
    STUDIENGESELLSCHAFT KOHLE, m.b.H., Plaintiff-Appellant, v. DART INDUSTRIES, INC., and Kraft, Inc., Defendants/Cross-Appellants.
    Nos. 88-1052, 88-1087 and 88-1088.
    United States Court of Appeals, Federal Circuit.
    Dec. 14, 1988.
    
      Arnold Sprung of Sprung Horn Kramer & Woods, New York City, argued for plaintiff-appellant. With him on the brief was Nathaniel D. Kramer.
    Stanton T. Lawrence, III of Pennie & Edmonds, New York City, argued for defendant/cross-appellant Dart. With him on the brief were Thomas F. Reddy, Jr. and James G. Markey.
    Thomas V. Heyman of Dewey, Ballan-tine, Bushby, Palmer & Wood, New York City, argued for defendant/cross-appellant Kraft. With him on the brief was Claire Ann Koegler. Of counsel were E. Norman Veasey and Robert H. Richards, III of Richards, Layton & Finger, Wilmington, Del.
    Before MARKEY, Chief Judge, and RICH and NEWMAN, Circuit Judges.
   RICH, Circuit Judge.

These appeals are from an accounting in a patent suit. The accounting trial was held before a special master who assessed damages, as of October 31, 1986, at $69,-942,450. The district judge reviewed the master’s report on the parties’ objections, finding certain errors. In an August 13, 1987, Opinion the district judge identified and corrected the errors and arrived at a revised award of $43,756,784.71 as of the date of judgment, September 30,1987. We affirm.

I. The parties and the Litigation

Plaintiff Studiengesellschaft Kohle m.b. H. (SGK) is successor in interest to Dr. Karl Ziegler, Nobel prize-winning scientist and inventor. This litigation began in July 1970 when SGK sued Dart Industries, Inc., in the District of Delaware, alleging infringement of Ziegler’s U.S. Patent No. 3,113,115 (’115), which covers broadly certain catalysts useful for commercial production of polymers of lower alpha-olefins. Kraft, Inc., the second defendant, only later became a party as a result of a corporate reorganization. For convenience, we refer to defendants jointly as “Dart.” We use the names “Ziegler” and “SGK” interchangeably.

Trial was held before District Judge Caleb M. Wright, who held that Dart had not carried its burden of proving the ’115 patent invalid and that Dart’s polypropylene operation in Odessa, Texas, infringed the patent. We affirmed that decision and remanded for an accounting. Studiengesellschaft Kohle mbH v. Dart Industries, 549 F. Supp. 716, 216 USPQ 381 (D.Del.), aff'd, 726 F.2d 724, 220 USPQ 841 (Fed.Cir. 1984). Judge Wright’s Opinion reviewing the master’s report is reported at 666 F.Supp. 674, 4 USPQ2d 1817. Familiarity with these opinions is assumed.

II. Standard of Review

We addressed the issue of appellate review of a decision of a district court which rejects findings of a master in Milliken Research Corp. v. Dan River, Inc., 739 F.2d 587, 222 USPQ 571 (Fed.Cir.1984). We apply the standard of review stated in Milliken, 739 F.2d at 592-93, 222 USPQ at 576.

III. Issues

The objections to the master’s report and the arguments here on appeal have centered on three areas: (1) the amount of damages to be awarded SGK; (2) whether Dart willfully infringed the '115 patent; and (3) whether SGK should be awarded prejudgment interest and, if so, the rate and periods for which it should be awarded. Since, as stated in Milliken, our task is to review the trial court’s judgment, the issues are:

1. Whether the district court erred in concluding that the master’s finding of a 4.0% reasonable royalty was clearly erroneous.

2. If not, whether the court’s substitute finding of a reasonable royalty of 2.5% plus a fully creditable down payment is clearly erroneous.

3. Whether the district court erred in concluding that the master’s finding that Dart willfully infringed the ’115 patent was clearly erroneous.

4. Whether the district court abused its discretion in adopting the master’s recommendation of an award of prejudgment interest at the prime rate compounded quarterly.

IV. Opinion

A. The Role of the District Court

Initially, SGK expresses concern that the district court reviewed the master’s findings of fact under an improper standard. SGK notes that while the district court paid “frequent homage” to the clearly erroneous standard it was bound to apply under Fed.R.Civ.P. 53(e)(2), “[nevertheless, some portions of the opinion read as if the Court were subconsciously applying the normal decision making authority of a federal district judge, i.e., a de novo consideration of the evidence in light of the arguments first made to him.”

We do not share this concern. Judge Wright devoted the better part of a printed page of his Opinion to scope of review, and he understood that the court’s “freedom to alter the Master’s determination [was] limited because the Master’s findings of fact must be adopted unless they are clearly erroneous.” So it is no accident that references to the clearly erroneous standard appear throughout the body of his Opinion. Moreover, the court did not merely give lip service to the standard. In each instance where a finding was held clearly erroneous, that conclusion was well supported by reason.

B. The Master’s Finding of a 3.7 to Jt.0% Floor

The master used a hypothetical negotiation to fix a reasonable royalty, after rejecting an argument that the evidence proved an established royalty. He considered a host of relevant factors and made many findings, most of which Judge Wright adopted. The master rejected the testimony of Dart’s expert, Mr. Goldscheider, and credited that of SGK’s expert, Professor Bischel. The master’s approach was to identify a range of royalties the parties would consider in the negotiations, and he fixed the lowest royalty or “floor” which Ziegler would consider at 3.7 to 4.0%, based on Ziegler’s 1950’s licenses, which contained most favored licensee clauses. He explained:

The negotiators would be aware of the 1950’s licenses entered into by Ziegler at the sliding scale of 4 — 3—2[%] plus up front payments. Ziegler’s negotiators would certainly point out that it could not license the '115 below the 4-3-2 scale, particularly in light of the most favored licensee clauses contained in those licenses. Professor Bischel testified, and I find, that the effective rate of the 4-3-2 [licenses] would be approximately 2.1% or 2.2% without consideration of the down payments made by the licensees. The up-front or down payments would have to be added into the royalty rate. Professor Bischel’s opinion was that the effective rate plus the down payment would lead to a hypothetical rate not less than 3.7% to 4.0%. (R..6151). That is the rate that would have to be entered into in order to avoid any most favored licensee clause in the 1950’s licenses so that SGK would not be required to refund money or lower rates to its earlier licensees. (R.6150-51).

Judge Wright decided the master’s determination that the floor should be between 3.7 and 4.0% was a clear factual and legal error. As to the fact error, Judge Wright saw two possible factual bases for the master’s arrival at a 3.7 to 4.0% floor. SGK does not argue the plausibility of the master’s first basis — that “the up-front or down payments would have to be added into the royalty rate” — which Judge Wright identified as clearly erroneous, so we need not consider that point.

The second possible basis for the master’s use of a 3.7 to 4.0% floor lay in the testimony of Professor Bischel, which is set out in the margin. Judge Wright accepted Bischel’s premise that Ziegler received certain economic benefits from the use of a down payment/running royalty arrangement as opposed to a straight running royalty, such as time use of the down payment money and decreased risk that future royalty payments might be withheld. Judge Wright rejected, however, Bischel’s factually unsupported conclusion that these benefits would translate into a jump from an effective royalty of 2.1 to 2.2% plus a creditable down payment, to a straight royalty of 3.7 to 4.0% if Ziegler had chosen to negotiate a straight running royalty.

