
761 F.Supp. 1420 (1991)
MICRO MOTION, INCORPORATED, Plaintiff,
v.
EXAC CORPORATION, Defendant.
No. C-89-1825 WHO.
United States District Court, N.D. California.
February 27, 1991.
*1421 *1422 John O. Tramontine, Jesse J. Jenner, David J. Lee, Fish & Neave, New York City, John W. Keker, Paul V. Carroll, Keker & Brockett, San Francisco, Cal., for plaintiff.
Sheldon W. Witcoff, Daniel A. Boehnen, Allegretti & Witcoff, Ltd., Chicago, Ill., Charles B. Cohler, Richard Haas, Lasky, Haas, Cohler & Munter, San Francisco, Cal., for defendant.

OPINION AND ORDER
ORRICK, District Judge.
This is the damages phase of a bifurcated patent infringement action involving Coriolis mass flowmeters, which measure the mass flow rate of liquids. Since 1977, plaintiff, Micro Motion, Incorporated ("Micro Motion"), a Colorado corporation and a wholly-owned subsidiary of Emerson Electric Company ("Emerson Electric") since 1984, has manufactured and sold Coriolis mass flowmeters and their accessories. Defendant, Exac Corporation ("Exac"), a California corporation, began to design Coriolis mass flowmeters in 1983, and to manufacture and market them beginning in 1984.
Micro Motion filed suit against Exac alleging that Exac's Model 7100 and Model 8100 flowmeters infringe Claims 8 and 57 of Micro Motion's U.S. Reissue Patent No. 31,450 and Claim 1 of U.S. Patent No. 4,491,025 under the doctrine of equivalents. In June 1987, a jury found that Exac's device infringed none of Micro Motion's patents. Micro Motion moved for a judgment notwithstanding the verdict ("JNOV") and a new trial. In December 1987, Judge Spencer M. Williams denied the motion for a JNOV but granted a new trial. Judge Williams later recused himself from the case, and it was reassigned to this Court.
The parties waived their right to a trial by jury in this Court. The second trial on the issue of infringement under the doctrine of equivalents began on March 12, 1990. On June 28, 1990, this Court issued an Opinion and Order finding that Exac's meters had infringed on Micro Motion's patents.
Trial of the damages phase of this action began September 17, 1990, and continued through October 4, 1990.[1] Micro Motion presented its case for lost profits due to lost sales, lost profits due to price erosion, reasonable royalty, prejudgment interest, and willfulness. Exac presented evidence in rebuttal to Micro Motion's case as well as evidence of the "tax windfall" that Micro Motion would enjoy if its award was not adjusted to reflect changes made to the tax code.
After considering the evidence placed before it in this action, the Court finds that Exac's actions caused Micro Motion to suffer damages in the following amounts: $1,694,444 in 1985; $3,910,383 in 1986; $4,409,075 in 1987; $4,806,064 in 1988; $3,198,797 in 1989; and $2,802,762 in 1990. The Court awards Micro Motion prejudgment interest of $5,409,481 on these damages, making a total award of $26,231,006.[2]

I. LOST SALES.
Micro Motion has claimed $5,782,234 as its damages for profits lost on sales taken from it by Exac. Micro Motion asserts that but for Exac's infringement, Micro Motion would have made eighty percent of Exac's domestic sales of Models 7100 and 8100 meters and sixty percent of Exac's sales of Model 8300 meters. Micro Motion estimates that it would have made a sixty-five percent profit on its lost meter sales. Exac disputes each of these claims.
To receive an award of lost profits, the patent owner must prove by a preponderance of the evidence that, but for the infringement, it either would have made the sales made by the infringer, charged higher prices for its patented products, or both. Marsh-McBirney, Inc. v. Montedoro-Whitney Corp., 882 F.2d 498, *1423 505 (Fed.Cir.1989). Once the Court determines that the infringer has indeed injured the patent owner, the Court may estimate the extent of the patent owner's damage by drawing a "just and reasonable inference" from the evidence: "The determination of a damage award is not an exact science, and `the amount need not be proven with unerring precision.' The trial court is required to approximate, if necessary, the amount to which the patent owner is entitled." Del Mar Avionics, Inc. v. Quinton Instrument Co., 836 F.2d 1320, 1327 (Fed.Cir. 1987) (quoting Bio-Rad Laboratories, Inc. v. Nicolet Instrument Corp., (citations omitted) 739 F.2d 604, 616 (Fed.Cir.1984)); see also, Yarway Corp. v. Eur-Control USA, Inc. 775 F.2d 268, 275 (Fed.Cir.1985) ("proof of lost profits need not be absolute but may not be speculative; lost profits must be proven to a reasonable probability"). When damage in fact is clear, but "the amount of the damages cannot be ascertained with precision, any doubts regarding the amount must be resolved against the infringer." Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed Cir.1983).
In Panduit Corp. v. Stahlin Bros. Fibre Works, Inc., 575 F.2d 1152, 1156 (6th Cir.1978), Judge Markey of the United States Court of Appeals for the Federal Circuit sitting by designation in the United States Court of Appeals for the Sixth Circuit, set forth a widely accepted method of proving lost profits:
To obtain as damages the profits on sales he would have made absent the infringement, i.e., the sales made by the infringer, a patent owner must prove: (1) demand for the patented product, (2) absence of acceptable non-infringing substitutes, (3) his manufacturing and marketing capability to exploit the demand, and (4) the amount of the profit he would have made.
Micro Motion need not present absolute proof of each of these elements; the cases make clear that Micro Motion's burden on all elements is one of reasonable probability. See Yarway, 775 F.2d at 275. Micro Motion has met this burden for each element of the Panduit test.

A. Demand for Coriolis Flowmeters.

In the early and mid-1980s, Micro Motion effectively marketed its Coriolis mass flowmeters and, by 1984, it was well known by, and its Coriolis mass flowmeters were popular with, firms in a wide range of industries, including chemical, food, and gas and oil. Micro Motion's flowmeters were popular because they provided a unique combination of capabilities. The meters were highly accurate over a wide range of flow rates, measured mass flow directly, were nonintrusive, and typically saved their users a great deal of money.
Moreover, during this period Micro Motion steadily improved the design of its flowmeters as it introduced new models. The B meter improved upon the A meter, the C meter improved upon the B meter, and the D meter improved upon the C meter. PX 185 at 11. The new models added features to or corrected problems with earlier models. For example, the D meter eliminated the sensitivity to external vibration that had plagued the C meter.
Micro Motion charged a high price for its flowmeters and achieved a high level of profitability. Micro Motion's customers were relatively insensitive to the price of Micro Motion's flowmeters because those flowmeters offered substantial benefits that nonCoriolis flowmeters did not offer. RT (Hunter) 167-68; RT (McConnell) 64-66.[3] Exac's own documents stress the superiority of and demand for Coriolis flow meters. For example, Exac's August 1984 business plan identified Micro Motion as the "only significant direct competition to Exac." PX 54 at 16. The plan put alternate technologies in "the second class of competitors" because "they do not measure flow directly." Id. at 17. Micro Motion's success led Exac to conclude that there was strong demand for Coriolis mass flowmeters: "The nearly 300% per year compounded *1424 annual growth rate of Micro Motion clearly indicates the market demand for mass flow sensors." Id. at 16. These statements demonstrates Exac's belief that there was significant demand for Coriolis flowmeters.
A Chem Systems study commissioned by Exac acknowledged the existence of other technologies but concluded that Micro Motion would be Exac's main or sole competitor. PX 185. Even though Mr. Swanson, Exac's former Chief Operating Officer and current Chief Executive Officer, may not have used the Chem System's report when formulating Exac's business strategy, the report offers further proof that at the time Exac began its operations, a separate market, distinct from that for other technologies, existed for Coriolis technology. Accordingly, the Court finds that even though other technologies may have sometimes competed with Coriolis technology for sales, Coriolis meters offered significant and distinct benefits to their primary users that distinguished Coriolis from nonCoriolis meters and created demand for Coriolis meters sufficient to satisfy the first element of the Panduit test.

