Business Valuation Review — Winter 2010 Page 1
Business Valuation Review
Volume 29 • Number 4
© 2010, American Society of Appraisers
Cost of Capital in Appraisal and Fairness Cases
Gilbert E. Matthews, CFA
include proof of value by any techniques or methods
which are generally considered acceptable in the financial
community.”3 It added that “elements of future value,
including the nature of the enterprise, which are known
or susceptible of proof as of the date of the merger and
not the product of speculation, may be considered” in
appraisals under Delaware law.4 It is in this decision that
the Supreme Court first approved the use of the DCF
method in a Delaware appraisal case. It pointed out
that the acquiring company’s officers had used the DCF
method in evaluating UOP’s earnings potential.
Since Weinberger, Delaware courts have adopted the
DCF method as their preferred method of valuation.5
A 2005 decision stated:
The DCF model of valuation is a standard one that gives
life to the ﬁ nance principle that ﬁ rms should be valued
based on the expected value of their future cash ﬂ ows,
discounted to present value in a manner that accounts for
risk. The DCF method is frequently used in this court and,
I, like many others, prefer to give it great, and sometimes
even exclusive, weight when it may be used responsibly.6
While DCF analyses have become the dominant approach
in appraisal proceedings since Weinberger, the ultimate
selection of a valuation framework remains within the
court’s discretion. In fact, the Court of Chancery has
rejected valuations based on the DCF method on several
occasions for various reasons, primarily because of the
quality of the projections.7 The Delaware courts continue
The cost of capital is a central issue in judicial business
valuations in statutory appraisal, stockholder oppression,
and “entire fairness” cases. The Delaware courts have
effectively set the standards for valuations related to cor-
porate disputes because Delaware law is widely accepted
on corporate legal issues. This chapter primarily discusses
Delaware Court of Chancery and Delaware Supreme
Court opinions involving the discounted cash flow (DCF)
method and its crucial component, the cost of capital.
Most of the Delaware decisions discussing cost of capital
have come from statutory appraisal cases, and the Court
does not differentiate in its approach to cost of capital in
It should be noted that some Delaware valuation
decisions—and most other states’ published valuation
decisions—contain neither an explanation of the court’s
methodology nor its calculations. A federal appellate
court decision under Missouri law commented:
It is unfortunate that, after performing such a well-reasoned
and thorough review of the record, the district court was
not more explicit in elaborating how it reached its ﬁ nal
calculation of price per share. Regardless, the district court
is not required to provide explicit detail or mathematical
precision in fair value cases [emphasis added], since “the
very nature of most cases precludes proof of value and
damage with the precision of mathematical computation.”
It is also permissible for a district court to arrive at a
determination of fair value that is not advocated by any of
State appellate court decisions seldom address these
details. Moreover, there are very few published state trial
court decisions outside of Delaware.
Discounted Cash Flow in Delaware Law
In Weinberger v. UOP, Inc., the Delaware Supreme
Court decided that a determination of fair value2 “must
Note: This paper is an update of Chapter 9 in Cost
of Capital in Litigation: Applications and Examples by
Shannon P. Pratt and Roger J. Grabowski (John Wiley &
Sons, 2011) and reprinted with permission of John Wiley
& Sons, Inc.
1Swope v. Siegel-Robert, Inc., 243 F.3d 486, 494–5 (8th Cir. 2001), citing
Phelps v. Watson-Stillman Co., 293 S.W.2d 429, 432 (Mo. 1956).
2Delaware’s statutory standard of value for dissenting stockholder actions
(as in most other states) is “fair value.” Fair value for statutory appraisals is
the value of an entity as it is being run, with no control premium and no
discount for lack of marketability or minority interest. See DEL. CODE ANN.
Tit. 8, § 262 (h).
3Weinberger v. UOP, Inc., 457 A.2d 701, 713 (Del. 1983), a seminal “entire
5See, e.g., Grimes v. Vitalink Comm. Corp., 1997 Del. Ch. LEXIS 124
(Aug. 26, 1997) at *3 (“[The] discounted cash ﬂ ow model [is] increasingly
the model of choice for valuations in this Court.”); Gholl v. eMachines, Inc.,
2004 Del. Ch. LEXIS 171 (July 7, 2004) at *20 (“This [DCF] method is
widely accepted in the ﬁ nancial community and has frequently been relied
upon by this Court in appraisal actions.”); Henke v. Trilithic Inc., 2005
Del. Ch. LEXIS 170 (Oct. 28, 2005) at *20 (citing Gholl).
6Andaloro v. PFPC Worldwide, Inc., 2005 Del. Ch. LEXIS 125 (Aug. 19,
2005) at *35.
7Harris v. Rapid-American Corp., 1990 Del. Ch. LEXIS 166 (Oct. 2, 1990)
at *17–18, *22 (speculative nature of forecasts) aff’d in part and rev’d in
part on other grounds, LeBeau v M.G. Bancorp., Inc., 1998 Del. Ch. LEXIS
9 (Jan. 29, 1998). at *36 (the Court could not rely on DCF valuation of
either expert), aff’d, 737 A. 2d 513 (Del. 1999); Bomarko, Inc. v. Inter-
national Telecharge, Inc., 794 A.2d 1161 (Del. Ch. 1999) at 1185 (unsup-
ported projections); aff’d 766 A.2d 437 (Del. 2000); Gray v. Cytokine
Pharmasciences, Inc., 2002 Del. Ch. LEXIS 48 (Apr. 25, 2002) at *26
(unreliable projections, terminal value high percentage of total value); Doft
& Co., Inc. v. Travelocity.com, Inc., 2004 Del. Ch. LEXIS 75 (May 21,
2004) at *32 (unreliable projections).
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Business Valuation Review
to use other valuation methods, principally the guideline
company method,8 but they do not value operating com-
panies based on asset value.9 A recent decision expressed
a preference for using more than one approach; Chancel-
lor Chandler stated, “If a discounted cash flow analysis
reveals a valuation similar to a comparable companies or
comparable transactions analysis, I have more confidence
that both analyses are accurately valuing a company.”10
Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is the
method by which the Court of Chancery most often
determines the cost of capital in a DCF method.11 CAPM
was first introduced in the 1990 Technicolor decision.12
Since then, experts in most Delaware appraisal cases have
used the CAPM to calculate the weighted average cost of
capital (WACC) for their DCF analyses, and subsequent
decisions show that the Court of Chancery is comfortable
The Court has elected to use the CAPM even in
situations where future results are highly speculative.
In one case, it rejected a 35% to 45% cost of equity based
on “a survey of venture capitalist [sic] firms” in favor
of an approximately 21% CAPM-based rate.13 In valuing
another speculative venture, the Court accepted a 30%
discount rate calculated using the CAPM and rejected a
17.7% rate that the Court believed inadequately reflected
the company’s risk.14 When cash flows are speculative,
the Court may allow the use of a venture capital rate.
In a case appraising a small biotech company, the
Court used a discount rate of 50% based on a report by
the investment banker who was an advisor in the
Components of Weighted Average Cost of
Delaware law requires that an appraisal be based on
information known or knowable at the valuation date.
All inputs into the WACC should therefore be based on
market information as of the valuation date.16 Inputs to
the WACC are discussed in the following pages.
Delaware accepts the 20-year Treasury rate as the
measure of the risk-free rate. The risk-free rate is rarely
a matter of dispute. In fact, only one Delaware decision
has addressed this issue. In a 2004 decision, the Court
rejected the 30-year U.S. government bond yield as
the risk-free rate and stated that “using the 20-year U.S.
government bond rate is more reasonable under the cir-
cumstances and in keeping with the accepted practice.”17
However, in a non-Delaware appraisal case, the U.S.