SGK argues it was the district court that erred because the master was not clearly erroneous in accepting Professor Bischel’s floor. First, SGK says that since Bischel was not cross-examined by Dart on his testimony concerning a floor, the master’s crediting of this “uncontroverted” expert testimony cannot be clearly erroneous. Acr cording to SGK, Federal Rule of Evidence 705 makes clear that Bischel did not have to affirmatively testify to his mental processes and calculations in arriving at his 3.7 to 4.0% floor. SGK adds that since the master required no underlying facts or data, if any were desired, it was incumbent on Dart to raise the same by cross-examination, citing United States v. Santarpio, 560 F.2d 448, 454-55 (1st Cir.), cert. denied sub nom. Schepici v. United States, 434 U.S. 984, 98 S.Ct. 609, 54 L.Ed.2d 478 (1977). Second, SGK asserts that the floor which Judge Wright ultimately adopted would have been more costly to Dart than the master’s 3.7 to 4.0% floor over the first five years of any agreement, the implication being that the master’s floor can hardly have been clearly erroneous.

We accept the premise of SGK’s first argument but reject the conclusion SGK draws. Rule 705 of the Federal Rules of Evidence, set out in the margin, addresses the circumstances under which an expert must disclose the facts or data underlying an opinion. We agree that pursuant to Rule 705 Bischel was not obligated to reveal the facts or data underlying his opinion on a floor, because Dart did not cross-examine on this issue and the master did not require otherwise. But nothing in Rule 705 bears on the circumstances under which the trier of fact or a reviewing court is required to credit expert testimony.

In the Santarpio case, an expert gave an opinion without describing or explaining the relevance of the factors upon which he based it. He was not cross-examined regarding his conclusion, and the First Circuit merely held that, under the circumstances of that case, the district court “was entitled to credit the expert’s conclusion.” Santarpio, 560 F.2d at 455 (our emphasis). Thus, Rule 705 and Santarpio do not support SGK’s conclusion that a court must credit expert testimony which goes uncross-examined, even if that testimony is inherently unbelievable. The flaw in Bis-chel’s testimony is demonstrated by Dart’s calculations, unrebutted by SGK, which show that the value of the interest earned on the up-front payments in the 1950’s licenses resulted in an effective royalty, based on Dart’s sales, approximately 0.1% greater than would have resulted if there had been no up-front payments.

SGK’s second argument is unpersuasive because it is based in part on an incorrect assumption. SGK’s showing that the floor ultimately adopted by Judge Wright was less favorable to Dart than that chosen by the master is based on Dart’s anticipated profits for the first five years of its polypropylene operation and therefore assumes that the negotiators would only have concerned themselves with the royalty picture through the first five years of any prospective agreement. This assumption renders SGK’s argument invalid because the parties would have negotiated an agreement for the entire seventeen year life of the '115 patent, not merely one for the first five years of its existence.

Judge Wright determined that the master also erred as a matter of law because he failed to consider the licensing approach SGK used in the 4-3-2 licenses that were the basis for establishing a floor rate. The 4-3-2 licenses provided for large down payments fully creditable towards running royalties, typically to the extent that fifty percent of any royalty payment falling due could be credited to the down payment. Nonetheless, the master selected a floor based on a straight running royalty. The master failed to explain why he did not impose a fully creditable upfront payment on Dart, “instead of undertaking speculation as to the economic value of the up-front payment.” 666 F.Supp. at 684, 4 USPQ2d at 1824. Judge Wright held this to be an error of law. He explained:

Even though this Court affirms the Master’s determination that the 4-3-2 Licenses do not establish a royalty rate, the licensing practice in these agreements is highly relevant in determining the floor royalty rate because it is these licenses that the Master used to justify imposing a floor rate. The Master’s failure to justify creating a different kind of royalty than existed in the 4-3-2 Licenses is an error of law.

Judge Wright relied on Stickle v. Heublein, Inc., 716 F.2d 1550, 219 USPQ 377 (Fed.Cir.1983), for the proposition that the patentee’s usual licensing approach should be considered in assessing a reasonable royalty. This court held in Stickle that a district court was clearly in error for basing a reasonable royalty on the use of a patented machine where the usual practice in the industry was to negotiate a paid-up license based on a lump sum payment for each machine. 716 F.2d at 1561-63, 219 USPQ at 386. The rule of Stickle applies with even greater force in this case to the subsidiary determination of a floor at the hypothetical negotiation, because that floor was based on specific, identifiable licenses granted by Ziegler. SGK’s attempt to distinguish Stickle on its facts is unavailing because Judge Wright drew on that case for a sound principle of law, commonly accepted. See, e.g., 5 D. Chisum, Patents § 20.03[3][b][i] (1988). If the master had looked to SGK’s actual practices as Judge Wright held he should have, the guessing game as to the economic value of the upfront payments would have been unnecessary. The law should make sense even in a field as murky as hypothetical negotiations to fix a reasonable royalty, and, under Judge Wright’s approach, it does.

SGK says Stickle is inapposite because the record in this case discloses the appropriateness of a straight running royalty as a floor. The other licenses SGK refers to, however, were not at any point relied upon as establishing a floor, and, as such, they are irrelevant to what SGK’s actual licensing practices were in the 4-3-2 licenses which were pointed to as establishing a floor. SGK also argues that as of the time of the hypothetical negotiation, the 4-3-2 licenses had become remote in time, and the basic reason for seeking and agreeing to large up-front payments at the expense of royalty points no longer existed. Perhaps if Ziegler were starting with a clean slate at the time of the hypothetical negotiation, SGK’s argument would make sense. But Ziegler did not start with a clean slate: he was contractually obligated to license at terms no more favorable than those granted in the 4-3-2 licenses if he wished to avoid difficulties arising out of the most favored licensee clauses in those licenses. Thus, a very good reason existed for Ziegler to seek large up-front payments as part of any license agreements, even at the time of the hypothetical negotiation.

SGK has also raised a procedural point. SGK says that because Dart did not urge upon the master any hypothetical negotiations result or “floor” setting forth a running royalty and a massive, specified down payment, it was not open to Dart to raise this argument on review before the district court. And, SGK says, the court in its Opinion erred by attempting to “re-write the [reasonable royalty] scenario” produced by Dart at trial, citing CPG Products Corp. v. Pegasus Luggage, Inc., 776 F.2d 1007, 227 USPQ 497 (Fed.Cir.1985).

This argument does not change our minds. Judge Wright held that the master erred in failing to account for SGK’s usual licensing practices. If that legal error was present in the submissions of both parties and the master failed to discern it, the district judge can hardly be criticized for pointing it out.

Nor does CPG help SGK. In CPG, the defendant Pegasus failed to introduce any evidence on damages. The district court fixed a reasonable royalty based on plaintiff’s evidence, and this court, in the course of affirming the denial of Pegasus’s subsequent Rule 60(b) motion for relief from judgment, observed that “[i]t is not among the purposes of the appellate process to re-write the scenario produced by an appellant at trial.” 776 F.2d at 1010, 227 USPQ at 498. Dart, however, did not ask Judge Wright to re-write the factual “scenario” of the 4-3-2 licenses. Instead, Dart challenged the legal theory underpinning SGK’s and the master’s approach to deriving a floor from those licenses. That Dart may initially have followed a similar approach should not preclude Dart from correcting that error, once realized. Nor was Judge Wright obligated on review to accept an erroneous legal theory of the case, even if both parties pursued that theory before the master. Compare CPG, supra, with United States v. Miller, 822 F.2d 828, 831-32 (9th Cir.1987).

In conclusion, SGK has not carried its burden of showing that Judge Wright erred in his determination that the master erred both in fact and in law in setting the floor for the hypothetical negotiation at 3.7 to 4.0%.

