WR Grace & Co.-Conn. v. Intercat, Inc.

OPINION LONGOBARDI, Senior District Judge. I. Introduction This is the damages phase of a patent infringement action. The Court conducted a bench trial over eight days beginning September 10, 1996 to determine liability. On September 8, 1997, the Court found that plaintiffs patents were valid and enforceable, were willfully infringed by defendant Intercat, both contributorily and by inducement, and were directly infringed by defendant Conoco. 1 The Court entered a permanent injunction against further infringement by defendants on November 3, 1997. The Court of Appeals for the Federal Circuit affirmed the findings of this Court on June 26,1998. 2 The parties stipulated before this trial that the assessment of damages would be based on a theory of lost profits. Plaintiff seeks damages based on lost sales and price erosion, as well as prejudgment interest, enhancement of damages based on willfulness, and an award of attorney fees based on the exceptional case standard. This Opinion represents this Court’s findings of facts and conclusions of law. II. Background Facts The relevant facts are set forth in detail in the Court’s opinion issued after the bench trial for the liability phase. To briefly summarize, W.R. Grace & Co.-— Conn. (“Grace”) is the owner of five patents relating to a composition, or the use of a composition, to reduce sulfur oxide (“SOx”) emissions from hydrocarbon conversion processes, such as fluid catalytic cracking (“FCC”) processes. The five patents at issue during the liability phase were U.S.Patents 4,469,589; 4,472,267; 4,495,305; 4,495,304; and 4,790,982. Grace is the producer of DESOX, which had attained a 95% market share by 1993. 7 F.Supp.2d at 434. Intercat introduced several products to compete in the SOx-removal additive market, but these were unsuccessful. Intercat then introduced No-SOx, and subsequently, No-SOx-PC, the infringing products, and was able to garner a 15% share of the relevant market. No other SOx-removal additive had any significant market share. Id. The primary alternatives for reduction of SOx emissions from an FCC unit are hydroprocessing and flue gas scrubbing. Id. at 431. The use of a flue gas scrubber requires significant investment of capital, requires time to construct and install the scrubber, and creates a solid waste problem stemming from the need to dispose of the byproducts of the scrubbing operation. Id. Installation of a hydroprocessor also requires a significant investment of capital and requires time to construct and install the equipment. Id. The use of a SOx-removal additive causes no solid waste disposal problems and requires neither a large capital investment nor significant time to implement. Id. III.International Sales As a threshold matter, the parties disagree as to whether plaintiff can recover damages based on Intercat’s sales of the infringing product in foreign countries. Defendants maintain that United States patent holders are entitled to assert a cause of action for infringing acts occurring outside of the United States only un *320 der certain limited conditions, which are not met in this case. The relevant statutory provision is 35 U.S.C. § 271(f): (1) Whoever ... supplies ... in or from the United States all or a substantial portion of the components of a patented invention ... in such a manner as to actively induce the combination of such components outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer. (2) Whoever ... supplies ... in or from the United States any component of a patented invention that is especially made or especially adapted for use in the invention and not a staple or commodity of commerce ... intending that such component will be combined outside of the United States in a manner that would infringe the patent if such combination occurred within the United States, shall be liable as an infringer. Defendants maintain that Section 271(f)(1) does not apply because Intercat’s sales of NO-SOx cannot be construed as “supplying and/or being a substantial portion of the components of a patented invention exemplified by claim 6 of Grace’s ’304 patent.” As for Section 271(f)(2), defendants maintain that while courts have applied it to apparatus patents, they have not applied it to process and design patents. 3 Furthermore, because Grace’s ’304 patent is a chemical composition patent, defendants allege that 271(f)(2) does not apply because the legislative history “states that the statute only covers components of machines and other structural combinations, since the section was enacted specifically to overrule” Deep-south Packing v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972). 4 Defendants also urge the Court not to follow Lubrizol Corp. v. Exxon Corp., 696 F.Supp. 302 (N.D.Ohio 1988), which appears to contradict defendants’ position, because it is a district court decision on a preliminary injunction application. Plaintiff argues that the plain language of Section 271(f)(2) makes it applicable to any “patented invention”, and that it is not limited to components of machines or other structural combinations. There is no limitation in the statute excluding protection for chemical composition inventions. Additionally plaintiff maintains that defendants misstate the legislative history, in that the Senate report cited by defendant nowhere states any limitation to components of machines and other structural combinations. Finally, plaintiff maintains that Lubrizol is directly on point, and because there is no contrary authority, this Court should follow its holding. The cases cited in support of defendants’ argument are irrelevant to the case at bar. Those cases involve patented processes and designs, which clearly are different from a “patented invention”. Here, we are dealing with a chemical composition, and therefore it falls under the holding in Lubrizol. In Lubrizol Corp. v. Exxon Corp., 696 F.Supp. 302, 325 (N.D.Ohio 1988), the court enjoined the defendant “from supplying in or from the United States any lubricant additive containing its product ECA 10444, including Paranox 300 and Paranox 600, for combination in a lubricating composition outside the United States (35 U.S.C. § 271(f)(1) and (2)).” While the court did not provide a rationale for its conclusion, this Court concurs in its result. *321 The plain language of the statute limits its application only to a “component of a patented invention”. Nowhere in the statute or its legislative history is there a limitation to components of machines and other structural combinations. A contrary holding, refusing to apply the statute to chemical compositions, would be tantamount to legislating additional language to a statute. That simply is not warranted. Furthermore, defendants’ argument that Lubrizol is distinguishable because it is a preliminary injunction decision is not persuasive. Therefore, plaintiff is entitled to damages based on Intercat’s international sales. IV. Damages in General A patent owner is entitled to “damages adequate to compensate for the infringement but in no event less than a reasonable royalty for the use made of the invention by the infringer.” 