  United States Court of Appeals
      for the Federal Circuit
                ______________________

                 FRANK GAYLORD,
                  Plaintiff-Appellee,

                           v.

                  UNITED STATES,
                 Defendant-Appellant.
                ______________________

                      2014-5020
                ______________________

    Appeal from the United States Court of Federal
Claims in No. 1:06-cv-00539-TCW, Judge Thomas C.
Wheeler.
               ______________________

               Decided: February 4, 2015
                ______________________

   HEIDI E. HARVEY, Fish & Richardson P.C., of Boston,
Massachusetts, argued for plaintiff-appellee.

    SCOTT BOLDEN, Assistant Director, Commercial Liti-
gation Branch, Civil Division, United States Department
of Justice, of Washington, DC, argued for defendant-
appellant. With him on the brief were STUART F. DELERY,
Assistant Attorney General, and JOHN J. FARGO, Director.
Of counsel on the brief were DAVID C. BELT and MICHAEL
F. KIELY, Attorney, United States Postal Service, Wash-
ington, DC.
                 ______________________
2                                            GAYLORD   v. US




    Before MOORE, REYNA, and TARANTO, Circuit Judges.
TARANTO, Circuit Judge.
    On remand from earlier holdings of this court, the
Court of Federal Claims held that ten percent of $5.4
million in revenue (which was almost pure profit) was a
reasonable royalty for the United States to pay as damag-
es for its unauthorized use of a distinctive copyrighted
work on a postage stamp. Finding an adequate basis for
the trial court’s determination, we affirm.
                      BACKGROUND
    Much of the background to the present appeal is de-
tailed in our prior opinions, Gaylord v. United States, 595
F.3d 1364 (Fed. Cir. 2010) (Gaylord I), and Gaylord v.
United States, 678 F.3d 1339 (Fed. Cir. 2012) (Gaylord II).
Frank Gaylord, a World War II veteran and renowned
sculptor, created The Column, consisting of nineteen
stainless steel statues depicting a squad of soldiers on
patrol, to form a central part of the Korean War Veterans
Memorial located on the National Mall in Washington,
D.C. The Memorial also includes a reflecting pool and a
mural wall, created by others. Mr. Gaylord was paid
$775,000 for his contribution, time and materials includ-
ed.
     In January 1996, roughly six months after the Memo-
rial was completed and dedicated, an amateur photogra-
pher named John Alli visited the Memorial during a
heavy snowstorm and photographed The Column, later
titling the resulting photograph Real Life. In 2002, the
United States Postal Service decided to issue a stamp to
commemorate the upcoming fiftieth anniversary of the
Korean War armistice. From the very outset of the pro-
cess of selecting an image for the commemoration, the
relevant Postal Service advisory committee fastened onto
the idea of using The Column on the stamp. It selected
GAYLORD   v. US                                          3



Mr. Alli’s photograph of The Column for the stamp face,
and it paid Mr. Alli a one-time fee of $1,500 for the right
to use his photo. The Postal Service did not seek Mr.
Gaylord’s consent to use The Column—the photograph
was a “derivative work” of The Column under 17 U.S.C.
§ 106(2)—before issuing the stamp in 2003, and Mr.
Gaylord never gave his consent. See Gaylord I, 595 F.3d
at 1370–71.
    Mr. Gaylord sued the United States for copyright in-
fringement in 2006. In Gaylord I, we held that the gov-
ernment was liable to Mr. Gaylord for copyright
infringement, because it used his work on the stamp
without his permission, The Column was not a “joint
work” (whose joint authors individually might grant
permission), and its use was not protected as fair use.
595 F.3d at 1371, 1376, 1381. In Gaylord II, we vacated
the Court of Federal Claims’ decision awarding Mr.
Gaylord $5,000 as the “reasonable and entire compensa-
tion” he was due under 28 U.S.C. § 1498(b). 678 F.3d at
1345. We remanded to determine the fair market value of
a license for Mr. Gaylord’s work based on a hypothetical
negotiation with the government. Id. at 1344–45.
    On remand after Gaylord II, the Court of Federal
Claims reopened the record to allow additional discovery
and expert reports, and it then held a two-day trial on
damages. As we had suggested, and the parties accept as
sound, the trial court broke down its consideration of
damages into three categories of infringing goods: (1)
stamps used to send mail; (2) commercial merchandise
featuring an image of the stamp; and (3) unused stamps
purchased by collectors. Gaylord v. United States, 112
Fed. Cl. 539, 542–43 (2013); see Gaylord II, 678 F.3d at
1344. The first two categories are not now in dispute: the
parties agreed that no damages would be awarded for
stamps used to send mail and that a per-unit royalty was
appropriate for the commercial merchandise, the trial
court setting the rate at 10% of revenue to produce a
4                                            GAYLORD   v. US