C. The Master’s Finding of a f0% Reasonable Royalty

Judge Wright concluded that the master’s error in calculating a floor, together with his failure to give proper weight to the terms of a settlement between Ziegler and Phillips Petroleum, rendered the master’s finding of a 4% reasonable royalty clearly erroneous. Judge Wright explained:

The errors in calculating the floor rate and in understanding the Phillips settlement’s significance render[ ] the Master’s determination that 4% is a reasonable royalty clearly erroneous. The Master’s determination of a floor erroneously limited the range of royalties he could consider. This is especially significant given that the royalty selected is within the range of the floor rate as found by the Master. If the lower most boundary had been properly determined, the Court finds that the Master would have awarded royalties at a lower rate. Second, his grounds for ignoring the Phillips settlement did not in fact apply to that settlement. The Phillips settlement thus stands as an existing royalty that should have been considered in the hypothetical negotiation.

1, The Floor

SGK argues that, even if the master erred in fixing the floor, he was not clearly erroneous in coming to a final royalty rate of 4%. SGK argues that the master credited Professor Bischel’s analysis leading to a 5% royalty, which he then “lowered ... by an additional 1%” to 4% in view of various factors including average royalty rates in the chemical industry. SGK says that since the master started at a higher preliminary rate and came down “as far as required” by the cited downward pressure, it is not at all clear that the master would have reached any other result if the floor were lower or, indeed, if there were no floor at all. Moreover, SGK suggests that if the master felt the determining factor in his final royalty rate were a floor, he could have eliminated a great deal of the analysis in his report and simply said so, but he did not.

What all this boils down to is that the master did not say how much reliance he placed on his 3.7 to 4.0% floor in arriving at a reasonable royalty of 4%. SGK’s position is that the master placed little, if any, reliance on the 3.7 to 4.0% floor; Judge Wright was of the opposite view.

The master’s report supports Judge Wright. First, the fact that the master discussed a floor indicates he thought it was important to his calculation of a reasonable royalty. Second, as Judge Wright noted, the 4% royalty which the master settled on is within the 3.7 to 4.0% range of the floor which the master used. Third, in a negative sense, the master did not say that the cited downward pressures added up to exactly one royalty point. There is nothing in his report to suggest that, if he had used a lower floor, he still would have found 4% to be a reasonable royalty. SGK’s argument in this regard is pure speculation.

SGK asserts that other portions of the record support the master’s determination of a 4% royalty. Dart’s 1962 estimate was that it would have to pay 5 to 7% royalties in toto on its polypropylene operation. Yet, SGK says, as of the date Dart’s plant went on stream, Dart had taken out only one license, with DuPont, thus obligating itself to pay a total of only 1% in royalties to third parties, leaving at least 4% for SGK. But any apparent relation between the 4% figure SGK obtains by this method and the 4% reasonable royalty found by the master is mere happenstance. In 1964, Ziegler and DuPont were not the only owners of intellectual property related to polypropylene; far from it. Thus, SGK and Dart would not have assumed at the hypothetical negotiation that 4% remained for SGK simply because Dart had already committed 1% of its 5 to 7% estimated outlays to DuPont.

2. The Phillips Settlement

The Fifth Circuit held in 1973 that the ’115 patent was valid and infringed by Phillips. Ziegler v. Phillips Petroleum Co., 483 F.2d 858, 177 USPQ 481 (5th Cir.), cert. denied, 414 U.S. 1079, 94 S.Ct. 597, 38 L.Ed.2d 485 (1973). The case was remanded for an accounting, and subsequently settled.

The master concluded that the Phillips settlement was relevant to this case. In discussing a reasonable royalty, however, he ignored the Phillips settlement. Judge Wright concluded he erred in so doing. He explained:

The settlement in Phillips transpired after the Fifth Circuit had reversed the District Court’s finding of no infringement. At the time of the Phillips negotiations, then, Ziegler had the same strength that is ascribed to him in a hypothetical negotiation — an unquestionably valid patent. Ziegler and Phillips agreed to a lump sum settlement of 5 million and a future running royalty of 1.5%. Taken together, as the Master properly held they should be, the effective rate of the Phillips agreement was 2.15%.
Contrary to the Master’s assertion, this settlement is highly probative evidence. The facts here are indistinguishable from those in Devex Corp. v. G.M. Corp., 494 F.Supp. 1369 (D.Del.1980), aff'd, 667 F.2d 347 (3d Cir.1981), aff'd, 461 U.S. 648, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983), where this Court held that the amount Devex offered the industry after a court held its patent valid was highly probative of a reasonable royalty. As in Devex, Phillips involved a licensing pat-entee who had a post-infringement determination of his patent’s validity and proceeded to agree to a rate of compensation for the patent. This brand of post-infringement evidence is distinct from other post-infringement evidence because both Phillips and Ziegler knew that the next step in the process was the exact type of accounting exercise that is being undertaken in this case.

SGK heads its arguments regarding the Phillips settlement: “The Master Was Not Clearly Erroneous in His Findings Relating to Phillips Petroleum” and “The District Court’s Substitute Findings Should, Therefore, Be Set Aside.” As a threshold matter, we think these headings confuse the issues. The master concluded the settlement was relevant; then, he ignored it. In other words, he admitted the settlement agreement as evidence but gave it no weight. The question for Judge Wright was whether the master, in casting aside the Phillips settlement, made a clear error of judgment. Judge Wright obviously thought so because he held that, in view of the undisputed fact of the Phillips settlement, the master’s arrival at a reasonable royalty of 4% was clearly erroneous. The question for us is whether Judge Wright erred in making that determination.

As to specific arguments, SGK first argues that Dart did not urge the master to accept the combined provisions of the Phillips settlement as probative of a reasonable royalty and that, therefore, it was not open to Dart to advance this position for the first time before the district court. SGK again cites CPG Products, supra, as support for its position. Judge Wright considered this exact argument in the context of the Phillips settlement and rejected it. We agree with his reasoning and conclusion, so we need not belabor this point.

Second, SGK argues that the royalty rate of the Phillips settlement was eroded by litigation and infringement and therefore was not probative of a reasonable royalty, and that furthermore, the settlement should be disregarded because it occurred after the date of the hypothetical negotiations:

In any event, reliance upon the eroded royalty rate of the 1974 Phillips license for hypothetical negotiations conducted ten years before, in 1964, whether direct (as Dart unsuccessfully sought before the Master) or indirect (as Dart successfully sought before the District Court) is contrary to the law of this circuit. Deere [& Co. v. International Harvester Co.] 710 F.2d 1551 at 1557 [(Fed.Cir.1983)]; Hanson v. Alpine Valley Ski Area, Inc., 718 F.2d 1075, 1078-79 (Fed.Cir.1983); see Sobering Corp. v. Precision-Cosmet Co., 614 F.Supp. 1368, 1377 (D.Del.1985). Not only are royalty rates eroded by infringement substantially worthless in hypothetical negotiations, but, as Dart’s own expert conceded, the hypothetical negotiations are conducted on the basis of information known to the parties at the time of the negotiations, and once a figure is reached in hypothetical negotiations, “it is not possible then to look at what would happen in the future and lower that figure....”

(record citations omitted). Placing SGK’s erosion argument to the side for one moment, we note that Deere and Alpine Valley do not establish any rule that all post-infringement evidence is irrelevant to a reasonable royalty calculation. Indeed, most recently, in discussing the hypothetical negotiations methodology, this court stated that “[t]he methodology encompasses ... flexibility because it speaks of negotiations as of the time infringement began, yet permits and often requires a court to look to events and facts that occurred thereafter and that could not have been knpwn to or predicted by the hypothetical negotiators.” Fromson v. Western Litho Plate and Supply Co., 853 F.2d 1568, 1575, 7 USPQ2d 1606, 1613 (Fed.Cir.1988). The court went on to hold that, under the circumstances of that case, it would be appropriate for the district court on remand to consider the infringer’s actual profits in calculating a reasonable royalty. Similarly, it was not error for Judge Wright to consider the Phillips settlement in this case, even though it was entered into in 1974 and the effective rate Phillips paid under the combined provisions of the settlement could not be determined until the '115 patent expired in 1981.