District Court in Nevada based the risk-free rate on 5-year
U.S. government bond yield at the time the transaction
Cost of equity
Until a few years ago, the Delaware decisions that used
the CAPM to calculate the cost of capital most frequently
used an equity risk premium (“ERP”) of 7.0% to 7.2%.
The Court of Chancery and other courts relied on experts
who used the older and more widely accepted ERP
estimates of 7.0% listed in the SBBI historical data (the
In 2003, however, highly regarded valuation experts
and academics began to question the automatic use of
the Historic ERP. Shannon Pratt wrote that he was “now
convinced that the long-term arithmetic average general
equity risk premium (currently 7.0%) is too high.”20 Pratt,
discussing the results of recent empirical research
8For a discussion of Delaware appraisal decisions, see Gilbert E. Matthews,
“A Review of Valuations in Delaware Appraisal Cases, 2004–2005,” Bus.
Val. Rev. (Summer 2006): 44.
9TV58 Limited Partnership v. Weigel Broadcasting Co., 1993 Del. Ch. LEX-
IS 146 (July 22, 1993) at *8, citing Shannon P. Pratt, Valuing a
Business: The Analysis and Appraisal of Closely Held Companies, 2d ed.
(Irwin, 1989), p. 106 (“The notion that a business interest is worth the value
of its underlying assets is basically fallacious in most cases, at least for an
10In re Hanover Direct, Inc. Shareholders Litigation, 2010 Del. Ch. LEXIS
201 (Sept. 24, 2010).
11Both experts performed a DCF analysis in the ﬁ rst Delaware appraisal
case after Weinberger, but neither expert used a discount rate based on
CAPM. Both used arbitrary rates: one expert chose a discount rate range
of 20% to 25%, the other chose 15% to 20%, and the court chose to use
the midpoint, 20%. Cavalier Oil Corp. v. Harnett, 1988 Del. Ch. LEXIS 28
(Feb. 22, 1988) at *59.
12Cede & Co. v. Technicolor, Inc., 1990 Del. Ch. LEXIS 259 (Oct. 19, 1990)
(“Technicolor 1990”) at *92–100, rev’d on other grounds, 634 A.2d 345
(Del. 1993). This case spawned 17 Chancery and Supreme Court decisions
over a 20-year span.
13Gilbert v. MPM Enterprises, Inc., 709 A.2d 663, 672–3 (Del. Ch. 1997),
aff’d, 731 A.2d 790 (Del. 1999).
14Ryan v. Tad’s Enterprises, Inc., 709 A.2d 682, 703 (Del. Ch. 1996), aff’d,
693 A.2d 1082 (Del. 1997).
15Gray at *31–33. Prior to the transaction, “the parties decided to save
money by asking Merrill Lynch to value the stock of both companies,
without opining as to fairness.” Gray at *14.
16See, e.g., Gilbert v. MPM Enterprises, Inc., 1998 Del. Ch. LEXIS 60
(Apr. 24, 1998) at *5, aff’d, Gilbert, 731 A.2d 790; Cede & Co. v. JRC
Acquisition Corp., 2004 Del. Ch. LEXIS 12 (Feb. 10, 2004) at *6–7.
17Cede & Co. v. MedPointe Healthcare, Inc., 2004 Del. Ch. LEXIS 124
(Sept. 10, 2004) at *69.
18Steiner Corp. v. Benninghoff, 5 F.Supp.2d 1117, 1133–35 (D. Nev. 1998).
19See, e.g., Swope at 493 (“Empirical evidence from Ibbotson’s includes
a long-term equity risk premium representing incremental rates of return
realized on large capitalization common stocks over the risk free rate
historically reported from 1929 [sic] to 1996.”); Cede & Co. v. Technicolor,
Inc., 2003 Del. Ch. LEXIS 146 (Dec. 31, 2003) (“Technicolor 2003”) at 177
(7.2%), aff’d, 884 A.2d 26 (Del. 2005); Lane v. Cancer Treatment Centers
of America “, 2004 Del. Ch. LEXIS 108 (July 30, 2004) at 43 (7.1%);
Andaloro at *57 (7.0%); Delaware Open MRI Radiology Associates v.
Kessler, 898 A.2d 290, 339 (Del Ch. 2006) (experts used 7.2% and 7.0%,
20Pratt, “Valuers Should Lower Equity Risk Premium Component of
Discount Rate,” Bus. Val. Update (Nov. 2003): 1.
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Business Valuation Review — Winter 2010 Page 3
Cost of Capital in Appraisal and Fairness Cases
published by Roger Ibbotson and Peng Chen in 2003,21 as
well as work conducted by Roger Grabowski and others,
stated that these results suggested that the ERP is actually
“about 1.25 percentage points lower than the historical
The Court of Chancery began to accept lower ERPs
derived from the Fama-French (FF) 3-factor model.
In 2004, Vice Chancellor Strine rejected a 7.3% premium
determined by the Historic ERP and accepted instead
a 4.5% equity premium derived from the FF model.
Relying on the alternate estimate, he stated:
Although the Fama-French three-factor CAPM model is
not wholly accepted, neither is the original CAPM itself.
By better factoring in the real risks of leverage, the
Fama-French model captures useful data that contributes to
a more reliable and real-world cost of capital.23
Shortly thereafter, Vice Chancellor Noble cited this
language when he employed the Fama-French model’s
estimate in determining ERP:
In calculating the risk premium, [petitioner’s expert] used
the relatively new research by Fama and French to ﬁ nd a
value of 4.5%. In contrast, [respondent’s expert] employed
the older and more widely accepted practice of using
the Ibbotson Associates data and used a value of 7.3%. The
Company’s main argument against the use of the Fama
and French research is that because it is “brand-new” and
“still under signiﬁ cant academic debate” it cannot satisfy
the standard that a valuation methodology be “generally
considered acceptable in the ﬁ nancial community,” as
required by Weinberger v. UOP.
The mere fact that it is new does not make this research
unreliable or outside of the Weinberger standard. A valua-
tion such as this is built on assumptions that will always be
under debate or attack in the academic community.24
His decision rejected the equity risk premium based on
the historic SBBI data and accepted the lower cost of
equity capital based on FF.25 The FF lower ERP was also
used in a 2006 decision that gave equal weight to both the
FF estimate and the Historic ERP.26
Vice Chancellor Strine centered on the debate over
how to calculate ERP in the recent and important 2010
Global GT decision.27 He sided with the petitioners by
rejecting a 7.1% ERP based on SBBI historical data and
accepting instead an ERP of 6.0%. He made his decision
based on the petitioner’s expert’s teaching experience, the
relevant academic and empirical literature, and the supply
side ERP reported in the 2007 Ibbotson Yearbook.28
The Vice Chancellor pointed out that the petitioners
had substantial support in the professional and academic
valuation literature for arguing that the continued use
of the simple historic ERP is unjustifiable and that there
are “persuasive reasons [that] support a lower forward-
looking real return on equity than the return found in the
Acknowledging that “the debate is not nearly so stark,”
he remarked that “[e]ach technique depends to a certain
extent on taking some combination of past data and using
it to predict a necessarily uncertain future.”30 He noted
that petitioner’s expert had relied upon the fact that
Ibbotson and his co-authors have themselves developed an
alternative model to forecast the long-term expected equity
return because of their view that the historic approach
wrongly assumes that the relationship between stocks and
bonds observed in the past would remain stable into the
future. . . . The supply side estimate that Ibbotson publishes
uses the Ibbotson historical sample from 1926 to the
present, but estimates which components of the equity risk
premium are driven by the price-to-earnings ratio of a
stock, and which components are driven by expected
earnings growth. The supply side rate assumes that actual
returns to equity will track real earnings growth, not the
growth reﬂ ected in the price-to-earnings ratio.31
Vice Chancellor Strine went on to state that the surveys
cited by petitioners’ expert suggested that current
academic thinking would put the ERP closer to 6.0% than
to 7.1%. He commented,
[T]o cling to the Ibbotson Historic ERP blindly gives undue
weight to Ibbotson’s use of a single data set. 1926 . . . has
no magic as a starting point for estimating long-term equity
returns. . . . [V]ery well-respected scholars have made
estimates in peer-reviewed studies of long-term equity
returns for periods much longer than Ibbotson, and have
come to an estimate of the ERP that is closer to the supply
side rate Ibbotson himself now publishes as a reliable ERP
for use in a DCF valuation. For example, Professor Jeremy
Siegel has examined the period from 1802 to 2004 and
come up with an ERP of 5.36%. Likewise, Professors
Eugene Fama and Kenneth French considered the period
from 1872 to 2000, and calculated an average ERP of
21Robert G. Ibbotson & Peng Chen, “Long-Run Stock Returns: Participat-
ing in the Real Economy,” Fin. Analysts J. (Jan./Feb. 2003): 88, 94.