merchandise award of $33,092 (plus prejudgment inter-
est), which neither side now contests. Gaylord, 112 Fed.
Cl. at 542–43.
    The only question disputed in this court concerns the
award regarding the third category—unused stamps.
“After a full review of the evidence presented by both
sides,” the trial court determined that a 10% per-unit
royalty was appropriate to calculate damages for stamps
purchased by collectors. Id. at 542. Based on evidence
from regularly conducted surveys that the Postal Service
commissions and relies on in its ordinary course of busi-
ness, the court determined that the Postal Service re-
ceived $5.4 million in revenue—which was “almost pure
profit”—from unused stamps of The Column sold to
collectors during the (now-ended) life of the issue. Id. at
541. The court therefore awarded Mr. Gaylord $540,000
for the unused stamps, plus prejudgment interest. Id. at
542–43.
   The government appeals the unused-stamp award.
We have jurisdiction under 28 U.S.C. § 1295(a)(3).
                       DISCUSSION
    We review legal conclusions by the Court of Federal
Claims de novo and its factual findings for clear error.
Gaylord II, 678 F.3d at 1342; Gargoyles, Inc. v. United
States, 113 F.3d 1572, 1576–77 & n.4 (Fed. Cir. 1997). “A
finding is ‘clearly erroneous’ when[,] although there is
evidence to support it, the reviewing court on the entire
evidence is left with the definite and firm conviction that
a mistake has been committed.” United States v. U.S.
Gypsum Co., 333 U.S. 364, 395 (1948). In the patent
context, we have treated the royalty determination as a
factual finding but certain methodological questions for
determining a fair market value as subject to abuse-of-
discretion review. See SmithKline Diagnostics, Inc. v.
Helena Labs. Corp., 926 F.2d 1161, 1164 & n.2 (Fed. Cir.
1991). Any difference in the standard of review does not
GAYLORD   v. US                                          5



matter here, however, as we find no clear error or abuse of
discretion in the Court of Federal Claims’ determinations
supporting its royalty award.
                            A
     In 28 U.S.C. § 1498(b), Congress waived the sovereign
immunity of the United States to allow “the recovery of
[the copyright owner’s] reasonable and entire compensa-
tion as damages” for copyright infringement. In Gaylord
II, we held that “the methods used to determine ‘actual
damages’ under the copyright damages statute, 17 U.S.C.
§ 504, are appropriate for measuring the copyright own-
er’s loss” under § 1498(b). 678 F.3d at 1343. Consistent
with the conclusions of other circuits that have considered
the issue, we held that actual damages for copyright
infringement may be based on a reasonable royalty repre-
senting “ ‘the fair market value of a license covering the
defendant’s use.’ ” Id. (quoting On Davis v. The Gap, Inc.,
246 F.3d 152, 172 (2d Cir. 2001)); see also Dowagiac Mfg.
Co. v. Minn. Moline Plow Co., 235 U.S. 641, 648–50 (1915)
(affirming that, in the patent context, a reasonable royal-
ty “afford[s] a basis for measuring the damages”); On
Davis, 246 F.3d at 168–69 (summarizing copyright cases).
    To calculate the fair market value, a court deciding a
copyright case may use a tool familiar from patent law,
without necessarily following every aspect of patent law’s
use of that tool. It may hypothesize a negotiation between
the parties before the infringement occurred and deter-
mine “ ‘the reasonable license fee on which a willing buyer
and a willing seller would have agreed for the use taken
by the infringer.’ ” Gaylord II, 678 F.3d at 1343 (quoting
On Davis, 246 F.3d at 167); see Sid & Marty Krofft Televi-
sion Prods., Inc. v. McDonald’s Corp., 562 F.2d 1157, 1174
(9th Cir. 1977) (approving instruction to jury to determine
“what a willing buyer would have been reasonably re-
quired to pay to a willing seller for plaintiffs’ work.”).
Several cases have stressed the use of “objective consider-
6                                             GAYLORD   v. US