B. Absence of Acceptable Noninfringing Substitutes.

Acceptable substitutes are noninfringing products that offer the key advantages of the patented device. An acceptable substitute must offer the advantages that the purchaser of the patented device values. Panduit, 575 F.2d at 1162 ("[a] product lacking the advantages of that patented can hardly be termed a substitute `acceptable' to the customer who wants those advantages"). Therefore, evidence showing that under some circumstances some other device could be used in place of Micro Motion's device does not by itself prove that acceptable substitutes were available to consumers.
Evidence that a patented device filled a long-felt need of its users and enjoyed commercial success indicates a lack of an acceptable noninfringing substitute. Id. In the liability phase of this action, this Court found that Micro Motion's invention represented a significant advance over earlierpatented devices and filled a long-felt need of some users. Indeed, Exac's internal documents support this conclusion. Exac's 1988 competitive portfolio stated the "Coriolis technology transcends the mediocrity of volumetric flowmeters," and a recent sales reference manual described in detail the disadvantages of volumetric flowmeters. PX 376 at XXXXXX-XXX; PX 388 at 500281.
Exac argues that these references to nonCoriolis technologies show only that it considered those technologies to be in competition with the Coriolis technology. These references, Exac argues, therefore do not support, but rather undermine, Micro Motion's claim that there were no acceptable noninfringing substitutes to Coriolis flowmeters. The Court, however, finds that when considered in light of other Exac documents, such as the 1984 business plan that identified Micro Motion as "the only significant direct competition to Exac" (PX 54 at 16), Exac's references to nonCoriolis technologies show that for those industries where direct measurement of liquid mass was important there were no acceptable noninfringing substitutes for Coriolis flowmeters. Although Coriolis flowmeters would sometimes compete with nonCoriolis flowmeters, Coriolis meters offered enough benefits that for many applications, such as oil and gas, food, chemicals, petro chemicals, and paper and pulp manufacturing, nonCoriolis meters were, at best, an imperfect substitute for Coriolis flowmeters.
Finally, evidence introduced at this trial clearly showed that Micro Motion's product enjoyed great commercial success. In the years following its introduction, Micro Motion enjoyed very rapid sales growth while maintaining high prices. Accordingly, the Court finds an absence of acceptable noninfringing substitutes for the users who purchased the bulk of Coriolis flowmeters.

C. Manufacturing and Marketing Capability.

The Court finds that Micro Motion had the ability to manufacture and market most of the flowmeters sold by Exac. As with the other Panduit factors, Micro Motion need not prove with absolute certainty *1425 that it could have made each of the sales it claims it lost to Exac; it need only show that it had the "potential capability" to manufacture and market those meters. It can meet its burden by showing that it would have expanded its manufacturing and marketing functions to meet the needs of Exac's customers.
Exac's total share of the domestic market was three percent in 1985, ten percent in 1986, thirteen percent in 1987, sixteen percent in 1988, and ten percent in 1989. PX 450. In order to manufacture all the infringing meters Exac sold domestically, Micro Motion would have had to increase its production by approximately one percent in 1985, six percent in 1986, ten percent in 1987, eleven percent in 1988, and two percent[4] in 1989. PX 450. To make eighty percent of Exac's sales, the amount Micro Motion asserts it would have made had Exac not entered the market, Micro Motion would have had to have increased its output by only one percent in 1985, five percent in 1986, eight percent in 1987, nine percent in 1988, and two percent in 1989. Id.

1. Manufacturing.
Exac points to Micro Motion's 1986-1987 production backlogs as evidence that Micro Motion could not have expanded its production to meet this demand. See Epping Dep. 7/25/87 at 63:11-64:3. The Court, however, finds this claim unconvincing. Even a substantial backlog does not necessarily indicate an inability to expand production: a manufacturing concern may simply find it more economical to work off a backlog. And Exac introduced no evidence to indicate that Micro Motion's backlog, ten percent to thirteen percent of total sales, was either unusually large or a reflection of the company's inability to expand its output. Moreover, every Micro Motion witness that testified on the subject stated that Micro Motion had sufficient capacity to make the number of meters sold by Exac. RT (McConnell) 72; RT (Wright) 563-65; PX 450. Accordingly, the Court finds that Micro Motion had the capacity necessary to produce the meters sold by Exac.

2. Marketing and Selling Capability.
Micro Motion was capable of marketing and selling most of the meters that Exac sold. Micro Motion had done a good job of marketing Coriolis flowmeters before it was acquired by Emerson Electric (RT (Swanson) 1056), and it stepped up its marketing efforts after the acquisition. RT (Hunter) 166-67, 171-72. Because Micro Motion and Exac sold to the same basic industries[5] and had many common customers,[6] one can assume that Micro Motion could have reached most of Exac's customers without expending an inordinately large amount of resources. And given Emerson Electric's interest in maximizing Micro Motion's profits, it is likely that Micro Motion would have committed the marketing resources necessary to make most of the sales that it lost to Exac.
Micro Motion, however, would not have made every one of Exac's sales. Micro Motion acknowledges that it might not have found every customer that Exac did; that some customers may have needed a feature that only Exac could provide; that some customers may have been dissatisfied with Micro Motion and would not have bought from it; and that some of Exac's customers may have purchased from a third-party Coriolis flowmeter vendor. Micro Motion estimates that it would have made eighty percent of Exac's sales of infringing devices. Exac argues that its entry caused no decrease in Micro Motion's sales.
It is unlikely that anyone could confidently state exactly which of Exac's sales of infringing and noninfringing meters Micro Motion would have made but for Exac's infringement, and this Court certainly cannot do so with the evidence before it. Micro Motion, however, need not prove with certainty what sales it would have made *1426 but for Exac's infringement; it need only prove that it probably would have made the percentage of Exac's sales that it claims it lost. And both parties have introduced enough evidence to allow the Court fairly and reasonably to estimate the percentage of Exac sales that Micro Motion would have made but for Exac's infringement.