22Pratt, “Valuers Should Lower Equity Risk Premium Component of
Discount Rate” at 1. Pratt “urged his readers who still use an ERP of 7% to
immediately make a downward adjustment to reﬂ ect recent research
results,” Id. at 6.
23Union Illinois 1995 Inv. Ltd. Partnership v. Union Financial Group, Ltd.,
847 A.2d 340, 363 (Del. Ch. 2004).
24MedPointe Healthcare at *69–70.
25MedPointe Healthcare at *72.
26PNB Holding at *114.
27Global GT LP v. Golden Telecom, Inc., 993 A.2d 497 (Del. Ch. 2010),
aff’d. __ A.3d. __ (Del. 2010).
28Id. at 514.
29Id. at 516, n.114, citing Jeremy J. Siegel, “Perspectives on the Equity Risk
Premium,” Fin. Analysts J. (Nov./Dec. 2005): 70.
30Id. at 514.
31Id. at 515.
32Id. at 516, citing Michael Devaney, “Will Future Equity Risk Premium
Decline?”, J. of Fin. Planning (Apr. 2008): 47; Jeremy J. Siegel, “Perspec-
tives on the Equity Risk Premium,” Fin. Analysts J. (Nov./Dec. 2005): 63;
and Eugene F. Fama & Kenneth R. French, “The Equity Premium,” J. of
Fin. (April 2002): 638.
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Additionally, the Vice Chancellor stated that “the
literature also suggests that the ERP for companies
operating in foreign markets [such as Golden GT] is, if
anything, lower than the Historic ERP for a domestic
Determining the cost of equity continues to be a major
disagreement among valuation experts. Vice Chancellor
Strine recognized this controversy when he carefully set
out his reasons for no longer following an approach—
Historic ERP—which “ha[d] met with the approval of
this court on prior occasions.”34 Elaborating, he said:
Ibbotson’s reasoning comports with the strong weight of
professional and academic thinking, which is accurately
represented by [petitioner’s] view that the most responsible
estimate of ERP is closer to 6.0% than 7.1%. . . . [W]hen
the relevant professional community has mined additional
data and pondered the reliability of past practice and come,
by a healthy weight of reasoned opinion, to believe that
a different practice should become the norm, this court’s
duty is to recognize that practice if, in the court’s lay
estimate, the practice is the most reliable available for
use in an appraisal. In reaching this conclusion, I give
heaviest weight to the published literature, but also ﬁ nd
the admittedly squishier academic survey data supportive.
Although that data is far from perfect, it does reveal that the
weight of academic thinking at our nation’s ﬁ nest ﬁ nance
departments places the ERP much nearer to [petitioner’s
expert]’s estimates than [respondent’s]. For all these
reasons, I adopt petitioner’s ERP of 6.0%.35
Although coming to the conclusion that, in this case,
there was solid academic and professional thinking
supporting the lower ERP, Vice Chancellor Strine fully
realized that any estimate of ERP remains just an estimate
based on uncertainty. He appropriately leaves to the valu-
ation profession the final responsibility for resolving the
debate: “[T]he relevant academic and professional com-
munity and not this court should develop the accepted
Cost of debt
In an appraisal, the acquirer’s cost of debt is not rele-
vant because the entity being valued is the company as it
existed prior to the transaction. Thus, the appropriate cost
of debt for determining cost of capital is the company’s
borrowing cost before it was acquired.37
There is one apparent exception to this rule that is not,
in fact, actually an exception: the Chancery Court’s use
of the acquirer’s cost of debt in Technicolor 2003. The
Supreme Court directed the Chancellor to appraise
Technicolor based on the acquirer’s business plan because
the acquirer had begun implementing its changes to
Technicolor shortly after it had taken control through
a 1982 tender offer and prior to the 1983 squeeze-out
merger.38 Because the entity being valued was Techni-
color under the new business plan which became opera-
tive after the tender offer (but before the squeeze-out),
not the old business plan prior to the tender offer, the
Chancellor ruled that it was not appropriate to use
Technicolor’s pre-tender offer borrowing cost. He decid-
ed that Technicolor’s cost of debt at the time of the
squeeze-out merger was the interest rate being paid on the
When the Court of Chancery computes a company’s
WACC, it normally tax-effects the cost of debt based on
the company’s marginal corporate tax rate.40 The proce-
dure for S corporations, which do not pay corporate tax,
differs: in one situation where the Court appraised an S
corporation in 1991, it did not tax-effect the cost of debt.41
The Court of Chancery took the same position in a 1992
valuation case.42 However, it is unlikely to take the same
position in the future; in a 2006 case valuing a debt-free
S corporation, the Court tax-effected earnings based on
taxes payable by shareholders.43
For a company that could deduct only a portion of
its debt for U.S. taxes, a federal court prorated the tax
[D]ebt is not as valuable to Steiner as to other companies,
due to the fact that only 62% of its interest expense
functions as a shield. . . . At least 62% of interest expense
would serve as a tax shield, so debt should have some value
* * *
No one [who testiﬁ ed] attempted to show that, although
Steiner does have limited deductibility of its interest
33Id. at 517.
35Id. at 517–8.
36Id. at 517.
37See, e.g., Hintmann v. Fred Weber, Inc., 1998 Del. Ch. LEXIS 26 (Feb. 17,
1998) at *17; In Re Emerging Communications, Inc. Shareholders Litiga-
tion, 2004 Del. Ch. LEXIS 70 (May 3, 2004) at *61; MedPointe Healthcare
at *41,*53; In Re United States Cellular Operating Company, 2005
Del. Ch. LEXIS 1 (Jan. 6, 2005) at *60. In a non-Delaware appraisal where
the experts based the yields of similarly rated debt, the court accepted this
approach (Albert Trostel & Sons Co. v. Notz, 2010 U.S. Dist. LEXIS 108778
(E.D. Wisc., Sept. 28, 2010)).
38Cede & Co. v. Technicolor, Inc., 684 A.2d 289, 300 (Del. 1996). The
company being appraised was not Technicolor as it existed at the time of
the tender offer, but as it existed at the time of the squeeze-out merger under
its new management, excluding the acquisition debt. The cost of debt
determined by the court was applied only to Technicolor’s pre-acquisition
39Technicolor 2003 at *177–178.
40See, e.g., id. at *178 (“Using the 46% tax rate agreed upon by both
experts, the resulting after-tax cost of debt is 7.54%.”)
