MARKEY, Chief Judge.
Dura Corp. and Kidde, Inc. (Dura) appeal from a judgment of the United States District Court for the Eastern District of Michigan, adopting a report of a special master awarding TWM Manufacturing Co., Inc. (TWM) $31,288,496 in damages for patent infringement. We affirm;
Background
U.S. Patent No. 3,285,621 (’621 patent) issued on November 15, 1966 to Stephen Turner, Jr. The patented device is a “Wheeled Vehicle Suspension” enabling trucks to engage an additional axle and wheels to carry heavy loads. Turner assigned the patent to TWM on August 28, 1969.
On December 19, 1966, Turner charged Dura with infringing the ’621 patent and tendered Dura a license. During negotiations, Dura said it believed the patent invalid. Negotiations ended on April 24, 1967. Dura did not hear from Turner again until his assignee, TWM, sued Dura on February 22, 1973.
Prior Proceedings
The district court granted Dura’s motion for summary judgment, holding TWM’s claim barred by laches and estoppel. 189 USPQ 274 (E.D.Mich.1975). On appeal, the Sixth Circuit reversed and remanded, holding that a genuine issue of material fact existed on whether Dura had engaged in egregious conduct that might undermine its laches and estoppel defenses. 592 F.2d 346, 201 USPQ 433 (6th Cir.1979). TWM had alleged that Dura “plagiarized” the claimed invention and harassed TWM by initiating or sponsoring third party litigation challenging the patent.
On remand, the district court found that: (1) Dura’s behavior was so egregious as to defeat the laches defense; (2) the absence of affirmative misconduct by TWM defeated the estoppel defense; (3) Dura had willfully infringed, and (4) Dura’s “copying” was not such bad faith as to warrant attorney fees. The court upheld the patent. 213 USPQ 423 (E.D.Mich.1981).
The district court entered judgment: reserving decision on enhanced damages; granting an immediate injunction against infringement; and ordering an immediate accounting. The accounting, but not the injunction, was stayed pending Dura’s appeal to the Sixth Circuit Court of Appeals. While that appeal was pending, the district
court found Dura in criminal contempt of the injunction because it sold repair parts for its infringing suspensions. Dura appealed that finding to the Sixth Circuit Court of Appeals.
The Sixth Circuit Court of Appeals: affirmed the rejection of the laches and es-toppel defenses and the upholding of the patent; held that Dura had violated the injunction, but was not guilty of criminal contempt; and remanded for determination of damages. 722 F.2d 1261, 221 USPQ 25 (6th Cir.1983).
The special master held an evidentiary hearing on damages and rendered her report. The district court orally adopted that report
in toto
as not clearly erroneous.
See
Fed.R.Civ.P. 53(e)(2).
The Special Master’s Report
The special master calculated compensatory damages as $8,511,596, the sum of: (1) a 30% royalty, and lost profits for the years proven ($6,465,714); (2) $100 for each sale made by TWM at prices forced lower by the infringement ($1,577,200); (3) special discounts by TWM on some sales to compete with Dura’s pricing practices ($468,-682); and (4) $100 for each sale by Dura in TWM’s lost profit years, because TWM would have made those sales at a $100 higher price ($366,900). The special master trebled the damages and added prejudgment interest, arriving at the ultimate figure of $31,288,496.
In this appeal, Dura does not contest the award of interest, but contests each calculation of damages by the special master as “grossly excessive.”
Issue
Whether the damages judgment appealed from rested on an abuse of discretion.
OPINION
Standard of Review
The methodology of assessing and computing damages under 35 U.S.C. § 284 is within the sound discretion of the district court.
Yarway Corp. v. Eur-Control USA, Inc.,
775 F.2d 268, 275, 227 USPQ 352, 357 (Fed.Cir.1985);
King Instrument Corp. v. Otari Corp.,
767 F.2d 853, 863, 226 USPQ 402, 409 (Fed.Cir.1985),
cert. denied,
— U.S. -, 106 S.Ct. 1197, 89 L.Ed.2d 312 (1986). Dura, as appellant, has the burden of convincing this court that the district court abused its discretion.
