’ expert believed that DFC’s forward beta as of 2014 would be more akin the market as a whole rather than like its earlier one. Perhaps there is a way to reconcile the petitioners’ point that DFC’s beta should also be seen as like the average market beta as of 2014, but that it should still be seen beyond 2018 as a hard-charging growth company. But, the rear-gument record does not do so, and there is an obvious rub beiween these contrary inferences, with the only coherent principle being that using both together inflates DFC’s discounted cash flow value.

⅝* ⅜ H* ⅝

It may be that after the period covered by the March Projections, there is a reasonable basis to assume a perpetuity growth rate higher than the 3.1% originally assumed by the Court of Chancery. But, as noted, any assumption of this kind has to address not only the possibility for an additional period of growth higher than the economy as a whole, but also the risk of industry contraction, or, even worse, company insolvency. An assumption of a perpetuity growth rate of 4% not only assumed that DFC would keep pace with inflation, but in fact would markedly exceed it. If that assumption is to be based on the working capital used in the March Projections themselves, there has to be some reliable evidence that the working capital in those projections was in fact somehow designed to generate future outsized growth in the years after 2018; The why for that has to relate to' DFC’s business and industry. As it stands, the record has nothing of that kind in it.

If, upon remand, the Chancellor decides to rely upon a discounted cash flow analysis generating a value higher than his original model after, it was adjusted to use the March Projections’ working capital figures, he must identify a basis in the record to assume that after 2018 the company would continue to grow át a rate above the 3.14% risk-free rate, in view of the .reality that: the growth rate in the management projection period was already aggressive and involved projections that the company did not meet even in the short-term period before closing; the fact that the company had already had a lengthy period of aggressive growth that brought on regulatory counteraction; and, the absence of evidence in. the record suggesting that the company had the ability to continue to expand in its markets, given its prior periods of rapid expansion.

E.

We now reach the petitioners’ cross-appeal. On cross-appeal, the petitioners argue that the Court of Chancery abused its.discretion by giving weight to its comparable companies analysis. Indeed, they argue that the result of the discounted cash'flow model should have been given predominant weight, - and the deal price little, if any, weight.

As to the Chancellor’s comparable companies analysis; the petitioners object for three reasons: i) the Chancellor,. using EBITDA metrics from fiscal years 2014 and 2015 for the three calculations, relied on “trough years” for DFC’s performance; ii) the comparable companies analysis would have yielded wildly different results if single years had been used and that draws,into question its accuracy; and iii) none of the six companies selected as peers were, in fact, comparable to DFC. None of these arguments persuade this Court that the Chancellor abused his discretion.

The petitioners’ first contention about the comparable companies analysis amounts to a recitation of its general, unsupported contention that DFC was primed for a surge .in growth that .was missed by the markets because of regulatory uncertainty and that market-based methods of valuation are inherently unreliable except when things are going really well. But, we are unaware of an accepted corporate finance or economic theory that suggests that market-based insights into value become inherently unusable in downturns or because of regulatory change. It was well within the Chancellor’s discretion to view the comparable companies analysis as providing relevant insights into DFC’s value based on inferences from how the market valued companies in the same industry, facing most of the same risks.

The petitioners’ second contention about the comparable companies analysis in some ways contradicts the first. The fair value figure DFC’s expert and the Chancellor used was derived from the median of full year 2013 and 2014 and part year 2014 financials. If DFC, and the industry as a whole, were truly in a period of volatile financial performance due to regulatory uncertainty, priming them for future growth, a blend of three of the, most relevant years of financial results was a reasonable way to be more accurate as. to DFC’s future performance than attempting to guess the single year that is most representative. When the petitioners’ expert conducted his comparable companies analysis, which admittedly he did not use as part of his fair value calculation, he did essentially the same thing, but used the 75th percentile figures rather than median. But, as the Chancellor noted, the petitioners’ expert admitted “that using the, median or 50th percentile is a more common benchmark, and that this was the only valuation he could recall in which he used the 75th percentile.” Indeed, in some ways using the median-figures was giving DFC the benefit of the doubt because most of its operating metrics, including revenue, gross profit, EBITDA, and EBIT, were below the median. Only gross profit margin, EBITDA margin, and EBIT margin were at or above the 75th percentile. ■

The petitioners’ third argument for the unreliability of the Court of Chancery analysis of the respondent’s comparable companies estimate of fair value was that the peer group companies were not comparable to DFC. But, the six companies comprising the peer group used by the Chancellor and DFC’s expert were in fact a subset of the seven companies the petitioners’ expert used in his comparable companies analysis. Although the petitioners’ expert argued that “none of the comparable companies had a mix of businesses and geographic locations that were sufficiently similar” to DFC, there was ample evidence in the record to support the Chancellor’s decision that the six comparable companies both experts used were, in fact, sufficiently-comparable for this analysis. As the Chancellor observed:

Each of the six companies both experts used was comparable to DFC, as evidenced by the experts’ agreement on them and by their use in peer group analyses that six different firms (including DFC itself, Lone Star, and Houli-han) used to evaluate DFC for various reasons from April 2013 to June 2014. Four of these peer companies were used by all six firms in their analyses.