41In Re Radiology Associates, Inc. Litigation, 611 A.2d 485, 492 (Del. Ch.
42MacLane Gas Company Limited v. Enserch Corporation, 1992 Del. Ch.
LEXIS 260 (Dec. 9, 1992) at *51–2.
43Delaware Open MRI at 330.
44Steiner at 1126.
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Cost of Capital in Appraisal and Fairness Cases
The Vice Chancellor assumed repayment of debt at
maturity, and discounted the debt to present value at a
13.5% equity rate.51
In contrast to Delaware, a U.S. District Court Judge
applying Nevada appraisal law did not accept the
company’s actual capital structure:
[W]e are not precluded from using the industry average, as
Steiner contends, because the existing Steiner management
has “no plans” to change the capital structure.
. . . [W]hile assuming that the particular capital structure
envisioned by a speciﬁ c investor will be implemented after
the merger would not be appropriate, considering changes
that market actors would assume on average in placing
a rational value on the company would. Using Steiner’s
actual debt to equity ratio, which has been established as
a result of the particular needs and desires of the Steiner
family, would be as improper as using the speciﬁ c capital
structure of any other particular investor. . . . The market
places a value on how it expects a company to perform in
the future. And over time, market participants will expect
a company to move to its optimal position in terms of
variables like debt structure . . . .
... [T]he 20%/80% ratio used by [plaintiff] is not the
actual industry average. Rather, it is signiﬁ cantly lower. . . .
The market would thus expect a capital structure for Steiner
to incorporate more than 4% debt, although not as much
as the actual industry average. Therefore, we will use the
The valuation standard for entire fairness in Delaware
differs from the appraisal standard. Although Delaware
uses the company’s own capital structure in appraisal
cases, it typically looks at optimal capital structure in
fairness cases. In fairness cases, the Court considers
acquisition value and gives weight to what a potential
acquirer might pay. Thus, in a 1994 fairness case, the
Court accepted a WACC that was computed using “an
‘optimal’ debt/equity structure.”53
Although the amount of debt is normally determinable
from a company’s financial records, the value of the
equity is not in the financial records, but is indeed the
very basis of the litigation. This problem of indeterminate
equity has rarely been discussed in Delaware decisions,
and it appears that experts have used either the book value
of equity or the transaction price to determine the debt/
equity ratio. However, a 2004 decision does examine the
issue of circularity in determining the equity portion of
The difﬁ culty is both that [defendant’s expert’s] assumed
$10.38 per share “enterprise value” and [plaintiff’s expert’s]
assumed $41.16 per share “enterprise value” are identical
expense, it is some percentage other than 62%. Thus we
ﬁ nd that, in effect, Steiner can only deduct 62% of its
interest expense. The WACC formula must consequently be
adjusted by multiplying Steiner’s tax rate of 43% by 62%
before inserting it into the WACC formula.45
When the Court of Chancery was faced with the issue
of how to tax-effect the cost of debt of a company with
tax-loss carryforwards, it applied a 40% rate to an 8%
cost of debt, reasoning
NOLs are to be calculated after applying the Code’s other
deductions, and any deductions for interest payments would
allow the Company to save its NOLs for subsequent years.
Based on the foregoing, the Court will apply a 4.8%
after-tax cost of debt.46
Once the cost of debt is determined, the court must
determine the amount of debt to which it applies. For
calculating WACC in appraisal cases, the Delaware courts
consistently favor using the company’s actual capital
structure at the valuation date, rather than a hypothetical
capital structure based on industry norms.47 As stated in
[Respondent’s expert] weighted FWI’s cost of debt and
equity in accordance with FWI’s actual capital structure
on the date of the merger: 98% equity and 2% debt. As with
all other areas of business valuation, this Court prefers
to use a company’s actual information when possible,
unless it is shown that the actual information would yield
The debt incurred in the transaction leading to the
appraisal cannot be considered part of the debt of the
The Court rejected a debt-free target capital structure
that the defendant’s expert based on similar companies
when the company being appraised actually had a lever-
aged structure. On the other hand, it did not accept
the plaintiff’s expert’s assumption that the control share-
holder would have rolled over the leveraged subsidiary’s
existing debt perpetually:
The minority stockholders had no right to beneﬁ t from
PFPC’s access to preferred ﬁ nancing from [parent] and
then turn around and demand that [parent] not receive a full
repayment of principal and interest.50
45Id. at 1135.
46Gholl at *49.
47See, e.g., In Re Radiology Associates at 493; MedPointe Healthcare at *67
(“While [petitioner’s expert] may well be correct than [sic] an 80/20 capital
structure would be typical for a company of this nature, Carter-
Wallace’s traditional aversion to debt could be expected to continue.”)
48Hintmann at *18.
49Technicolor 2003 at *169 (“The [amount of] debt used to acquire the com-
pany cannot be ﬁ gured into the calculation when determining
Technicolor’s long-term debt.”)
50Andaloro, 2005 Del. Ch. LEXIS 125 at *54.
51Id. at *55.
52Steiner at 1125–26.
53Wacht v. Continental Hosts, Ltd., 1994 Del. Ch. LEXIS 171 (Sept 16,
1994) at *17.
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to the ultimate “fair value” that each expert determined
for ECM. Those values exemplify the ultimate circularity
inherent in WACC. . . . [T]he Court is unable to adopt
the “enterprise value” assumed by either expert with any
degree of conﬁ dence.
. . . [T]he only sensible way (in the Court’s view) to avoid
the circularity in this case is to use an enterprise valuation
of ECM that is not litigation-driven. On this record, the
only such valuation is the $ 27.84 per share value . . . that
the RTFC determined and actually used for purposes of
ﬁ nancing the Privatization. Having no better or more reli-
able information, the Court adopts that value for purposes
of determining the percentage of ECM’s capital structure
represented by long term debt and by equity on the merger
Interestingly, no decision discusses the fact that the
cost of equity itself is a function of the capital structure.
For any given company, the cost of equity will be lower
with an unleveraged structure and greater if it is highly
The Court of Chancery accepts the concept that the
equity risk premium must be adjusted for an appropriate
beta. When shares of a company being valued are pub-
licly traded in an active market, customary practice is to
determine beta by reference to the company’s own market
prices. However, if a company is private or if it is thinly
traded, the Court will look at the betas of guideline
publicly traded companies.56 The Court wrote in 1998
that using “the median beta of comparable companies . . .
is the customary method of determining a beta for a
privately held company.”57 However, in 2006, Vice Chan-
cellor Strine expressed concern about determining beta
for private companies based on the betas of guideline
I am chary about concluding that corporations that issue
illiquid securities for which beta—a measure of covariance
of the company’s trading price with overall market prices—
is indeterminable have a lower cost of equity than publicly-
listed corporations whose durability is reﬂ ected in a trading
history producing a reliable beta. The real world capital
markets seem to reject that odd notion.58
The period during which beta is determined should
exclude dates on which the market was inﬂ uenced by the
transaction which led to the appraisal. In Technicolor 1990,
Chancellor Allen rejected a beta of 1.7 based on the com-
pany’s market prices in a period which included the tender
offer through which control was purchased and instead
adopted a beta of 1.27, based on Technicolor’s pre-tender
market prices.59 On remand 13 years later, Chancellor
Chandler adopted a beta of 1.6 based on the single month
preceding the squeeze-out merger, reasoning that the beta
for earlier periods reﬂ ected prior management’s business
plan that the Supreme Court had ruled was not applicable
under the facts of the case.60
The Court generally prefers betas based on longer time
[Petitioner’s expert] calculated a beta of .62 based on a
period beginning six months after JR Cigar’s IPO.