As to its erosion argument, SGK additionally states that, “[a]s Chief Judge Mar-key of this Court has cautioned:”

“a royalty, if any, resulting from [settlement of a prior litigation] should not be considered evidence of an ‘established’ royalty and thus a measure of adequate damages here.” Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1164, n. 11 (6th Cir.1978).

(brackets in original). Chief Judge Markey has also cautioned that cases should not be cited for mere words. Fromson, supra. The rest of the Panduit footnote reads:

License fees negotiated in the face of a threat of high litigation costs “may be strongly influenced by a desire to avoid full litigation. Rude v. Westcott, 130 U.S. 152, 164, 9 S.Ct. 463 [468], 32 L.Ed. 888 (1888).” Tights, Inc. v. Kayser-Roth Corp., 442 F.Supp. 159 at 166, 196 USPQ 750 at 755[ (M.D.N.C.1977) ]. See also R. Stroup, Patentee’s Monetary Recovery from an Infringer, 59 J.P.O.S. 362 at 384 (1977).

Panduit, 575 F.2d at 1164 n. 11,197 USPQ qt 736 n. 11. Thus put in context, it is clear that the settlement Panduit refers to took place under a threat of litigation. Rude v. Westcott is not as clear, but to the Supreme Court it “seem[ed] that [payment] was made in part under a threat of suit, and in part as the result of an arbitration after litigation on the subject had been commenced, and to avoid future litigation.” 130 U.S. at 164, 9 S.Ct. at 468. As to Hanson v. Alpine Valley Ski Area, there this court cited Panduit and stated that offers to license made at a time when “litigation was threatened or probable” should not be considered evidence of an established royalty. 718 F.2d at 1078-79, 219 USPQ at 682. In the Deere case, this court held that the district court “could properly discount the probative value of the White license” because that license “was negotiated against a backdrop of continuing litigation and International] Harvester] infringement of the Schreiner patent.” 710 F.2d at 1557, 218 USPQ at 486. From the facts of the case it appears that Deere’s suit against Harvester was filed in 1976, White was granted a license in 1977, and the district court entered a judgment finding Harvester liable in 1978.

The circumstances of the Phillips settlement were obviously much different than the circumstances present in these cases. There was no “threat” of litigation against Phillips in 1974; nor was the Phillips settlement negotiated “against a backdrop of continuing litigation” on validity and infringement. The only “threats” Phillips faced were an impending accounting and a permanent injunction which would have forced it to shut down its Adams Terminal plant. Phillips’ overall agreement with Ziegler was more along the lines of a shotgun wedding than a situation where Phillips could impose upon Ziegler to grant a license at an eroded rate. That is why Judge Wright held that this type of evidence was “distinct” from other types of post-infringement evidence and highly probative of a reasonable royalty: “because both Phillips and Ziegler knew that the next step in the process was the exact type of accounting exercise that is being undertaken in this case.” We agree.

Finally, SGK attacks Judge Wright’s reliance on his earlier decision in the Devex case. SGK asserts that in Devex, in contrast to this case, “there was no acceptable evidence of the defendant’s projected profits (or savings) available to the parties at [the] hypothetical negotiations.” What SGK implies is that Judge Wright completely rejected any reliance on Dart’s anticipated profits, but that is not what happened here. The overarching theme of Judge Wright’s opinion in this case is “that the necessarily speculative hypothetical negotiation is rendered less speculative by use of as many facts as can be gleaned from the evidence to create a reasonable royalty.” Even if we assume, which is not at all clear, that Bischel’s 5% figure the master found “credible” was based entirely on Dart’s anticipated profits, Judge Wright did not reject that figure. Instead, he accepted that figure when he modified the master’s report and adjusted it in light of the additional factors — the lowered floor and the Phillips settlement — which the master had mistakenly calculated and ignored, respectively. Thus, Judge Wright’s entirely proper approach was to create a reasonable royalty from as many facts as possible, and he did not simply treat this case as some sort of replay of Devex.

SGK’s other attempts to distinguish De-vex have no merit.

3. Conclusion

In sum, Judge Wright concluded that the master’s errors in calculating a floor and in failing to account for the Phillips settlement rendered his conclusion that 4% was a reasonable royalty clearly erroneous. SGK has not persuaded us that Judge Wright erred in that conclusion.

D.The District Court’s Modification of the Master’s Report

Judge Wright’s methodology was to modify the master’s report in view of the two clear errors the court found: the reliance on a 3.7 to 4.0% floor rate, and the failure to take into account the Phillips settlement. After doing so, he found that a reasonable royalty would consist of a $1.18 million up-front payment, fully creditable towards a running royalty of 2.5%, with the up-front payment to be credited to the extent of 50% of each royalty payment due. For the most part, SGK has directed its arguments against the district court’s rejection of the master’s 4% rate as clearly erroneous. To the limited degree SGK has addressed itself to the court’s “substitute findings,” Milliken, supra, or to its modification of the master’s report, we are not persuaded of any error.

E.Willful Infringement 1. Introduction

The consequences of a finding of willful infringement being serious, we have held that such a finding, an ultimate finding of fact, is to be made only after due consideration of the totality of the circumstances. E.g., Amstar Corp. v. Envirotech Corp., 823 F.2d 1538, 1547, 3 USPQ2d 1412, 1418 (Fed.Cir.1987). Concomitantly, we have held that there are no hard and fast per se rules in respect of willfulness. Rolls-Royce Limited v. GTE Valeron Corp., 800 F.2d 1101, 1110, 231 USPQ 185, 191 (Fed.Cir.1986).

The master found that Dart willfully infringed the ’115 patent. The duty to finally adjudicate the rights of SGK and Dart, however, rested on Judge Wright. He reversed the master’s determination. We conclude that Judge Wright did not err in doing so. And since Dart’s infringement was either willful or it was not, we need not review separately Judge Wright’s “substitute” finding of non-willfulness. Kloster Speedsteel AB v. Crucible Inc., 793 F.2d 1565, 1577, 230 USPQ 81, 88-89 (Fed.Cir.1986), modified, 231 USPQ 160, cert. denied, 479 U.S. 1034, 107 S.Ct. 882, 93 L.Ed.2d 836 (1987). Underlying or subsidiary findings we review as stated in Milliken, supra.

Judge Wright identified several errors the master made in arriving at his finding of willfulness which rendered that ultimate finding clearly erroneous. We begin with the master’s imposition of particular legal requirements on Dart with regard to Dart’s choice of counsel.

2. The Use of Inside Counsel

Dart relied upon the opinions of its assistant patent counsel, Mr. Valles, with respect to the ’115 patent. The master concluded that Dart’s use of inside counsel in this case “did not conform to the requirement of the law.” How the master approached the use of inside counsel is seen from Ms report, some relevant portions of which are set forth in the margin. Two of the four major reasons the master gave for his finding of willful infringement related to Dart’s use of inside counsel (numbering ours):

Based upon the facts stated above and particularly because [1] the pre-infingement [sic] opinions relied upon by Dart were provided by in-house counsel, [2] with mere conclusionary statements without analytic backup, and [3] were based on conclusions mostly irrelevant to infringement and [4] Dart deviated from its usual practice of getting opinions from competent counsel not employed by it, I find that Dart has not complied with its affirmative duty to exercise due care to determine whether or not it was infringing after having notice of the ’115 patent and before it commenced infringement. (Rep. at 37).