Finally, as to the petitioners’ argument that the discounted cash flow analysis was the most reliable indicator of fair value, and should have been given more weight than the comparable companies analysis, there were ample reasons for the Chancellor to doubt the reliability of the discounted cash flow model on this record. It was therefore not an abuse of discretion for him to consider other factors in reaching a decision about DFC’s fair value.

F.

Finally, we will address an issue implied in DFC’s argument, that the Court of Chancery’s decision to give equal weight to the deal price, its comparable companies valuation, and its discounted cash flow valuation cannot be justified by reference to the record. Because we have determined that the Court of Chancery’s reasons for giving the weight it did to the deal price were not supported by the record, we arguably do not need to reach this larger issue. But, because this issue is present in many appraisal cases, we will address it. When faced with briefs and expert reports written by highly-skilled litigators in concert with men and women of valuation science that often come to ridiculously varying positions, the Court of Chancery may well feel tempted to turn its valuation decisions into a more improvisational variation of the old Delaware Block Method, but one in which the court takes every valuation method put in the record, gives each equal weight, and then divides by the number of them. When life is sloppy and unpredictable, the visual appeal of a mathematical formula to create an impression of precision is understandable.

But, in keeping with our refusal to establish a “presumption” in favor of the deal price because of the statute’s broad mandate, we also conclude that the Court of Chancery must exercise its considerable discretion while also explaining, with reference to the economic facts before it and corporate finance principles, why it is according a certain weight to a certain indicator of value. In some cases, it may be that a single valuation metric is the most reliable evidence of fair value and that giving weight to another factor will do nothing but distort that best estimate. In other cases, it may be necessary to consider two or more factors. As one appraisal treatise points out, “laying down in advance fixed rules that state how competing approaches are to be weighted is impossible.” What is necessary in any particular case though is for the Court of Chancery to explain its weighting in a manner that is grounded in the record before it. That did not happen here. In this case, the decision to give one-third weight to each metric was unexplained and in tension with the Court of Chancery’s own findings about the robustness of the market check.

III.

Taken together, our findings require us to reverse and remand this case to the Chancellor to reassess his conclusion as to fair value in light of our decision. We do not retain jurisdiction, and leave the Chancellor with the discretion to address the open issues using procedures he finds the most helpful. The Chancellor need not reopen the evidentiary record, and the extent of further submissions of the parties, if any, is entirely within his discretion, based on his determination as to what is most helpful to him. 
      
      . 8 Del C. § 262(h).
     
      
      . 11 A.3d 214 (Del. 2010).
     
      
      . In re Appraisal of DFC Glob. Corp., 2016 WL 3753123, at *21 (Del. Ch. July 8, 2016).
     
      
      . Id. at *22. .
     
      
      .App. to Appellant's Opening Br. at A844 (Petitioners’ Expert Report). This Opinion will refer to the Petitioners’ Expert Report as PER, and the Petitioners’ Expert Rebuttal Report as PERR. The Respondent’s Expert Report will be referred to as RER, and the Respondent’s Expert Rebuttal Report as RERR. In general, citations to the record have been shortened to a short name of the document, "at,” and the appendix page number. Page numbers beginning with "A” refer to the Appendix to the Appellant’s Opening Brief, and page numbers beginning with "B” refer to the Appendix to the Appellees/Cross-Appellants’ Answering Brief and Opening Brief on Cross-Appeal. Certain Joint Exhibits, which did not appear in the appendices are cited as JX_, "at,” and the relevant page number of that document.
     
      
      . PER at A847.
     
      
      . DFC, Form 10-K, 2013 at 4, 7. We take judicial notice of DFC’s public filings with the SEC. See, e.g., Hazout v. Tsang Mun Ting, 134 A.3d 274, 280 n.13 (Del. 2016).
     
      
      . JX 409: DFC Investor Presentation at A444.
     
      
      . JX 487: DFC, Rating Agency Presentation at B253.
     
      
      . JX 309: DFC Global Corp. Investor Presentation at A388.
     
      
      . RER at A974.
     
      
      . RER at A977.
     
      
      . Id.
      
     
      
      . Id. at A974.
     
      
      . DFC,. Form 1.0-K, 2008 at 32 (2004-08 , figures): DFC, Form 10-K, 2013 at 39 (2009-13 figures); see also RER at A977.
     
      
      . RER at A986.
     
      
      . Id. at A987.
     
      
      ; JX 462: David M. Scharf & Jeremy Frazer, DFC Global Corp., JMP Securities at 1.
     
      
      . PERat A893.
     
      
      . RER at A1024 n.407; PER at A882.
     
      
      . PER at A882.
     
      
      . Id.
      
     
      
      . JX 533: Igor Koyfman & Kevin Cole, Sterling Mid-Holdings Assigned ‘B’ Rating, DFC Global ‘B’ Rating Affirmed, Off Watch on Sale Approval; Outlooks Negative, Standard & Poor’s Rating Servs. at 3.
     
      
      . JX 358: Bill Carcache, DFC Global Corp., Nomura at 1.
     
      
      . JX 468: Igor Koyfman & Kevin Cole, DFC Global Ratings Placed on CreditWatch Negative After Weaker Business Performance and Definitive Buyout Agreement, Standard & Poor’s Rating Servs. at 2.
     
      
      . JX 533, supra note 23, at 3.
     