[Respondent’s expert] calculated a beta of .67 based on a
period beginning a week after the IPO. Neither period is
presumptively valid. A longer period of time . . . is gener-
ally preferred. A ﬁ ve-year period, longer than the period
used by either expert, is the most common.61
A 2005 decision gave equal weight to two-year betas
and five-year betas of guideline companies. For both
periods, it gave greater weight to betas of companies
deemed to be more comparable.62
The use of a “predictive beta” from Barra was rejected
by Vice Chancellor Strine in 2010. He observed, “No
neutral academic support for the predictive power of the
Barra beta has yet been published.”63 The Vice Chancellor
explained his reservations about the Barra model:
[T]he Barra forecasting model is proprietary, and cannot
be reverse-engineered. The Barra predictive beta, which is
a forecast of a stock’s future looking beta using past data,
is based on a thirteen-factor model, but the weight given to
each of the factors is not publicly available. In fact, Barra
has used three different versions of its model without
explaining why or what changes have been made, and it is
not apparent whether Barra retroactively updates its past
beta calculations . . . The only thing [petitioner’s expert]
knows about the model is that it lists certain valuation-
relevant factors, including factors relevant to the historical
beta such as volatility, leverage, and trading activity, and
throws them in a stew pot in undisclosed proportions to
come up with an outcome.64
However, he added:
59Technicolor 1990 at *96–97.
60Technicolor 2003 at *174. Using this very short period for determining
beta was unique to the facts and judicial history of the protracted litigation.
61JRC Acquisition at *39 n. 94, citing Pratt, Cost of Capital: Estimations
and Applications, 2d ed. (John Wiley & Sons, 2002): 82.
62Andaloro at *57–60.
63Global GT LP at *67.
64Global GT LP at *65–66.
54Emerging Communications at *67–68. The issue of circularity was subse-
quently addressed in relation to the size premium in In Re Sunbelt Beverage
Corp. Shareholder Litigation, 2010 Del. Ch. LEXIS 1 (Jan. 5, 2010), which
is discussed below.
55See Pratt and Roger J. Grabowski, Cost of Capital: Applications and
Examples, 4th ed. (John Wiley & Sons, 2010), Chapter 7, for a discussion
on the relationship between leverage and the cost of equity.
56Gotham Partners, L.P. v. Hallwood Realty Partners, L.P., 855 A.2d 1059,
1077 (Del. Ch. 2003) (“Given what Gotham itself contends was an
‘inefﬁ cient’ market in the Partnership’s units . . . , the judgment that the
Partnership’s published beta was out of line strikes me as reasonable.”)
57Hintmann at *14.
58PNB Holding at *113 n. 149.
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I wish to emphasize that I do not reject the Barra beta for
use in later cases. . . . If the Barra beta is to be used in
appraisal proceedings, a more detailed and objective record
of how the Barra beta works and why it is superior to other
betas must ﬁ rst be presented.65
The Court’s view as to whether to use “raw beta” or
“adjusted beta” is unsettled. In 1998 Vice Chancellor
Steele stated that he had not heard testimony that
explained to his satisfaction the reasons why raw beta
should be adjusted, and wrote:
Based on the remaining evidence in the record, I conclude
that “raw” beta should be used to calculate the discount
rate. Although “adjusted” beta may be appropriately used
in future cases when supported by a record subject to
the crucible of cross-examination, I ﬁ nd that petitioner did
not meet his burden to prove why “adjusted” beta should
be used in this case.66
Six years later, however, Chancellor Chandler ques-
tioned the use of a raw beta and instead utilized an
Petitioner suggests that [the company’s] raw beta is more
appropriate than the adjusted beta. Petitioner’s own expert
did not use the raw beta, probably because doing so is
inaccurate. Betas based on observed historical data are
more representative of future expectations when they are
In 2010 Vice Chancellor Strine did not accept a
Bloomberg adjusted beta, commenting that “no reliable
literature or evidence was presented to show that the beta
of a telecom company like Golden, which operates in
a risky market [Russia], will revert to 1.0.”68 Instead, he
looked at industry betas:
According to the Ibbotson telecom (SIC 4813) beta, which
gives the beta values for approximately 50 telecom com-
panies that are traded in the United States including
Golden, the median industry beta as of December 2007
was 1.45, and the SIC composite beta was 1.24. . . . Golden
was a much larger, less levered company than the median
company on the Ibbotson SIC 4813 list and, therefore, the
composite beta of 1.24 is more appropriate than the median
beta of 1.45.69
The Court concluded, “I find that a beta that gives
2/3 weight to the Bloomberg historic raw beta of 1.32 and
1/3 weight to the 1.24 industry beta is the best approach
to this DCF analysis.”70
When beta is determined based on guideline com-
panies, it is important to consider the risks of those guide-
line companies relative to the subject company. It may
be appropriate to adjust the selected beta to reflect the
incremental risk when the court does not incorporate a
company-specific risk premium and when the subject
company is smaller and more vulnerable than the guide-
line companies.71 The Court of Chancery adopted this
approach in a 1996 case:
The plaintiffs’ expert relied primarily upon a New York
Stock Exchange-traded company that had a beta of 2.2. . . .
The plaintiff’s expert derived Cell Tech’s beta of 2.0
from this “comparable” company’s beta of 2.2, thereby
suggesting that Cell Tech involved lower risk than did
the “com parable” company. The comparison is factually
* * *
The defendants calculated a discount rate of 26.5% using
the CAPM. The defendants’ expert explained that on
the basis of his experience, he considers 30% to be more
appropriate, given the risks associated with Cell Tech.73
* * *
I recognize that the defendants’ 30% discount rate is unusu-
ally high, but the record demonstrates that Cell Tech, at the
time of the Merger, was an unusually risky investment. . . .
Accordingly, I adopt 30% as the appropriate discount
rate . . .74
In another case, the Court rejected a market beta
of 0.63 for thinly traded limited partnership units and
accepted defendant’s expert’s beta of 3.35.75 The Court
then ruled that the 3.35 beta subsumed other adjustments
to the cost of equity:
What I believe unreasonable, though, is compounding that
substantial adjustment to beta—based on ﬁ rm speciﬁ c
characteristics of the Partnership—with the further addi-
tion of small company and speciﬁ c company adjustments.
Although such adjustments have been accepted in certain
decisions of this court involving different circumstances,
I ﬁ nd them to be inappropriate here. The adjustment to
beta alone was sufﬁ cient to account adequately for those
Industry risk premium
In corporate valuation cases, courts have rarely dis-
cussed the concept of adjusting the cost of equity by
65Global GT LP at *68–69.
66Gilbert, 1998 Del. Ch. LEXIS 60 at *9.
67JRC Acquisition at *39 n. 96, citing Pratt, Cost of Capital, 2d ed.: 89.
68Global GT, 993 A.2d 497, 523.
69Global GT, 993 A.2d 497, 523.
70Global GT, 993 A.2d 497, 524.
71See, e.g., Matthews, “Errors and Omissions in DCF Calculations: A
Critique of Delaware’s Dr. Pepper Appraisal,” Bus. Val. Update (October
72Ryan, 709 A.2d 682, 703.
73Id., n. 26.
74Id. at 704.
75Gotham Partners at 1077.