(a) Sales of Infringing Meters.
Exac argues that its aggressive marketing campaign and superior features allowed it to make sales that Micro Motion would not have made. It contends that although Micro Motion put on evidence that it and Exac sold to the same basic industries, Micro Motion did not show that Exac either targeted existing Micro Motion customers or took any particular sales from Micro Motion.
Micro Motion introduced evidence by Professor Wright that indicated that all but thirteen percent of Exac's sales were made to customers with names that matched those of earlier-established Micro Motion customers, and all but four percent of Exac's sales were to customers operating in industries to which Micro Motion sold. PX 390; PX 391; PX 392. Professor Wright drew these conclusions after building a database of Exac and Micro Motion invoices and comparing the customer names on Exac invoices to those on Micro Motion invoices. Although this approach has some significant limitations (it cannot distinguish between different locations of a multilocation customer, and it cannot show whether a common customer would have bought from Micro Motion but for Exac's infringement), it nevertheless indicates the large extent to which Exac depended on past, current, or potential Micro Motion customers for sales.
Exac argues that Professor Wright's findings are unreliable because they depend solely on customer name matches and are not supported by any customer interviews showing what caused the customers to purchase from Exac. Because the Court uses Professor Wright's database comparison only as a means of measuring customer overlap and not as a way of estimating what percentage of Exac customers would have purchased from Micro Motion but for Exac, Professor Wright's failure to interview customers is irrelevant. And as long as Micro Motion and Exac never sold to different companies with a common name[7] and the customer names were properly entered into the database, there is no risk of a false name match.
Professor Wright's study does, however, overstate the overlap between Exac and Micro Motion customers in that it counts different plants of a multiplant concern as a single customer. Exac introduced evidence that indicated that individual plants in a multiplant firm may make independent buying decisions so that a sale to one location does not necessarily establish a relationship with other locations. RT (Swanson) 986. Professor Wright's analysis of his invoice database shows that Exac made about ten percent of its sales to locations that had not purchased from Micro Motion but were part of a company that had done so. PX 452.
Although the evidence before the Court was inconclusive as to the extent to which decision makers in remote locations of multiplant companies look either to similarly situated decision makers in other remote locations or to some central authority for direction on purchasing decisions, the bulk of the anecdotal information introduced at trial and common sense lead the Court to believe that most, but not all, multiplant concerns either encourage or require their plant managers to seek advice from other plants or approval from a central authority before investing in a Coriolis flowmeter. RT (Hunter) 285-86; RT (Smith) 1743; RT (Wright) 550-53. Accordingly, the Court finds that decision makers at some, but not many, locations that purchased only from Exac but were part of a multiplant concern that also dealt with Micro Motion did not know of Micro Motion and, therefore, might not have bought from it even if Exac had not entered the market.
*1427 Exac's meters offered some features not available on Micro Motion's meters. Mr. Swanson stated that Exac's first model featured a cross-over loop design that caused a lower pressure drop, an absence of tube cracks, and a digital computer microprocessor that gave the device greater accuracy and communications capability. RT (Swanson) 969-970. And its later-introduced Model 8100 meter had a "dry solids feature," an alarm system that would alert the operator when a critical material was about to run out, and a membrane panel keyboard by which an unsophisticated operator could control the amount of solids that flows through the pipe. Id. 972-76. But although no Micro Motion meter had all of Exac's features, all of Exac's "distinguishing features" (save the dry solids feature) were available at one time or another on one or more of Micro Motion's meters.
More important, Exac offered little evidence that its customers bought its meters because of their distinctive features and would not have bought a Micro Motion meter that lacked one or more of them. For example, in the 1987 trial, Mr. Swanson testified that only ten percent of Exac's customers were interested in its densitybased features. RT (Swanson) 1987 Trial 1791-93. And at this trial, Mr. Swanson, who had never discussed a flowmeter buying decision with an Exac customer, could identify only four customers for whom he thought Exac's dry solids features were critical. RT (Swanson) 1023-24. Although it is very difficult to determine what features were critical to Exac's customers, it seems likely that the advantages inherent in a Coriolis flowmeter, and not any feature unique to Exac, led the overwhelming majority of Exac's customers to purchase their meters.
To the extent that Exac sold to customers that knew of, but would not buy from, Micro Motion, Exac's sales do not represent a loss to Micro Motion. The only evidence as to the size of this group is a Dean Witter report stating that customers had returned as defective ten percent of the meters Micro Motion sold in 1985. DX SM. But there is no evidence as to either what portion of this group turned to Exac for replacements, or what portion of that subgroup would have stayed with Micro Motion but for Exac's infringement. Nevertheless, it is reasonable to infer that at least some of Micro Motion's dissatisfied customers turned to Exac for relief and would not have bought from Micro Motion again even had Exac not entered the market.
Finally, some of Exac's sales would have gone to third-party manufacturers of Coriolis technology. Although they began market entry activities as early as 1985, third-party providers of Coriolis mass flowmeters enjoyed little success before late 1987. Micro Motion estimated that the combined market share of third-party Coriolis competition was about two percent of Micro Motion's sales in 1987, four percent of Micro Motion's sales in 1988, and nine percent of Micro Motion's sales in 1989. RT (Hunter) 182-83. Because neither party provided data as to total third-party sales of Coriolis flow meters, Micro Motion's estimates of third-party market share is the best information available to the Court. Increasing these numbers to reflect the possibility that (1) Exac's customers might have been more likely than other customers to purchase from third-party vendors,[8] and (2) Micro Motion might have underestimated the sales made by third parties,[9] the Court estimates that the percentage of Exac's sales that would have gone to third party vendors would still be only about three percent for 1987, seven percent for 1988, and twelve percent for 1989.
After considering the evidence presented by both parties, the Court finds that although *1428 Exac made some sales that Micro Motion would not have otherwise made, Micro Motion would have made most of Exac's Model 7100 and Model 8100 sales had Exac not sold those infringing devices. More specifically, the Court finds that Micro Motion would have made seventy percent of Exac's Model 7100 and Model 8100 sales had Exac not entered the market.

(b) Sales of Noninfringing Meters.
The Court rejects Micro Motion's claim to lost sales damages on Exac's Model 8300 meter sales. Micro Motion asserts that Exac's experience with its infringing devices directly benefited its later sales of its Model 8300 meter. Specifically, Micro Motion argues that the name recognition, customer contacts, and marketing and production knowledge Exac gained by manufacturing and selling its infringing meters allowed it to sell far more Model 8300 meters than it otherwise would have sold.
Although the experience and credibility Exac gained while selling its infringing meters undoubtedly helped it sell its Model 8300 meter, the net effect of Exac's early activities on its Model 8300 sales is uncertain. The competitive threat posed by Exac's infringing devices may well have driven Micro Motion both to improve the design of its flowmeters and to keep the prices of its meters down. It is, therefore, quite possible that had Exac not infringed, the Model 8300 would have been introduced into a less competitive market in which it might have enjoyed even more sales than it in fact did.
Accordingly, the Court finds the relationship between Exac's earlier infringement and its later sales of its Model 8300 too speculative to merit compensation. The Court awards Micro Motion no lost sales damages for Exac's sales of its Model 8300.

D. The Amount of Profit Micro Motion Would Have Made on Its Lost Sales

Having determined that Micro Motion would have made seventy percent of Exac's domestic sales but for Exac's infringement, the Court must determine the profit Micro Motion lost on those sales. Lost profits are equal to the revenue that Micro Motion would have received from the lost sales (both meters and accessories) less the cost of making those sales.
The first step in this process is to quantify Micro Motion's lost sales. To do this, the Court (1) determines Exac's total domestic sales for the infringing period by model, (2) converts Exac's sales for each model into their Micro Motion equivalents, (3) determines lost sales units by subtracting the Exac sales that Micro Motion would not have made, (4) multiplies the lost sales of each Micro Motion meter by that meter's estimated sale price, (5) adjusts the resulting figure to account for anticipated returns, and (6) adds reasonably expected accessory sales.
Ms. Dancik determined Exac's domestic sales for the relevant time period by reviewing Exac sales invoices. She found that Exac's sales were as follows: 423 EX 12 meters; 663 EX 120 meters; 973 EX 1200 meters; and 138 EX 6000/9000 meters. PX 450. The Court accepts this finding.[10]
Converting these Exac meters into their Micro Motion equivalents entails some guesswork because both Exac and Micro Motion sold several different meters and none of Exac's meters had an identical Micro Motion counterpart. Micro Motion proposed a conversion scheme based on each meter's flow rate. See PX 453. The Court accepts this approach as fair and reasonable. Under this approach, Exac's domestic sales convert to Micro Motion sales as follows: 85 D6 meters; 212 D12 meters; 127 D25 meters; 398 D40 meters; 654 D100 meters; 584 D150 meters; 124 D300 meters; and 14 D600 meters. PX 450.
Reducing these numbers by thirty percent to reflect the Court's finding that Micro Motion would have made only seventy percent of Exac's domestic sales yields lost sales as follows: 59 D6 meters; 148 D12 *1429 meters; 89 D25 meters; 278 D40 meters; 458 D100 meters; 409 D150 meters; 87 D300 meters; and 10 D600 meters.
The total meter revenue lost during the infringement period is $6,851,334. PX 518. Total returns and allowances on the lost sales would have been $203,387. Id. Thus, the net lost sales revenue is $6,647,947.
Although very little evidence was presented on the issue, the Court accepts Ms. Dancik's assertion that Micro Motion historically sold about $15 of accessories for every $100 of meters it sold.[11] PX 450. Adding lost accessory sales of $992,584 to net lost sales revenue of $6,647,947 gives a total lost sales revenue of $7,640,531.
Both Exac and Micro Motion presented evidence as to the costs Micro Motion would have incurred had it produced and sold the units that it lost to Exac. Micro Motion relied primarily on the testimony of Ms. Dancik, who performed a detailed account analysis on Micro Motion's financial records. Exac relied primarily on the testimony of Mr. Holdren who performed regression and historical analyses as well as an account analysis on Micro Motion's financial records. Ms. Dancik estimated Micro Motion's lost profit rate to be about sixty-five percent; Mr. Holdren estimated it to be about forty-five percent.
At least in part, both experts base their profit rate estimates on an incremental income approach, which "recognizes that it does not cost as much to produce unit N + 1 if the first N (or fewer) units produced already have paid the fixed costs. Thus fixed costs ... are excluded when determining profits." Paper Converting Machine Co. v. Magna-Graphics Corp., 745 F.2d 11, 22 (1984). Incremental costs are distinct from marginal costs in that marginal costs include only those costs that vary when producing one more unit, whereas incremental costs include any costs that increase as production expands over a relevant range  in this case up to nine percent.
Recognizing that "[t]he incremental approach to the computation of lost profits is well established in the law relating to patent damages," id., and finding that, when properly followed, an incremental cost analysis can yield an accurate estimate of the cost of meeting increased demand, the Court chooses to follow the incremental approach in this case.
The Court finds Mr. Holdren's historical and regression analyses to be of little probative value. An historical or regression cost analysis may be quite useful in a case involving a well-established firm with relatively constant costs and sales. But it is less useful where, as here, the firm can incur substantial nonrecurring costs, which because they can vary significantly[12] from year to year may appear to be, but are not, incremental costs. Moreover, the database Mr. Holdren used for his historical and regression analyses included data not at issue in this case, such as costs and revenues associated with international sales, and sales of meters not affected by Exac's infringement. RT (Holdren) 1322-46.
Ms. Dancik based her conclusions on a detailed review of almost six thousand Micro Motion accounts. After interviewing knowledgeable Micro Motion personnel and reviewing available records, she classified each account as variable, semivariable, or fixed. PX 450. A variable account was one whose costs would increase as Micro Motion increased its production and marketing activity to make the sales that it lost to Exac; a semivariable account was one containing some components the costs of which would increase and others the cost of which would not change as production increased over the relevant range; and a fixed account was one whose cost would not change as production and sales changed. Id.
Mr. Holdren engaged in a similar exercise but received somewhat different results, finding more accounts to be variable than did Ms. Dancik. Based on Ms. Dancik's *1430 responses to the challenges Exac put to her at trial and the apparent thoroughness of her work, the Court finds her testimony to be very reliable.
Exac argued that Ms. Dancik's classification of some sales and marketing and engineering and product support expenses are emblematic of the problems with her approach. But in both these instances Ms. Dancik's judgment appears to be as sound and as well-informed as Mr. Holdren's. Mr. Holdren argues that Ms. Dancik erred by allocating some variable selling expenses to intercompany sales, by making salesmen's meals and auto expenses fixed, and by making utility expenses only semivariable.
But her errors are not obvious to the Court. It seems likely that there would be some cost associated with making intercompany sales, and that salesmen's meal expenses should not increase with their sales (they should be making the same number of calls but having more success). And Micro Motion introduced evidence showing that it heats, cools, and lights its plant all day thereby making its utility expenses only semivariable. Given that these account classifications are representative of those to which Exac objects and that Exac had six thousand classifications from which to pick those it challenged, the Court does not view Exac's objections to Ms. Dancik's work to be compelling.
Finally, although he would have liked to have done so, Mr. Holdren did not speak with any Micro Motion employees. RT (Holdren) 1360. Consequently, he lacked Ms. Dancik's insight into how Micro Motion's costs would vary with a change in sales. Accordingly, the Court accepts Ms. Dancik's estimate of Micro Motion's incremental expenses.
Applying Ms. Dancik's analysis, the incremental cost associated with the lost meter sales is $2,350,505, and the incremental cost associated with producing the accessories that would have been sold along with those meters is $412,208, making a total cost of $2,762,713. PX 518. Subtracting that amount from the total lost sales revenue of $7,640,532 gives a profit on lost sales of $4,877,819.