      
      . 2016 WL 3753123, at *3.
     
      
      . DFC, Form 10-K, 2013 at B144.
     
      
      . JX 478: Consumer Lending, First Research at 3.
     
      
      . Testimony of Kenneth Kaminski at A252.
     
      
      . RER at A993.
     
      
      . JX 478, supra note 29, at 4.
     
      
      . • Testimony of John Gavin, DFC former board member at A154.
     
      
      . Id. at A155 (recording testimony that the board was "always considering strategic alternatives .... But we probably got a little more focused on it in the 2012 time frame. As the regulatory environment looked to become more onerous in the U.K., and that was the biggest part of our business, we decided that we needed to make sure we understood what all of our options were ....”).
     
      
      . PER at A859; RERat A981.
     
      
      . RER at A982.
     
      
      . JX 320: Moshe Orenbuch & Lesley Robert-shaw, DFC Global Corp., Credit Suisse at 1.
     
      
      . PER at A945.
     
      
      . Id.
      
     
      
      . Stipulated Joint Pre-Trial Order at Al 16.
     
      
      . Id.
      
     
      
      . 2016 WL 3753123, at *4.
     
      
      . PER at A945.
     
      
      . Id. at A936.
     
      
      . RER at A1015; DFC, Form 10-K, 2013 at 82.
     
      
      . JX 444: March Projections Email at A475; id. at A477.
     
      
      . PER at A883.
     
      
      . JX 444: March Projections Email at A477; RER at A1008-09.
     
      
      . Although the Court of Chancery’s opinion refers to a peer group of nine companies, 2016 WL 3753123, at *19, that group was used by the petitioners’’ expert for beta estimation only and not'the comparable compa- . nies analysis, compare PER at A949, id. at A950, and id. at A951, with id. at A952; see also RERR at A1070.
     
      
      . PER at A907-11, A942-44.
     
      
      . Id. at A911.
     
      
      . The petitioners’ expert did not give the comparables valuation methodology any weight because, according to that expert, none of the peer companies were sufficiently similar to DFC and, the petitioners’ expert argued, multiples-based valuation methods do not necessarily reflect the fundamental value of a company, do not allow for the inclusion of company-specific operating characteristics, and do not take into account expected long-term growth in cash flow. The last argument in particular is; of course, odd. The whole point of a comparables analysis is to infer the value of the ■ subject company by looking at how the market views the value of other comparable companies. Joshua Rosenbaum & Joshua Pearl, Investment Banking 11 (2009). The market’s assessment of the industry and the comparables are, of course, supposed to -be primarily based in its view of the future earnings.
     
      
      . PER at A937; JX 402: John Hecht & Kyle Joseph, Financial Services: Specialty Finance, Stephens (March 6, 2014), at 19.
     
      
      . RER at A1034.
     
      
      . 2016 WL 3753123, at *6.
     
      
      . Id. at* 16,
     
      
      . Id. at *17.
     
      
      . Id. (emphasis added).
     
      
      . Id. at *20.
     
      
      . Id. at *21 (emphasis added).
     
      
      . Id.
      
     
      
      . Id.
      
     
      
      . Id. (emphasis added).
     
      
      . Id. at *22.
     
      
      . Id.
      
     
      
      . Id.
      
     
      
      . Id.
      
     
      
      . Id. at *23.
     
      
      
        .Id.
      
     
      
      . The respondent’s expert derived that figure by only replacing the working capital figures in the Court of Chancery’s model. In response to some of the petitioners' other contentions in their Response to the respondent’s motion, he used the petitioners’ expert’s model and derived a $8.30 per share value from the discounted cashflow model and an $8.62 per share fair value. Respondent’s Expert's Aff. on Reargument at A1389-90.
     
      
      . Id. at A1388, A1390.
     
      
      . Petitioners’ Reargument Motion at A1341-49.
     
      
      . Id. at A1352.
     
      
      . Id.
      
     
      
      . Appellant’s Opening Br. Ex. B at 5 (Rear-gument Order).
     
      
      . Id.
      
     
      
      . Id. at 6.
     
      
      , Petitioners’ Expert's Aff, .on Reargument at A1352-S3,
     
      
      . Golden Telecom, Inc. v. Glob. GT LP, 11 A.3d 214, 217 (Del. 2010).
     
      
      . In re Shell Oil Co., 607 A.2d 1213, 1219 (Del. 1992).
     
      
      . Respondent's Pretrial Brief at A58.
     
      
      . Respondent’s Post-Trial Brief at A1271-81.
     
      
      . Sup. Ct. R. 8.
     