Seattle Box Co. v. Industrial Crating and Packing, Inc.,
756 F.2d 1574, 1581, 225 USPQ 357, 363 (Fed.Cir.1985);
Paper Converting Machine Co. v. Magna-Graphics Corp.,
745 F.2d 11, 21, 223 USPQ 591, 598 (Fed.Cir.1984). “Abuse of discretion may be established by showing that the district court either made an error of law, or a clear error of judgment, or made findings which were clearly erroneous.”
Seattle Box Co.,
756 F.2d at 1581, 225 USPQ at 363;
see also American Original Corp. v. Jenkins Food Corp.,
774 F.2d 459, 462-64, 227 USPQ 299, 300-02 (Fed.Cir.1985).
Reasonable Royalty
35 U.S.C. § 284 governs the award of damages for patent infringement. It provides:
Upon finding for the claimant the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer, together with interest and costs as fixed by the court.
* * * * * *
The court may receive expert testimony as an aid to the determination of damages or of what royalty would be reasonable under the circumstances.
For the years TWM could not establish its lost profits, TWM and Dura agreed that the district court should determine a reasonable royalty based on a “hypothetical royalty resulting from arm’s length negotiations between a willing licensor and a willing licensee.”
Hanson v. Alpine Valley Ski Area, Inc.,
718 F.2d 1075,1078, 219 USPQ 679, 682 (Fed.Cir.1983);
see Tektro-nix, Inc. v. United States,
552 F.2d 343, 348-49, 213 Ct.Cl. 257, 193 USPQ 385, 390-
392 (1977),
cert. denied,
439 U.S. 1048, 99 S.Ct. 724, 58 L.Ed.2d 707 (1978);
Georgia-Pacific Corp. v. U.S. Plywood Corp.,
318 F.Supp. 1116, 1120-22, 166 USPQ 235, 238-39 (S.D.N.Y.1970),
modified,
446 F.2d 295, 170 USPQ 369 (2d Cir.),
cert. denied,
404 U.S. 870, 92 S.Ct. 105, 30 L.Ed.2d 114 (1971). The parties recognize that no established royalty exists in this case.
The special master, citing
Georgia-Pacific
and
Tektronix,
used the so-called “analytical approach”, in which she subtracted the infringer’s usual or acceptable net profit from its anticipated net profit realized from sales of infringing devices.
Relying principally on a memorandum written by “Dura’s top management” before the initial infringement, the special master found that Dura projected a gross profit averaging 52.7% from its infringing sales. From that figure, she subtracted overhead expenses to get an anticipated net profit in the range of 37% to 42%. Subtracting the industry standard net profit of 6.56% to 12.5% from that anticipated net profit range, she arrived at a 30% reasonable royalty.
Dura says the special master erred as a matter of law in failing to analyze all factors delineated in
Georgia-Pacific.
Had she done so, says Dura, she would have found the “analytical approach” inapplicable. Unlike the situation in
Georgia-Pacific,
Dura argues, Turner had an unproven product he was desperate to license to a company like Dura with marketing and manufacturing expertise, and there was a market leader with an established non-infringing product. Dura contends that it was error for the special master to rely on Dura’s estimate of future profit in a purely speculative memorandum. Having reevaluated the
Georgia-Pacific
factors, Dura strenuously argues that the 30% royalty was “exorbitant” and “totally at odds with the result indicated by the other factors.”
Dura has cited nothing which would limit the district court’s discretion in choosing the analytical approach to determine a reasonable royalty. Section 284 does not mandate how the district court must compute that figure, only that the figure compensate for the infringement.