II. PRICE EROSION CLAIM.
Lost profits as a result of price erosion are compensable damages that stand on the same ground as damages caused by lost sales. Lam, 718 F.2d at 1065. In most price erosion cases, a patent owner has reduced the actual price of its patented product in response to an infringer's competition. Yale Lock Mfg. Co. v. Sargent, 117 U.S. 536, 553, 6 S.Ct. 934, 943, 29 L.Ed. 954 (1886). But a patent holder who proves that he would have increased his prices had the infringer not been in competition with him can also sustain a price erosion claim. Kalman v. Berlyn Corp., 914 F.2d 1473, 1485 (Fed Cir.1990); TWM Mfg. Co. v. Dura Corp., 789 F.2d 895, 902 (Fed.Cir.1986).
Micro Motion claims that it suffered price erosion losses when Exac's infringement forced it to forego four percent price increases in 1985, 1986, and 1987 on those products that competed directly with, or were linked for pricing purposes to meters competing directly with, Exac's meters. Micro Motion argues that had it imposed the price increases in question, it could have maintained its prices at the resultingly higher levels in the years that followed. It therefore seeks price erosion damages for 1988, 1989, and 1990. Micro Motion also seeks damages to compensate for the losses it suffered when it discounted its products in 1986 and 1987.

A. Would Micro Motion Have Raised Prices But for Exac?

Before Exac entered the market, Micro Motion was the only supplier of Coriolis mass flowmeters. Because the Coriolis technology offered substantial benefits over other flow measurement technologies and Micro Motion was that technology's only source, Micro Motion faced a relatively price insensitive market. In 1984, Chem Systems concluded in a market study commissioned by Exac that "if a mass flow meter is needed to do the required job, price does not appear to be a problem except for some truck applications." PX 185 at 3.
*1431 Micro Motion's experts also found demand for Coriolis flowmeters to be inelastic. Professor Rubinfeld stated that he "believe[s] that the market demand for Coriolis meters has been highly inelastic (insensitive to price) at the actual market prices [and] had Micro Motion increased its prices by 4% during fiscal years 1985-1987, the number of meters sold would have declined by less than 1%." PX 454 at 8-9. Based on this evidence, the Court concludes that Micro Motion could have raised prices had it not faced competition from Exac.
Micro Motion's ability to raise prices, however, does not dispose of the issue: the question of whether Micro Motion would have raised prices remains. Micro Motion had no contemporaneously prepared documents showing that it would have increased its prices but for Exac's presence in the marketplace. Smith Dep. 1/17/89 126:16-127:6.
Micro Motion's lack of documentation on this issue, however, is of little probative value. It does not seem at all unusual that businessmen not concerned about generating paper trails for use in future litigation would not think to record their reasons for not taking a particular action. And Micro Motion introduced some evidence that its managers both considered and discussed Exac's effect on their pricing decisions. The testimony at trial of Micro Motion managers responsible for its pricing decisions uniformly supports the proposition that Micro Motion would have increased prices had Exac not been in the market. Messrs. McConnell, Hunter and Smith each stated that they had made a conscious decision to forego a contemplated price increase because of Exac.[13] And Mr. Smith testified that he spoke with both Messrs. McConnell and Perkins about Exac's effect on his pricing recommendations. RT (McConnell) 66, 76-77; RT (Hunter) 280; RT (Smith) 724-29. Although the Court recognizes the dangers of giving effect to management's self-serving testimony about price increases they would have recommended years earlier, the Court finds the testimony of Micro Motion's former managers to be creditable. Accordingly, the Court concludes that Micro Motion would have raised its prices more frequently than it did had Exac not entered the market.