      
      . 11 A.3d 214 (Del. 2010). Golden Telecom was an odd case to argue for deference to the deal price. The transaction in this case and the ones in the many cases when the Court of Chancery has found that the deal price was the best evidence of value reflected the results of a non-conflicted, open market check. E.g., In re PetSmart, Inc., 2017 WL 2303599, at *27-*31 (Del. Ch. May 26, 2017); Merion Capital LP v. BMC Software, Inc., 2015 WL 6164771 (Del. Ch. Oct. 21, 2015); LongPath Capital, LLC v. Ramtron Int’l Corp., 2015 WL 4540443, at *25-*26 (Del. Ch, June 30, 2015); Merlin P'rs LP v. AutoInfo, Inc., 2015 WL 2069417 (Del. Ch. Apr. 30, 2015); In re Appraisal of Ancestry.com, Inc., 2015 WL 399726 (Del. Ch. Jan. 30, 2015); Huff Fund Investment Partnership v. CKx, Inc., 2013 WL 5878807, at *11-*14 (Del. Ch. Nov. 1, 2013); Union Illinois 1995 Inv. Ltd. P’ship v. Union Fin. Grp., Ltd., 847 A.2d 340, 357-58 (Del. Ch. 2004). By contrast, the transaction in Golden Telecom was conflicted and did not involve a process whereby buyers not tied to the company's major stockholders would have felt welcome to bid and succeed. In fact, Golden Telecom’s two largest shareholders owned more of the buyer than they did of Golden Telecom. Glob. GT LP v. Golden Telecom, Inc., 993 A.2d 497, 508 (Del. Ch. 2010), aff'd, 11 A.3d 214 (Del. 2010).
     
      
      . Golden Telecom, 11 A.3d at 216.
     
      
      . 8 Del. C. § 262.
     
      
      . Id. at § 262(h).
     
      
      . Golden Telecom, 11 A.3d at 217.
     
      
      . Id. at 217-18 (second emphasis added).
     
      
      . 457 A.2d 701 (Del. 1983). Weinberger was itself not an appraisal case but this Court recognized its interpretation of the appraisal statute as binding on appraisal proceedings as well. See, e.g., Cede & Co. v. Technicolor, Inc., 684 A.2d 289, 296 (Del. 1996).
     
      
      . Edward P. Welch et al., Folk on the Delaware General Corporation Law§ 262.10, at 9-229 (6th ed. 2017).
     
      
      . Joseph Evan Calio, New Appraisals of Old Problems: Reflections on the Delaware Appraisal Proceeding, 32 Am. Bus. L.J. 1, 30 (1994).
     
      
      . Paskill Corp. v. Alcoma Corp., 747 A.2d 549, 555 (Del. 2000).
     
      
      . Cede & Co. v. Technicolor, Inc., 1990 WL 161084, at *18 n.39 (Del. Ch. Oct. 19, 1990).
     
      
      . Folk, supra note 91, § 262.10
     
      
      . Bradford Cornell, Corporate Valuation 39 (1993) (describing, in a book published in 1993, the “voluminous” literature on the efficient market hypothesis and pointing to two papers, including one from 1970, as the "best summaries”); Richard A. Brealey et al.. Principles of Corporate Finance 214 (2008) ("In the mid-1960s three economists — William Sharpe, John Litner, and Jack Treynor — produced an answer to [the problem of determining expected risk premia]. Their answer is known as the capital asset pricing model or CAPM.”); Calió, supra note 92, at 48 n.222 (“A - 1975 survey of 33 major corporations revealed that 94% of those companies used the discounted cash flow technique to evaluate investment projects.”).
     
      
      . 60 Del. Laws, c. 371, § 7 (1976) (“[T]he Court shall appraise the shares, determining their fair value exclusive of any element of value arising from the accomplishment or expectation of the merger.”).
     
      
      . 63 Del. Laws, c. 25, § 14 (1981) (“In determining such fair value, the Court shall take into account all relevant factors.”).
     
      
      . Weinberger, 457 A.2d at 714.
     
      
      . Id. at 704.
     
      
      . Id. at 713.
     
      
      . See cases cited supra note 84.
     
      
      . 2016 WL 3753123, at *20 ("The merger price in an arm’s-length transaction that was subjected to a robust market check is a strong indication of fair value in an appraisal proceeding as a general matter and this Court has attributed 100% weight to-the market price in certain circumstances.”); see also, e.g., cases cited supra note 84.
     
      
      . See, e.g., Cornell, supra note 96, at 47 (“[T]he [efficient market hypothesis] .states that the market assessment of value is more accurate, on average, than that of'any individual, including an appraiser.”); Barry M. Wertheimer, The Shareholders’ Appraisal Remedy and How Courts Determine Fair Value, 47 Duke L.J. 613, 655 (1998) ("The best evidence of value, if available, is third-party sales value.”); Brealey et al., supra note 96 at 373; Burton G. Malkiel, Are Markets Efficient?, Wall St. J.(Dec. 28, 2000) ("Most of us economists who believe in this efficient market theory do so because we view markets as amazingly successful devices for reflecting new information rapidly and, for the most part, accurately.”).
     
      
      . See Brealey et al., supra note 96 at 373.
     
      
      . 8 Del. C. § 262.
     
      
      . 564 A.2d 1137, 1144 (Del. 1989).
     
      
      . See e.g., Cede & Co., 684 A.2d at 298; TriCont'l Corp. v. Battye, 74 A.2d 71, 72 (Del. 1950).
     
      
      . Cavalier Oil, 564 A.2d at 1144.
     
      
      . Id. at 1145.
     
      
      . Id. at 1144 (“[T]he company must be first valued as an operating entity by application of traditional value factors, weighted as required, but without regard to post-merger events or other possible business combinations.”). The Court later said that, in order to value a company as a going concern, synergies must be excluded. M.P.M. Enterprises, Inc. v. Gilbert, 731 A.2d 790, 797 (Del. 1999) (”[S]ection 262(h) requires that the Court of Chancery discern the going concern value of the company irrespective of the synergies involved in a merger.”).
     