Aro Manufacturing Co. v. Convertible Top Replacement Co.,
377 U.S. 476, 507, 84 S.Ct. 1526, 1543, 12 L.Ed.2d 457, 141 USPQ 681, 694 (1964).
In arguing against the district court’s application of the analytical approach, Dura deals mostly with events subsequent to its initial infringement. Although evidence of actual profits is generally admissible,
Trans-World Manufacturing Corp. v. Al Nyman & Sons, Inc.,
750 F.2d 1552, 1568, 224 USPQ 259, 269 (Fed. Cir.1984), the district court here correctly focused on the date when the infringement began.
Hanson,
718 F.2d at 1079, 219 USPQ at 682;
Panduit Corp. v. Stahlin Bros. Fibre Works, Inc.,
575 F.2d 1152, 1158, 197 USPQ 726, 731 (6th Cir.1978).
On appeal, an infringer cannot successfully argue that the district court abused its discretion in awarding a “high” royalty by simply substituting its own re-computation to arrive at a lower figure.
See Paper Converting Machine Co.,
745 F.2d at 21, 223 USPQ at 598-99. That argument does not show error, but merely indicates the damages an infringer-appellant would prefer to pay. That the district court might have viewed the infringer’s evidence more favorably is not a basis for reversal.
See American Original Corp., 774
F.2d at 462-64, 227 USPQ at 300-02.
Whether Dura’s computation was more accurate than that proffered by TWM’s experts was for the special master to decide. Dura’s pointing to facts that might have supported a lower royalty does not sustain its burden of showing that the district court abused its discretion in adopting the facts found by the special master. Nor does it establish that the master’s findings were clearly erroneous. Dura’s oversimplified argument that the special master considered only one
Georgia-Pacific
factor will not withstand analysis in light of the master’s extensive report.
The special master gave weight to the testimony of TWM’s witnesses, who said
their computations were derived from the factors in
Georgia-Pacific.
On the other hand, Dura offered no testimony from any of its present or former employees who were familiar with Dura or TWM. Dura has given no basis for this court to take the highly unusual step of rejecting credibility determinations of the special master.
Moreover, Dura disregards the effect of the special master’s specific rejection of many of the “facts” Dura urges on appeal. For example, Dura insists that there existed non-infringing alternatives. However, the special master found that the
absence
of such alternatives was indicated by Dura’s: (1) failure to design its own device, despite the alleged availability of other suspensions now characterized by Dura as “acceptable”; (2) election to infringe, despite having expended only minimal sums when notified of infringement; (3) willful infringement; (4) failure to successfully market other allegedly “acceptable” designs; (5) violation of the 1981 injunction, and (6) withdrawal from the business after enforcement of the injunction.
The special master’s notation that the Turner invention’s immediate commercial success, its satisfaction of a long-felt need, and the absence of a competing suspension possessing all its beneficial characteristics, were factors tending to support a 30% royalty, is supported in the record.
The special master properly rejected Dura’s effort to downplay the significance of its pre-infringement internal memorandum, because it was more probative than profits realized shortly after the infringement, because Dura’s loss of its documents precluded TWM from showing lost profits, and because Dura used the figures in the memorandum in deciding whether to manufacture and market the infringing device.
On appeal, this court may not exercise
de novo
review over the special master’s finding on Dura’s anticipated profit. That rule is unaffected by the basis for that finding, i.e., by whether it is based on testimony or on physical or documentary evidence.
Anderson v. City of Bessemer, N.C.,
— U.S.-, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985). The special master thoroughly considered and weighed the Dura memorandum, and this court may not reweigh it. “Determining the weight and credibility of the evidence is the special province of the trier of fact.”
Inwood Laboratories, Inc. v. Ives Laboratories, Inc.,
456 U.S. 844, 856, 102 S.Ct. 2182, 2189, 72 L.Ed.2d 606, 214 USPQ 1, 7 (1982).
The special master properly resolved difficulty in determining the royalty figure against Dura as an infringer which had lost its records.
Gyromat Corp. v. Champion Spark Plug Co.,
735 F.2d 549, 554-55, 222 USPQ 4, 8 (Fed.Cir.1984). She recognized that “any adverse consequences must rest on the infringer when the inability to ascertain lost profits is due to the infringer’s own failure to keep accurate or complete records.”