ations” in the determination of a copyrighted work’s
market value using that method. Jarvis v. K2 Inc., 486
F.3d 526, 534 (9th Cir. 2007); see Oracle Corp. v. SAP AG,
765 F.3d 1081, 1088 (9th Cir. 2014); On Davis, 246 F.3d
at 166–67. The court is not constrained to accept particu-
lar practices of the parties on either side—either to allow
owners to charge what they “would like to have charged if
unconstrained by reality,” Oracle, 765 F.3d at 1088, or to
“shield [infringers] from paying fair market value for
what they took,” Gaylord II, 678 F.3d at 1343 (citing to
patent law).
    Determining a reasonable royalty does not require
“mathematical exactness,” but a “reasonable approxima-
tion” under the circumstances of a given case. See Dowa-
giac, 235 U.S. at 647 (discussing the degree of precision
required in the sometimes-similar process of apportioning
profits).   Other circuits have recognized the often-
unavoidable uncertainties in establishing the fair market
value of a reasonable license fee as well as the importance
of avoiding undue speculation. Oracle, 765 F.3d at 1088–
89; On Davis, 246 F.3d at 166. “[S]ome difficulty in
quantifying the damages attributable to the infringement
should not bar recovery.” On Davis, 246 F.3d at 167.
    The hypothetical-negotiation determination must be
tied to the particular work at issue and its marketplace
value—much as, in patent law, the determination must be
tied to the particular patented technology and its foot-
print in the market. See VirnetX, Inc. v. Cisco Sys., Inc.,
767 F.3d 1308, 1327 (Fed. Cir. 2014); LaserDynamics, Inc.
v. Quanta Computer, Inc., 694 F.3d 51, 67, 79 (Fed Cir.
2012); Uniloc USA, Inc. v. Microsoft Corp., 632 F.3d 1292,
1315–18 (Fed. Cir. 2011); ResQNet.com, Inc. v. Lansa,
Inc., 594 F.3d 860, 869 (Fed. Cir. 2010). Different kinds of
evidence may be relevant, as long as it is viewed for what
it says about the work-specific value. For example, past
arms-length licensing practices by the copyright owner or
the infringer for similar uses and “benchmark” licenses by
GAYLORD   v. US                                             7



others in the industry may be useful. See Oracle, 765
F.3d at 1093; Jarvis, 486 F.3d 534–35. But the use of
past licenses as evidence must always take account of
economically relevant differences between the circum-
stances of those licenses and the circumstances of the
matter in litigation—as we have said in the related pa-
tent-law context. Ericsson, Inc. v. D-Link Sys., Inc., 773
F.3d 1201, 1227–28 (Fed. Cir. 2014); VirnetX, 767 F.3d at
1330–31; Finjan, Inc. v. Secure Computing Corp., 626
F.3d 1197, 1211–12 (Fed. Cir. 2010). Thus, in the copy-
right context, the unique features of a particular work
(including its recognized stature and symbolic value) may
be important in assessing the ultimate significance of past
practices in licensing other works.
                              B
    The basic premise of the hypothetical negotiation in
this case would have been the opportunity for making
substantial profits if the two sides were willing to join
forces, which we must assume they were. See Gaylord II,
678 F.3d at 1343 (“ ‘a willing buyer and a willing seller’ ”).
The Court of Federal Claims in this case determined that
the negotiators, presented such an opportunity and acting
under assumptions designed to identify market value,
would have agreed to a 90/10 split of the revenue from
retained stamps, which, here, is in substance a 90/10 split
of profits, because the revenue for the unused stamps is
almost pure profit to the Postal Service. The question for
us is whether that result—giving the Postal Service 90%
of the profits and Mr. Gaylord 10%—is within the range of
reasonable findings from the evidence. See Polar Bear
Prods., Inc. v. Timex Corp., 384 F.3d 700, 709 (9th Cir.
2004) (affirming jury award that was “within the range of
the fair market value” justified by the evidence).
     In answering that question, “[w]e presume that a fact
finder reviews all the evidence presented unless he explic-
itly expresses otherwise.” Medtronic, Inc. v. Daig Corp.,
8                                             GAYLORD   v. US



