This is an action for patent infringement. Marlee Electronics Corporation (Marlee) appeals from an award of damages based on its contributory infringement of Anders Trell's patent. We vacate and remand.

Anders Trell, a citizen and resident of Sweden, owns United States Letters Patent 3,974,641, issued to him on March 30, 1976. Trell's system, when used in combination with a public telephone network, enables visitors to gain entrance to locked buildings such as apartment houses. The patent claim at issue covers a feature of the electrical system that Trell created, the "common combination lock device," which allows a visitor or tenant to open a locked door directly by entering a special code. In approximately 1976, Marlee included this feature in its products, calling it ENTRAKEY.

On November 9, 1985, Trell filed a complaint against Marlee in the district court, charging Marlee with patent infringement. The district court held that Marlee's systems did not infringe Trell's patent. On appeal, in an unpublished opinion, we reversed, holding that Marlee was liable for contributory infringement of Trell's patent, and remanded with instructions to calculate damages. Trell v. Marlee Electronics Corp., 867 F.2d 615 (Fed.Cir.1989). Upon remand, the district court awarded Trell partial damages for the period from January 1, 1980 to January 1, 1987 in the amount of $504,000, and prejudgment interest in the amount of $298,166. Marlee has timely appealed the damage award.

Marlee first argues that Trell failed to sustain his burden of proving any direct infringement for which Marlee would be liable as a contributory infringer. "[I]f there is no direct infringement of a patent there can be no contributory infringement." Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336, 341, 81 S. Ct. 599, 602, 5 L. Ed. 2d 592 (1961) (Aro I ) (emphasis in original). Marlee thus asserts that the district court erred in awarding damages to Trell. In our prior review of this matter, we concluded that the record showed contributory infringement by Marlee. Our judgment concerning liability is the law of this case, and cannot be reviewed unless one of three exceptional circumstances exists: "the evidence on a subsequent trial was substantially different, controlling authority has since made a contrary decision of law applicable to such issues, or the decision was clearly erroneous and would work a manifest injustice." Yachts America, Inc. v. United States, 779 F.2d 656, 659-70 (Fed.Cir.1985), cert. denied, 479 U.S. 832, 107 S. Ct. 122, 93 L. Ed. 2d 68 (1986); Smith Int'l v. Hughes Tool Co., 759 F.2d 1572, 1576 (Fed.Cir.1985) (same) (quoting Central Soya Co. v. George A. Hormel & Co., 723 F.2d 1573, 1580-81 (Fed.Cir.1983)), cert. denied, 474 U.S. 827, 106 S. Ct. 87, 88 L. Ed. 2d 71 (1985); see also Eichman v. Fotomat Corp., 871 F.2d 784, 791 (9th Cir.1989) ("Under the law of the case doctrine a decision of the court in a prior appeal must be followed in all subsequent proceedings in the same case."). Because Marlee has invoked none of the exceptions to the law of the case doctrine, the issue of liability cannot be revisited.

Marlee next challenges the district court's method of calculating damages. "Assessing and computing damages under 35 U.S.C. Sec. 284 is a matter within the sound discretion of the district court." Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1576 (Fed.Cir.1988). "Abuse of discretion may be established by showing that the district court's decision was based on an error of law or on clearly erroneous fact findings, or that the district court made a clear error of judgment." Id. at 1577. Marlee argues that the district court's finding of fact that "[s]ix (6) percent of the net selling price of Defendant Marlee's infringing entry control system is an established and reasonable royalty rate pursuant to 35 U.S.C. Sec. 284" is clearly erroneous.

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 of the invention by the infringer, together with interest and costs as fixed by the court.

35 U.S.C. Sec. 284 (1982). The two methods by which damages are usually calculated under Sec. 284 are assessment of actual damages (the profits the patentee lost due to the infringement) or, if actual damages cannot be ascertained, determination of a reasonable royalty. Hanson v. Alpine Valley Ski Area, Inc., 718 F.2d 1075, 1078 (Fed.Cir.1983). Because Trell did not sell its invention in the United States, he could not seek damages on the basis of lost profits. Lindemann Maschinenfabrik GmbH v. American Hoist & Derrick Co., 895 F.2d 1403, 1406 n. 2 (Fed.Cir.1990). Thus, Trell was required to present evidence of a reasonable royalty. Hanson, 718 F.2d at 1078.

