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 *1581Parchment 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).
*158235 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.