Judge Wright carefully reviewed the master’s report and concluded that the master had, in effect, “imposed a requirement that Dart use outside counsel unless Dart could prove why outside counsel was not required in this case.” Judge Wright concluded that the master committed a basic error of law when he stated: “Dart appears to have followed the policy of getting an [outside] opinion when it feared the patent holder would enforce its rights or it was going to be sued for failure to take a license. This ‘policy’ does not conform to the requirement of the law. (Radio Steel and Underwater Devices, supra).” Judge Wright reasoned that there are no particular requirements in a totality of the circumstances determination and that creating such a requirement is an error of law. He explained:

Though the Master is correct that use of in-house counsel is a factor to be weighed, he is incorrect when he approaches the factor with the view that use of in-house counsel is inherently wrong. Western Electric Co. v. Stewart-Warner Corp., 631 F.2d 333, 337 (4th Cir.1980), cert. denied, 450 U.S. 971, 101 S.Ct. 1492, 67 L.Ed.2d 622 (1981) (“Just because an attorney is in-house counsel does not mean that his opinions are necessarily suspect.”). Just as the overall determination of willfulness is dependent on the totality of the circumstances, so too should the infringer’s decision to use a particular counsel be viewed on a case by case basis.

SGK responds that the master correctly recognized that the use of inside counsel was only “a factor” to consider. This response, however, begs the question of whether the master blew this factor entirely out of proportion. Since two of the master’s four principal reasons for finding willful infringement concerned Dart’s choice of counsel, Judge Wright hardly exaggerated when he stated that this factor was “paramount” in the master’s determination. SGK’s only other argument is that Judge Wright read the master’s words out of context. We disagree. The relevant paragraph of the master’s report has been set out in the margin. In context, it is clear that when the master referred to Dart’s apparent “policy of getting an opinion,” he meant an opinion of outside counsel. The master then stated the circumstances in which Dart’s apparent policy was to get an outside opinion: “when it feared the patent holder would enforce its rights or it was going to be sued for failure to take a license.” These two circumstances are the same thing; what the master was saying is that Dart’s apparent policy was to obtain an opinion from outside counsel when Dart feared the patentee would sue. The master concluded that “[t]his ‘policy’ does not conform to the requirement of the law,” citing Radio Steel & Mfg. Co. v. MTD Products, Inc., 788 F.2d 1554, 229 USPQ 431 (Fed.Cir.1986), and Underwater Devices, Inc. v. Morrison-Knudsen Co., 717 F.2d 1380, 219 USPQ 569 (Fed.Cir.1983). Those cases set forth no such rule and the master’s creation of such a rule was, as Judge Wright properly held, an error of law. SGK has not persuaded us otherwise.

Judge Wright also concluded that the master committed clear factual error in finding that Dart’s use of in-house counsel was unjustified, because the master failed to consider all the facts that entered into that determination. Notably, the master made a specific finding “that Valles’ request for an opinion from Dean Laurence in 1967 and his request for an opinion from outside counsel with respect to the Monte-catini ’300 patent in 1964 are not explainable in the context of his rationalization for not seeking outside counsel with respect to the ’115 in 1963 or 1964.” Judge Wright explained that the master failed to consider the fact that Montecatini informed the industry that it would enforce its patent and that it believed the entire industry needed to buy a license to operate. By contrast, Judge Wright noted, Dart told Ziegler, through Ziegler’s agent Montecatini, that it did not believe it needed a license, and neither Ziegler nor Montecatini contested that assertion in 1964. Judge Wright found that the difference in Dart’s approach to the two patents was justified by the difference in approach taken by the two patentees, citing American Original Corp. v. Jenkins Food Corp., 774 F.2d 459, 465-66, 227 USPQ 299, 303 (Fed.Cir.1985). Additionally, Judge Wright explained:

[T]he decision to get an outside opinion from Dean Laurence in 1967 was a result of Ziegler’s decision to sue Phillips on a patent related to the ’115. Only at that time could it be said that the circumstances of the Montecatini patent and the Ziegler patent were sufficiently alike to justify a similar approach to both patents by Dart. In short, the Master failed to consider a key fact, the patentee’s response to Dart’s assertions, in doubting the propriety of Dart’s reliance on Valles’ opinion.

SGK responds that reliance upon the different reactions of Montecatini and Ziegler is absurd because Montecatini could easily study Dart’s polypropylene and compare it with its ’300 product patent claims, while Ziegler had no way of knowing what Dart’s secret polymerization catalyst was. This argument is not persuasive. Whatever the reason for Ziegler’s silence in the face of Dart’s assertions may have been, the relevant inquiry is whether Dart acted reasonably under the circumstances in deciding to rely on its in-house counsel. Given that Montecatini stated its position that all producers would require a license under the ’300 patent, while Ziegler remained silent with respect to the ’115, we cannot say that Judge Wright erred in his conclusion that the master should have considered this fact in justification of Dart’s use of its inside counsel for the '115 patent. American Original, supra.

SGK next asserts that even if Ziegler had known the identity of Dart’s catalyst, that should not affect “Dart’s affirmative duty to seek and obtain a competent opinion of counsel before it started to infringe.” SGK points out that Dart began infringing in February, 1964, while the meeting in question did not take place until May of that year. This argument makes no sense. Ziegler and his agent Montecatini were silent regarding the ’115 not only at the May meeting, but before it as well. Moreover, the master relied upon Dart’s reaction to Montecatini’s position on the ’300 patent as well as Dart's 1967 request for an opinion from Dean Laurence to arrive at his conclusion that Dart’s initial reliance on in-house counsel for the ’115 patent was suspect. If, as SGK says, these post-February 1964 events cannot be considered, then the master’s reasons for his conclusion are taken away.

A final error the court identified in the master’s approach to the counsel issue was that the master considered Mr. Valles’ qualifications on an improper standard:

The only mention of Valles’ qualifications is in stating that “he did not possess special knowledge in this area that put him in a superior position to qualified patent counsel in this field.” Rep. at 28. That finding requires too much of Dart. Valles need not be in a “superior position” to qualified counsel; the question is whether Valles was qualified to render an opinion. The Master only viewed Valles’ qualifications as they could be used as a justification for deviating from the Master’s requirement that Dart get outside counsel. Rep. at 28. To justify such a deviation, the Master believed that Valles’ qualifications had to be superior to that of outside counsel. The Master failed to consider whether, Valles’ knowledge relative to outside counsel notwithstanding, Valles was sufficiently qualified to render an opinion on the ’115 patent.

Judge Wright then reviewed Valles’ undisputed qualifications and found “that Dart acted reasonably in electing to rely on the opinion of a qualified patent attorney who had been monitoring the relevant field for three years prior to the issuance of the ’115.” SGK has completely ignored this finding. It is not clearly erroneous.

In view of the errors he identified and his substitute findings, Judge Wright held that the master’s great reliance on the in-house counsel factor was erroneous. Again, SGK has not shown any error in this determination.

3. Valles’ Opinions

Judge Wright next reviewed the master’s analysis of Valles’ two opinion letters of December 5, 1963, and January 8, 1964. The December 5th letter, rendered two days after the ’115 patent issued, was a preliminary opinion suggesting the further study that resulted in the January 8th letter. The master’s first criticism of the January 8th letter was that it was not definitive because Valles used the word “believe” and he later wrote that his conclusions were “conclusions of my own.” Judge Wright rejected as clearly erroneous this ground for the master’s finding of willful infringement because: (1) Valles reached the definite conclusion that the ’115 was not infringed; (2) whether stated or not, any opinion letter is implicitly based upon counsel’s belief; and (3) as a matter of law, Dart was only required to form a good faith belief that the patent was invalid or not infringed. Also, Judge Wright determined that the master should not have given any weight to Valles’ comment that his conclusions were “conclusions of my own,” because that did not mean that they were bald and conclusory: the conclusions would have been Valles’ own whether based upon a full year of study or no study at all. Accordingly, this ground for the master’s finding was clearly erroneous. SGK has offered no response.