A reasonable royalty "may be based upon an established royalty, if there is one, or if not upon a hypothetical royalty resulting from arm's length negotiations between a willing licensor and a willing licensee." Id. On remand, Trell presented evidence of its license agreement with Bewator Svensk Teleproduktion AB (Bewator), which provided for a royalty rate of 6 percent for the exclusive right to sell Trell's system in Europe. The district court concluded that 6 percent was the "established and reasonable royalty rate."

Marlee contends that the district court erred in concluding that the royalty payment under the Bewator license constituted proof of an established royalty. We agree. A single licensing agreement, without more, is insufficient proof of an established royalty. As we noted in Hanson v. Alpine Valley Ski Area, Inc., for a royalty to be established, it "must be paid by such a number of persons as to indicate a general acquiescence in its reasonableness by those who have occasion to use the invention." Hanson, 718 F.2d at 1078 (citing Rude v. Westcott, 130 U.S. 152, 165, 9 S. Ct. 463, 468, 32 L. Ed. 888 (1889)).

Because no established royalty existed for licensing the Trell patent, the district court "necessarily had to use 'a willing-buyer/willing-seller concept, in which a suppositious meeting between the patent owner and the prospective [user] of the infringing [method] is held to negotiate a license agreement.' " Id. at 1079 (quoting Tektronix, Inc. v. United States, 213 Ct. Cl. 257, 552 F.2d 343, 349 (1977), amended, 213 Ct. Cl. 307, 557 F.2d 265 (1977)). In determining the result of such a hypothetical negotiation, the district court may consider the infringer's anticipated profits, as indicated by evidence of actual profits. Trans-World Mfg. Corp. v. Al Nyman & Sons, Inc., 750 F.2d 1552, 1568 (Fed.Cir.1984). The court may also "receive expert testimony as an aid to the determination of damages or of what royalty would be reasonable under the circumstances." 35 U.S.C. Sec. 284. The court may also evaluate evidence of what rate the patentholder itself would have required to grant a license. CPG Prods. Corp. v. Pegasus Luggage, Inc., 776 F.2d 1007, 1010 (Fed.Cir.1985). Although "there is room for exercise of a common-sense estimation of what the evidence shows would be a 'reasonable' award," Lindemann, 895 F.2d at 1406, the district court must consider what is reasonable "under all the circumstances." Fromson, 853 F.2d at 1575.

The district court in this case failed to determine what royalty a negotiated license agreement between Trell and Marlee would have produced. Instead, the Court appears to have based its award of damages on the royalty paid for the Bewator license. At the damage hearing, the Court commented as follows:

THE COURT: See, here's [what] I'm having problems with. I'm having problems, you see, going beyond the evidence of this case, remaking what a willing buyer and willing seller, that have negotiated on as to the applicable royalty to be paid ... for this particular feature.

The evidence is that, Mr. Trell, gets six percent in Europe for selling whatever rights [are] patented over there. That's the only evidence introduced at this trial.

Now, what you're asking me to do now is to really come up with a figure from the defendant's perspective here, allocating an amount you contend is fair for the royalty that the defendant [has] to pay, in view of the Appellate decision, to Mr. Trell.

The only evidence that I have is six percent. For me to select anything other than six percent, would[ ] it be sustained by the evidence?

....

And I have got to look at the evidence. The evidence is that, there is only one royalty amount that has been set and that's six percent....

A. 774-75, 777. The court, however, failed to consider all of the evidence in the record, some of which tends to negate reliance on the Bewator license fee as a reasonable royalty. For instance, the evidence suggests (1) that the Bewator agreement was an exclusive license and conveyed rights more broad in scope than those covered by Trell's patent; (2) that the infringement of claim 9 of Trell's patent, for which Marlee was found liable, relates to only one aspect of its accused device; and (3) that the cost of producing that infringing aspect, i.e., the ENTRAKEY feature, was relatively small and did not contribute appreciably to Marlee's sales price or profit.

Thus, the district court erred in relying solely on the fee set forth in the Bewator license as a reasonable royalty to compensate for Marlee's infringement. "[A] particular fee is not the correct measure of damages unless that which is provided by the patentee to its licensees for that fee is commensurate with that which the defendant has appropriated." Bandag, Inc. v. Gerrard Tire Co., Inc., 704 F.2d 1578, 1582 (Fed.Cir.1983). Marlee's infringement related to only one aspect of Trell's invention, as compared with the scope of the Bewator license. The district court's apparent failure to consider the fact that the Bewator license was exclusive and that it encompassed the right to other inventions compels reversal.