      
      . Union Illinois 1995 Inv. Ltd. P’ship v. Union Fin. Grp., Ltd., 847 A.2d 340 (Del. Ch. 2004).
     
      
      . Id. at 356.
     
      
      . 8 Del. C. § 262(h).
     
      
      . E.g., Harold Winter, Issues in Law & Economics 39 (2017) ("To an economist, when considering a seller 'who is willing, but not required to sell’ a property at some price, that price would have to exceed a value based on whatever is important to the seller.”); N. Gregory Mankiw, Principles of Economics 390 (8th ed. 2016) ("According to neoclassical theory, the amount paid to each factor of production depends on the supply and demand for that factor.”).' This understanding has a long pedigree. E.g., Alfred Marshall, Principles of Economics 8 (1895) (citing Adam Smith and observing "[t]he value ... of one thing in terms of another at any place and time, is the amount of that second thing which can be got there and then in exchange for the first.”).
     
      
      . Applebaum v. Avaya, Inc., 812 A.2d 880, 889-90 (Del. 2002); see also Poole v. N. V. Deli Maatschappij, 243 A.2d 67, 70 n.1 (Del. 1968) ("Fair market value is defined as ... the price which would be agreed upon by a willing seller and a willing buyer under usual and ordinary circumstances, after consider- ' ation of all available uses and purposes, with- ■ out any compulsion upon the seller to sell or upon the buyer to buy."); State ex rel. Smith v. 0.15 Acres of Land, More or Less, in Mew Castle Hundred, New Castle Cty., 53 Del. 372, 376, 169 A.2d 256, 258 (Del. 1961) (“Fair market value has been defined ... as the 'price which would be agreed upon by a willing seller and a willing buyer under usual and ordinary circumstances, without any compulsion whatsoever on the seller to sell or the buyer to buy’ ”) (quoting Wilmington Housing Auth. v. Harris, 47 Del. 469, 93 A.2d 518, 521 (Del. 1952)).
     
      
      . One of the reasons, of course, why a •control block trades at a different price than a minority block is because a- controller can determine key issues like dividend policy.
     
      
      . Of course, some businesses provide certain non-common benefits, such as those that might come from owning a sports team or entertainment business, beyond what their cash returns-would suggest. But, the typical approach teaches "[cjompanies create value by investing capital to generate future cash flows at rates of return that exceed their cost of capital.” Tim Roller et al„ Valuation: Measuring and Managing the Value of Companies 15 (2010); see also id. at 101 ("In broad terms, a company’s value is driven by its ability to earn a healthy return on invested capital (ROIC) and by its ability to grow. Healthy rates of return and growth result in high cash flows, the ultimate source of value.”). This is, after all, one of the reasons why discounted cash flow models are so often used in appraisal proceedings when the respondent company was not public or' was not sold in an open market check: “The enterprise [discounted cash flow] model is a favorite of academics and practitioners because it relies solely on how cash flows in and out of the company.” Id. at 115. The reason for that is not that an economist wouldn’t consider the best estimate of a private company’s value to be the price it sold at in an open, sale process of which all logical buyers were given fulhinformation and an equal opportunity to compete. Rather, the reason is that if such a process did not occur, corporate finance instructs that the value of the company to potential buyers should be reflected in its ability to generate future cash flows.
     
      
      
        . See, e.g., Brealey et al. supra note 96, at 91 ("This discounted-cash-flow (DFC) formula for the present value of a stock is just the same as it is for the present value of any other asset. We just discount the cash flows — in this case the dividend stream — by the return that can be earned in the capital market on securities of equivalent risk.”).
     
      
      . See e.g., Cornell, supra note 96, at 35-38.
     
      
      . Koller et al., supra -note 118, at 326 (”[T]he extent to which company valuations based on the fundamental approach have matched stock market values over the past four decades is remarkable.”); id. ("[MJanag-ers can safely assume that share prices reflect the markets’ best estimate of. intrinsic value.”); id. at 333 ("Market valuation levels are determined by the company’s absolute level of long-term expected growth and performance — that is, expected revenue and earnings growth and. expected ROIC.”); id. at 354 . (”[S]tock price data suggest that the market digs deeply beneath not just reported earnings but all of a company's accounting information in order to understand the underlying economic fundamentals.”).
     
      
      . Brealey et al., supra note 96, at 373.
     
      
      . Id. at 13.
     
      
      . See Rosenbaum & Pearl, supra note 52, at 109 (“[Discounted cash flow models are] an important alternative to market-based valuation techniques .... A [discounted cash flow model] is also valuable when there are limited (or no) pure play, peer companies or comparable acquisitions.”)’; see also Cornell, supra note 96, at 100 ("The strength of [a discounted cash flow model] is that it can be applied in virtually any situation”).
     
      
      . See, e.g., Cornell, supra note 96, at 35-38.
     
      
      . Cinerama, Inc. v. Technicolor, Inc., 663 A.2d 1134, 1143 (Del. Ch. 1994), aff'd, 663 A.2d 1156 (Del. 1995).
     
      
      . Revlon, Inc. v. MacAndrews & Forbes Holdings, Inc., 506 A.2d 173, 182 (Del. 1986).
     