35 U.S.C. § 284. The purpose of the damage award is to place the patent owner in the same financial position that it would have been in had the infringement not occurred. Aro Mfg. v. Convertible Top Replacement Co., 377 U.S. 476, 507, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964); Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1545 (Fed.Cir.1995); Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1574 (Fed.Cir.1988). In calculating damages, the focus is on the financial harm to the patent owner caused by the infringement. No consideration is given to whether the defendant gained or lost by the infringing act. State Indus. v. Mor-Flo Indus., 883 F.2d 1573, 1577 (Fed.Cir.1989); Weinar v. Rollform, Inc., 744 F.2d 797, 807 (Fed.Cir.1984). “The general rule for determining the actual damages to a patentee that is itself producing the patented item, is to determine the sales and profits lost to the patentee because of the infringement.” Del Mar Avionics, Inc. v. Quinton Instr. Co., 836 F.2d 1320, 1326 (Fed.Cir.1987); Kori Corp. v. Wilco Marsh Buggies & Draglines, 761 F.2d 649, 653 (Fed.Cir.1985). A patent owner need not prove patent infringement damages with absolute certainty. Mobil Oil Corp. v. Amoco Chemicals Corp., 915 F.Supp. 1333, 1350-51 (D.Del.1994). Rather, a patent owner need only show a reasonable probability that it would have made the sales. Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed.Cir.1983). If a patent owner is unable to determine the amount of damages with precision, the court resolves doubts against the infringer. Id. V. Lost Profits on Diverted Sales Grace first seeks damages for the lost sales resulting from defendants’ infringement. Grace has the burden of proving by a reasonable probability that the adjudged infringing activity of defendants caused it to lose profits it would have made in the absence of infringement, and providing sufficient evidence to compute the loss. King Instrument Corp. v. Otari Corp., 767 F.2d 853, 863 (Fed.Cir.1985). The first inquiry is essentially whether, “but for” the infringement, the patent owner would have made the sales made by the infringer. Paper Converting Mach. v. Magna-Graphics Corp., 745 F.2d 11, 21 (Fed.Cir.1984); Gyromat Corp. v. Champion Spark Plug Co., 735 F.2d 549, 553 (Fed.Cir.1984). With respect to lost sales, the “but for” rule requires the patentee to provide proof to a reasonable probability that the sale would have been made but for the infringement. Minco v. Combustion Eng’g, Inc., 95 F.3d 1109, 1117 (Fed.Cir.1996); Paper Converting Mach., 745 F.2d at 21. The defendant has stipulated that Grace would have made each and every domestic sale made by Intercat. See Defendants’ brief (D.I.319) at 9. The general rule and method for lost profits due to lost sales is set forth in Panduit Corp. v. Stahlin Bros. Fibre Works, 575 F.2d 1152, 1156 (6th Cir.1978): To obtain as damages the profits on sales he would have made absent the infringement, i.e., the sales made by the *322 infringer, a patent owner must prove: (1) demand for the patented product, (2) absence of acceptable noninfringing substitutes, (3) his manufacturing and marketing capability to exploit the demand, and (4) the amount of profit he would have made. This method of establishing lost profits on lost sales has been adopted by the Court of Appeals for the Federal Circuit. Rite-Hite, 56 F.3d at 1545. The three threshold factors have either already been established or are uncontested by the defendants. A. Demand Demand for the patented products is evidenced by sales of the patented products made by the patent owner and the infringer. “The substantial number of sales ... of infringing products containing the patented features itself is compelling evidence of the demand for the product.” Gyromat Corp. v. Champion Spark Plug Co., 735 F.2d 549, 552 (Fed.Cir.1984). Demand for the SOx-removal additive products was established during the liability phase. DESOX controlled up to 95% of the market, and Intercat was unable to capture a significant market share until it introduced the infringing products. 7 F.Supp2d. at 464-65. No other SOx-re-moval additive had any appreciable market share during the relevant time period. Id. The infringer’s willingness to risk suit to enter and stay in the market is also evidence of demand. Gyromat, 735 F.2d at 552. Intercat continued to sell NO-SOx and then introduced NO-SOx-PC after the filing of this action. These facts establish the demand for the Sox-removal additives. B. Lack of Non-Infringing Substitutes The claims of the patents-in-suit define the market used to assess whether or not acceptable non-infringing substitutes existed. Datascope Corp. v. SMEC, Inc., 879 F.2d 820, 824 (Fed.Cir.1989). The Court found in the liability phase that there are no non-infringing substitutes to use in the FCC units. 7 F.Supp.2d at 464-65. Moreover, Intercat admitted prior to trial that there were no such alternatives, and the Court precluded Intercat from contesting that issue at the damages trial. See Order, D.I. 309. C. Capacity To prove capability to meet demand for lost sales, the patent owner need only show a reasonable probability that its manufacturing and marketing efforts were adequate, or could have been made adequate, to make the additional sales. Yarway Corp. v. Eur-Control USA, Inc., 775 F.2d 268, 276-77 (Fed.Cir.1985). Plaintiff has presented evidence of its capacity to meet demand, and defendants have not contested this issue. 