We recognize that an assessment of a royalty based on a fictional negotiation is not a simple task. "Determining a fair and reasonable royalty is often, ... a difficult judicial chore, seeming often to involve more the talents of a conjurer than those of a judge." Fromson, 853 F.2d at 1574. Nevertheless, the court must exercise its discretion in a manner consistent with the law of this circuit. As discussed above, acceptance of the rate contained in a single, broader existing license as an established royalty is contrary to our decision in Hanson.

Trell had the burden of persuading the court with legally sufficient evidence regarding the amount that should be awarded as a reasonable royalty. Having erroneously concluded that the Bewator license was proof of an established royalty, the district court appears to have fixed 6 percent as a reasonable royalty because of Marlee's failure to offer evidence that this rate was unreasonable. Marlee, however, did not have the burden of going forward with evidence to rebut proof of a royalty paid by another for an exclusive license involving additional inventions. We cannot sustain the district court's award on the ground that Marlee did not present evidence to show that a rate less than 6 percent would be reasonable. The record does not contain legally sufficient proof of an established rate or any evidence showing that 6 percent was a reasonable royalty.

3. DAMAGES FOR PERIOD PRIOR TO MARLEE'S KNOWLEDGE OF PATENT

Marlee maintains that the district court erred in awarding Trell damages for sales made prior to Marlee's knowledge of Trell's patent. 35 U.S.C. Sec. 271(c) provides:

(c) Whoever sells a component of a patented machine, manufacture, combination or composition, or a material or apparatus for use in practicing a patented process, constituting a material part of the invention, knowing the same to be especially made or especially adapted for use in an infringement of such patent, and not a staple article or commodity of commerce suitable for substantial noninfringing use, shall be liable as a contributory infringer.

35 U.S.C. Sec. 271(c) (1982) (emphasis added). The district court awarded damages to Trell for the period from January 1, 1980 to January 1, 1987, in addition to prejudgment interest from January 1, 1980 to date. The Pre-Trial Order in the original infringement action included as an admitted fact: "In a letter dated April 2, 1985, Plaintiff's attorney advised Defendant of Plaintiff's patent 3,947,641." Trell introduced no evidence that Marlee had the requisite knowledge prior to that date.

Section 271(c) "require[s] a showing that the alleged contributory infringer knew that the combination for which his component was especially designed was both patented and infringing." Aro Mfg. Co. v. Convertible Top Replacement Co., 377 U.S. 476, 488, 84 S. Ct. 1526, 1533, 12 L. Ed. 2d 457 (1964) (Aro II ). In Aro II, the Supreme Court held that the knowledge requirement of section 271(c) limited an alleged contributory infringer's liability to sales made after it received a letter from the patentholder informing it of the existence of the patent. Id. at 491, 84 S.Ct. at 1534. The Court directed the district court to make a finding of fact on the question of the alleged contributory infringer's knowledge of the existence of the patent prior to receipt of the letter. Id. The district court was also instructed that, if the alleged contributory infringer did not have such knowledge, the judgment imposing liability had to be vacated as to any sales made before the date it received the letter. Id.

Trell maintains that Marlee is estopped from raising this issue before this court because it failed to raise the issue before the district court. Failure to raise issue of knowledge of contributory infringement does not bar consideration of this question for the first time on appeal. In Aro II, the Supreme Court raised this issue sua sponte: "[T]he language of Sec. 271(c) presents a question, apparently not noticed by the parties or the courts below, concerning the element of knowledge that must be brought home to [the contributory infringer] before liability can be imposed." Id. at 488, 84 S.Ct. at 1533 (emphasis added). We note also that, at oral argument, Trell's counsel admitted that he was cognizant at the time of trial of the rule that damages cannot be awarded for contributory infringement unless there is evidence of knowledge of the existence of a patent. On remand, the district court shall determine whether and when Marlee knew of the existence of Trell's patent.

The district court improperly construed the 6 percent rate in the Bewator license as an established royalty and failed to calculate a reasonable royalty based upon the amount a willing buyer and seller would have negotiated to license the device covered by the Trell patent.

Upon remand, the district court is directed to determine a reasonable royalty consistent with the methodology set forth in our opinion in Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568 (Fed.Cir.1988), and to determine the date of Marlee's first knowledge of Trell's patent.

Each party shall bear its own costs.

VACATED AND REMANDED.