B. The Threat Posed by Exac.

In April 1984, Hambrecht and Quist, an investment banking and venture capital firm, asked Mr. Swanson to prepare a business plan for Exac, which was then staffed largely by technical people. RT (Swanson) 951. Exac hired Mr. Swanson as its Chief Operation Officer after he made a May 1984 presentation to Exac's board on Exac's need for more financing. The board charged Mr. Swanson with converting Exac from a technical organization into a functioning business. Id. at 951-52, 1577-78. Shortly thereafter, Exac began to market its product aggressively. It began to sign up and train distributors, it wrote to and met with representatives of trade magazines, and it called on potential customers. Id. at 848-62. By October 1984, Exac had held successful sales training meetings in California and Pennsylvania, and nearly one hundred independent sales representatives carried Exac's products. Id. at 859-60; PX 473A; PX 474. In late October 1984, Exac entered the market at the annual meeting of the Instrument Society of America ("ISA") in Houston. This was the first time that customers of Micro Motion had another source of supply for mass flowmeters. RT (McConnell) 68-69. Exac organized a reception for the press and interested potential customers at the ISA show. During that reception, Mr. Swanson stated that Exac had made a quantum jump in Coriolis technology, had secured significant financing from Hambrecht & Quist, and was "poised to become the leader in mass flow measurement for all sectors of the industrial and commercial community where measurement and control of process and end product fluids is vital to profitability." PX 195 at 2.
Exac brought to the show a price list that included prices for a full range of meters. PX 369. Exac continued to sign up representatives, including some former Micro Motion representatives. PX 466. In *1432 February 1985, Exac announced that it had obtained financing from Fisher Controls, a prominent supplier of process control instrumentation. PX 217A at 58. In December 1984, Exac instituted a volume discount for large purchasers and a discount for OEM manufacturers. RT (Swanson) 869-70. Although Exac did not subsidize any discounts given by its representatives to other customers, it authorized them to take lower commissions so that they could cut prices from list in individual customer transactions. Id. at 871-72.
Exac capitalized directly on the popularity Micro Motion had established for Coriolis mass flowmeters. Because its target market was companies that stood to profit from the use of Coriolis mass flowmeters, many of Exac's principal customers had either been or were current or potential Micro Motion customers. RT (Hunter) 186-87; PX 452. In April 1986, Exac entered into a national sales agreement with Procter & Gamble, a large customer of Micro Motion, under which all facilities of Procter & Gamble could purchase Exac flowmeters at a discount of at least five percent off list price. RT (Swanson) 1631. Exac dropped the effective price of its meters over time by adding additional features but not increasing prices. PX 369. For example, in October 1985, Exac made standard features that had once been options and priced the new package below the previous cost of a comparably equipped machine. When Micro Motion increased prices in May 1986, Exac made no corresponding move. PX 347.
Exac experienced rapid growth. Mr. Swanson publicly characterized Exac's growth as "phenomenal" in October 1987. PX 219A. Exac's market share grew with corresponding rapidity. Its share was three percent in 1985, ten percent in 1986, and thirteen percent in 1987. PX 444.

C. Effect Exac's Entry Had on Marketplace.

Exac's entry into the market for Coriolis mass flowmeters significantly changed the structure of that market. Exac's entrance subjected Micro Motion to a substantial risk that a price increase in its meters would lead customers to switch to Exac. Between 1984 and 1987, Micro Motion rapidly lost market share to Exac, suffered flat sales, and failed to meet its targets for marginal profits, growth in absolute dollars, and growth rate. RT (McConnell) 151-53; RT (Holdren) 1317, 1358. Exac's presence in the marketplace led to an increase in Micro Motion's selling costs as Micro Motion began to hold mass flow seminars and spend more time working with its existing customers. PX 450. Exac's entry changed what had been exclusively Micro Motion's market into a two-supplier market and, thus, limited Micro Motion's ability to realize monopolistic profits on its Coriolis mass flowmeters.
Exac recognized that the market would be price sensitive in the context of competition between Micro Motion and Exac and took Micro Motion's prices into account in setting its initial prices in October 1984. RT (Swanson) 1632-36; PX 485. Exac's prices for its basic meters were somewhat higher than Micro Motion's prices, but Exac priced its optional features, which were important to some customers, lower than Micro Motion's options. And Exac's meter prices remained competitive with Micro Motion's prices when Exac made some of its options standard without increasing its meters' prices to reflect the full value of the added features. PX 368; PX 369.
Micro Motion's managers stated that but for Exac they would have raised prices at least as quickly as prices were rising for comparable equipment  about four percent per year. RT (Hunter) 280; RT (McConnell) 66-80; PX 454; PX 531. But with Exac in the market, Micro Motion did not impose a real price increase until 1988. In May 1986, Micro Motion announced a price increase of about four percent, but the effect of that increase was offset at least in part by the introduction of discount programs.
Micro Motion introduced evidence showing that it raised prices when it believed that it could do so without losing sales to Exac. In 1987, Micro Motion began to raise prices on models, such as the D600, for which Exac offered no substitute. RT (Hunter) 173-75, 180-81. And in 1988, Micro Motion began increasing prices in its main line of stainless steel meters where it competed directly with Exac. These increases *1433 coincided with the end of Exac's rapid growth, which came to an abrupt halt in 1988.[14] Micro Motion's reaction to Exac's troubles and its policy of increasing prices on meters that did not compete directly with Exac give indirect support to Micro Motion's claim that it would have raised its prices but for Exac. The Court finds that, but for Exac's infringement, Micro Motion would have raised its prices four percent more than it did in both 1985 and 1986.
The Court, however, rejects Micro Motion's claim to price erosion damages for discounts it offered to compete with Exac's discounts and to counter Exac's disparagement of Micro Motion's C meters. The Court finds that Micro Motion's desire to upgrade the meters it had in the field motivated its C to D discount program, which was similar to the B to C discount program it had implemented before Exac entered the field.

D. Effect of Third-Party Coriolis Manufacturers.

In the late 1980s, several flowmeter companies began to get involved in the business of making and selling their own Coriolis mass flowmeters. The companies that attempted to enter the United States market for Coriolis mass flowmeters included Bailey Controls, Endress & Hauser, K-Flow, Neptune and Smith Meter. Dan Foss and Krohne also participated in the Coriolis mass flowmeter market, but only abroad. RT (Hunter) 200, 277; RT (Smith) 1688-90.
Some of these companies began marketing their "products" before they could deliver a commercially viable Coriolis flowmeter to the United States market. For example, Dan Foss began distributing promotional literature in the United States in 1985, even though it had no United States distribution capability. RT (Hunter) 276. And Smith Meter appeared at a trade show with Coriolis mass flowmeters in late 1985, but apparently had not yet developed a commercially viable design. By early 1988, Smith had modified its design several times and had sold few meters. PX 388.
Third-party competitors in the market for Coriolis mass flowmeters enjoyed little success before late 1987, when a jury rendered a verdict of noninfringement in the first trial between Micro Motion and Exac. Micro Motion lost, at most, one to two percent of its sales to third-party Coriolis competitors in 1987. RT (Hunter) 182-83. And some of the third-party meters in the field in 1987 had not been sold, but rather had been provided free of charge for field testing. Id. Micro Motion estimated that the combined market share of third-party Coriolis flowmeters grew to four percent of Micro Motion's sales in 1988 and nine percent of Micro Motion's sales in 1989. Id.
Micro Motion claims that Exac's activities kept it from increasing prices in 1985, 1986, and 1987. And based on the evidence before it, the Court has found that Micro Motion would have raised prices by four percent in both 1985 and 1986 but for Exac's infringement. The Court, however, does not believe that Exac's infringement was the proximate cause of Micro Motion's decision not to raise prices in 1987.
In 1987, third-party manufacturers of Coriolis mass flowmeters enjoyed a market share similar to that held by Exac in 1985. It is, therefore, likely that even though no single new entrant posed a risk to Micro Motion's market share as great as that which Exac posed in 1985, the combined threat of the new entrants in 1987 would have been enough to discourage Micro Motion from announcing any new price increases. Consequently, the Court finds that Exac's infringement resulted in Micro Motion charging only eight percent less for its meters than it otherwise would have for the period 1987-1989.[15]


*1434 E. Damages.

Price erosion damages on Micro Motion's actual sales equal the cumulative erosion percentage multiplied by Micro Motion's eroded sales volume. To calculate Micro Motion's eroded sales volume, sales of products the pricing of which were unaffected by Exac's activities (i.e., products for which Exact offered no substitute and products sold to intercompany entities such as Oval Engineering and Brooks Instruments), are subtracted from Micro Motion's net sales. Micro Motion's annual sales of products with eroded prices are as follows: $32,561,157 in 1985; $28,801,254 in 1986; $27,600,913 in 1987; $30,818,088 in 1988; $37,383,742 in 1989; and $35,034,524 in 1990. PX 518. Multiplying the yearly eroded sales volume by the percentage of price erosion suffered (four percent for 1885, and eight percent for 1986-1990) gives price erosion damages on Micro Motion's actual sales in the amount of $14,073,527.
Price erosion damages on Micro Motion's lost sales are calculated using the same methodology but substituting Micro Motion's lost sales for its actual sales. Micro Motion's lost sales for each of the relevant years are as follows: $540,347 in 1985; $1,980,140 in 1986; $2,772,196 in 1987; $3,106,408 in 1988; and $332,944 in 1989. PX 518. Multiplying the yearly eroded sales volume by the percentage of price erosion suffered (four percent for 1885, and eight percent for 1986-1989) gives price erosion damages on Micro Motion's actual sales in the amount of $575,562. Adding these figures to Micro Motion's total price erosion damages on its actual sales gives total price erosion damages of $14,649,084.