5 D. Calculation of Lost Profits In making the calculation of lost sales, the Court applies the incremental income method: The incremental income approach to the computation of lost profits is well established in the law relating to patent damages. The approach 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 — those costs which do not vary with increases in production, such as management salaries, property taxes, and insurance — are excluded when determining profits. Paper Converting Mach. Co. v. Magna-Graphics Corp., 745 F.2d 11, 22 (Fed.Cir.1984). At trial, plaintiff presented evidence seeking to show that its incremental lost profits based on lost sales during the period of infringement was $4,145,356. *323 Plaintiffs testimony was presented by its damages expert, Mr. Kevin Dennis. Defendant presented evidence that plaintiffs damages due to lost sales was $3,067,000. Defendants’ evidence was presented through the testimony of their damages expert, Mr. John Bone. For a number of reasons, the Court finds the presentation by Mr. Bone flawed, and therefore, unpersuasive. The parties agree on the methodology used to calculate lost profits based on lost sales: (1) Determine the volume of NO-SOx and NO-SOx-PC sold during the damages period. (2) Determine Grace’s lost volume of DESOX based on the efficiency ratio between DESOX and NO-SOx and NO-SOx-PC. (3) Determine the price per pound of DESOX at which Grace would have made the lost sales. (4) Calculate Grace’s lost revenue by multiplying Grace’s lost DESOX volume [step 2] by price [step 3]. (5) Determine Grace’s additional incremental costs incurred to make the lost DESOX sales. (6) Subtract total incremental costs [step 5] from Grace’s lost revenue [step 4] to arrive at Grace’s lost profits. The parties disagree on the calculation of price per pound (step 3) and incremental costs (step 5). 1.Volume Sold During the Damages Period Intercat’s sales of the infringing NO-SOx and NO-SOx-PC products were set forth in Intercat’s answers and supplemental answers to Interrogatory 3 and its answers to Interrogatory 21. (See PTX-37, 42, 244, 245, 426, 554). Intercat sold 555,-470 pounds of NO-SOx in 1993 (in the applicable period from April - December); 135,118 pounds of NO-SOx and 695,145 pounds of NO-SOx-PC in 1994; 353,258 pounds of NO-SOx-PC in 1995; and 35,-790 pounds of NO-SOx-PC in 1996. (See id. PTX-560-D). 2. Grace’s Lost Volume Adjusted for Efficiency The parties agree that DESOX performed in a superior fashion to the original NO-SOx product. Both parties’ experts based their calculations on the assumption that NO-SOx was 83% as effective as DE-SOX. This figure is based on a comparative study performed by Conoco. (See PTX-108). While both parties made other representations of the efficiency in their marketing efforts during the damages period, the Court is satisfied that 83% is the proper efficiency ratio. Thus, Grace would have sold .83 pound of DESOX for each pound of NO-SOx sold by Intercat. Additionally, the parties agree that NO-SOx-PC was equal in efficiency to DE-SOX. Therefore, Grace’s sales of DESOX would have been equivalent in volume to the sales of NO-SOx-PC. To determine Grace’s lost volume, the sales of NO-SOx are multiplied by .83, and then added to the sales of NO-SOx-PC. Applying this conversion factor leads to the result that in 1993, Grace would have sold 461,040 pounds of DESOX in place of NO-SOx. In 1994 Grace would have sold 112,148 pounds of DESOX in place of NO-SOx, and 695,145 pounds in place of NO-SOx-PC, for a total lost volume in 1994 of 807,293 pounds of DESOX. In 1995, Grace would have sold 353,258 pounds of DESOX in place of NO-SOx-PC. In 1996, Grace would have sold 35,790 of DESOX in place of NO-SOx-PC. (See PTX-560-D). 3. Price per Pound of Lost Sales Grace contends that the price per pound of the lost sales should be at a price equal to Grace’s actual average selling price at the time of sale. Mr Dennis calculated Grace’s average per-pound sales price for DESOX for each year. (See PTX-515). Defendants argue that in the international *324 market, it is unreasonable to assume that Grace would have been able to achieve these prices. Grace’s prices for DESOX in the international market were up to 60% higher than Intercat’s prices for its NO-SOx products, and defendants maintain that Grace produced no evidence to indicate that international customers would have been willing to pay Grace’s higher prices. Defendants’ expert, Mr. Bone, also used a different method to ascertain the equivalent price in the domestic market. Mr. Bone calculated the total number of pounds of NO-SOx sold, and the cost each customer incurred annually to meet its desired level of SOx reduction. Because NO-SOx was only 83% as efficient as DE-SOX, Mr. Bone determined that the NO-SOx customers would buy less DESOX, and thus would be willing to pay a higher price per pound; therefore, spending the same total amount of money. Thus, according to defendants, the equivalent price that NO-SOx customers would pay for DESOX was higher than the actual average price of DESOX. Defendant also used this methodology to determine an equivalent price for international sales. Defendants’ use of equivalent price, both for domestic and international sales is flawed. Defendants’ methodology is incorrect because it uses prices set by Intercat as its starting point. In Inter-cat’s absence, however, customers would have been forced to' pay Grace’s prices. This is true even in the international market, where Grace’s prices were significantly higher. In a two supplier market, such as the SOx-removal additive market, it is presumed that 'the patentee would have made the sales made by the infringer. Kaufman Co. v. Lantech, Inc., 926 F.2d 1136, 1141 (Fed.Cir.1991); Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed.Cir.1983). Therefore, while Grace’s international prices were higher than Intercat’s, the Court presumes that Grace would have made those sales at its average price. Defendants’ methodology also is flawed because it uses Intercat’s price as its starting point. The purpose of the damages inquiry is to place the patent owner in the same financial position that it would have been in had the infringement not occurred. Aro Mfg. v. Convertible Top Co., 377 U.S. 476, 507, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964); Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1545 (Fed.Cir.1995); Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1574 (Fed.Cir.1988). That means the Court must assume that no competition existed for DE-SOX, and the customers were never aware of Intercat’s products. While defendants point out the use of its method results in greater damages for Grace from the domestic market, it results in less damages from the international market. “The defendant may ‘not take advantage of any reduction in price caused by its ... wrongdoing.’ ” Saf-Gard Products, Inc. v. Service Parts, Inc., 491 F.Supp. 996, 1009 (D.Ariz.1980) (quoting Overman Cushion Tire Co., Inc. v. Goodyear Tire and Rubber Co., 66 F.2d 361, 362 (2d Cir.1933)). In Saf-Gard, the court held that plaintiffs lost profits cannot be based on “any reduced selling price occasioned by the defendant’s unlawful competition.” Id. at 1009. That holding is applicable here as well. Grace’s damages must be based on its own pricing structure, not that of the infringer. Accordingly, the price per pound of Grace’s lost sales is: $7.06 in 1993; $7.23 in 1994; and $7.52 in both 1995 and 1996. Mr. Dennis calculated these average prices directly from Grace’s sales invoices for DESOX. (See PTX-515). 