      
      . Unocal Corp. v. Mesa Petroleum Co., 493 A.2d 946, 955 (Del. 1985).
     
      
      . G. Andrade, M, Mitchell, & E. Stafford, New Evidence and Perspectives on Mergers, 15 J. Econ. Persp. 103 (2001).
     
      
      . E.g., Bos. Consulting Grp. & Technishe Universitat München, Divide and Conquer: How Succesful M & A Deals Split the Synergies 9 (2013) (“To arrive at a transaction price acceptable to the seller, in most cases,’ the acquirer must agree to share expected synergies.”).
     
      
      . As to this point, it is notable that under the leading corporation statute used outside of Delaware, the Model Business Corporation Act, an appraisal petition cannot be filed in a public company merger, for cash or the stock of another public company, unless it is an “interested transaction,” Model Bus. Corp, Act §§ 13.02(b) (Am. Bar Assoc. Bus. L. Section 2016) (denying appraisal'rights’for shareholders of public companies who receive cash or stock in a merger unless the merger is an "interested transaction”); 13.01 (defining "interested transaction”). In those cases, stockholders who wish to challenge the merger must do so by filing an equitable action arguing that the merger. resulted from a breach of fiduciary duty.
     
      
      . Koller, et al., supra note 118, at 434-35.
     
      
      . Andrade et al, supra note 129, at 110; cf. U. Malmendier et al., "Winning by Losing; Evidence on the Long-Run Effects of Mergers,” NBER Working Paper No. 18024, Apr, 2012 (describing findings that, in close bidding contests for corporate control, winners tend to underperform losers over the following three years).
     
      
      . 2016 WL 3753123, at *6; PER at A935; see also supra chart accompanying note 19.
     
      
      . PER at A883.
     
      
      . 2016 WL 3753123, at *22.
     
      
      . Since the 1980s, a robust economics literature has developed around the premise that "unanticipated changes in regulation result in a current change in security prices, and the price change is an unbiased estimate of the value of the change in future cash flows to the firm.” G. William Schwert, Using Financial Data to Measure Effects of Regulation, 24 J.L. & Econ. 121, 121-22 (1981); see also John J. Binder, Measuring the Effects of Regulation with Stock Price Data, 16 RAND J. Econ. 167, 181 (1985) (conducting event studies around regulatory changes in regulated industries and finding "it is extremely difficult to find announcements in the regulatory process that are unanticipated by the market, even when the announcements are carefully studied to eliminate those that do not appear to have a major effect on expectations”). And, the corollary of that is "[i]f regulation has implications for the value of securities, the effects of regulation are impounded into prices at the time when they are first anticipated. Subsequent security returns only reflect the equilibrium expected returns to assets of comparable risk, unless the actual effects of regulation deviate from the originally anticipated effects.” Schwert, supra, at-122.
     
      
      . See supra pp. 353-55.
     
      
      . JX 554: John Hect et al„ Initiating on Non-Prime Cons. Fin, Jeffries at 1. •
     
      
      . See sources cited, supra note 137.
     
      
      . See also supra chart accompanying note 19.
     
      
      . Id.
      
     
      
      . Cooper v. Pabst Brewing Co., 1993 WL 208763, at *8 (Del. Ch. June 8, 1993) ("Where there is an established market for a corporation’s stock, market value must be considered in appraising the value of the corporation’s shares.”); Cede & Co., 1990 WL 161084, at *18 (“[M]arket price is a relevant factor of some weight where the market is active and where no special consideration indicating that it should be given no weight is present.”).
     
      
      . See, e.g., Brealey et al., supra note 96, at 373 (“In an efficient market you can trust prices, for they impound - all available information about the value of each security.”); ' Cornell, supra note 96, at 39 ("[0]n average, market forecasts and market valuations will be at least as accurate as those produced by individual investors and appraisers, no matter how expert.”).
     
      
      . Admittedly, the petitioners point to evidence from Lone Star's files indicating that it ' thought it was taking an opportunity to buy DFC at trough pricing and that it could reap the upside of this risk. Stipulated Joint PreTrial Order at A136, One would expect a buyer to think it made a wise decision with an upside, and, to be candid,, it is in tension with the statute itself to argue that the subjective view of post-merger value of the acquirer can be used to value the respondent company in an appraisal, as ■ the statute’s, exclusion of transaction-specific value seems to be directed at the concern a buyer who pays fair value should not have its economic upside for faking that risk expropriated in the appraisal process, a result that if it were the law, would discourage sales transactions valuable to selling stockholders. That a buyer views itself as having struck a good deal is far from reliable evidence that the resulting price from a competitive bidding process is an unreliable indicator ' of fair value. For starters, here the Court of Chancery’s own comparable companies analysis and that of the petitioners’ expert if he used the median multiple resulting from his analysis suggested that Lone Star was .paying a substantial premium to gain control of DFC at $9.50. So did the Court of Chancery’s discounted cash flow model when calculated in accordance with the original assumptions, the Court of Chancery adopted in its post-trial decision. And, one would think that the buyer who paid the highest price in a competitive process had the most confidence there was ati upside and must think that post-purchase gains would justify its purchase; otherwise, no sale would ever occur in the world. That Lone Star expected to profit does not mean that the collective view of value that results from the deal price is not a reliable indicator of fair value; to hold otherwise, is to adopt a non-binary view of fair value in which only the upside view of what could happen in the future is taken, into account. Perhaps most importantly, under the Court of Chancery's view, the discounted cash flow value of DFC was somehow 62% above the value implied by a consideration of its worth when valued on par with public companies like it, and 38% above the deal price resulting from a lengthy open market check. This suggests that daily traders in the company’s equities, Wall Street lenders who passed on the chance to refinance DFC's debt and to syndicate even more acquisition debt, and the types of buyers who would consider buying a payday lender all missed out on a big chance to reap outsized gains,
     
      
      . DFC Rating Agency Presentation at B261,
     
      
      . Id. at B262.
     