III. REASONABLE ROYALTY ANALYSIS.
A reasonable royalty is determined by conducting a hypothetical negotiation between the patent owner and infringer at the time infringement began. The parties are assumed to be reasonable businessmen willing to enter into a licensing agreement. Trans-World Mfg. Corp. v. Al Nyman & Sons, Inc., 750 F.2d 1552, 1568 (Fed Cir. 1984).
"The key element in setting a reasonable royalty after determination of validity and infringement is the necessity for return to the date when the infringement began." Panduit, 575 F.2d at 1158. As the Court found in its earlier decision on liability, infringement began in December 1983. Opinion and Order filed June 28, 1990, at 17.
Under Georgia-Pacific Corp. v. United States Plywood Corp., 318 F.Supp. 1116, 1120 (S.D.N.Y.1970), modified 446 F.2d 295 (2d Cir.1971), a court can consider a number of factors when determining what a reasonable royalty rate should be. All of the factors listed in Georgia-Pacific are probative to the extent that they indicate the royalty rate to which reasonable businessmen would agree. Under Georgia-Pacific, a court determining the terms to which a willing buyer and seller would agree can consider:
[the parties'] relative bargaining strength; the anticipated amount of profits that the prospective licensor reasonably thinks he would lose as a result of licensing the patent as compared to the anticipated royalty income; the anticipated amount of net profits that the prospective licensee reasonably thinks he will make; the commercial past performance of the invention in terms of public acceptance and profits; the market to be tapped; and any other economic factor that normally prudent businessmen would, under similar circumstances, take into consideration in negotiating the hypothetical license.
Id. at 1121. Under this approach, the reasonable royalty rate does not reflect the infringer's actual profits, but rather the parties' expectations and bargaining positions at the time of the first infringement. State Indus. Inc. v. Mor-Flo Indus., Inc., 883 F.2d 1573, 1580 (Fed.Cir.1989).
Micro Motion would have come to the negotiating table with a strong negotiating position. Its mass flowmeter was a significant improvement over previous measurement technologies, and it had enjoyed tremendous sales growth. PX 487. At the time of the hypothetical negotiation Micro *1435 Motion had enjoyed five years of sales growth and three years of high profit margins. Id.
Exac would have been anxious to strike a deal with Micro Motion. Exac recognized the advantages of the Coriolis mass flowmeter and the clear market potential for those products. Exac's 1984 financial plans, which anticipated a high profit margin (39.5 percent) in its fifth year of operation, support this conclusion.[16] PX 54.
Exac would compete directly with Micro Motion for most of its sales. And for each sale that it lost to Exac, Micro Motion would forego a profit margin of sixty-five percent. Accordingly, Micro Motion would have sought a high royalty rate. But Exac would not offer to pay a royalty rate so high that it could not profitably enter the Coriolis meter market.
There was no established royalty for the patents in suit at the time of the hypothetical negotiation. The license agreement between Exac and Chevron Corporation (DX HJ) is of little probative value. That agreement was not between competitors and covered a device that applied only to a narrow segment of the flowmeter market. In 1985, Micro Motion entered into two licenses with Emerson Electric affiliates  Brooks Instrument and Oval Engineering. Because both arrangements were with sister companies doing business outside the United States they, too, are of little probative value. PX 487.
In order to reach a deal with Exac and thereby derive some profit on those units it would not have otherwise sold, Micro Motion would have been willing to surrender some profit on the sales it lost to Exac. Similarly, because Exac would have been unable to enter business without first securing a license from Micro Motion, Exac should have been willing to pay a significant portion of its expected profits as a royalty to Micro Motion.
A reasonable royalty that would adequately compensate Micro motion for Exac's infringement is fifteen percent. This is the amount that the Court believes the parties would have settled on in a hypothetical negotiation held in December 1983. This rate reflects the Court's determination that for each new sale Exac made it also made two and one-third sales that would have gone to Micro Motion. The Court declines to add a five percent "Panduit kicker". This royalty rate applies to the thirty percent of Exac's domestic meter and accessory sales that Micro Motion would not have made and to all of Exac's foreign sales of meters and accessories. The reasonable royalty is $536,097 for domestic meters and accessories, $758,520 for foreign meters and accessories, and $1,294,617 in total. PX 518.
Micro Motion suffered $20,821,525 in damages as a direct result of Exac's patent infringement. The total damages consist of the lost profits due to Exac's infringement ($4,877,819) plus the damages due to price erosion ($14,649,089) plus the reasonable royalty on the Exac sales that Micro Motion would not have made ($1,294,617). PX 518.
Accordingly, The Court awards Micro Motion $20,821,525 in damages.

IV. TAX WINDFALL.
Exac asks this Court to consider recent changes in corporate federal income tax rates when determining Micro Motion's award. Through Mr. Holdren, Exac introduced evidence showing that the maximum marginal federal tax rate for corporations has fallen from forty-six percent in 1985 and 1986, to forty-three percent in 1987, and to thirty-four percent in 1988, 1989, and 1990. DX ACS at 11. Exac argues that Micro Motion will enjoy an unfair "tax windfall" because the taxes it will pay on the damage award it receives in this case may be substantially less than the taxes it would have paid had it actually earned those amounts in 1985, 1986, and 1987. Exac, therefore, suggests that the Court *1436 adjust Micro Motion's award to reflect the difference between the marginal corporate tax rate in place when Micro Motion sustained its injury and the marginal corporate tax rate in place when it receives it award.
Although it finds Exac's tax windfall theory quite interesting, the Court declines to apply it in this case. First, Exac failed to prove that Emerson Electric, Micro Motion's parent, paid taxes at the top marginal rate for corporations. Second, to be completely fair, a tax adjustment would have to take into account changes to a firm's entire tax burden, not just changes to its federal taxes. Such an inquiry, which was not performed in this case, would add to the complexity of already difficult damage cases and could add significantly to the cost of litigating such actions. Moreover, even though the federal tax rates changed four years ago, Exac identified no patent infringement case in which a court has made an adjustment to reflect a change in the tax code.

V. PREJUDGMENT INTEREST.
In General Motors Corp. v. Devex Corp., 461 U.S. 648, 655, 103 S.Ct. 2058, 2062, 76 L.Ed.2d 211 (1983), the Supreme Court clearly set forth the objective of a prejudgment interest award: "In the typical case an award of prejudgment interest is necessary to ensure that the patent owner is placed in as good a position as he would have been in had the infringer [not infringed]." The interest to which Micro Motion is entitled depends on two factors: (1) the appropriate interest rate, and (2) the appropriate base of damages.
Exac states that this Court should award Micro Motion interest at a rate equal to that paid on the relevant one-year treasury bills. Exac argues that this rate is appropriate because Micro Motion incurs no risk on its prejudgment interest award and should, therefore, be paid interest at the prevailing rate for risk-free investments  the treasury bill rate. DX ACS. The interest rate on T-bills over the relevant period was as follows: 8.28 percent in 1985, 6.54 percent in 1986, 6.01 percent in 1987, 6.84 percent in 1988, 8.07 percent in 1989, and 7.52 percent in 1990. Id. at 13.
From 1985 to the present, Micro Motion has swept its cash accounts into an Emerson Electric account each night. PX 450. Micro Motion states that it should receive prejudgment interest at the rate paid on the Emerson Electric sweep account because the money it would have earned but for Exac's infringement would have been placed in that account and would have earned that interest. That account paid 10 percent in 1985, 10 percent in 1986, 8.5 percent in 1987, 8.5 percent in 1988, 8.5 percent in 1989 and 9.5 percent in 1990. PX 381 at 13.
The Court has discretion in deciding the rate of interest and whether the interest should be compounded. General Motors Corp., 461 U.S. at 655-57, 103 S.Ct. at 2062-63. Because Micro Motion would have placed its additional cash, as it placed all its cash, in the Emerson sweep account, using that account's performance to determine the prejudgment interest rate would best "ensure that [Micro Motion] is placed in as good a position as [it] would have been in had [Exac not infringed]." Id. at 655, 103 S.Ct. at 2062. Accordingly, the Court will apply those rates.
Exac argues that to allow Micro Motion to receive prejudgment interest based on the entire pretax amount of its damage award would put Micro Motion in a better position than it would have been in but for Exac's infringement. Although this position has some merit, there is not enough evidence before the Court to allow it to determine what tax rate should be applied to each year's earnings when calculating the post-tax base on which it should award interest. Therefore, prejudgment interest will be paid on the full amount of damages awarded, but the interest payments will not be compounded.
The Court has found that Micro Motion suffered damages in each of the years at issue as follows: $1,694,444 in 1985; $3,910,383 in 1986; $4,409,075 in 1987; $4,806,064 in 1988; $3,198,797 in 1989; and $2,802,762 in 1990. Applying the relevant percentage rates to Micro Motion's damages for each year yields a prejudgment interest total of $5,409,481.