4. Lost Revenue Grace’s lost revenue is calculated by multiplying Grace’s lost volume (step 2) by the price per pound (step 3). Broken down into yearly figures, Grace’s lost revenue is: $3,254,942 for 1993; $5,836,728 for 1994; $2,656,500 for 1995; and $269,141 for 1996. Grace’s total lost revenue is $12,017,311. *325 5. Additional Incremental Costs Under the incremental income approach, profit is computed by deducting from the selling revenue only the variable or incremental costs that the patent owner would have incurred in making the additional sales. Fixed costs have already been incurred and are not deducted. Paper Converting Mach., 745 F.2d at 22; Kerwit Medical Prods, v. N & H Instruments, 224 U.S.P.Q. 679, 689, 1984 WL 63520 (N.D.Tex.1984); Lam, Inc. v. Johns-Manville Corp., 219 U.S.P.Q. 599, 601 (D.Colo.1982), aff'd in part, rev’d in part, 718 F.2d 1056 (Fed.Cir.1983). The patent owner’s view as to which of its costs are fixed or variable is entitled to credit based on its familiarity with its own costs. Kalman v. Berlyn Corp., 9 U.S.P.Q.2d 1191, 1198 (D.Mass.1988), aff'd in part, rev’d in part, 914 F.2d 1473 (Fed.Cir.1990). Once the patent owner has presented evidence of the amount of lost profits, it is up to the infringer to establish that the patent owner’s proofs are unreasonable. Paper Converting Mach., 745 F.2d at 21. Grace has reasonably set forth the costs it would incur to make the lost sales of DESOX. These costs are the fee paid to United Catalysts, Inc. (“UCI”) to toll manufacture DESOX, the cost of raw materials Grace purchased for UCI, the royalties paid to AMOCO and UOP (for ARCO) for the right to manufacture and sell DESOX, and any commissions applicable for the foreign sales of DESOX. DESOX was manufactured under contract with UCI pursuant to a Toll Conversion Agreement. (See PTX-27). The fees charged by UCI changed annually, on the June 1 anniversary of the agreement. The agreement provided for a reduced fee for quantities of DESOX exceeding one million pounds tolled by UCI in an agreement year (June 1 - May 31). Grace produced evidence to demonstrate that in each agreement year, it met that threshold with the amount of DESOX it sold. Therefore, the toll cost Grace would have incurred for its sales to replace the infringing sales would have been at the discounted rate. The per-pound cost Grace would have incurred to have UCI convert additional quantities of DESOX to cover the sales of the NO-SOx products would have been: $1.92 from April through May 31, 1993; $1.72 from June 1993 through May 31, 1994; $1.78 from June 1994 through May 31, 1995; $1.84 from June 1995 through May 31, 1996; and $1.87 from June through December 1996. (See PTX-560F). Accordingly, the tolling costs were calculated by Mr. Dennis by multiplying the lost DESOX sales by the applicable tolling costs for the year. Because the costs changed in June of each year, Mr. Dennis divided the lost volume into two periods: January through May and June through December. Mr. Dennis allocated the volume based on Intercat’s interrogatory answers, and assumed Grace would have made the sales at the same time. Defendants have presented no evidence to counter this assumption. Accordingly, Grace’s “would have been” toll costs are: 1993— $800,552; 1994 — $1,421,662; 1995 — $637,-257; 1996 — $66,511. Grace’s total toll manufacturing costs would have been $2,925,982. Grace would also have had costs for supplying raw materials to UCI. These raw materials included tetrasodium pyro-phosphate, Pural SB alumina, cerium nitrate, vanadium pentoxide, magnesium oxide, oxalic acid, and formic acid. These materials are available on the open market and Grace would have been able to purchase sufficient quantities to manufacture enough DESOX to cover all of Intercat’s sales, without a substantial increase in the costs of the materials. The unit cost for the raw materials (per pound) was: 1993— $1.81; 1994 — $1.74; 1995 — $1.81; and 1996 — $1.82. The “would have been” costs of raw materials was calculated by multiplying the unit cost by the volume of lost sales for that year. The raw material costs that Grace would have incurred were: 1993 — $834,482; 1994 — $1,404,690; *326 1995 — $639,397; 1996 — $65,138. Grace’s total cost of raw materials for the damages period would have been $2,943,707. The third component of Grace’s “would have been” costs is the royalties that Grace would have paid for the sale of additional quantities of DESOX. Grace paid a royalty of 7% of the net sales of DESOX to UOP (for ARCO) from the date Grace acquired the DESOX business from UOP in April, 1993 until ■ July 1995, at which time the license from ARCO was paid in full. (See PTX-9). Grace also paid a royalty according to the formula: $.45 + $.05(DESOX net sales price — $3.00) to AMOCO throughout the entire damages period. These royalties would have been $525,586 for 1993; $944,533 for 1994; $370,333 for 1995; and $24,338 for 1996; for a total of $1,864,790. The final component of Grace’s “would have been” costs is the commissions to sales agents that Grace would have paid for the sale of additional quantities of DE-SOX into certain foreign countries. Grace pays commission for all DESOX sales in Mexico, Japan and Taiwan of 5% of the net sales value. These commissions would have been: $70,903 for 1993; $43,742 for 1994; and $22,831 for 1995; for a total of $137,476. Defendants maintain that Grace’s selling and general and administrative costs should be included as well, because these costs increase with increased sales activity. However, Mr. Steve Davey, Grace’s Business Manager for FCC Additives and thereafter the Director of FCC Additives throughout the damages period, testified otherwise, and defendants have not refuted this testimony. Mr. Davey testified that the staff in place to handle the DE-SOX sales was capable of handling the increase in sales, even in 1994, when Inter-cat’s sales were at their highest point. Therefore, it is proper to not include this in Grace’s incremental costs. Accordingly, Grace’s total incremental costs for the lost sales during the damages period is $7,871,955. 