      
      . 2016 WL 3753123, at *22.
     
      
      . See id. at *3 (“On January 30,. 2014, DFC cut its adjusted EBITDA projections again, lowering its fiscal year 2014 forecast from $200-240 million to $170-200 million, noting the continued difficulties with the U.K. regulatory transition.’’).
     
      
      . JX 320, supra note 37, at 1; JX 468, supra note 25, at 2-3.
     
      
      . 2016 WL 3753123, at *22.
     
      
      . Consistent with the market’s reaction, there is also evidence in the record to support the proposition that DFC was not going to navigate the U.K. regulatory changes it faced in 2014 without experiencing commercial losses as it did the’ Canadian changes. See supra page 354.
     
      
      . Brealey'et al., supra note 96, at 129-30 (describing internal rates of return as a prevalent form of analysis for companies engaging in new.projects); see also id. at 118 fig. 6.2 (describing survey result that seventy-six percent of CFOs use internal rate of return for evaluating investment projects); cf. id. at 891-93 (arguing that mergers should be analyzed based on determining if the merger results in economic gain, i.e., if the two firms are worth more together than apart).
     
      
      . Indeed, were it true that hitting an internal rate of return was somehow incompatible with .achieving fair value, it would be.hard to explain the results of studies that have shown that for specific sets of targets in auction-type situations, financial sponsor buyers, who ostensibly are the most disciplined users of internal rates of return to make investment decisions, place a higher value on them than strategic buyers, despite the conventional wisdom that strategic buyers can count on greater value from mergers through synergies. Alexander S. Gorbenko & Andrey Malenko, Strategic and Financial Bidders in Takeover Auctions, J. Corp. Fin. (forthcoming) (manuscript 4-5), https://ssrn.com/abstract= 1559481. And, of course, private equity buyers have to compete with strategic buyers and thus the potential synergy gains of other buyers and its effect on the bids they can make will influence the price any buyer of any type has to pay to prevail/ Relatedly, the absence of synergistic buyers for a company is itself relevant to its value.
     
      
      . 2016 WL 3753123, at *21.
     
      
      . William J. Carney, Corporate Finance 195 (2005) (comparing equity and debt as substitutes and noting that debt instruments “are promises to pay a fixed sum on a specified date, together with periodic payments of interest” distinct from equity, which is "a residual claim, entitled to all remaining assets on liquidation after all other claims are paid.”).
     
      
      . Respondent's Expert’s Aff. on Reargument at A1338.
     
      
      . Petitioners’ Reargument Motion at A1342.-
     
      
      . Id.
      
     
      
      . Id. at A1342-44.
     
      
      . Id. at A1344.
     
      
      . Id.
      
     
      
      . Id. at A1345. The lack of development of the record for this crucial change to the discounted cash flow model is also a good illustration of why all parties are poorly served . when this sort of material change is raised for the first time in a motion for reargument.
     
      
      . Respondent’s Opposition to Petitioners’ Reargument Motion at A1376-77.
     
      
      . Id. at A1381.
     
      
      . Appellant’s Opening Br. Ex. B at 4-6 (Reargument Order).
     
      
      . Id. at A1342.
     
      
      . Aswath Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Company 323-24 (2002).
     
      
      , Rosenbaum & Pearl, supra note 52, at 132; Roller, supra note 118, at 214.
     
      
      . Petitioners’ Expert’s Aff. on Reargument at A1351.
     
      
      . Roller, supra note 118, at 214; Cornell, supra note 96, at 144; cf. Brealey et al., supra note 96, at 95 (”[R]esist the temptation to apply the [constant-growth discounted cash flow] formula to firms having high current rates of growth. Such growth can rarely be sustained indefinitely, but the constant-growth DCF formula assumes it can.”).
     
      
      .Roller Et Al, supra note 118, at 95-96 ("[D]eveloping reasonable [long-term growth] projections is a challenge, especially given the upward bias in growth expectations .... [G]rowth decays Very quickly; high growth is not sustainable for the typical company. [CJompanies struggle to maintain high growth because product life cycles are finite and growth gets more difficult as companies get bigger.”).
     
      
      . PER at A844.
     
      
      . Id. at A936.
     
      
      . Id.
      
     
      
      . 2016 WL 3753123, at *22.
     
      
      . Id.
      
     
      
      . PER at A883.
     
      
      . JX 444: March Projections Email at A477; RER at A1008-09.
     
      
      . RER at A973.
     