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applying an industry risk premium. The only extensive
discussion was in a decision by Vice Chancellor Strine
that treated a negative industry risk premium as a proxy
for a private company’s beta:
More important, I regard [plaintiff’s expert’s] consideration
of the lower industry risk for companies like Delaware
[Open MRI] Radiology to be a fair proxy for beta in a cir-
cumstance when beta cannot be measured directly. Under
the CAPM, the equity risk premium is not used in isolation
to estimate the subject company’s cost of capital. Rather
the equity risk premium is adjusted by an estimate of the
systematic risk of the subject company reﬂ ected by its
actual or estimated beta. The industry return data that
[plaintiff’s expert] uses is an acceptable substitute for
that adjustment in this situation when a beta cannot be
estimated. [Plaintiff’s expert] testiﬁ ed that the negative
risk premium he employed was consistent with market
return data from Ibbotson’s indicating that investments in a
health care industry business present less market risk than
Courts have often considered the application of a
size premium in calculating the cost of equity. A small
company premium was first applied in Delaware to a cost
of equity calculation in a 1991 decision.78
In 1999 the Court of Chancery wrote, “This Court has
traditionally recognized the existence of a small stock
premium in appraisal matters.”79 The role of a testifying
expert is to demonstrate whether the size premium is
appropriate in a given situation and, if so, the amount of
the premium.80 The Court stated in 2004:
There is ﬁ nance literature supporting the position that
stocks of smaller companies are riskier than securities of
large ones and, therefore, command a higher expected rate
of return in the market. Our case law also recognizes
the propriety of a small ﬁ rm/small stock premium in
appropriate circumstances. The issue, therefore, is not
whether a small ﬁ rm/small stock premium is permissible
theoretically, but whether the defendants have shown that
a premium of 1.7% is appropriate in this particular case.
The Court concludes that the defendants have made that
An Alabama appraisal case also accepted a size pre-
mium for calculating a discount rate. The court accepted
the defendant’s expert’s testimony as to both a “micro-
capitalization risk premium” of 3.5% (because “[t]he
typical small company has a higher degree of investment
risk than a similar, but larger company”) and a “company
size premium” of 4.35% (“[s]ince a small, closely held
company is usually restricted to narrower markets than
publicly-traded companies, an additional small company
premium is warranted”).82 Similarly, a Maine court
rejected a 0.5 beta based on betas of companies in the
same industry because it was not adjusted to reflect the
issuer’s small size.83
The Court may decide, however, that based on facts
and circumstances, a size premium should not be
In these circumstances, I cannot conclude that it has
been persuasively shown that the statutory fair value of
Technicolor stock would more likely result from the
inclusion of a small capitalization premium than from its
exclusion. In this circumstance, I conclude it should not be
In a very recent 2010 case, Chancellor Chandler raised
another issue with regard to determining the size pre-
mium. He termed it the “issue of circularity,” which arises
from the fact that the selection of a size premium is a
function of the assumed value of the enterprise:
[A] discounted cash ﬂ ow analysis both values the size of
a company (and thus points to the appropriate Ibbotson
premium to use) and relies on the appropriate Ibbotson
premium to determine the value of the company. This
process is circular; which should come ﬁ rst, the valuation
of the company or the selection of the Ibbotson risk
He criticized defendant’s expert for his “methodologi-
cally problematic” argument:
[He] goes as far as to say that because his selection of a
5.78% premium results in a valuation that places Sunbelt in
the tenth decile—the decile with a corresponding premium
of 5.78%—I should take this as evidence that the 5.78%
premium is appropriate. I cannot accept this asserted
mathematical proof and proposed ﬂ ow of causality.86
The Court concluded that it was appropriate to use the
weighted average of the SBBI (Ibbotson) size premiums
for the two deciles into which the subject company’s
value might fall:
According to Ibbotson, the 3.47% premium is a weighted
balance between the ninth-decile premium of 2.65% and
the tenth-decile premium of 5.78%. Given the uncertainty
in Sunbelt’s own value and whether Sunbelt falls on the
77Delaware Open MRI at 340.
78In Re Radiology Associates, 611 A.2d 485, 490.
79ONTI, Inc. v. Integra Bank, 751 A.2d 904, 920 (Del. Ch., 1999). See also,
e.g., Hintmann at *14 (“This Court has accepted the addition of small stock
premia.”); Delaware Open MRI at 340 ([“The expert’s] inclusion of a small
stock premium is consistent with a good deal of academic and practitioner
thinking about CAPM.”)
80ONTI at 921.
81Emerging Communications at *71.
82Ex parte Baron Services, Inc., 874 So.2d 545, 552 (Ala. 2003).
83In re Valuation of Common Stock of Penobscot Shoe Company, 2003 Me.
Super. LEXIS 140 (May 29, 2003) at *98–100.
84Technicolor 1990 at *99.
85Sunbelt Beverage at *41.
86Id. at *43.
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Cost of Capital in Appraisal and Fairness Cases
smaller or larger side of the line between the ninth and
tenth deciles, I believe it is more appropriate to select
3.47%, a small-ﬁ rm risk premium that accounts for the
possibility that the company is on either side of the line
and that Ibbotson itself seems to have applied to all ﬁ rms
within (or between) the ninth and tenth deciles.87
The Court of Chancery understands that the size
premium measures risk is not measured by beta, and rec-
ognizes that the concepts of beta and the small company
premium are distinct:
[T]he size premium is not dependent on the beta of the ﬁ rm.
In fact, it is because the beta does not capture all the
systematic risk that a size premium is included. “Even after
adjusting for the systematic (beta) risk of small stocks, they
outperform large stocks.”88
An additional issue is that the Court must consider
whether to use size premiums based on data starting in
1926 or starting at a later date. In one case, the Court
weighted the historical premium data for various
Thus, it seems to me that a small stock premium exists,
but just as the difference in returns over sixty-nine years
is much greater than that over other, perhaps equally valid
periods of time. . . . I think the better approach is to weight
the more recent results more heavily than the older ones.
To accomplish that, I will take the returns over the past 14,
28, 42, 56, and 69 years and average them, generating a
weighted return over the past 69 years for both the smallest
quintile and the entire NYSE universe of stocks. This
will have the effect of weighting the most recent period
ﬁ ve times as much as the ﬁ rst period, the second most
recent period four times as much as the earliest, and so on.
I believe this to be a more accurate method of determining
the existence and magnitude of any small stock
The application of the size premium to foreign
businesses was discussed in a 2006 Court of Chancery
decision. The Vice Chancellor reviewed the academic
literature and concluded:
The general weight of the scholarship, in summary, seems
to be that the small-size premium might well apply in the
same way as in the U.S. in more highly developed foreign
markets, and would not apply to the same extent, or at all,
in newly developing markets.”90
Company-specific risk premium
The Chancery Court has expressed skepticism as to the
use of a company-specific risk premium in computing
The calculation of a company speciﬁ c risk is highly sub-
jective and often is justiﬁ ed as a way of taking into account
competitive and other factors that endanger the subject
company’s ability to achieve its projected cash ﬂ ows.
In other words, it is often a back-door method of reducing
estimated cash ﬂ ows rather than adjusting them directly.
To judges, the company speciﬁ c risk premium often seems
like the device experts employ to bring their ﬁ nal results
into line with their clients’ objectives, when other valuation
inputs fail to do the trick.91
The Court has accordingly declined to apply a
company-specific risk premium on several occasions,
stating its view that company-specific risk premiums
cannot be included without “fact-based evidence pro-
duced at trial” by expert testimony that persuades the
Court to accept the adjustment.