6. Lost Profit Grace’s lost profits based on lost sales is calculated by subtracting “would have been” costs from lost revenue. These values are: YEAR LOST DESOX REVENUE INCREMENTAL COSTS LOST PROFIT — 1993 — $ 3,254,942 $2,231,523 $1,023,419 — 1994 — $ 5,836,728 $3,814,627 $2,022,101 — 1995 — $ 2,656,500 $1,669,818 $ 986,682 — 1996 — $ 269,141 $ 155,987 $ 113,154 TOTAL $12,017,311 $7,871,955 $4,145,356 7. Conoco’s Contribution During the liability phase, the Court found that Conoco directly infringed the patents-in-suit by using the infringing NO-SOx products it purchased from Intercat. 7 F.Supp.2d at 455, 477. Every Conoco purchase deprived Grace of a sale it would have otherwise made. Thus, Conoco is jointly and severally liable for the amount of damages attributable to its purchases. FMC Corp. v. Up-Right, Inc., 816 F.Supp. 1455, 1461 (N.D.Cal.1993) (“Under federal patent law, when infringement results from the participation and combined or *327 successive action of several parties, those parties are joint infringers, and are jointly liable.”) The methodology to calculate Conoco’s joint liability is the same as outlined above. Conoco’s purchases of the infringing product are set forth as part of the sales figures in Intercat’s interrogatory answers. (See PTX-37, 42, 244, 245, 426, 554). In 1993 (April through December), Conoco purchased 62,002 pounds of NO-SOx from Intercat for use in its FCC units; in 1994, 28,800 pounds of NO-SOx and 138,945 pounds of NO-SOx-PC; in 1995, 70,000 pounds of NO-SOx-PC. Using the same efficiency ratios as above, Conoco would have purchased 51,461 pounds of DESOX in 1993, 162,849 pounds in 1994, and 70,000 pounds in 1995. Mr. Dennis, using the same methodology described for Intercat’s sales, calculated Grace’s lost profits on DESOX sales it would have made to Cono-co. These are $121,332 for 1993; $418,671 in 1994; and $202,940 in 1995; for a total of $742,943. Therefore, Conoco is jointly and severally liable for this amount. VI. Price Erosion In addition to lost profits from diverted sales, Grace seeks lost profits from defendants’ price competition. A patent owner may recover lost profits for price erosion by showing that the infringement caused the patent owner to charge lower prices than the market otherwise would have dictated. Amstar Corp. v. Envirotech Corp., 823 F.2d 1538, 1543 (Fed.Cir.1987). In a market with only two viable competitors, a court may infer that the patentee would have charged higher prices but for the infringement. Id. Price erosion damages can be described as “the difference between actual costs of goods and potential price — the price [that the patent holder] could have realized had there been no competition from the in-fringers.” 6 In re Mahurkar Double Lumen Hemodialysis Catheter Patent Litig., 831 F.Supp. 1354, 1386 (N.D.Ill.1993). As with lost profits for diverted sales, the patent holder must show that it would have been able to charge higher prices but for the infringement, Minco, Inc. v. Combustion Eng’g, Inc., 95 F.3d 1109, 1120 (Fed.Cir.1996), and it must prove the amount of its loss. Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1065 (Fed.Cir.1983). Its burden of proof on these issues is only to a reasonable probability. Yarway Corp. v. Eur-Control USA, Inc., 775 F.2d 268, 275 (Fed.Cir.1985). The determination of price erosion damages is not, and is not expected to be, exact. It is enough if the evidence shows that the damages are a matter of just and reasonable inference, even though the result is only approximate. King Instr. Corp. v. Otari Corp., 767 F.2d 853, 863 (Fed.Cir.1985). A patent holder may recover for price reductions incurred both On its own sales as well as on the sales that the infringer made. In the absence of infringement, the sales made by the infringer would have been made by the patent owner, at the same non-reduced price, as the sales that the patent owner actually made of its own product. TWM Mfg. Co. v. Dura Corp., 789 F.2d 895, 902 (Fed.Cir.1986). A. Plaintiffs Price Erosion Calculations Grace argues that but for the infringement of the defendants, it would have been able to charge a higher price for its DE-SOX product. Grace argues that it could have raised prices annually by just under 5.0% per year. Each year of Intercat’s presence in the market, Grace fell further behind its projections. This would amount to price erosion damages of $3,837,930. Grace arrived at this figure based on its *328 projected price increases that it drafted in 1992, when it considered the purchase of the DESOX technology. (See PTX-20). In support of this 5% annual price increase, Grace argues that before Intercat began selling the infringing products, the price that Grace’s predecessor, UOP, had been charging for DESOX had increased at an average rate of approximately 5.4% each year between 1987 and 1991. During this period, DESOX had no significant competition in the SOx-removal additive market. This time period reflects a more true non-competition scenario than Grace’s own projections. Furthermore, Grace maintains that in 1992, when Intercat was considering purchasing the DESOX technology, Intercat projected that if it acquired DESOX, in could maintain annual increases of 10% per year. Accordingly, Grace maintains that while its price erosion damages are based on a speculative projection made in 1992 of 5% annual price increases„.this is a reasonable projection in light of UOP’s and Intercat’s higher projection for the same time period. B. Defendants’ Price Erosion Calculation Defendants maintain that Grace’s price erosion calculation is based solely on its 1992 projection, and is not an analysis of the but-for world, which never included the infringing competitor. Defendants argue that there are many flaws in the plaintiffs calculation. Defendants argue that plaintiffs projected price increases were based on projected cost increases, however, the actual cost increases were lower; therefore, Grace’s actual price increases would have been lower, even without Intercat in the market. Additionally, defendants maintain that Grace set a goal of a 33% profit margin for the DESOX product, and that Grace maintained this profit margin during the damages period. Defendants also maintain that Grace could have charged higher prices during the damages phase, but chose not to. Defendants base this argument on Grace’s marketing, which claimed that DESOX outperformed NO-SOx by 2 to 2.4 times. Accordingly, defendants argue that Grace could have charged double Intercat’s price and still have been competitive based on Grace’s claims of DESOX’s efficiency. Finally, defendants maintain that market factors other than Intercat’s presence caused Grace to charge a lower price for DESOX. These factors include: (1) Grace’s normal discounts; (2) decline in the total volume of SOx