Lam, Inc. v. Johns-Manville Corp.,
718 F.2d 1056, 1065, 219 USPQ 670, 675 (Fed.Cir.1983).
Dura has not persuaded this court that a 30% royalty does not reflect what a willing licensor and licensee would have agreed to in 1967, based on the present record. That Turner might have agreed to a lesser royalty is of little relevance, for to look only at that question would be to pretend that the infringement never happened. “It would also make an election to infringe a handy means for competitors to impose a ‘compulsory license’ policy upon every patent owner.”
Panduit Corp.,
575 F.2d at 1158, 197 USPQ at 731. The willing licensee/licensor approach must be flexibly applied as a “device in the aid of justice.”
Cincinnati Car Co. v. New York Rapid Transit Corp.,
66 F.2d 592, 595, 19 USPQ 40, 43 (2d Cir.1933).
Entire Market Value Rule
Dura argues that the special master erroneously included unpatented wheels and axles in the royalty base and in the lost profits award. Dura contests the applicability of the “entire market value” rule here because TWM did not manufacture the unpatented parts, but merely pro
vided them as a “convenience to its customers.”
We reject Dura’s argument that the inclusion of unpatented items in the royalty base or lost profits determination is dependent on who manufactures those items, or on whether they are supplied for “convenience”.
The entire market value rule allows for the recovery of damages based on the value of an entire apparatus containing several features, when the feature patented constitutes the basis for customer demand.
See, e.g., King Instrument Corp. v. Otari Corp.,
767 F.2d 853, 865, 226 USPQ 402, 410-11 (Fed.Cir.1985),
cert. denied,
— U.S. -, 106 S.Ct. 1197, 89 L.Ed.2d 312 (1986);
Paper Converting Machine Co.,
745 F.2d at 22, 223 USPQ at 599 (Fed.Cir. 1984). It is the “ ‘financial and marketing dependence on the patented item under standard marketing procedures’ which determines whether the non-patented features of a machine should be included in calculating compensation for infringement.”
Kori Corp. v. Wilco Marsh Buggies and Draglines, Inc.,
761 F.2d 649, 656, 225 USPQ 985, 989 (Fed.Cir.),
cert. denied,
-U.S.-, 106 S.Ct. 230, 88 L.Ed.2d 229 (1985) (quoting
Leesona Corp. v. United States,
599 F.2d 958, 974, 220 Ct.Cl. 234, 202 USPQ 424, 439,
cert. denied,
444 U.S. 991, 100 S.Ct. 522, 62 L.Ed.2d 420 (1979)). In establishing lost profits, “[t]he deciding factor ... is whether ‘[njormally the patentee (or its licensee) can anticipate sale of such unpatented components as well as of the patented’ ones.”
Paper Converting Machine Co.,
745 F.2d at 23, 223 USPQ at 599 (quoting
Tektronix,
552 F.2d at 351, 193 USPQ at 393).
Where a hypothetical licensee would have anticipated an increase in sales of collateral unpatented items because of the patented device, the patentee should be compensated accordingly.
Cf. Trans-World Manufacturing Co.,
750 F.2d at 1568, 224 USPQ at 269-70 (increased sales of unpatented items may be relevant in determining reasonable royalty). That correlation was shown to exist in this case. Because Dura did not show how many, if any, of the patented devices were sold alone without wheels and axles, the special master could not have apportioned the infringing sales if such apportioning had been appropriate. The special master correctly included unpatented items in the royalty base.
Having shown each of the elements for lost profits, TWM established that in all reasonable probability it would have made the sales that Dura made. The special master therefore correctly included the un-patented wheels and axles in her lost profits determination.
Lost Profits
Dura says TWM should get no lost profits because it did not establish absence of acceptable non-infringing substitutes, which, says Dura, need not possess all the beneficial characteristics of the patented device. Alternatively, Dura says the concession of a TWM witness (that competition existed in 30% of the market) means there must have been non-infringing substitutes in at least that portion of the market.