The remaining ground for the master’s finding of willful infringement was his evaluation of the substance of Valles’ opinions. The master accepted the assessment of SGK’s expert, Marvin Soffen, of the nature of Valles’ opinions. The master concluded that the Valles opinion letters “were flawed for several reasons”:

(1) they were largely conclusionary statements by in-house counsel without analytic backup.
(2) they failed to provide reasons for the conclusions and the conclusions were not based on documented laboratory tests for infringement.
(3) In one instance the statement is made that it is rumored that the Ziegler patent was opposed by Bayer and that Bayer was successful in Germany. The subject German patent was the Fischer patent and the rumor was apparently not correct. I question the reliance upon rumor in an opinion of this importance.
(4) The opinion letter fails to discuss the reverse doctrine of equivalents.

Later, in concluding his discussion, the master stated that besides Dart’s use of in-house counsel and its deviation from its apparent policy of obtaining opinions of outside counsel, the two principal reasons for his finding of willfulness were that Valles’ opinions constituted “mere conclu-sionary statements without analytic backup,” and “were based on conclusions mostly irrelevant to infringement.”

Upon review, Judge Wright was left with a definite and firm conviction that the master erred in analyzing Valles’ opinions. Again, SGK raises the specter of de novo review, arguing that the district court’s result, “reached after a de novo review of the record, was legal error.” But Judge Wright cannot be faulted for undertaking a detailed and conscientious review, because the test is whether, “on the entire evidence,” the reviewing court is left with a definite and firm conviction that a mistake has been committed. United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948).

Judge Wright concluded that the master’s determination that Valles’ opinions “were based on conclusions mostly irrelevant to infringement” was clearly erroneous. The master reached this conclusion through Soffen’s testimony that the reasons stated were irrelevant, but Judge Wright concluded that Soffen’s testimony was, in reality, proof that Valles’ reasons were wrong, not irrelevant.

In response, SGK says the reasons Valles gave in his Opinion were shown to be irrelevant because: (1) Valles in his testimony tried to rely on various other arguments, not made in the opinion; (2) Judge Wright, in discussing infringement in his Opinion on liability, never raised or addressed any of the arguments in the Valles opinion; and (3) Judge Hughes used none qf the arguments made by Valles in her district court opinion in Phillips, later reversed, finding the ’115 not infringed by an identical catalyst.

These factors do not convince us that Judge Wright erred in rejecting the master’s conclusion that Valles’ reasons were irrelevant to infringement. First, Valles’ deposition testimony and his testimony at the accounting trial were given after the Fifth Circuit’s decision in Phillips, the district court’s decision on liability in this case, and this court's affirmance. Valles knew that, in the judgment of courts, his advice to management in 1963 and 1964 was off the mark. So it is not surprising that Valles in his testimony, given more than two decades after his initial opinion, referred to other grounds to support his initial conclusion. But that does not mean his initial reasoning was irrelevant as opposed to simply wrong. As to Judge Wright’s discussion of infringement in his Opinion on liability, we think his role in the liability trial should place him in an excellent position to determine what considerations are and are not relevant to infringement of the '115 patent. He determined that Valles’ reasons were wrong, not irrelevant. Finally, Judge Hughes’ opinion in Phillips not only does not support SGK’s position, it cuts strongly against it. She construed the claims of the ’115 patent in light of the specification and, presumably, the prosecution history, and concluded that the claims did not read on the Stauffer AA — DEAC catalyst. Valles did the same thing and reached the same conclusion. From the Fifth Circuit’s opinion, it is clear that at least two of Valles’ reasons — that Dart’s use of TÍCI3 took it out of the scope of the ’115 claims because the claims did not encompass TiCl3 and were limited to TiCl4, and his reliance on authority that TÍCI3 is not the chemical equivalent of TiCl 4 — were presented to and apparently accepted by Judge Hughes in the context of the Phillips case. Thus, her decision shows, not that Valles’ reasons were irrelevant, but that the issue of what the ’115 patent covers was not, even seven years after Valles considered the question in 1964, as clear as it is today.

The master’s other determination — that Valles’ opinions constituted “mere conclu-sionary statements without analytic backup” — is plainly wrong. Judge Wright found that “[o]n the face of Valles’ letter scientific reasons are clearly stated” to support Valles’ conclusion that Dart’s catalyst would not infringe the ’115 patent. He further found:

[T]he Valles’ letter contains much more than unsupported conclusions. Valles referred to a file history search. He also discussed a Hoechst study and the ’471 Du Pont patent as factors justifying distinguishing the Dart catalyst from the reach of the ’115 patent. Though Valles was ultimately shown to be incorrect, he presented scientific justifications for distinguishing between a titanium tetrachloride catalyst and a titanium trichloride catalyst.

Judge Wright then concluded that, when viewed from the perspective of Dart management, Dart’s reliance on Valles’ opinion was justified:

The Dart management knew that Valles had a good understanding of the Dart catalyst and what could distinguish it from the patent’s claims. From the perspective of a Dart manager, these are significant, scientifically based reasons to justify the opinion. Valles applies the kind of analysis that would give a manager confidence that a proper opinion had been reached. Valles may have made errors in reaching his conclusion or in undertaking his analysis, but his opinion contains objective factors justifying it. Whether or not these factors later proved to be incorrect or, in the judgment of courts, insubstantial does not detract from the fact that at the time the decision not to license was made, the Dart management had within the “four corners [of Valles’ letter] ... sufficient internal indicia of credibility,” Underwater Devices, 717 F.2d at 1390, to justify Dart’s reliance on Valles’ opinion.

SGK challenges the fact of Dart’s reliance and asserts there is no evidence to show that Valles’ January 8th opinion was given to Dart management before Dart started infringing. But the master found that Dart management did rely on Valles’ opinion, and from the context of his discussion it is clear that he meant before the start of Dart’s infringement. Judge Wright held that this finding was not clearly erroneous and that, in any event, SGK’s objection on this point was untimely. We find SGK’s contrary position too strained to be persuasive.

SGK also asserts that Judge Wright erred in evaluating Valles’ opinions from the perspective of Dart management:

Moreover, a corporation cannot rest on the mere fact that an opinion is prepared by an attorney and talks in “patent-ese” in order to discharge its affirmative duty. Such a “clean heart and empty head” doctrine would gut this court’s requirement that the potential infringer obtain “competent legal advice,” Underwater at 1389-90 (emphasis added), and transmogrify it into a requirement of obtaining an opinion having “an appearance of competence.”

First, it bears repeating that this court has not issued any edict “requiring” a potential infringer to obtain advice of counsel. The affirmative duty is to exercise due care. Whether a potential infringer obtains counsel’s advice may be an important consideration, but “that does not mean ... that absence of an opinion of counsel alone requires in every case a finding of willful infringement.” Rolls-Royce Limited v. GTE Valeron Corp., 800 F.2d 1101, 1109, 231 USPQ 185,191 (Fed.Cir.1986). Second, Judge Wright did not apply a “clean heart, empty head” standard. He found that Dart acted reasonably in electing to rely on Valles, a qualified patent attorney who had been monitoring the relevant field for three years, and furthermore, he found that Valles’ opinion, although later shown to be incorrect, contained significant, scientifically based objective factors to justify Valles’ conclusion of no infringement. He contrasted Valles’ opinion to those in other cases which lacked any appearance of competence, authoritativeness, or internal indi-cia of credibility, which, he recognized, are some of the important factors to consider when evaluating an opinion letter. See Radio Steel, 788 F.2d at 1558-59, 229 USPQ at 434. We see no error in this approach.

J. Conclusion on Willful Infringement

The parties have raised other arguments. We have considered them fully but do not deem it necessary to address them explicitly. While we may not agree with Judge Wright’s reasoning in its entirety, we conclude, in view of the master’s errors which we have discussed and the overall record on appeal, that Judge Wright committed no reversible error in rejecting the master’s finding of willful infringement. Accordingly, it was proper for Judge Wright to reverse the master’s award of enhanced damages and attorney fees.