*1437 VI. WILLFULNESS.
Under the patent statute, "the court may increase the damages up to three times the amount found or assessed," 35 U.S.C. § 284, if it finds willful infringement. Datascope Corp. v. SMEC, Inc., 879 F.2d 820, 829 (Fed.Cir.1989). A finding of literal infringement is not a necessary predicate for a finding of willful infringement; infringement under the doctrine of equivalents can be willful. Great Northern Corp. v. Davis Core & Pad Co., 782 F.2d 159, 166-67 (Fed.Cir.1986).
In determining whether the infringement was willful, the Court must consider "`whether, under all the circumstances, a reasonable person would prudently conduct himself with any confidence that a Court might hold the patent invalid or not infringed.'" State Industries, 883 F.2d at 1581 (quoting Ryco, Inc. v. Ag-Bag Corp., 857 F.2d 1418, 1428 (Fed.Cir.1988)).
Once "a potential infringer has actual notice of another's patent rights, he has an affirmative duty to exercise due care to determine whether or not he is infringing." Underwater Devices, Inc. v. Morrison-Knudsen Co., 717 F.2d 1380, 1389 (Fed.Cir.1983).
Willfulness must be proved by clear and convincing evidence, E.I. Du Pont de Nemours & Co. v. Phillips Petroleum Co., 849 F.2d 1430, 1439-40 (Fed.Cir. 1988), but there is no requirement that the patent holder show that the infringer acted in bad faith. TWM Mfg., 789 F.2d at 902. Factors relevant to a finding of willfulness include:
(1) whether the infringer deliberately copied the ideas or design of another; (2) whether the infringer, when he knew of the other's patent protection, investigated the scope of the patent and formed a good-faith belief that it was invalid or that it was not infringed, and (3) the infringer's behavior as a party to the litigation.
Bott v. Four Star Corp., 807 F.2d 1567, 1572 (Fed.Cir.1986).
In both stages of this trial, Micro Motion introduced significant evidence indicating that Exac's designers had access to Micro Motion's technology while they were designing Exac's Coriolis flowmeter. Exac's founders, Drs. Young and Dahlin, designed the Exac mass flowmeters in suit. Opinion and Order filed June 28, 1990, at 8. By the end of 1982, Drs. Young and Dahlin had gained experience with Micro Motion's C meter, and Dr. Young had obtained a copy of Micro Motion's '721 patent, which was later reissued as the '450 patent. Id. In early 1983, Dr. Dahlin obtained a copy of the Cox '028 patent. Id. In June 1983, Dr. Dahlin obtained information on and drawings of the Micro Motion D meter through a Mr. Bottom. And Dr. Dahlin received a Micro Motion C meter in August 1983 and a D meter in December 1983 from a Mr. Tanner.
Exac, however, introduced evidence that Drs. Dahlin and Young obtained information on Micro Motion's patents so that they could ensure that the device they developed would not conflict with Micro Motion's patents. RT (Young) 1492. This assertion is reasonable given Drs. Young and Dahlin's strong financial interest in developing a patentable product. At trial, Dr. Young testified to the design differences that he felt distinguished the Exac device from Micro Motion's. Id. at 1493-94. Based on the testimony of Dr. Young and Mr. Swanson, the Court believes that Exac did not intentionally copy Micro Motion's design.
That determination, however, does not end the Court's inquiry. Once Exac had "actual notice of [Micro Motion's] patent rights, [it] had an affirmative duty to determine whether or not [it] is infringing. Such an affirmative duty includes, inter alia, the duty to seek and obtain competent legal advice from counsel before the initiation of any possible infringing activity." Underwater Devices, 717 F.2d at 1389-90 (citations omitted). Because Exac made a tactical decision during the liability phase of this action to withhold as privileged evidence of the patent advice it received from counsel, the Court refused to allow Exac to introduce such evidence at this trial. On redirect, however, the Court allowed Mr. Hamrick, Exac's patent counsel, to testify that, prior to June 1983 and January 1984, he gave Exac oral opinions on whether its proposed designs infringed Micro Motion's patents. RT (Hamrick) 1551-63. No evidence *1438 was presented as to that opinion's content.
Although absence of proof of advice of counsel can give rise to an inference against the infringer, the Court draws no such inference in this case. Unlike defendants in most cases in which no advice of counsel proof is entered, Exac strenuously sought to introduce its advice of counsel evidence. Moreover, Exac allowed Micro Motion to depose Mr. Hamrick on the subject of the opinions he gave Exac.
Mr. Swanson and Dr. Young each testified convincingly as to their belief of noninfringement and of the procedures that they followed in reaching and validating that belief. See e.g., RT (Swanson) 1560-64; RT (Young) 1483-95. In light of the testimony of Mr. Swanson and Dr. Young as to the steps that they took to insure that their device did not infringe Micro Motion's patents, the Court finds that Exac conducted itself as a reasonably prudent person seeking to avoid infringement and, therefore, did not willfully infringe Micro Motion's patents. The question of infringement was a difficult one, and Mr. Swanson and Dr. Young took reasonable, although ultimately insufficient, precautions to assure themselves that their design was not infringing.
Because the Court does not find Exac's infringement to be willful, it does not find this to be an exceptional case. Accordingly, it denies Micro Motion's request for attorney's fees.

VII. CONCLUSION.
Accordingly,
IT IS HEREBY ORDERED that:
1. Based on the above findings of fact and conclusions of law, the Court finds that Micro Motion has established by a preponderance of the evidence that Exac's infringement caused it to suffer $20,821,525 in damages. Exac shall pay to Micro Motion that amount plus $5,409,481 in prejudgment interest, making a total award of $26,231,006.
2. Micro Motion's request for attorney's fees is denied.
3. The foregoing constitutes the findings of fact and conclusions of law required by Rule 52 of the Federal Rules of Civil Procedure. The Court will not entertain any motions for reconsideration.
4. Appendix II, attached hereto and incorporated herein by reference, states the Court's rulings on the admission of exhibits during the trial.

APPENDIX I


                         1985          1986         1987           1988           1989          1990  
Lost Sales Revenue     $ 472,804   $1,732,623   $2,425,672    $2,718,107      $ 291,326
Lost Sales Cost        (152,338)     (554,860)    (896,324)   (1,017,092)       (142,099)
                       _________   ___________  ___________   ___________    ___________
Lost Sales Profits      320,466     1,177,763    1,529,348     1,701,015         149,227
Reasonable Royalties     52,620       290,461      483,334       431,952          36,250
Price Erosion on
Micro Motion Sales    1,302,446     2,304,100    2,208,073     2,465,447       2,990,699   2,802,762
Profit Erosion on
Lost Sales               18,912       138,059      188,320       207,650          22,621
                     __________     _________    _________     _________       _________   _________
Total Damages         1,694,444     3,910,383    4,409,075     4,806,064       3,198,797   2,802,762
Interest on Award       847,222     1,564,154    1,355,790     1,069,349         439,835     133,131