additives sold during the damages period; (3) operation of refineries at low margins; (4) consolidation among refineries; (5) Grace’s competition for cracking catalysts and other FCC additives; and (6) potential entrants into the market. Because of these alleged flaws in Grace’s calculations, defendants’ expert presented his own calculation of Grace’s price erosion damages. Mr. Bone based his calculation on a customer-by-customer analysis of Grace’s 13 largest customers, which accounted for 85% of Grace’s domestic sales. Mr. Bone determined the total percentage price erosion for these 13 customers, and applied that price erosion rate to Grace’s remaining domestic sales and Grace’s international sales. After reviewing a customer’s sales records, Mr. Bone determined the “normal discount” that Grace provided each of its customers off the list price. Mr. Bone defined “normal discount” as the percent discount off list price that Grace provided before any evidence of Intercat’s activity. Any discount other than this “normal discount” was attributed to In-tercat’s presence in the market, where there was evidence of Intercat’s activity with that particular customer, such as a NO-SOx trial. According to Mr. Bone, Grace suffered price erosion at a rate of 3.33%. Therefore, defendants argue that Grace suffered price erosion damages totaling $1,746,000. Defendants maintain that because Grace failed to meet its burden in proving price erosion damages, the Court should reject Grace’s calculation and adopt the findings made by Mr. Bone. *329 C. The Court’s Price Erosion Analysis For the reasons that follow, the Court holds that plaintiff has met its burden in demonstrating price erosion damages, and the Court accepts Mr. Dennis’ calculations. The testimony at trial of Mr. Steve Da-vey supports the proposition that Grace would have charged higher prices but for Intercat’s presence in the market. The Court’s accepts plaintiffs representation that it would have raised its price by 5% annually but for the infringing product. While this is speculative in nature, price erosion damages must be speculative, because the Court is required to examine a fictitious market, without the presence of the infringing product. See In re Mahurkar Double Lumen Hemodialysis Catheter Patent Litig., 831 F.Supp. 1354, 1387-92 (N.D.Ill.1993) (awarding price erosion damages even though hypothesis about price and output effects in a world without imitators is speculative). Therefore, the speculative nature of Grace’s evidence does not trouble the Court. To the contrary, other Courts have also accepted this type of speculative evidence in fixing price erosion damages. See, e.g., Micro Motion, Inc. v. Exac Corp., 761 F.Supp. 1420, 1431 (N.D.Cal.1991) (“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 credible. Accordingly, the Court concludes that Micro Motion would have raised its prices more frequently that it did had Exac not entered the market.”). Additionally, other evidence demonstrates the reasonableness, and conservative nature, of the 5% projection. Most importantly, historical data showed that when UOP marketed DESOX in the pre-infringement market, UOP was able to maintain average price increases of over 5%. Moreover, when Intercat contemplated purchasing the DESOX technology from UOP, it projected annual price increases of 10%. Therefore, the Court finds that it is reasonably probable that Grace would have increased prices 5% annually in a market without Intercat’s infringing products. Defendants’ arguments attacking plaintiffs calculations are without merit. Defendant argues that because Grace’s price projections were based on cost projections, and the actual costs were lower than the projected costs, Grace would not have raised prices as it projected. Defendant also argues that Grace was already meeting its goal of a 33% profit margin, and therefore, would not have raised prices by 5% annually in Intercat’s absence. These arguments are without merit. In a market without Intercat, the Court presumes that Grace would have been able to raise prices. See Amstar Corp. v. Envirotech Corp., 823 F.2d 1538, 1543 (Fed.Cir.1987). Grace’s price projections, and its 33% profit margin were projections, and not a price ceiling. Grace’s goal was a minimum gross margin of 33%. It is reasonable to assume that Grace would have attained a higher margin if the opportunity was available, which in Intercat’s absence, would have been the case. Similarly, there is no reason to assume that Grace’s price increase would mirror its cost increase. Grace certainly would have increased price at a rate greater than its costs if the market would accept these prices. In the SOx-removal additive market, with Grace as the only supplier, the market would have accepted these increases. Defendants’ argument that Grace could have raised prices during the damages period based on its own marketing representations of DESOX’s efficiency is also without merit. The market clearly did not accept Grace’s representations that DE-SOX was at least 2-2.4 times as effective as NO-SOx. If the market had accepted this premise, refineries would only have been willing to pay 40%-50% of the price of DESOX for a pound of NO-SOx. No customer of Intercat, however, paid that little. The representations made by Grace *330 and Intercat regarding the efficiencies of their products were only accepted by the refineries as “best light” marketing vehicles. Mr. Bone and Mr. Davey both testified that refineries were the best judge of the products’ efficiency, and it was their judgment that dictated the relative pricing. Accordingly, Grace was not able to raise prices in conjunction with its representation of DE SOX’s efficiency. These representations were marketing tools, and were, not a true representation of what each customer was willing to pay. Therefore, Grace’s failure to raise prices during the damages period is not a factor in computing its damages for price erosion. Defendants also maintain that several other market factors contributed to Grace’s lower prices. They argue that Grace’s discounts to customers, most of which were given before Intercat entered the market, should result in less damages for price erosion. Without Intercat in the market, however, Grace’s list price would have been higher. Therefore, even if Grace gave a customer the same percentage discount, it would still have received a higher price from the customer than it did with Intercat in the market. Discounts were always computed from the list price, and without Intercat, Grace’s list price would have been higher. Defendants also maintain that a decrease in volume and demand