F. Prejudgment Interest

The final issue to be considered is prejudgment interest, which accounts for many millions of dollars of the award in this case. Judge Wright concluded that the master’s award of prejudgment interest at the prime rate compounded quarterly was within his discretion.

Dart in its cross-appeal disagrees and argues that the master erred as a matter of law in awarding interest at the prime rate because SGK did not affirmatively demonstrate that it was entitled to a rate higher than what Dart calls a reasonable commercial rate for an investor. Dart relies on Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 219 USPQ 670 (Fed.Cir.1983), and concludes that

the proper rule of law and the rule of this Court in Lam is that, without “affirmative demonstration” of entitlement to a higher rate, a factor indispustably [sic] absent in this ease, a patent owner, particularly a licensing patentee, should receive interest at a “reasonable commercial rate” for an investor, not at a lender’s rate such as, for example, the prime rate.

We reject Dart’s argument because our considered view of Lam is that it did not establish any “rule” requiring what Dart calls an “affirmative demonstration,” i.e., proof of borrowing at or above prime, for a plaintiff to be entitled to an award of prejudgment interest at the prime rate. Nor do we intend to establish any rule that prejudgment interest at the prime rate should be awarded as a matter of course in every case. Simply put, the question of the rate at which such an award should be made is a matter left to the sound discretion of the trier of fact, Bio-Rad Laboratories Inc. v. Nicolet Instrument Corp., 807 F.2d 964, 969, 1 USPQ2d 1191, 1194 (Fed.Cir.1986), and despite the paucity of evidence on this issue, Dart has not shown that the master’s award of prejudgment interest at the prime rate compounded quarterly was outside his discretion.

G. Conclusion

The judgment of the district court is affirmed.

AFFIRMED.

PAULINE NEWMAN, Circuit Judge,

concurring in part, dissenting in part.

I respectfully dissent from that portion of the court’s decision that relates to the measure of damages. I join the court’s affirmance of the measure of prejudgment interest.

Upon reference to a master under Fed.R.Civ.P. 53(b), the district court “shall accept the master’s findings of fact unless clearly erroneous”. Rule 53(e)(2). It is not enough that the district court would have decided the matter differently. TWM Mfg. Co. v. Dura Corp., 789 F.2d 895, 898-900, 229 USPQ 525, 527-28 (Fed.Cir.), cert. denied, 479 U.S. 852, 107 S.Ct. 183, 93 L.Ed.2d 117 (1986). In this case the district court incorrectly rejected the findings and conclusions of the master.

A. Royalty Determination

The methodology of assessing compensatory damages under 35 U.S.C. § 284 is committed to the sound discretion of the trier of fact. TWM Mfg., 789 F.2d at 898, 229 USPQ at 526; King Instrument Corp. v. Otari Corp., 767 F.2d 853, 863, 226 USPQ 402, 409 (Fed.Cir.1985), cert. denied, 475 U.S. 1016, 106 S.Ct. 1197, 89 L.Ed.2d 312 (1986). The district court upheld the master’s choice of the reasonable royalty as a measure of damages, recognized that there was no established royalty rate for licenses to the ’115 patent, and thus upheld the master’s methodology of hypothetical negotiations between a willing licensor and willing licensee.

The early Ziegler licenses were negotiated, as the district court as well as the master recognized, at the threshold of this technology, before its value was manifest, and before the ’115 patent was issued. Many uncertainties as to isotactic polypropylene manufacture were dissipated by the time Dart entered the business, including any question about whether it was necessary to use a Ziegler catalyst. The district court erred when it rejected the master’s premise that Dart and SGK, in hypothetical negotiations, need not have concluded a license in the identical format to that of the Ziegler licenses of the 1950s.

Neither party had argued for a combination of lump-sum and running royalty, the absence of which was cited by the district court as the principal error in the master’s analysis. The master correctly recognized that there were not analogous values between an up-front payment by Dart, twenty-four years after the “front” has passed (Dart’s infringement commenced in 1964), and the up-front payments of the 1950s, paid several years before a commercial process and running royalties were generated. The early up-front payments were plainly of different value to the licensor, for they produced immediate income to Ziegler, and were non-returnable even if no commercial production was ever achieved by the licensee. The master did not err in crediting the expert’s testimony that the royalty equivalent of the early licenses would be an overall rate of 3.7-4.0% if the up-front payments were appropriately valued.

The district court rejected the master’s reliance on this expert’s testimony, apparently for the reason that details of the arithmetic calculation were not given. This criticism was not raised by Dart before the special master. Further, the opinion testimony of expert witnesses need not contain step-by-step calculations. See, e.g., Story Parchment Co. v. Paterson Parchment Paper Co., 282 U.S. 555, 568, 51 S.Ct. 248, 250, 75 L.Ed. 544 (1931) (“while the damages may not be determined by mere speculation or guess, it will be enough if the evidence show the extent of the damages as a matter of just and reasonable inference, although the result be only approximate”); Terrell v. Household Goods Carriers’ Bureau, 494 F.2d 16, 25 (5th Cir.1974) (“the expert on damages need not be armed on the right hand with a slide rule, on the left hand with a computer. He is allowed some economic imagination so long as it does not become fantasy”). Professor Bischel’s estimate of the royalty equivalent was not shown to be in clear error.

The master also considered relevant the 1974 settlement between Phillips and Ziegler, entered into after the ’115 patent had been upheld by the Fifth Circuit Court of Appeals. That license provided for a lump sum payment for past infringement, equivalent to a royalty rate of 6.3%; and a royalty rate of 1.5% for future production over the remaining six years of patent life. The master also considered the profitability to Dart of 36.5% as projected in 1964; and received testimony from experts for both sides that it is “customary” in the chemical industry to measure royalties at 15-25% of projected profits.

Although the district court appears to place weight on Dart’s argument that in 1964 it was not known for certain whether there were non-infringing alternatives, it seems more correct to observe that in 1964 no non-infringing alternatives were known. Judge Wright, deciding the merits in 1984, so recognized. The many parties licensing the Ziegler invention so recognized, starting in the 1950s. I remark that the 1963 Nobel Prize committee did not reflect such uncertainty. Nor, apparently, did Dart.

The willing licensor/licensee hypothesis need not ignore the value of the Ziegler invention; nor the infringer’s profits; nor the circumstances of continuing infringement. See Sinclair Ref. Co. v. Jenkins Petroleum Process Co., 289 U.S. 689, 698-99, 53 S.Ct. 736, 739-40, 77 L.Ed. 1449, 17 USPQ 522, 525-26 (1933) and the discussion thereof in Fromson v. Western Litho Plate and Supply Co., 853 F.2d 1568, 1575-76, 7 USPQ2d 1606, 1613-14 (Fed.Cir.1988). The master’s decision reflects a solid understanding of the realities of the risks assumed by the parties:

The setting of a reasonable royalty after infringement cannot be treated ... as the equivalent of ordinary royalty negotiations among truly “willing” patent owners and licensees. That view would constitute a pretense 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. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1158, 197 USPQ 726, 731 (6th Cir.1978) (Markey, C.J., sitting by designation). The law governing compensatory damages does not require SGK to be “willing” to license Dart at the lowest rate paid by others under other circumstances. The law does not so heavily favor the tort-feasor. See Fromson, 853 F.2d at 1574-75, 7 USPQ2d at 1612-13.

The district court erred in rejecting the master’s methodology, in the absence of clear error in the premises adopted by the master or in his application of law. Because the 4% assessed is well within the range of royalties reasonably available in light of all the evidence, I would reinstate the master’s judgment.