*1439 APPENDIX II
During the course of this trial, each side made numerous offers to introduce trial exhibits, interrogatory answers, and deposition testimony into evidence. The opposing party often objected to the proffered evidence. In an attempt to streamline the trial process, the Court asked the parties to exchange with each other their offers of and objections to evidence before submitting those offers and objections to the Court. In late October, the parties submitted their final offers of evidence and objections to offers of evidence. The Court's rulings on the contested offers of evidence are as follows.[1]
The following exhibits are admitted into evidence: PX 490; PX 491; PX 218A; PX 219A; PX 410; PX 450 (excluding ¶ 45); PX 453; PX 528; PX 529; PX 541; PX 346A; PX 538; PX 366; PX 381; PX 400; PX 401; PX 402; PX 466; PX 467; PX 474 (excluding the last page); PX 476A; PX 477; PX 332; PX 333; PX 334; PX 335; PX 336; PX 337; PX 338; PX 339; PX 340; PX 343; PX 344; PX 347; PX 350; PX 366; PX 369; PX 382; PX 473; BE; DX HJ; DX HS; DX MC; DX MD; DX ME; DX MF; DX MG; DX MH; DX MI; DX MJ; DX MK; DX NB; DX OY; DX PA; DX PB; DX PC; DX PD; DX SN; DX SO; DX TG; DX VE (excluding pages 3-6); DX XR; DX XS.
The following exhibits are admitted only to show when the statements were made: DX XF; DX YD; DX YE; DX YF; DX YG; DX YH; DX YI; DX YJ; DX YK; DX YL; DX ACI;
The following exhibits are admitted only as illustrative of the witnesses' testimony: PX 499; PX 510; PX 511; DX ZS; DX AAB; DX ABO; DX ABP; DX ABQ; DX ACM;
The following exhibits are not admitted: PX 532; PX 533; PX 534; PX 535; PX 536; PX 537; PX 349; PX 374; PX 394; PX 403; PX 404; PX 405; PX 406; PX 407; PX 408; PX 409; PX 415; PX 416; PX 417; PX 418; PX 421; PX 346; PX 476; DX UW; DX AAA; DX ABN; DX ABR; DX ABZ; DX ACG; DX ACU; DX ACW; DX ACX;
The following depositions are admitted into evidence: All portions of Daniel H. Case III's 6/26/85  6/27/85 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of Daniel H. Case III's 8/20/85 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of Donna Erickson's 5/27/86  5/28/86 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of Robert J. Kunze's 6/18/86 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of Joseph S. Maloney's 7/11/85 deposition designated by Micro Motion;
All portions of Joseph S. Maloney's 2/17/87 deposition designated by Micro Motion;
All portions of Loren Puck's 12/6/88 deposition designated by Micro Motion;
All portions of Keith Swanson's 2/11/85  2/12/85 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of Keith Swanson's 4/1/87 deposition designated by Micro Motion or counterdesignated by Exac except 31:20-23, which Micro Motion has withdrawn;
All portions of Keith Swanson's 7/14/87 deposition designated by Micro Motion;
All portions of Keith Swanson's 7/25/87 deposition designated by Micro Motion;
All portions of Keith Swanson's 1/24/89 deposition designated by Micro Motion or counterdesignated by Exac;
All portions of David E. Wiklund's 7/10/85 deposition designated by Micro Motion;
All portions of Gordon Woolbert's 11/29/88 deposition designated by Micro Motion, except 101:15-17;
All portions of Alan Young's 2/13/85 deposition designated by Micro Motion;
All portions of Alan Young's 7/13/87 deposition designated by Micro Motion;
*1440 All portions of Julius Adorjan's 12/16/88 deposition designated by Exac or counterdesignated by Micro Motion, except 73:8-74:1;
All portions of Jacob Beck's 1/5/89 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Brent Carpenter's 5/21/86 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Daniel Case III's 6/26/85  6/27/85 deposition designated by Exac or counterdesignated by Micro Motion, except 28:1-21 and 29:8-24 of the 6/26/85 deposition;
All portions of Daniel Case III's 8/20/85 deposition designated by Exac or counterdesignated by Micro Motion, except 21:5-11, and 26:14-24;
All portions of Bruce Cox's 6/7/82 deposition designated by Exac;
All portions of Erik Dahlin's 2/12/85  2/13/85 deposition designated by Exac or counterdesignated by Micro Motion, except 74:22-75:25 of the 2/12/85 deposition;
All portions of William Epping's 7/25/87 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Edward Groner's 6/8/82 deposition designated by Exac;
All portions of Robert Kunze's 6/18/86 deposition designated by Exac;
All portions of Joseph Maloney's 2/17/87 deposition designated by Exac;
All portions of James McConnell's 7/10/87 deposition designated by Exac;
All portions of Dennis Perkin's 6/30/87 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Dennis Perkin's 3/12/90 deposition designated by Exac;
All portions of Dennis Perkin's 9/15/90 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Loren Puck's 12/06/88 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Wilfred Roth's 4/21/86  4/22/86 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of William Epping's 7/25/87 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Harold Schindler's 5/21/86 deposition designated by Exac;
All portions of James Smith's 1/9/85 deposition designated by Exac;
All portions of Lee Smith's 5/30/86 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of Lee Smith's 1/17/89 deposition designated by Exac or counterdesignated by Micro Motion, except 162:21-164:17;
All portions of Keith Swanson's 4/1/87 deposition designated by Exac or counterdesignated by Micro Motion;
All portions of John Tregoning's 3/25/82 deposition designated by Exac;
All portions of Gordon Woolbert's 11/29/88 deposition designated by Exac or counterdesignated by Micro Motion.
The following deposition testimony is not admitted into evidence: All portions of Steve Bayles' 12/14/88 deposition designated by Exac or counterdesignated by Micro Motion.
NOTES
[1]  The Court asked both parties to submit in writing at the end of the trial their offers of evidence and objections to offers of evidence. Appendix II contains the Court's rulings on those objections.
[2]  Appendix I contains a breakdown of the award by year and by injury.
[3]  "RT" refers to the trial transcript and the name of the witness is indicated in the parentheses. "PX" refers to plaintiff's trial exhibits; "DX" refers to defendant's trial exhibits. Excerpts from designated deposition testimony are indicated by the witness' name followed by "Dep."
[4]  This number is low relative to Exac's market share because most of Exac's 1989 sales were of noninfringing meters.
[5]  Ninety-six percent of Exac's sales went to companies with four-digit Standard Industry Classification ("SIC") Codes that put them in industries also served by Micro Motion. PX 392.
[6]  Eighty-eight percent of Exac's sales went to companies that also purchased from Micro Motion. PX 391.
[7]  Given the relatively small number of industries to which Micro Motion and Exac sold, it is unlikely that two unrelated customers would share a common name.
[8]  This would be the case if some Exac customers had bought from Exac because they either disliked something about Micro Motion or its meters or liked working with a newer company with a smaller market share.
[9]  Neither party introduced any documents that purported to account for all sales of Coriolis flowmeters. Micro Motion knew of only those third-party sales for which they had competed. RT (Hunter) 288-93. Because it is likely that third-party vendors made some sales for which they had not competed with Micro Motion, it is reasonable to assume that the total sales made by third parties exceeded Micro Motion's estimate of sales lost to third parties.
[10]  Exac presented no evidence to challenge Ms. Dancik's estimate of Micro Motion's lost sales revenues.
[11]  Other than asserting that Exac's infringement resulted in no lost sales to Micro Motion, Exac did not challenge this figure.
[12]  The costs would vary most where, as here, the firm is young, has had rapid and uneven growth, and has spent substantial resources developing new products.
[13]  The Court accepts Professor Rubinfeld's testimony that Micro Motion's prices were not flat in 1985-87 because of extraneous factors such as problems in the oil and gas industry.
[14]  Exac was in the process of terminating its existing representatives and switching to the representative organization of Fisher Controls. The Fisher representatives were unable to sell Exac flowmeters as effectively and efficiently as Exac's original representative organization, and Exac's sales slumped. RT (Swanson) 1620-25.
[15]  The court further finds that while these new entrants might have kept Micro Motion from raising its prices more than it did, they would not have caused micro motion to roll its prices back to the level that existed with Exac's infringement. The little evidence introduced as to these third parties showed them to be price takers.
[16]  Because it finds is no reason to believe that Exac was more hopeful in August 1984 than it would have been in December 1983, the Court finds that the August 1984 financial projections offer some insight into Exac's expectations even though the projections were developed after the hypothetical negotiations would have taken place and may have reflected an optimistic mind set.
[1]  This appendix addresses only those exhibits and declarations whose admissability is currently disputed. Accordingly, it contains no discussion of items no longer offered into evidence by their sponsor, items that have already been admitted, or items whose admission is unopposed.