Vice Chancellor Steele,92 in a 1998 Delaware decision,
was the first to discuss extensively the rejection of a
company-specific risk premium. Although he did note
that this premium could occasionally be appropriate,
he concluded, “Respondent has failed to carry its burden
of proving the appropriateness of adding a 3% company
specific risk premium.”93 He explained:
An investment speciﬁ c premium may be appropriate to
account for risks not captured in the equity risk premium
and the small size premium. Unlike those two premia,
which are commonly determined by reference to the pub-
lished results of empirical research, a company speciﬁ c
risk premium “remains largely a matter of the analyst’s
judgment, without a commonly accepted set of empirical
support evidence.” Thus, the factors relied upon in assess-
ing an investment speciﬁ c premium should be carefully
explained to the Court. As with all aspects of a party’s
valuation for purposes of section 262, the proponent of a
company speciﬁ c premium bears the burden of convincing
the Court of the premium’s appropriateness.94
The company-specific risk premium was rejected again
in a 2004 decision:
By adding a second incremental premium to ECM’s cost of
equity to account for the risk of size, [defendant’s expert]
appears to have performed a mechanical exercise, rather
than make a nuanced, textured judgment. Accordingly, the
Court determines that the defendants have not established
a credible justiﬁ cation for their incremental “supersmall”
ﬁ rm premium, and declines to add that premium to the
87Id. at *44.
88JRC Acquisition at *39, citing Pratt, Cost of Capital, 2d ed. at 82.
89ONTI at 922. The valuation date was in 1995, so that the periods started in
1981, 1967, 1953, 1939, and 1926, respectively.
90Gesoff v. IIC Industries Inc., 902 A.2d 1130, 1161 (Del. Ch. 2006).
91Delaware Open MRI at 339.
92Now Chief Justice of the Delaware Supreme Court.
93Hintmann at *20.
94Id. at *18–19, citing Pratt, Robert F. Reilly, and Robert P. Schweihs, Valu-
ing a Business: The Analysis and Appraisal of Closely Held Companies,
3d ed. (Irwin, 1996), 164. Section 262 is the section of the Delaware
Corporation Law relating to appraisals.
95Emerging Communications at *76.
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Rejection of this premium persisted in a 2006 case,
in which defendant’s expert applied company-specific
risk premiums to each constituent business of the subject
company. The Court of Chancery stated “[O]ur courts
have not applied company-specific risk premia without
fact based evidence produced at trial on which to base
that discount.”96 It then concluded, “In this case, the court
finds that the defendants did not carry their burden of
proving the appropriateness of company-specific premia
for IIC constituent companies.”97
In the latest denial of a company-specific premium, the
Court, in the 2010 Sunbelt Beverage decision, reiterated
the rule regarding the evidentiary burden for accepting a
company-specific risk premium. The Chancellor said:
Defendants offer three primary justiﬁ cations for including
a company-speciﬁ c risk premium: (1) the at-will termina-
tion of supplier agreements that prevails throughout the
wholesale alcohol distribution industry; (2) the competition
Sunbelt faces from speciﬁ c players such as Southern
Wine & Spirits; and (3) the level of optimism contained in
Sunbelt’s management projections.
I conclude that none of these justiﬁ cations merits inclu-
sion of a company-speciﬁ c risk premium for Sunbelt. The
ﬁ rst and second justiﬁ cations clearly relate to the industry
as a whole, rather than speciﬁ cally to Sunbelt. 98
Defendants thus have failed to meet their evidentiary
burden to demonstrate to me that it was riskier for Sunbelt
to rely on its speciﬁ c management projections than it is
for all companies to rely on management projections. . . . I
do not believe a company should be able to manufacture
justiﬁ cation for a company-speciﬁ c risk premium (and all
the quantitative uncertainty accompanied therewith) simply
by adjusting its management projections such that there
is a heightened risk in relying on those projections, no
matter how unique that risk-thirsty practice may be to the
The Court further stated, “It is important for any
proposed company-specific risk premium to be based on
a specific financial analysis, so that the Court can verify
both the propriety of including the risk premium and the
appropriate level of the premium.”100 This explicit instruc-
tion regarding the necessity for both factual evidence
and specific financial analysis is a warning to any expert
that without these two essentials, the Court is unlikely to
accept a company-specific risk premium.
It should be noted, however, that the Court accepted
a company-specific risk premium in a 1999 decision in
which Chancellor Chandler reviewed the prior status of
this adjustment in Delaware. He found that “the party
seeking to add the premium,” who bore “the burden of
showing that the premium [was] appropriate,” had “only
partly met that burden.”101 Noting that no beta had been
calculated by the experts, he explained, “I am willing to
accept that the addition of a company-specific premium is
appropriate in the absence of beta [emphasis added].”102
He reviewed the six factors that respondent’s expert listed
in support of the premium, and concluded that since the
expert’s valuation “does not state how much impact on
the company specific premium each of these factors has,
I will estimate that they are approximately equal; there-
fore, because I have eliminated half of them, I reduce
[defendants’ 3.4%] company specific risk premium by an
equal amount, to 1.7%.”103
In contrast, in a 1994 Delaware decision in a fairness
case, the Court criticized the plaintiff’s expert for not
using a company-specific premium.104 The Court rejected
certain factors that defendant’s expert considered in sup-
port of a 5% company-specific premium and accepted
other factors, ruling that “an appropriate premium is 3%,
based on the other factors considered by [defendant’s
expert] in determining the target rate of return, such as
pending litigation . . . and the competitive environment
in which Continental operated.”105 On balance, the reluc-
tance of the courts to accept company-specific premiums
means that the expert who includes this premium in his
calculation of WACC may expect a strong challenge on
the stand. However, as discussed in the following section,
the company-specific risk premium is acceptable in the
Most expert testimony in Delaware has used CAPM
for calculating cost of capital, but the Court has some-
times utilized the build-up method for calculating it.
The Delaware Court of Chancery explicitly rejected the
build-up method in a 1998 decision, stating that “[t]he
CAPM would seem to be more useful than the ‘build up’
method because it offers more complete information.”106
It has, however, been accepted in later decisions,107 and in
Delaware Open MRI in 2006, the Court not only explic-
itly accepted the build-up method, but also provided the
rationale for doing so and also for accepting a company-
specific risk premium in that case. Observing that the
96Gesoff at 1158.
97Id. at 1158.
98Sunbelt Beverage at *47.
99Id. at *49–50.
100Id. at *50.
101ONTI at 920.
102The Chancellor noted that in Gilbert, “Vice Chancellor Steele applied . ..
a beta . . . with the beta perhaps acting as a surrogate company speciﬁ c risk
104Wacht at *13.
105Wac h t at *21.
106Hintmann at *16.
107Gholl at *47,*49; Henke, 2005 Del. Ch. LEXIS 170 at *40.
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Cost of Capital in Appraisal and Fairness Cases
build-up method could reluctantly be accepted as a
substitute for CAPM, it wrote:
[N]ot all public companies have a sufﬁ cient public ﬂ oat
for trading in their shares to provide a reliable beta for
use in calculating their cost of capital, forcing a resort to
the use of data from the industry or so-called comparable
companies. . . .
The experts in this case have used the proxy [for CAPM]
that has found the most favor among professional apprais-
ers: the so-called “build-up model.” The build-up model
begins with the core factors considered by CAPM, a risk-
free rate and an equity premium rate. From there, however,
the build-up model begins to diverge from CAPM. Under
the build-up method, beta is not considered. A size pre-
mium, used consistently with the practice of most current
users of CAPM in the appraisal and valuation context, is
de rigueur under the build-up model. Much more heretical
to CAPM, however, the build-up method typically incor-
porates heavy dollops of what is called “company-speciﬁ c
risk,” the very sort of unsystematic risk that the CAPM
believes is not rewarded by the capital markets and should
not be considered in calculating a cost of capital. [italics
The build-up method has seldom been discussed in
other jurisdictions. However, in a Missouri appraisal
case in federal court, the decision discussed both experts’
use of the build-up method and applied it.109 A Vermont
decision accepted a discount rate calculated using the
build-up method; it criticized respondent’s expert’ CAPM
calculation that was inconsistent with his CAPM inputs
as dissenters’ expert in another Vermont case.110
The Delaware courts have considered two additional
and unrelated points that should be noted by valuation
experts: (1) the mid-year convention is acceptable, and
(2) DCF valuations using CAPM should not be adjusted
for a minority discount.