Dura’s arguments are without merit. As above indicated, the special master found many facts clearly establishing absence of acceptable substitutes. Dura has failed to show that any of the many findings on which the magistrate’s no-substitutes determination was based was clearly erroneous.
Mere existence of a competing device does not make that device an acceptable substitute. The special master committed no error in noting that none of the alleged substitutes had all beneficial characteristics of the patented device.
See Central Soya Co. v. Geo. A. Hormel & Co.,
723 F.2d 1573, 1579, 220 USPQ 490, 494 (Fed. Cir.1983). That finding supported the determination that there were no acceptable substitutes. “A product lacking the advantages of that patented can hardly be termed a substitute ‘acceptable’ to the customer who wants those advantages.”
Panduit Corp.,
575 F.2d at 1162, 197
USPQ at 734. Moreover, Dura ignored those substitutes while it sold the patented invention and thus its acceptable substitute argument “must be viewed of limited influence.”
Id.
at 1162 n. 9, 197 USPQ at 734 n. 9.
Dura has shown no error in the special master’s determination that TWM is entitled to lost profits for the years its lost profits exceeded its reasonable royalty.
Diminished Sales Prices and Special Discounts
Dura argues that the special master should not have awarded TWM $100 for each TWM sale and Dura sale in the lost profit years 1976-1979 because that award was based on testimony which is “totally fallacious and contrary to other evidence in the case.” Dura argues that nothing in the record supports the finding that TWM could have sold its patented product for $100 more had Dura not infringed.
The special master credited the testimony of TWM’s witnesses, Messrs. Wilkof and Van Denberg, who testified that Dura’s infringement caused TWM to keep its prices down $100 on the average. Dura presented no rebuttal witnesses to that testimony. When no contrary evidence exists in the record, bald assertions that the testimony is self serving and defies common sense cannot form a “basis on which this court could engage in the normally inappropriate process of substituting a contrary credibility determination for that of the district court.”
Windsurfing International, Inc. v. AMF Inc.,
782 F.2d 995, 999, 228 USPQ 562, 565 (Fed.Cir.1986).
In addition to the $100 price reduction, substantial evidence supports the special master’s finding that TWM had to give special discounts to compete with Dura’s pricing practices. Dura’s argument that there was no correlation between the special discounts and its infringing activity is contrary to the record and must be rejected.
In determining an award “adequate to compensate”, 35 U.S.C. § 284, there must be room to take into account the totality of the circumstances. The sale price and discount elements employed here may be unusual. Their employment under the circumstances of this case, however, did not constitute an abuse of discretion.
Because Dura has shown no evidence contradicting the special master’s findings concerning the $100 on each TWM sale, $100 on each Dura sale, and TWM’s special discounts, those awards must be affirmed.
Enhanced Damages
Dura concedes that the district court’s finding of willfull infringement is the law of the case. Dura contends, however, that absence of a finding of its “bad faith” precludes an award of enhanced damages for that willful infringement.
This court reviews an award of enhanced damages under an abuse of discretion standard,
See, e.g., Rosemount, Inc. v. Beckman Instruments, Inc.,
727 F.2d 1540, 1547-48, 221 USPQ 1, 8-9 (Fed. Cir.1984), and has repeatedly affirmed enhanced awards based on findings of willful infringement. See cases cited in
S.C. Johnson & Son, Inc. v. Carter-Wallace, Inc.,
781 F.2d 198, 200, 228 USPQ 367, 368 (Fed.Cir.1986). Dura cites no law requiring a finding of “bad faith” before awarding increased damages for willful infringement. Nor has Dura shown an abuse of discretion in the district court’s response to Dura’s “bad faith” arguments after the remand. The treble damage award must be affirmed.
Conclusion
The judgment appealed from is affirmed in all respects.
AFFIRMED.