      
      . United Kingdom; Geography, CIA World Factbook, https://www.cia.gov/libraiy/ publications/the-world-factbook/geos/uk. html#Geo (last visited July 18, 2017).
     
      
      . Petitioners’ Reargument Motion at A1347.
     
      
      . Petitioners' Expert’s Aff. on Reargument at A1351.
     
      
      . Id. at A1353.
     
      
      . PER at A877.
     
      
      . Id. at 878. The petitioners’ expert also points out that at least some economists believe that the ceiling for a company’s long-term growth should be the relevant risk-free rate, which, here, is lower than nominal gross domestic product growth. Id.
      
     
      
      . RER at A1007.
     
      
      . PER at A847.
     
      
      . Id.
      
     
      
      . Testimony of John Gavin, DFC 'former board member at A184 (describing the new Canadian regulations as “at price points and with restrictions that were very palatable and allowed us to operate profitably. That’s not where the U.K. ended up.’’).
     
      
      . "Melissa Soper, Senior Vice President-of Government Relations and Corporate Administration, described the United Kingdom’s restrictions on relending as 'more stringent' as compared to those in Canada.” RER at A994.
     
      
      . See supra pp. 353-55.
     
      
      . RER at A990 (reporting DFC “experienced higher loan defaults” during U.K. regulatory transition); id. (describing 32% year-over-year increase in loan loss provisions from 2012-13); id. ("[DFC] experienced higher costs and higher delinquencies as a result of the change from automatically withdrawing funds from customers’ accounts .... ”); id. at A1015 (describing DFC’s shifts in lending that required more working capital); id. at A1016 (finding that working capital as a •percentage of revenue "could increase over time”); JX 309: DFC Investor Presentation at A403 (showing 29% jump in loan losses as U.K. regulatory transition began); JX 444: March Projections Email at A510 (describing “lower effective pricing” on new loan types being used more frequently to help comply with U.K. regulations).
     
      
      . Id. at A990. These effects continued in 2014. Id. at A1007-08.
     
      
      . Petitioners' Reargument Motion at A1344-45.
     
      
      . 2016 WL 3753123, at *17.
     
      
      . Id. at *16.
     
      
      . PER at A905.
     
      
      . Id. at A879-80 (emphasis added).
     
      
      . Shannon P. Pratt & Roger J. Grabowski, Cost of Capital 271 (5th ed. 2014) (“[B]eta is a function of the expected relationship between the return on an individual security (or portfolio of securities) and the return on the market.”).
     
      
      . Rosenbaum & Pearl, supra note 52, at 128; Shannon P. Pratt & Roger J. Grabowski, Cost of Capital in Litigation 35 (2011); see also id. at 160.
     
      
      . Id. at 35.
     
      
      . Pratt & Grabowski, supra note 200, at 203; id. at 194 ’("Many high-tech companies are good examples of stocks with high betas.... The classic example of a low-beta stock would be a utility that has not diversified into riskier activities.”).
     
      
      . "Published and calculated betas for publicly traded stocks typically reflect the capital structure of each respective company. These betas are sometimes referred to- as levered betas, that is, betas reflecting the leverage in the company's capital structure.” Pratt & Gra-bowski, supra note 200, at 243. “If the leverage of the [company to be valued] differs significantly from the leverage of the [comparable companies] selected for analysis ... it typically is desirable to remove the effect that leverage has on the betas,” i.e., unlevering, "before using them as a proxy to estimate the beta of the subject company ... on one or more assumed capital structures (i.e., relever the beta).” Id. at 244.
     
      
      . PER at A952.
     
      
      . A887-88 (emphasis added).
     
      
      . Pratt & Grabowski, supra note 200, at 211 ("Over time, a company’s beta tends toward its industry average beta.”).
     
      
      . This would, of course, not be the first case in which experts’ assumptions about future growth and their estimate of forward-looking beta were at odds. In Golden Telecom, Glob. GT LP v. Golden Telecom, Inc., 993 A.2d 497 (Del. Ch. 2010), aff'd, 11 A.3d 214 (Del. 2010), for example, the respondent’s expert opined that the subject company did not have any reasonable expectations for above-market growth, but that its beta should be relatively high, id, at 511-12, 518, By contrast, the petitioners' expert testified that the company would grow rapidly beyond the projection period, but argued for using a forward beta trending toward a. lower industry average, using betas from companies operating in more mature markets. Id. at 513, 518. As in this case, what tended to render, their analy-ses consistent, was that by using contrary inferences for different parts of their models, they generated results benefitting, their clients. What these situations make clear is the often impossible task the Court >of Chancery has in sifting through this 'kind of input to make an underlying determination of fair value that is reliable.
     
      
      . PER at A910-11.
     
      
      . 2016 WL 3753123, at *20.
     
      
      . PER at A942,
     
      
      . 2016 WL 3753123, at *20.
     
      
      . PER at A908.
     
      
      . E.g., id, at A938-41.
     
      
      . 2016 WL 3753123, at *9.
     
      
      . Cornell, supra note 96, at 263. That treatise recommends great weight to market-based approaches and caution with discounted cash flow models because those models are "easily abused” such that "value can be created out of thin air by optimistic forecasting. Therefore, the weight applied to a [discounted cash flow model] forecast should be directly proportional to the confidence that can be placed in the cash flow forecasts.” Id. at 264.
     