Enhanced Damages — Attorney Fees

Enhanced damages are awarded, and an “exceptional case” determined, in the discretion of the decision-maker, based on all the circumstances of the case. King Instrument, 161 F.2d at 867, 226 USPQ at 412 (Fed.Cir.1985). Such determinations by a special master are set aside only in the event of a clear error of judgment, or an error of law, or if the master relied on clearly erroneous findings of fact. TWM v. Dura, 789 F.2d at 898, 229 USPQ at 526. Seattle Box Co. v. Industrial Crating and Packing Inc., 756 F.2d 1574, 1581, 225 USPQ 357, 363 (Fed.Cir.1985).

35 U.S.C. § 284 provides no well-marked threshold, across which damages are rigorously trebled, on the other side of which there is no increase at all. Nor is there always a clear boundary between what we have sweepingly called “willfulness”, with its overtone of defiance or bad faith, and the business decision to take a chance in the courts, based on a calculated balance of the legal risk and the commercial stakes. Such a commercial gamble may be tempting indeed when there is no risk of an injunction if the gambler loses — as here, with a licensing patentee as well as the probability that the litigation would extend beyond patent expiration (the ’115 patent expired in 1980). When these elements are present, this factor may be considered in the decisions of enhancement of damages and “exceptional case” attorney fees.

This court has not spoken for all situations on the question of whether the willfulness analysis, as applied to the entire term of infringement, must be based solely on the facts existing the day the infringement started; or whether the question can be reviewed by the court — as it was by the infringer — based on changed circumstances during continuing infringement. Such change in this case was the Fifth Circuit’s 1974 decision holding the ’115 patent valid and infringed. Thus the master could have considered the advice given by counsel to Dart after the Fifth Circuit decision, such advice being, in sum, that another forum can always hold differently. Dart, knowing that the most it had at risk was a “reasonable royalty”, might have made the business decision to litigate rather than license. This litigation continued for fourteen years after the Fifth Circuit upheld the ’115 patent, preserving the cloud on the patent: a factor that need not be ignored when the decision-maker turns to the equitable purposes of Sections 284 and 285.

I think too much emphasis has been placed on the issue of in-house counsel versus outside counsel. It is a question of the nature of the legal advice, not its source. Ongoing legal review by an accused infringer is highly relevant, for each fresh infringing act incurs liability as of its occurrence. The advice after the Fifth Circuit’s decision was not on the side of probable non-infringement or invalidity.

We observed in Fromson that through Sections 284 and 285 a just result may be reached, invoking the court’s equitable discretion. The special master awarded an increase of one half the compensatory damages, and finding exceptional circumstances awarded SGK attorney fees. The district court pointed to no error in judgment or law or factual premise in these rulings, and erred in rejecting the master’s decision and substituting its own. 
      
      . Professor Bischel testified:
      Therefore, as a floor, I don’t believe this licensor would have negotiated a royalty agreement with anyone which was less than 4, 3, 2, plus the equivalent, the equivalent of the up-front payment, since in a hypothetical negotiation we cannot have an up-front payment. In this particular case it has to be adjusted in some way by adjusting the royalty rate.
      We look at an effective rate of 2.1 or 2.2 percent per year on all production. In my opinion, we would have to add a percent and a half to 2 percent to that royalty to adjust for the fact that this licensee was not going to have to make a substantial up-front payment.
      I should point out in at least one license agreement which was negotiated, I believe it was the Exxon agreement which was negotiated, one of the later agreements negotiated in the 1950’s, the down payment was in the range of approximately a million dollars.
      So in order to compensate for that, it would seem to me that this licensor could not have negotiated a royalty of less than about a 3.7 to 4 percent rate. So that would be the minimum rate.
     
      
      . Rule 705: Disclosure of Facts or Data Underlying Expert Opinion
      The expert may testify in terms of opinion or inference and give reasons therefore without prior disclosure of the underlying facts or data, unless the court requires otherwise. The expert may in any event be required to disclose the underlying facts or data on cross-examination.
     
      
      . Excerpts from the master’s report, with record citations omitted, include the following:
      Dart's pre-infringement investigation was performed by Valles who was employed by Dart as assistant patent counsel. The fact that Dart’s pre-infringement investigation was done by in-house counsel is a factor in the determination of whether or not Dart discharged its affirmative duty. (Rep. at 25).
      Since Dart relied upon Valles after having notice of the ’115 patent and the fact that Dart’s catalyst might infringe it, it is relevant to determine whether it was Dart’s practice at that time to rely upon the assessment of Mr. Valles in such matters. (Rep. at 26).
      A fair reading of Mr. Vallesf] testimony at the liability trial was that he considered he had such special knowledge in this area dating from 1961 and 1962 that he did not believe he had the need to go to outside counsel. He was in a superior position to outside counsel in these subjects. Yet he admits that he didn’t consider himself qualified as a chemist. Yet he sought outside patent counsel with regard to the Montecatini ’300 patent which involved much of the same chemistry as the ’115. It would seem he would consider himself in a superior position as to both, not one. I find that he did not possess special knowledge in this area that put him in a superior position to qualified patent counsel in this field.
      I find that Valles’ request for an opinion from Dean Laurence in 1967 and his request for an opinion from outside counsel with respect to the Montecatini ’300 patent in 1964 are not explainable in the context of his rationalization for not seeking outside counsel with respect to the '115 in 1963 or 1964.
      Mr. Valles testified on a number of occasions that Dart sought outside counsel’s opinion when it believed the patentee would enforce its patent rights or when it believed it would be sued. [H]e also testified that Dart’s policy was to seek outside counsel's opinion if it was not taking a license. On one occasion he said Dart had no policy. Regardless of the apparent inconsistency in testimony, Dart failed to get outside opinion on the ’115 until after infringement began in 1964. Dart appears to have followed the policy of getting an opinion when it feared the patent holder would enforce its rights or it was going to be sued for failure to take a license. This "policy” does not conform to the requirement of the law. (Radio Steel [& Mfg. Co. v. MTD Products, Inc., 788 F.2d 1544, 229 USPQ 431 (Fed.Cir.1986)] and Underwater Devices[, Inc. v. Morrison-Knudsen Co. 717 F.2d 1380, 219 USPQ 569 (Fed.Cir.1983)], supra). (Rep. at 28-29).
     
      
      . Judge Wright identified several other factors which confirmed the reasonableness of Dart’s actions. First, the reason Dart had notice of the '115 was because Valles monitored the patents in the field; he learned of the '115 patent only two days after it issued. Second, that Valles learned of the patent himself and proceeded to study it indicated "that he was doing his job and that neither he nor Dart was ignoring relevant patents in the field." Third, Dart’s in-house counsel “exercised the independence to recommend that the company license some patents,” and there was no evidence that Valles was under any pressure "to recommend in favor or against licensing any particular patent.”
     
      
      . The master stated:
      Mr. Valles’ letter to Whipple [Dart’s chief inside patent counsel] dated January 8, 1964 is not definitive. Valles states "[t]he claims of the Ziegler patent ... are not believed to extend to titanium trichloride.” He also stated "[s]ince the broadest Ziegler claim, claim 1, does not distinguish over the Bayer reference by at least reciting separate addition or 
        mixing of the catalyst components, these broad claims are believed to be weak.” Mr. Valles does not state that the claims do not extend to titanium trichloride or that the broad claims are invalid, but merely stated they are not believed to extend or that the broad claims are believed to be weak. These statements indicate to me that Mr. Valles was less than fully convinced of the conclusions he was announcing. In a letter dated November 4, 1969, to Thomas Reddy, Mr. Valles admitted that his early opinions were "conclusions of my own ...” Mere bald, conclusory statements do not satisfy one's affirmative duty to obtain competent legal advice before infringement. (Underwater Devices Inc., supra, at 1390). [First brackets ours; record citations omitted.]
     