789 F.2d 903, 906 (Fed. Cir. 1986). Here, the trial court,
far from stating otherwise, expressly stated that it con-
ducted “a full review of the evidence presented by both
sides.” Gaylord, 112 Fed. Cl. at 542. We therefore con-
sider the entirety of the evidence, not just the evidence
expressly recited in the trial court’s opinion. Plant Genet-
ic Sys., N.V. v. DeKalb Genetics Corp., 315 F.3d 1335,
1343 (Fed. Cir. 2003) (“The fact that the district court did
not in its opinion recite every piece of evidence does not
mean that the evidence was not considered.”). We con-
clude that the trial court’s determination must be upheld.
                             1
    As a threshold matter, the trial court could reasona-
bly find that a per-unit royalty, and not a one-time lump-
sum payment, would have been the outcome of the nego-
tiation. The familiar advantages of a per-unit royalty can
readily be found present here. A per-unit royalty is a
logical way to tie the amount paid for the asset to the
marketplace success it helps produce, which fits the
objective of measuring market value. Moreover, by using
a per-unit royalty, the licensee avoids the risk of making a
fixed payment that overvalues the asset before its market
performance occurs, and the licensor avoids the risk that
a sure up-front payment might undervalue the asset. In
an important respect, it is the licensor that takes more of
the risk in such an arrangement, because it typically
retains little or no control over the efforts required to
produce the revenue that would generate per-unit royal-
ties. Lucent Techs., Inc. v. Gateway, Inc., 580 F.3d 1301,
1325–26 (Fed. Cir. 2009).
    No evidence required the trial court to reject a per-
unit royalty here. For example, there is no overriding
evidence of the kinds of difficulties of monitoring the
number of sales or amount of revenue that would neces-
sarily persuade rational negotiators that a per-unit royal-
ty was inefficient. To the contrary, the evidence shows
GAYLORD   v. US                                            9



that the Postal Service has long conducted quarterly
surveys to track the retention rate of commemorative
stamps, surveys the Postal Service considered statistically
accurate and relied on its business. J.A. 1844, 6605 n.4.
     The government argues that industry practice, by
which it means its own past licensing practices, shows
that it would not have agreed to a per-unit royalty. In the
first trial on damages, the Court of Federal Claims found
that Mr. Gaylord would have received a flat fee of $5,000,
based primarily on the government’s evidence that it had
never agreed to a per-unit royalty for stamps. Gaylord II,
678 F.3d at 1341. The trial court has now found other-
wise. The government challenges the new finding, point-
ing to witness testimony that, in the past, the Postal
Service had found alternatives rather than agree to what
it deemed excessive demands from a rights holder. But
the issue is “first and foremost a question of fact,” with
the trial court’s finding reviewed only for clear error based
on what the record says about the particular circumstanc-
es defining the hypothetical negotiation. Bruce v. Weekly
World News, 310 F.3d 25, 29–30 (1st Cir. 2002) (finding
no clear error in trial court’s adoption of lump-sum license
based on industry practice). In this case, the record does
not allow us to conclude that the Court of Federal Claims
committed a clear error.
    We do not question the government’s suggestion that
alternatives available to a potential licensee provide an
important constraint in a hypothetical negotiation. “[T]he
buyer will not ordinarily pay more for a license than its
anticipated benefit,” a benefit measured relative to avail-
able alternatives. Oracle, 765 F.3d at 1089; see Aqua
Shield v. Inter Pool Cover Team, 774 F.3d 766, 771 & n.1
(Fed. Cir. 2014) (applying the same concept in the patent
context). But given the uniqueness of the work at issue
here, including its status as a distinctively recognized
symbol of the Korean War for most Americans, the trial
court could properly discount the significance of potential
10                                            GAYLORD   v. US