forced Grace to keep its prices lower. Defendants, however, presented no evidence to support this theory. Mr. Bone interviewed no refineries, and presented no economic analysis of the alternatives to DESOX. Mr. Davey testified that while several refineries did switch to flue scrubbers or hydroproces-sors, this did not affect Grace’s pricing. Because of the large capital costs of these alternatives, Mr. Davey testified that a refinery’s decision to implement these methods is independent of the price of DESOX. Defendants did not present enough evidence to demonstrate that a lower market volume contributed to Grace’s price depression. Defendants also maintain that Grace’s prices were depressed because refineries were operating at low margins. Again, however, defendants have presented no evidence to support this contention. Mr. Bone made no calculations to demonstrate the relationship between the refineries’ margins and Grace’s prices. Grace demonstrated that the amount a refinery spends on a SOx-removal additive is less than one half of one percent of its operating costs. Therefore, a refinery’s low operating margin would have no effect on Grace’s pricing. Defendants’ remaining arguments are also unsupported. Refinery consolidation had no effect on prices. Mr. Davey testified that no newly-enlarged, consolidated refinery ever demanded a price reduction on DESOX based on its consolidation. Furthermore, Grace’s other FCC business did not enter into its pricing for DESOX. Mr. Davey testified that no large-volume customer of its other FCC products threatened to purchase those products elsewhere if Grace did not lower its price for DESOX. Defendants final contention, that Grace lowered its prices because of potential entrants into the market, is also without merit. Mr. Bone identified no possible entrants, and could not testify as to the cost of designing a SOx-removal additive without infringing Grace’s patents. Intercat was the only competitor, albeit with an infringing product, and there is no evidence that any other competitor could enter the market with a non-infringing product. The Court also finds that defendants’ price erosion calculation is legally incorrect. Defendants base their price erosion calculation on Grace’s list price during the damages period. Grace, however, set its list price incorporating Intercat’s presence in the market. Therefore, any calculation that is based on the list price does not reflect a true “but for” scenario. The purpose of the damages inquiry is to place the patent owner in the same financial position that it would have been in had the infringement not occurred. Aro Mfg. v. *331 Convertible Top Replacement Co., 377 U.S. 476, 607, 84 S.Ct. 1526, 12 L.Ed.2d 457 (1964); Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1545 (Fed.Cir.1995); Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1574 (Fed.Cir.1988). Defendants’ calculation does not accomplish this task. Without Intercat in the market, Grace’s list price would have been higher. Mr. Bone testified that he assumed that Grace’s list price would not have been higher, and that if his assumption was wrong, his price erosion calculation would be too low. Indeed, Mr. Bone’s assumption is incorrect, and therefore, defendants’ price erosion calculation is flawed. Mr. Bone’s calculation of the “normal discount” is also flawed. In some circumstances, Grace gave customers “sole-source” agreements, which gave the customer a lower price in exchange for making Grace its sole supplier of SOx-removal additives. Grace would only revoke this discount if the refinery purchased SOx-removal additive from another source, namely, Intercat. Therefore, these discounts should not have been included in the calculation of the “normal discount” because the discounts were a direct result of Intercat’s infringement, even when they were given before any evidence of a refinery conducting a test of the two products. Accordingly, inclusion of the sole-source discount in the “normal discount” resulted in a calculation of price erosion damages that understates Grace’s actual price erosion damages. Accordingly, the Court accepts plaintiffs price erosion calculations. Intercat’s infringement is the sole reason that Grace was unable to meet its projected prices. Therefore, the difference between the actual price and the projected price per pound represents Grace’s damages for price erosion. Year Grace’s Actual Selling Price (per pound) Grace’s Projected Selling Price (per pound) Price Differential — 1993 — $7.06 $7.31 $0.25 — 1994 — $7.23 $7.67 $0.44 ' — 1995 — $7.52 $8.05 $0.53 — 1996 — $7.52 $8.45 $0.93 The difference between the actual and projected price is multiplied by the DESOX sales affected in each year. This is the amount of DESOX actually sold by Grace, in addition to the amount of DESOX Grace would have sold in place of Intercat’s sales 0f NO-SOx and NO-SOx-PC. Year Total DESOX Sales (lbs.) for Price Erosion — 1993 — 1,612,367 — 1994 — 2,774,485 — 1995 — 1,792,509 — 1996 — 1,777,472 Total 7,956,833 *332 After multiplying the price differential by the affected DESOX sales, Grace reduced the resulting figures by the incrementally increased costs that Grace would have incurred for royalties and commissions, which were based on Grace’s sales price. Defendants did not oppose plaintiffs calculation of these costs. Year Price Erosion Before Royalties/Commissions Price Erosion After Royalties/Commissions — 1993 — $ 403,092 $ 352,027 — 1994 — $1,220,773 $1,065,813 — 1995 — $ 950,030 $ 856,687 — 1996 — $1,653,049 $1,563,403 Total $4,226,944 $3,837,930 Conoco is jointly and severally liable for price erosion damages for its purchase and use of the infringing NO-SOx products, at a lower price than had it purchased DE-SOX from Grace in Intercat’s absence. Conoco’s contribution to the price erosion damages is $108,139. In summary, Intercat is liable for $4,145,356 for lost sales, and $3,837,930 for price erosion, for a total of $7,983,286. Conoco is jointly and severally liable for $742,943 for lost sales, and $108,139 for price erosion, for a total of $851,082. VII. Prejudgment Interest The Supreme Court has held that an award of damages under 35 U.S.C. § 284 requires an award of prejudgment interest from the time infringement began until judgment. General Motors Corp. v. Devex Corp., 461 U.S. 648, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983). Prejudgment interest does not apply to any enhanced or punitive portion of an award. Lam, Inc. v. Johns-Manville Corp., 718 F.2d 1056, 1066 (Fed.Cir.1983). Prejudgment interest does apply to recoveries for both lost sales and price erosion. Both