The mid-year convention has been explicitly used in
DCF calculations in every Delaware case where the
Court stated that a testifying expert had used it.111 Several
other jurisdictions have also accepted the mid-year
The Delaware courts recognize that DCF analyses
based on discount rates derived either using CAPM (from
SBBI data or the FF 3-factor model) or the build-up
method should not be adjusted for an implied minority
discount. The Court of Chancery first rejected this adjust-
ment in 1991113 and, except for one anomalous excep-
tion,114 it has continued to reject adding a control pre mium
to DCF valuations. A 2001 decision cited Shannon Pratt’s
reasoning for not permitting the discount:
Some analysts believe that the income approach always
produces a publicly traded minority basis of value because
the Capital Asset Pricing Model (CAPM) and the buildup
model develop discount and capitalization rates from
minority transaction data in the public markets. This is a
very common and highly ﬂ awed conclusion. There is little
or no difference in the rate of return that most investors
require for investing in a public, freely tradable minority
interest versus a controlling interest.115
Role of the Expert
Testifying experts need to be familiar both with perti-
nent valuation literature and relevant case law regarding
cost of capital and related issues. This base of knowledge
will not only help experts assist the judge, but will also
protect them in cross-examination.
Even when experts are well-qualified, the courts often
express skepticism as to testimony regarding discount
rates. Vice Chancellor Strine writes:
Testimonial feuds about discount rates often have the
quality of a debate about the relative merits of competing
alchemists. Once the experts’ techniques for coming up
with their discount rates are closely analyzed, the court
ﬁ nds itself in an intellectual position more religious than
empirical in nature, insofar as the court’s decision to prefer
one position over the other is more a matter of faith than
This citation illustrates why an expert fails to serve
the judge and the client by acting as a partisan in court.
Testifying experts are most valuable when they can
inform and educate the judge to understand, and then
hopefully adopt, the reasoning underlying the expert’s
report, testimony, and methodologies.
108Delaware Open MRI at 338–9.
109Swope at 493–498 and 503.
110In re Shares of Madden, 2005 Vt. Super. LEXIS 112.
111See, e.g., Hintmann at *16; PNB Holding at *105.
112See. e.g., Steiner at, 1136; U.S. Inspect, Inc. v. McGreevy, 57 Va. Cir. 511,
524 (2000); 2000 Va. Cir. LEXIS 524 (Nov. 7, 2000) at *28; Matter of
Murphy. v. United States Dredging Corp., 2008 N.Y. Misc. LEXIS 9900,
(N.Y. Supr., May 19, 2008) at **52, aff’d in part and rev’d in part on other
grounds, 74 A.3d 815 (N.Y. App. 2010).
113In re Radiology Associates at 494 (“The discounted cash ﬂ ow method
purports to represent the present value of Radiology’s cash ﬂ ow.... The
discounted cash ﬂ ow analysis, as employed in this case, fully reﬂ ects this
value without need for an adjustment.”)
114The Court added a 20% control premium (based on “control premia paid
for publicly-held companies”) to a DCF valuation in Hintmann at *31. In
contrast, the Court has frequently added a premium to guideline company
valuations to offset a supposed “implicit minority discount.” This adjust-
ment has, however, been questioned by some legal and valuation commen-
tators. See, e.g., Lawrence A. Hamermesh and Michael L. Wachter, “The
Short and Puzzling Life of the ‘Implicit Minority Discount’ in Delaware
Appraisal Law,” 156 U. Pa. L. Rev. (2007): 1; Matthews, “Misuse of Control
Premiums in Delaware Appraisals,” Business Valuation Review (Summer
115Pratt, Business Valuation Discounts and Premiums (Wiley, 2000), p. 30,
cited in Lane at *118.
116Delaware Open MRI at 338.
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Business Valuation Review
Sometimes the court merely needs help in understand-
ing technical issues. For example, one Vice Chancellor
appears to have misunderstood the definition of deciles:
[Defendant] asserts [in its brief] that “the Ibbotson year-
book clearly states that the capitalization cut-off between
deciles 10a and 10b is $48,345,000. That is, all companies
with market capitalizations of $48,345,000 or less fall
within decile 10b, while companies with market capitali-
zations greater than $48,345,000 but no greater than
$84,521,000 fall within decile 10a.” This is not what the
Ibbotson Associates yearbook says. Rather, it merely pro-
vides that the largest company within decile 10b has a
market capitalization of $48,345,000 and the company with
the largest capitalization within decile 10a has a market
capitalization of $84,521,000. There is no indication of
whether a company with a market capitalization of less
than $48,345,000 may nonetheless fall within decile 10a or
even decile 9 given certain characteristics.117
The Court’s misunderstanding of deciles demonstrates
the importance of articulate testimony by an expert
witness to explain concepts to a judge. If an experienced
Delaware Vice Chancellor can be confused by a basic
statistical concept, experts testifying in other jurisdictions
where judges are usually less familiar with valuation
methods and literature must be clear in their testimony.
Sometimes, as Vice Chancellor Strine articulates
above, the court’s fear that the judge must operate “more
[from] a matter of faith than reason” is much more seri-
ous. The court’s apprehension arises from what Strine
calls the “status of principles of corporate finance,”118 that
is, the valuation profession’s continuing but incomplete
development of the academic and intellectual principles
which underlie valuation methodologies. In these
situations, the court does not expect the expert to cure the
theoretical inadequacies. What it requests is that experts
aid the judge by, in Strine’s words, “trying to come up
with a proxy that takes into account concerns addressed
by CAPM.”119 As Strine elucidated:
Even as to public companies, there is much dispute about
how to calculate the discount rate to use in valuing their
future cash ﬂ ows, even when one tries to stick as closely
as possible to the principles undergirding the capital asset
pricing model and the semi-strong form of the efﬁ cient
capital markets hypothesis. Witness the serious academic
debate about whether the so-called size premium received
by investors in smaller public companies is a durable
indicia of their greater risk, or whether there are attributes
of stocks with a low book-to-market ratio that require the
consideration of that factor in estimating a discount rate.120
In addition, he points out that a reliable beta cannot be
calculated directly for thinly traded public companies,
so that valuators are forced to employ the less desirable
alternative of using guideline companies or industry data,
as discussed previously in relation to the build-up model.
Situations like [Delaware Open MRI] inspire even less
conﬁ dence, when experts are required to calculate a cost
of capital for a very small, non-public company, for which
neither of the experts has identiﬁ ed reliable public com-
parables. In this context, the ability of the experts or the
court to hew literally to the teaching of the high church
of academic corporate ﬁ nance is essentially non-existent.
At best, the experts and the court can express their rever-
ence by trying to come up with a proxy that takes into
account concerns addressed by CAPM and ECMH
[Efﬁ cient Capital Market Hypothesis].121
The Delaware Court of Chancery is the leading court
on valuation issues in corporate disputes. That court has
declared its preference for the DCF method of valuation,
including all elements of the expanded CAPM to
determine the cost of capital. It has, however, rejected the
company-specific adjustment in the calculation of WACC
unless there are unusual circumstances to validate it.
The author thanks Michelle Patterson, Ph.D., J.D., for
her assistance in the research, organization, and writing
of this article.
117Taylor v. American Specialty Retailing Group, Inc., 2003 Del. Ch.
LEXIS 75 (July 25, 2003) at *17, n. 18.
118Delaware Open MRI at 338.
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