alternatives. In fact, the government’s witnesses testified
that the Memorial was the immediate and fixed focus of
the stamp-selection committee as the subject for com-
memorating the Korean War armistice and that all of the
images considered by the committee were photographs of
The Column, not of less recognizable portions of the
Memorial or other subjects.
    Accordingly, the trial court could plausibly discount as
insufficiently analogous the government’s examples from
other stamp-selection processes—such as replacing a
stamp honoring one celebrity with a stamp honoring
another. As already noted, see supra pp. 6–7, taking
account of significant differences in circumstances is
essential to a sound evaluation of evidence of payments
for other works in a hypothetical negotiation. There is
only one nationally recognized Korean War memorial, and
the evidence readily allows the finding that, by 2003, that
memorial—and particularly The Column within it—was a
distinctively valuable subject for a commemoration of the
veterans who sacrificed through service in that war.
Under these circumstances, the trial court did not err in
concluding that, faced with limited alternatives, the
Postal Service would have agreed to a per-unit license.
                             2
    As to the particular amount of the royalty, the trial
court awarded a 10%-per-unit royalty amounting to a
90/10 split of profits between the Postal Service and Mr.
Gaylord. We see no clear error in the trial court’s deter-
mination of the royalty amount, considering the perspec-
tives of the two parties to the hypothetical negotiation.
    We begin with Mr. Gaylord’s perspective. In his other
licenses for derivative works incorporating The Column,
one of which was entered as a litigation settlement, Mr.
Gaylord had obtained a per-unit royalty of revenue on t-
shirts, miniature replicas, and other collectibles. J.A.
1180–81 (10% of “Product Revenue”); J.A. 1201 (10% of
GAYLORD   v. US                                            11



“wholesale sales”); J.A. 1721 (10% of “gross proceeds”).
And the government now accepts that rate for the mer-
chandise portion of the award in this case. Moreover, in a
1998 agreement, the contractor that oversaw the design
and construction of the Memorial demanded and obtained
a royalty “of 10% of the retail sales price” from Mr. Alli for
the latter’s sales of Real Life, Mr. Alli believing the con-
tractor to own the copyright to The Column. J.A. 1311,
1784. Consistent with that pre-litigation result, Mr. Alli
agreed in a 2007 litigation settlement—of less significance
for that reason—to pay Mr. Gaylord 10% of “net retail
sales” for his direct sales of Real Life. J.A. 1599.
    The per-unit royalty here gives Mr. Gaylord, if any-
thing, a lower share of the joint gains from the stamp—
the profits—than The Column fetched in the foregoing
licenses. In those other circumstances, where costs of
production are substantial, revenues do not effectively
equal profits, so that 10% of revenues represented a
higher percentage of profits, leaving the licensee with less
than 90% of the jointly earned profits. For example, if a
manufacturer’s costs of creating a miniature of The Col-
umn accounted for 50% of its revenue from that product,
Mr. Gaylord’s 10% share of revenue would amount to a
20% share of the profits, with the licensee keeping 80%.
For the unused stamps at issue, in contrast, the revenues
are almost pure profit, and the trial court’s royalty left the
Postal Service with 90% of profits. 1 Under the trial



    1   The Postal Service produced 86.8 million stamps
featuring Mr. Gaylord’s work, at a printing cost of
$181,412. Other costs were minimal. Each stamp had a
face value of 37 cents, for a total face value of $31.82
million. The parties stipulated that the Postal Service
sold at least 47.9 million stamps (generating $17.73
million), though the evidence suggested the number was
much higher.
12                                           GAYLORD   v. US



court’s royalty award, therefore, Mr. Gaylord would
actually come out of the negotiation with a smaller share
of the net gains from the joint project than was paid by
the licensee of the same work in other licenses.
    An additional common-sense factor supports the 10%
figure from Mr. Gaylord’s perspective. At the time of the
hypothetical negotiation here, Mr. Gaylord was not in a
position like that of other copyright owners—e.g., The
Walt Disney Company, an example the government
cites—who might obtain appreciable indirect economic
benefits from the publicity generated by a stamp and who,
therefore, might have a strong economic incentive to
accept less than their usual amount as a royalty. Before
July 2003, when the parties agree the hypothetical nego-
tiation would have occurred, Mr. Gaylord had retired,
closed his studio, and was no longer seeking new opportu-
nities as an artist. The record here permits a finding that
Mr. Gaylord would have focused on a direct monetary
royalty as the primary compensation for licensing his
work on a stamp.
    We turn to the perspective from the other side of the
negotiating table. The trial court could reasonably con-
clude that the Postal Service had sufficient incentive to
agree to a 10% per-unit royalty for sales of unused stamps
to collectors. The evidence shows that the Postal Service
knew that retained stamps were a source of significant
revenue, which was almost pure profit, and tracked
estimates of that revenue on a quarterly basis. The
Postal Service knew, too, that past military-themed
stamps had performed well with collectors, and it ex-
pected the Korean War Veterans Memorial stamp to sell
well, as evidenced by its choice to print roughly 50% more
of the Memorial stamps than was typical for its commem-
orative stamps (86.8 million compared to 50 to 60 million).
An arrangement under which it kept 90% of the profits
from this opportunity was a good economic deal.
GAYLORD   v. US                                           13