parties agree that prejudgment interest should be at the prime rate, compounded annually, applied according to the “mid year” convention. According to this method, it is assumed that profits lost in any given year were lost evenly throughout the year, so that a representative interest loss can be calculated by applying the prime rate existing at the middle of the year to the full profits lost over that year. Once the first year’s interest is so determined, it is compounded annually, at the middle of each succeeding year, to bring it up to the present. Interest is calculated on profits lost for each year of the infringement in the same manner. Plaintiff has submitted the prejudgment interest totals through March 1, 1999. The plaintiff shall submit its calculations on prejudgment interest on the damages for lost sales and price erosion, through the date of the opinion. VIII. Enhanced Damages A summary of the authority for increased damages is set out in BIC Leisure Products v. Windsurfing Int’l, Inc., 1 F.3d 1214, 1222-23 (Fed.Cir.1993): The patent statute authorizes courts to award increased damages. 35 U.S.C. § 284 (1988). A court may award enhanced damages under this section upon a finding of willful infringement. Avia Group Int’l, Inc. v. L.A. Gear California, Inc., 853 F.2d 1557, 1566 (Fed.Cir. *333 1988). In “exceptional cases” the district court may award attorney fees to the prevailing party. 35 U.S.C. § 285 (1988). Both willfulness and exception-ality are questions of fact that this court reviews under the clearly erroneous standard. See State Indus. v. Mor-Flo Indus., Inc., 883 F.2d 1573, 1581 (Fed. Cir.1989); Fromson v. Western Litho Plate & Supply Co., 853 F.2d 1568, 1573 (Fed.Cir.1988). Windsurfing had the burden of proving by clear and convincing evidence that BIC’s infringement was willful and that the case was exceptional. State Indus., 883 F.2d at 1581; Badalamenti v. Dunham’s Inc., 896 F.2d 1359, 1364 (Fed.Cir.1990). In State Indus., supra, at 1581, the court further explains: To establish willful infringement, a plaintiff must prove by clear and convincing evidence that the defendant acted with no reasonable basis for believing it had the right to do so. E.I. du Pont de Nemours & Co. v. Phillips Petroleum Co., 849 F.2d 1430, 1440 (Fed.Cir.1988). There are no “hard and fast per se rules,” and the finding is based on the totality of the circumstances. Rolls-Royce Ltd. v. GTE Valeron Corp., 800 F.2d 1101, 1110 (Fed.Cir.1986). The court in Badger Meter, Inc. v. Grinnell Corp., 13 F.3d 1145 (7th Cir.1994) noted that “exceptional cases” have been interpreted to mean cases where the acts of infringement can be characterized as malicious, fraudulent, deliberate, or willful. This Court has already determined that Intercat willfully infringed the patents-in-suit. 7 F.Supp.2d at 472-77. More specifically, the Court held: In sum, Grace has proven by clear and convincing evidence that Intercat did not act reasonably and prudently to avoid infringement of Grace’s patent rights. Intercat deliberately copied the invention of the patents-in-suit and the highly successful DESOX product. Regis Lip-pert, the President of Intercat, plainly had knowledge of Grace’s patent rights, yet failed to obtain competent advice of counsel before initiating or continuing infringing activities. Although Mr. Lip-pert claims to have formed a good faith belief that NO-SOx and NO-SOx-PC did not infringe the patents-in-suit and that those patents were invalid, he formed his belief (if indeed he actually held such a belief) without preforming an adequate investigation into the scope of Grace’s patent rights. As a consequence, the Court finds as fact that In-tercat willfully infringed the patents-in-suit. 7 F.Supp.2d at 476-77. Therefore, in light of this Court’s prior finding of Intercat’s willfulness, the total of lost sales plus price erosion damages, or the sum of $7,983,286, will be doubled for an award of $15,966,572. Conoco remains jointly and severally liable for $851,082, as there was no evidence presented that its infringement was willful. Additionally, the Court holds that this is an exceptional case justifying an award of attorneys fees. In addition to the facts of willfulness set forth above, this Court has previously held that Intercat’s defense of non-infringement was “litigation-inspired.” 7 F.Supp.2d at 438. Accordingly, the Court finds that this is an exceptional case, and Grace is awarded attorney fees. IX. Conclusion For the reasons set forth herein, and in the Court’s prior opinion set forth at 7 F.Supp.2d 425, the Court finds that Grace is entitled to recover from Intercat lost profits for lost sales of $4,145,356 and price erosion damages of $3,837,930, plus prejudgment interest at the prime rate, compounded annually. Because the Court finds that this infringement was willful and that this is an exceptional case, the total of $7,983,286 will be doubled for an award of $15,966,572 plus attorney fees. Prejudgment interest does not apply to the enhanced portion of the damage award. Co-noco is jointly and severally liable for a *334 total of $851,082, plus prejudgment interest. Footnotes [1] The Court's opinion is reported at 7 F.Supp.2d 425. [2] Reported at 155 F.3d 572 (1998). [3] Defendants rely on Standard Havens Prods., Inc. v. Gencor Indus., Inc., 953 F.2d 1360 (Fed.Cir.1991) (holding that sale of a plant used in a patented process to customers abroad was improperly included in the damages award); Enpat, Inc. v. Microsoft Corp., 6 F.Supp.2d 537 (E.D.Va.1998) (holding that § 271(1) did not apply to Microsoft’s sales of its software abroad where use of the software infringed a United States process patent); Robotic Vision Sys. v. View Eng'g Inc., 39 U.S.P.Q.2d 1117, 1995 WL 867456 (C.D.Cal.1995); Aerogroup Int’l, Inc. v. Marlboro Footworks, Ltd., 955 F.Supp. 220, 231-32 (S.D.N.Y.1997). [4] Defendants cite S.Rep. No. 663, 98th Cong., 2d Sess.1984; and 1984 U.S.C.C.A.N. 5828. [5] Plaintiff presented the deposition testimony of Kent Keys, the plant manager at UCI, Inc., which toll manufactured DESOX for Grace. He testified that UCI could have produced enough DESOX to meet even the highest yearly amount of combined sales of DESOX and the NO-SOx products. [6] Price erosion damages are normally the difference between potential price and actual cost. However, the Court has already awarded damages for lost sales, which was the difference between actual price and actual costs for the sales lost to Intercat. Therefore, price erosion is the difference between potential price and actual price of both the sales made by Grace, and the sales it lost to Inter-cat.