    The government argues that the availability of alter-
natives and its past licenses show that the royalty rate
would have been lower. We have already explained why
the trial court could appropriately discount the alleged
effect of alternatives on the hypothetical negotiation in
this case. The trial court could likewise justifiably find
that the government’s past negotiations regarding other
stamps are of limited probative value. As already noted,
respecting economically relevant differences in evaluating
evidence about other works is critical to the royalty as-
sessment.
    The government points to past licenses of sculptural
and architectural works as examples of licenses contain-
ing a much lower royalty. But the works can easily be
found to be quite different for licensing purposes. Some,
such as the sculptures Akari 25N or Mother and Child,
1944-45, do not have the household recognition and
symbolic value of The Column. Others, such as the Walt
Disney Concert Hall, might not have copyright protection
for pictorial representations at all, see Gaylord I, 595 F.3d
at 1380–81 (discussing the Architectural Works Copyright
Protection Act, applicable to buildings but not The Col-
umn, a sculptural work), and involve owners with appar-
ent indirect interests in stamp-generated publicity. The
government has not pointed to such clear evidence of past
similar licensing situations as could warrant overturning
the trial court’s finding regarding the distinctive work at
issue here.
                             3
    The remaining issue is whether the trial court erred
in using $5.4 million as the base for the Postal Service’s
revenue from sold but unused stamps. We find no clear
error in the trial court’s determination.
    The government argues that the trial court should not
have relied on the survey data estimating $5.4 million in
revenue from retained copies of The Column stamp,
14                                            GAYLORD   v. US



because a later study conducted by the same survey
company concluded that its earlier methodology overesti-
mated the number of unused stamps for some types of
stamps. The trial court had sufficient reason not to alter
the $5.4 million base. The later study focused on the
retention of “forever stamps,” 2 J.A. 6605, and the Postal
Service itself did not apply the results to non-forever
stamps, like the stamp at issue here, in its internal ac-
counting procedures, J.A. 6603. That decision squares
with the Postal Service’s position that non-forever stamps
“have different consumer behavior characteristics” from
forever stamps. J.A. 6375. On these facts, the trial court
did not err by relying on the same data the Postal Service
has relied on for decades to track the retention of stamps.
    The government also challenges use of the $5.4 mil-
lion figure by invoking our patent-law decisions involving
multi-component products, where we have insisted that
the base of a running-royalty calculation presented to a
jury generally be tied realistically to the component
embodying the invention. Ericsson, 773 F.3d at 1226–27;
Virnetx, Inc., 767 F.3d at 1327–28; LaserDynamics, 694
F.3d at 67. But even aside from the fact that this is a
copyright case, and one not tried to a jury, it is enough to
say that the principles of the cited line of patent-law
authorities do not undermine the use of the $5.4 million
figure based on the price of the stamp here. The stamp
consists, essentially in full, of the image of Mr. Gaylord’s
work and is not a multi-component product in a meaning-
ful sense. There are two copyrights in that stamp, but



     2 Forever stamps, which first issued in 2007, “can
be used to mail a one-ounce letter regardless of when the
stamps are purchased or used and no matter how prices
may change in the future.” USPS, Forever Stamp Fact
Sheet,    https://about.usps.com/news/fact-sheets/forever-
stamp-facts.htm.
GAYLORD   v. US                                     15



Mr. Alli has already been paid, and the government does
not seek reversal to subtract that $1,500 payment. What
remains is to apportion the revenues, here equaling the
gains, to Mr. Gaylord’s contribution. The 90/10 split
accomplishes that goal.
                     CONCLUSION
   For those reasons, we affirm the judgment of the
Court of Federal Claims.
   No costs.
                     AFFIRMED
